Movatterモバイル変換

[0]ホーム
URL:

Uploaded byRosaTarekAyyash
PPTX, PDF725 views

5 Qubit Modalities Used In Quantum Computing.pptx

Qubit modalities in quantum computing include superconducting qubits and trapped ion qubits. Superconducting qubits use superconducting circuits containing Josephson junctions to define discrete energy levels for qubits. Trapped ion qubits encode information in the internal states of trapped ions. Both approaches require initialization to a fiducial state, long coherence times enabled by techniques like dressed states, and methods for single and two-qubit gates using electromagnetic fields and measurement of qubit states.

Embed presentation

Downloaded 22 times
Qubit ModalitiesUsed in QuantumComputingWOMANIUM Quantum Program 2023By Rosa Ayyash 1
Qubit Modalities• The classical bits in traditional computers can represent either a 0 or a1, while qubits can exist in a superposition of 0 and 1.• This property allows quantum computers to perform parallelcomputations on a scale that was previously unattainable.• As the field of quantum computing matures, the development ofrobust and scalable quantum hardware becomes paramount.• This involves creating physical systems that can maintain the delicatequantum states required for computation, while also addressingchallenges like noise, error rates, and decoherence.By Rosa Ayyash 2
Qubit Modalities• This rapid progress in quantum hardware and qubit modalities has ledto a spectrum of applications with far-reaching implications.• Quantum computers hold the potential to revolutionize fields such ascryptography, optimization, material science, drug discovery, andartificial intelligence.• They can potentially solve complex problems exponentially faster thanclassical computers, opening doors to novel solutions that werepreviously unattainable.By Rosa Ayyash 3
Di Vincenzo’s CriteriaCriteria for constructing a Quantum Computer:1. A scalable physical system with well-characterized qubit2. The ability to initialize the state of the qubits to a simple fiducial state3. Long relevant decoherence times4. A "universal" set of quantum gates (single and two-qubits gates)5. A qubit-specific readout capabilityBy Rosa Ayyash 4
1. Scalable CharacterizedQubit• As the number of qubits increase, theybecome less characterized, hence, less usefulfor a computation, until they cross a limitafter which they are not useful.By Rosa Ayyash 5• A qubit is a two-level system with some energy gap.• For a well characterized qubit, we require that the qubit remains inthe subspace of these two states.• Scalability is the problem as the creation and incorporation ofadditional qubits requires an exponential growing experimentalsetup.
2. Initialization of QubitsBy Rosa Ayyash 6• All operations and measurements are dependent on the initial stateof the qubit (unitary nature of quantum mechanics).• In most cases, the initialization is realized by letting the systemanneal to its ground state• In quantum annealing, we start with aquantum system in a known configuration( high-energy state) and evolve thesystem's Hamiltonian in such a way that iteventually settles into the ground stateconfiguration (lowest energy state).
3. Long Decoherence TimesBy Rosa Ayyash 7• Decoherence describes the loss of quantum coherence and theemergence of classical behavior in a quantum system due to itsinteraction with an external environment.• Superposition and entanglement can belost due to Decoherence.• Long Decoherence times are required,longer than the lifetime of quantumgates, in order to use error correctiontechniques.
4. Quantum GatesBy Rosa Ayyash 8• A specific set of elementary quantum logic operationsthat, when combined in various ways, can approximateany unitary transformation on a quantum system.• Quantum gates can be single-qubit gates or mutli-qubitgates (where the state of qubit(s) affect the state of otherqubit(s))• Quantum Gates should conserve unitarity, quantuminformation, probability and most importantly coherence.
5. Qubit-Specific MeasurementBy Rosa Ayyash 9• Measurement is projecting the quantum state onto one of its basis.• It is at the foundation of all quantum algorithms.• If our system allows for non-destructive projective measurements,then, in principle, this can be used for state preparation (the qubitcan be re-used all over again).• Measurement techniques that are not 100% efficient are typicallyrepeated to increase the success rate.
1.Superconducting QubitsBy Rosa Ayyash 10
Criteria 1: Well Defined Qubit• Superconducting qubit can be described asHarmonics Oscillators, specifically an LC circuitwith well defined, quantized energy states.• The circuit consists of an inductor and acapacitor connected in series.• The kinetic energy of the system is associatedwith the oscillations of the voltage of thecapacitor.• The potential energy is associated with theflux of the inductor.By Rosa Ayyash 11
Criteria 1: Well Defined Qubit• The Hamiltonian describing the system:𝐻 =12𝐶𝑉2+12𝐿𝐼2• The flux within the inductor, the charge stored in the capacitor arerespectively written as:𝜑 𝑡 =−∞𝑡𝑉 𝑡′ 𝑑𝑡′ ; 𝑄 𝑡 =−∞𝑡𝐼 𝑡′ 𝑑𝑡′• Hence, the Hamiltonian is rewritten as:𝐻 =12𝐶𝑄2 +12𝐿𝜑2By Rosa Ayyash 12
Criteria 1: Well Defined Qubit• In the context of dimensionless quantities, charge can be mapped tocooper pair number:𝑛 =𝑄2𝑒• Similarly, the flux can be mapped to the superconducting phase:𝜓 = 𝜑𝑛2𝑒−1• The capacitive and inductive energies can thus be written as:𝐸𝑐 =𝑒22𝐶; 𝐸𝐿 =𝜑02𝐿By Rosa Ayyash 13𝜑0 is the reduced quantum flux
Criteria 1: Well Defined Qubit• A well defined qubit is characterized by two discrete energy levels.• Josephson Junction is thus added to the circuit to introduce non-linearity, disrupting the equidistance of the energy levels and enablingthe two-state system.By Rosa Ayyash 14This is thesuperconducting qubit
Criteria 1: Well Defined Qubit• For Charge Qubits: Charge qubits are based on the quantization of electriccharge on a superconducting island.|0⟩ state: No excess Cooper pairs (or electrons) on the superconducting island.|1⟩ state: One excess Cooper pair (or electron) on the island.• For Transmon Qubits: Transmon qubits are a variation of charge qubitsdesigned to have longer coherence times by suppressing the charge noisethat can degrade qubit performance|0⟩ state: Ground state of the anharmonic oscillator.|1⟩ state: First excited states of the anharmonic oscillator• For Phase Qubits: Phase qubits encode quantum information in the phasedifference across a Josephson junction, which is a key component of manysuperconducting qubits.The qubit states |0⟩ and |1⟩ correspond to different values of the phase difference.By Rosa Ayyash 15
Josephson Junction• It is superconducting electrodes separated by a thin insulating barrier• The Josephson junction exhibits a quantum mechanical phenomenon (Josephsoneffect) which involves the tunneling of Cooper pairs across the insulating barrier.By Rosa Ayyash 16• When a voltage is applied across aJosephson junction, a supercurrent can flowwithout the need for an applied electricfield. The supercurrent is directlyproportional to the sine of thesuperconducting phase difference ψ acrossthe junction. 𝐼 = 𝐼𝑐𝑠𝑖𝑛𝜓
Josephson JunctionWhy add a Josephson Junction to an LC circuit?• Nonlinearity for Two-Level System:An LC circuit alone behaves as a linear harmonic oscillator, which means that its energylevels are equidistant, forming a continuous spectrum. The Josephson junctionintroduces nonlinearity, disrupting the equidistant energy levels of the LC circuit andcreating a potential energy landscape with distinct quantum states.• Quantization of Phase Difference:The Josephson junction's function is to quantize the phase difference (𝜓) across it. Bycombining the Josephson effect with the LC circuit, the phase difference becomes aquantized variable.• Energy Levels and Qubit States:The Josephson junction introduces energy levels that depend on the quantized phasedifference. These energy levels can be manipulated using external control parameters,such as magnetic flux or applied voltages.By Rosa Ayyash 17
Josephson JunctionBy Rosa Ayyash 18A linear LC circuit /Harmonic Oscillatorwith evenly spacedenergy levels.A non linear LC circuitwith the introduction ofa Josephson junctiondisrupts the evennessthe energy level makingthe circuit operationseasier to implement
Criteria 2: Initialization• Such systems exhibit quantum behavior only atextremely low temperatures, where interactionswith the environment are extremely low𝑘𝐵𝑇 ≪ ∆𝐸• The superconducting is thus initialized bycooling down the system to low temperatures(≈ 10 𝑚𝐾) where thermal noise is almostnegligible; hence the need of dilutionrefrigerators.By Rosa Ayyash 19
Criteria 3: Long DecoherenceTimesThe best way to improve the coherence time is by improving on thematerials and design:• Material Selection: Choosing high-quality superconducting materialswith low loss and minimal defects can help improve coherence.Materials with longer coherence times, like certain types of aluminumor niobium, can be used.• Geometry Optimization: Careful design of qubit components, such asthe Josephson junction and resonators, can reduce the susceptibilityof the qubit to noise and interference.By Rosa Ayyash 20
Criteria 4: Quantum Gates• Microwave pulses are applied to the qubits todrive transitions between different energylevels, creating superposition or changing thequantum state of the qubit.• The frequency of the microwave pulses ischosen to match the energy difference betweenthe desired qubit states.• Single-qubit gates, such as the X, Y, and Z gates,correspond to rotations around the Blochsphere.By Rosa Ayyash 21
Criteria 4: Quantum Gates• In superconducting qubit systems, qubits are designed to couple toeach other through capacitive or inductive interactions.• These interactions create a link between the qubits, allowing them toinfluence each other's quantum states.• To implement a two-qubit gate, specific control pulses are applied tothe qubits. These control pulses are carefully designed microwavesignals that induce changes in the qubit states.• When the interactions between the qubits are turned, their quantumstates start to evolve in a correlated manner. The qubits' statesbecome entangled as they exchange information due to theinteraction.By Rosa Ayyash 22
Criteria 5: Measurement• Measurement, or qubit readout, is achieved through a process thatconverts the quantum state of the qubit into a measurable electricalsignal.• This process typically involves coupling the qubit to a microwaveresonator, allowing the qubit state information to be extracted aschanges in the microwave signal.• A readout pulse (short microwave pulse) is applied to the resonator toprobe the qubit's state. This pulse interacts with the qubit andresonator, causing a symmetric shift in the resonator's frequency basedon the qubit state.By Rosa Ayyash 23
Advantages & DisadvantagesAdvantages DisadvantagesStrong Qubit-Qubit Interactions: They can beengineered to have relatively strong interactions,enabling two-qubit gates and multi-qubit operationsOperation at low temperature: Superconducting qubitsrequire extremely low temperature (≈ 10 𝑚𝑘) inorder to execute quantum behaviors.High-fidelity gate: With advances in control techniquesand error correction methods, superconducting qubitshave achieved high fidelity single and two-qubit gatesDecoherence: Superconducting qubits are susceptibleto various sources of decoherence, such as charge andflux noise.Integrated electronics: can be fabricated using standardsemiconductor manufacturing techniques, allowing forthe integration of qubits with classical electronics onthe same chip.Sensitivity to Environmental Factors: Superconductingqubits are sensitive to external electromagnetic fields,temperature variations, and other environmentalfactors, requiring careful shielding and control.Speed: Superconducting qubits can be manipulatedand measured quickly, preserving coherence betweenqubits.By Rosa Ayyash 24
2.Trapped-ions QubitsBy Rosa Ayyash 25
Criteria 1: Well Defined Qubit• Trapped-ion qubits are a type of qubitrealized using individual ions, usually 𝑌𝑏+that are confined (Pauli Trap) andmanipulated using electromagnetic fields.• Information are encoded in the internalstates of the ion.• The two states are associated with the twolong-lived energy levels (intrinsic); namely,the ground state and an excited state.By Rosa Ayyash 26
Trapping the IonBy Rosa Ayyash 27• The ion(s) is trapped in 3D, between six electrodes.• A charged particle will naturally tend to move fromhigher potential to lower potential regions, influencedby the forces exerted by electric fields.• In a static situation where the potentials areunchanging, it is not possible to create a stable trappingenvironment for the ion.• The introduction of dynamic changes in electrode polarities overcomes this limitation.• By altering the potentials applied to the surrounding electrodes, this adjustmentcreates a delicate balance between repulsive and attractive forces, resulting in anequilibrium point where the ion is confined to a specific region, the trap.
Trapping the IonBy Rosa Ayyash 28• Another key step is the use of laser cooling to slow downthe motion of ions, reducing their thermal motion andbringing them close to their lowest possible energy state.• Further, It enables precise initialization, enhancescoherence times, improves state manipulation andmeasurement, and facilitates the implementation ofquantum logic gates.
Criteria 2: InitializationBy Rosa Ayyash 29• The initialization of trapped-ion qubit involves using externalelectromagnetic fields, often lasers and sometimes microwave radiation, toprepare the ion in a specific quantum state.• Laser beams are directed towards the trapped ion with specific frequenciesmatching the energy difference between the ion's ground state and anauxiliary excited state.• This excited state is chosen such that it has a relatively short lifetime andcan rapidly decay back to the ground state.• As the ion transitions back to the ground state, it emits a photon carryingaway the excess.• The emitted photon can be detected, signaling that the ion has returned toits ground state, and thus initialized.
Criteria 3: Long DecoherenceTimesStarting with some definitions:• Decoherence-free manifold: Subspace within thelarger Hilbert space of a quantum system wherecertain quantum states are more robust againstcertain types of noise.• Dressed states: Quantum states that emergefrom the interaction between a quantum systemand an external field, such as a laser field. Whena quantum system interacts with a strongexternal field, its energy levels can shift leadingto the creation of new eigenstates, known asdressed states.By Rosa Ayyash 30
Criteria 3: Long DecoherenceTimes• To improve the decoherence times of trapped-ion qubits, the setup shouldbe moved to a decoherence-free manifold using dressed states.• The idea is to manipulate the qubits' energy levels using appropriately tunedlaser fields so that they become entangled with the environmental degreesof freedom that cause decoherence.• This entanglement can lead to the formation of dressed states, which areeigenstates of the total Hamiltonian, including interactions.• When the qubits are in these dressed states that create a decoherence-freemanifold, the coherence time of the qubits can be significantly extended.• This happens because the dressed states are prone against types ofenvironmental noise.By Rosa Ayyash 31
Criteria 4: Quantum Gates• A single qubit can be controlled using resonant electromagneticradiation to move the ion between the two chosen states.• When the trapped ion is exposed to resonant electromagneticradiation, the interaction allows the qubit to absorb a photon from theradiation field and transition from one state to the other.• By controlling the duration and intensity of the applied radiation,quantum engineers can tailor the qubit's transition probabilities.By Rosa Ayyash 32
Criteria 4: Quantum Gates• To realize two-qubit gates, we need to assure the communicationbetween the ions through a common mode, which is the motional /vibrational mode.• This can be achieved by creating a “quantum bus” which in principle isthe coupling of qubits via their common motion, initiated by theexcitation of one ion.• The momentum is then transferred throughout the line of ions. Thistransfer necessitates the use of short wavelengths, often in the opticalrange.By Rosa Ayyash 33
Criteria 5: Measurement• Measurement is done using laser light that is resonant with a specificqubit energy transition. This resonance means that the frequency ofthe laser light matches the energy difference between the qubit's twostates.• When the laser light is resonant with one of the qubit states, it caninteract with the qubit in that state, leading to fluorescence.• Fluorescence occurs when the qubit absorbs a photon from the laserand transitions to a higher-energy state.• If the ion is in state | ⟩1 , the fluorescent light can be observed.Inversely, the state | ⟩0 is when the fluorescent light is absent.By Rosa Ayyash 34
Advantages & DisadvantagesAdvantages DisadvantagesLong Coherence Times: demonstrated some of thelongest coherence times. Their ability to be isolatedfrom external noise sources and cooled to very lowtemperatures helps maintain quantum coherence.Complex Setup: require sophisticated setups involvingvacuum chambers, lasers, and electromagnetic fields.These setups can be complex and costly to build andmaintain.High Fidelity Gates: manipulated with high precisionusing laser pulses and electromagnetic fields.Limited Qubit Connectivity: the physical arrangement ofions can result in limited qubit connectivity comparedto other platforms.Highly Controllable: The precise control over theinternal and external states allows for the creation ofwell-defined qubits and reliable qubit-qubitinteractions.Qubit Initialization and Measurement Overheads: Theprocess of initializing and measuring trapped-ionqubits can be time-consuming due to the need forlaser cooling, state manipulation, and detection ofemitted photons. This can affect the overall speed ofquantum computations.By Rosa Ayyash 35
3.Neutral-Atoms QubitsBy Rosa Ayyash 36
Criteria 1: Well Defined Qubit• Neutral atom qubits are often realized by trapping individual neutralatoms using electromagnetic fields in devices known as atom traps.• Optical traps, such as optical tweezers, are frequently used to confineand manipulate these atoms.By Rosa Ayyash 37
Criteria 1: Well Defined Qubit• Rydberg atoms, arranged in a lattice are oftenused for this purpose.• The information is encoded within the internalenergy levels of the atom (hyperfine energylevels).• The lowest energy level (state | ⟩0 ) is known asthe ground state, the higher level (state | ⟩1 ) isknown as Rydberg energy level.By Rosa Ayyash 38
Criteria 2: Initialization• Initialization is done using laser pulses, driving the atom into thedesired initial state.• The atom's temperature should also reduced to nearly absolute zero(≈ 100 𝜇𝐾), which minimizes its motion and thermal excitation andprepares it in a well-defined quantum state.By Rosa Ayyash 39
Criteria 3: Long DecoherenceTimes• Neutral atom qubits are relatively immune to certain types ofdecoherence, such as electromagnetic interference, which can affectcharged qubit platforms.• Environmental interactions and spontaneous emission, can still degradethe performance of neutral atom qubits.• External sources of noise, like laser phase noise, can also lead todecoherence.• Laser phase noise refers to random fluctuations in the phase of a laserbeam's electromagnetic wave.By Rosa Ayyash 40
Criteria 4: Quantum Gates• By exciting the atoms from one energy stateto another using carefully designed laserpulses, we can perform single-qubit gateoperations.• We use lasers to induce transitions betweenthe chosen energy levels. By carefully tuningthe frequency of the laser, we can cause theatom to absorb a photon and transition fromone state to another.By Rosa Ayyash 41
Criteria 4: Quantum Gates• To realize two-qubit gates, the dipole-dipole interaction between theRydberg atoms is used.• When two Rydberg atoms are brought close together, their electricdipoles can interact with each other, leading to a controlled exchangeof quantum information between the atoms.• By carefully controlling the positions ofthese atoms and the timing of theirinteractions, two-qubit quantum gates can beachieved.By Rosa Ayyash 42
Criteria 5: Measurement• Measurement is done by detecting the light emitted fromthe atoms when they are probed with a laser beam. Thisprocess is known as fluorescence measurement.• When a neutral atom undergoes a transition between twoenergy states, it absorbs energy and then releases it in theform of light. The frequency and intensity of the emittedlight depend on the specific energy levels involved in thetransition.By Rosa Ayyash 43
Advantages & DisadvantagesAdvantages DisadvantagesIdentical: Being natural atoms, neutral-atom qubit areperfectly identical to each other.Thermal Effects: Even with laser cooling, residualthermal motion can lead to qubit errors and reducedcoherence times.Long Coherence Times: Neutral atoms are relativelyisolated from their environment, leading to longercoherence times compared to charged particles likeions or electrons.Limited Interaction Strength: While neutral atoms havestrong dipole-dipole interactions at long distances,these interactions can be relatively weak compared toother qubit platform.Well-Defined Qubit States: The energy levels are well-defined and controllable, which allows for accuratequbit initialization, manipulation, and measurement.Complex Experimental Setup: The construction andoperation of setups for trapping, cooling, andmanipulating neutral atoms can be challenging.Low Crosstalk: Neutral atoms are localized and interactweakly with each other, reducing the chances ofcrosstalk and unwanted interactions between qubits.Slow Gate Operations: The interaction times betweenneutral atoms can be relatively slow, which mightaffect the speed of quantum computations.By Rosa Ayyash 44
4.Photonic QubitsBy Rosa Ayyash 45
Criteria 1: Well Defined Qubit• The first approach is Discrete Variable encoding.• The photonic mode is represented by a harmonicoscillator with two energy levels.• Any two energy levels consist the two-level system.• The polarization state of a photon is used to encode the qubit. Ahorizontal polarization state |H⟩ corresponds to the qubit |0⟩, and avertical polarization state |V⟩ corresponds to the qubit |1⟩.• This approach requires a large number of photons to create the logicalqubit, which worsens the error correction process.By Rosa Ayyash 46Approach1
Criteria 1: Well Defined Qubit• The second approach is continuous variableencoding.• The photonic mode is represented by a harmonicoscillator with multiple energy levels.• This is known as multi-level encoding; the photonsare used to access multiple levels of the harmonicoscillator.• Error correction can be done in a single mode whichis easier to implement. However, manufacturing themulti-photon state, the GKP state, is a realchallenge.By Rosa Ayyash 47Approach2
Criteria 2: Initialization• To initialize a photonic qubit, we use a carefully designed setup ofoptical components, specifically a “beam splitter network” thatincludes beam splitters, wave plates and detectors to generate aspecific quantum state of a photon.By Rosa Ayyash 48
Criteria 3: Long DecoherenceTimes• To enhance the coherence time, it is imperative to minimize the phasenoise within the system.• Phase noise refers to the random and undesired fluctuations in thephase of a quantum state.• This can involve utilizing precision opticalcomponents, employing error correctionmethods, and applying advanced noisefiltering and suppression protocols.By Rosa Ayyash 49
Criteria 4: Quantum Gates• Implementing single-qubit gates on photonic qubits involves theconcept of measurement-induced teleportation within a cluster state.• A cluster state is a specific type of highly entangled quantum state thatserves as a resource for quantum computation.• These measurements trigger the teleportation of quantuminformation, including the desired single-qubit gate operation, to thetarget qubit.• The specifics of the measurement settings are chosen to correspondto the desired gate operation, allowing for the realization of quantumgates such as rotations.By Rosa Ayyash 50
Quantum TeleportationBy Rosa Ayyash 51• Alice and Bob share an entangled quantum state, often referred to as an EPR pair.• Alice possesses a qubit. This qubit is in an unknown quantum state that she wishes totransmit to Bob.• Alice performs a Bell State Measurement, a joint measurement involving her qubit andher portion of the entangled pair.• This measurement projects the joint state of the qubit and the entangled pair onto one ofthe four Bell states.• The Bell State Measurement yields two classical outcomes. These outcomes provideinformation about the correlations between Alice's qubit and her entangled particle.• Alice communicates her measurement outcomes to Bob using classical communicationchannels.• Upon receiving Alice's classical information, Bob applies a series of quantum operations tohis particle.• These operations are designed to transform Bob's particle into a state that approximatesthe original state of Alice's qubit.
Quantum TeleportationBy Rosa Ayyash 52
Criteria 4: Quantum GatesBy Rosa Ayyash 53• An optical parametric oscillator is a device that exploits nonlinearinteractions in materials to produce pairs of entangled photons.• Within an OPO, the entangled pair is typically generated through aprocess known as spontaneous parametric down-conversion, where ahigh-energy photon is converted into two lower-energy entangledphotons.• The nonlinearity of the OPO's interactionscan be harnessed to perform two-qubitquantum gate operations on the entangled photonpairs.
Criteria 5: Measurement• In the context of quantum optics, qubits can berepresented using the properties of light, such as itsamplitude and phase.• These properties can be quadratures of the light, whichencode information about the quantum state of thequbit.• Quadrature measurements refer to measurementsof a pair of complementary quantum observables knownas quadratures. These observables are related to theposition and momentum of the quantum system, and theycan be precisely determined using specific optical techniques.• By measuring one of the quadratures of light associated with the qubit, itbecomes possible to distinguish between different qubit states.By Rosa Ayyash 54
Advantages & DisadvantagesAdvantages DisadvantagesScalability: The compatibility of photonic systems withexisting fiber-optic infrastructure provides a promisingpathway for scalability.Difficulty in generating GKP states: GKP states arecharacterized by their narrow Gaussian distribution inthe phase-spaceOperation at room temperature: This significantlysimplifies the experimental setup and reduces thecomplexity and cost of maintaining extremely lowtemperaturesError Correction Complexity: implementing errorcorrection codes can be complex and resource-intensive, requiring additional qubits and operationsthat increase the overall computational overhead.Modularity & Networkability: naturally suited formodular quantum systems. Multiple photonic qubitscan be generated, manipulated, and entangled usingstandard optical components.Low overheads for fault-tolerance: error resilience dueto their weak interaction with the environment.By Rosa Ayyash 55
5.Silicon-Based QubitsBy Rosa Ayyash 56
Criteria 1: Well Defined Qubit• This approach involves trapping electrons in silicon quantum dots, asemiconductor material, as qubits.• The spin of the electron (up and down) consists our two-level system.By Rosa Ayyash 57Approach1
Criteria 1: Well Defined Qubit• Another method involves using the nuclearspins of a donor atom embedded in Silicon asqubits.• A single Silicon atom is replaced by a Group Vdonor (P, As, Sb, Bi)• An extra electron is bonded to the donornucleus via the Coulomb potential• These qubits have relatively long coherencetimes, which is important for error correctionin quantum computing.By Rosa Ayyash 58Approach2
Criteria 2: Initialization• Initialization can be achieved using a single electron transistor (SET)and the energy levels associated with the electron's spin states.• To initialize the qubit, the Fermi level of the single electron transistor isadjusted or tuned to a specific energy level.• By tuning the Fermi level, it's possible toposition it between the energy levels ofthe spin-up and spin-down states of theelectron in the qubit.By Rosa Ayyash 59
Criteria 3: Long DecoherenceTimes• To improve on the decoherence time, one should use isotopicallypurified Silicon; Natural Silicon is not recommended for this purpose.• Natural Si is composed of approximately:1628𝑆𝑖 𝑏𝑦 92%1629𝑆𝑖 𝑏𝑦 5%1630𝑆𝑖 𝑏𝑦 3%• 1629𝑆𝑖 which has an odd number of nucleons, has a non-zero nuclearspin. This nuclear spin can interact with the spins of electrons, othernuclei in the silicon lattice, or any eternal magnetic field leading todecoherence of the quantum states of qubits.By Rosa Ayyash 60
Criteria 4: Quantum Gates• To execute a single-qubit quantum gate, an oscillating magnetic field isapplied.• This magnetic field is generated using an on-chipmicrowave antenna, which emits microwaves at a specificfrequency.• The frequency of the microwave field is chosen to beresonant with the energy gap between the spin-down andspin-up states of the qubit.• The oscillating magnetic field effectively drives the qubit between itstwo quantum states, implementing a controlled evolution thatcorresponds to a specific quantum gate operation.By Rosa Ayyash 61
Criteria 4: Quantum Gates• Two qubits can be entangled by utilizing flip-flop qubits, which resultfrom the antiparallel spin states of a donor nucleus and an electron.• The interaction between these qubits can be established through theelectric dipole interaction.• This interaction occurs when eachelectron is pulled away from its donornucleus.• The spatial separation of the electronand the nucleus leads to a coupling between their spin states, enablingthe creation of entanglement.By Rosa Ayyash 62Approach1
Criteria 4: Quantum Gates• Entanglement can also be generated between two donor nuclear spinsby exploiting their hyperfine interaction with a shared electron spin.• The hyperfine interaction is a magnetic interaction between a nuclearspin and an electron spin.• By manipulating the shared electron spin,the nuclear spins of the two donors canbecome entangled through their interactionswith this common mediator.By Rosa Ayyash 63Approach2
Criteria 4: Quantum Gates• When particles with antisymmetric wave functions (such as fermions) areexchanged, their spatial and spin coordinates become correlated in a waythat influences their overall behavior. This is known as exchange interaction(SWAP or CROT gates in quantum computing)• Two electron spins can be entangled through the exchange interaction iftheir wavefunctions overlap significantly.• This overlap occurs when the spatial separation between the electronwavefunctions is minimized.• In this scenario, the exchange interaction becomes significant, leading to thecreation of entanglement between the electron spins.By Rosa Ayyash 64Approach3
Criteria 5: MeasurementIn state |1> In state |0>• The associated electron has sufficient energy totunnel from its current location onto a singleelectron transistor (SET) island.• As the electron tunnels onto the SET island, italters the local charge environment.• This change in the charge state of the SET islandaffects the electrical properties of the singleelectron transistor, leading to a measurablechange in the current passing through thetransistor.• This change in current serves as an indication thatthe qubit is in the |1⟩ state.• The associated electron does not possess enoughenergy to overcome the energy barrier andtunnel onto the SET island.• Consequently, the charge environment of the SETisland remains unchanged, and the currentflowing through the single electron transistorremains unaffected.• This lack of change in current serves as anindicator that the qubit is in the |0⟩ state.By Rosa Ayyash 65
Advantages & DisadvantagesAdvantages DisadvantagesIntegrated Electronics: Silicon qubits can be integratedwith classical electronic components on the same chip,enabling hybrid quantum-classical systems and easingqubit control and readout.Fabrication Challenges: The design and fabrication ofsilicon-based qubits with high fidelity can be complexand may require advanced nanofabrication techniques.Potential for Room Temperature Operation: Somesilicon-based qubits show promise for operation athigher temperatures compared to other qubitplatforms, potentially reducing the need for extremecooling.Isotope Enrichment: Enhancing coherence oftenrequires isotopic enrichment of silicon, which can betechnically challenging and increase production costs.Decoherence: Despite relatively long coherence times,silicon qubits still suffer from decoherence due tointeractions with their environment, which can limitthe performance of quantum operations.By Rosa Ayyash 66
ReferencesBy Rosa Ayyash 67
From Womanium YT ChannelBy Rosa Ayyash 68• https://youtu.be/qhLSuF_42hE?list=PL_wGNAk5B0pUVk2G7VvjHWA-P_uorDB7X• https://youtu.be/4HqDZ22yWS4?list=PL_wGNAk5B0pUVk2G7VvjHWA-P_uorDB7X• https://youtu.be/TFL-N0hRBkI?list=PL_wGNAk5B0pUVk2G7VvjHWA-P_uorDB7X• https://youtu.be/ieKG8firTOU?list=PL_wGNAk5B0pUVk2G7VvjHWA-P_uorDB7X• https://youtu.be/mBEFGbYMMuU?list=PL_wGNAk5B0pUVk2G7VvjHWA-P_uorDB7X• https://youtu.be/pFP7RvD9HvQ?list=PL_wGNAk5B0pUVk2G7VvjHWA-P_uorDB7X• https://youtu.be/tWdC50pUqus?list=PL_wGNAk5B0pUVk2G7VvjHWA-P_uorDB7X• https://youtu.be/7AQDTM-vw60?list=PL_wGNAk5B0pUVk2G7VvjHWA-P_uorDB7X
DiVincenzo, David P. "The physical implementation of quantum computation." Fortschritte der Physik:Progress of Physics 48.9‐11 (2000): 771-783.• Superconducting qubits:Vool, Uri, and Michel Devoret. "Introduction to quantum electromagnetic circuits." InternationalJournal of Circuit Theory and Applications 45.7 (2017): 897-934.Kjaergaard, Morten, et al. "Superconducting qubits: Current state of play." Annual Review ofCondensed Matter Physics 11 (2020): 369-395.Guo, Shaojun, et al. "Scalable quantum computational chemistry with superconducting qubits." arXivpreprint arXiv:2212.08006 (2022).Hyyppä, Eric, et al. "Unimon qubit." Nature Communications 13.1 (2022): 6895.• Neutral Atom Qubits:Henriet, Loïc, et al. "Quantum computing with neutral atoms." Quantum 4 (2020): 327.Ravets, Sylvain, et al. "Coherent dipole–dipole coupling between two single Rydberg atoms at anelectrically-tuned Förster resonance." Nature Physics 10.12 (2014): 914-917.By Rosa Ayyash 69
• Si-based Qubits:Kane, B. A silicon-based nuclear spin quantum computer. Nature 393, 133–137 (1998).https://doi.org/10.1038/30156Pla, J., Tan, K., Dehollain, J. et al. A single-atom electron spin qubit in silicon. Nature 489, 541–545(2012). https://doi.org/10.1038/nature11449Morello, A., Pla, J., Zwanenburg, F. et al. Single-shot readout of an electron spin in silicon. Nature 467,687–691 (2010). https://doi.org/10.1038/nature09392• Photonic Qubits:Duan, L-M., and H. J. Kimble. "Scalable photonic quantum computation through cavity-assistedinteractions." Physical review letters 92.12 (2004): 127902.• Trapped-ions Qubits:Bruzewicz, Colin D., et al. "Trapped-ion quantum computing: Progress and challenges." AppliedPhysics Reviews 6.2 (2019).https://www.iqsdirectory.com/articles/chiller/laser-coolers.htmlBy Rosa Ayyash 70

Recommended

PDF
Quantum Computing: The Why and How
PDF
Quantum Computers New Generation of Computers PART1 by Prof Lili Saghafi
PPTX
Quantum computing
PDF
Quantum computation with superconductors
PPT
Ibm quantum computing
PDF
Quantum Computing and Qiskit
PPT
Quantum Computing Lecture 1: Basic Concepts
PPTX
Shors'algorithm simplified.pptx
PPTX
Quantum computing
PPTX
Quantum computing seminar
PPTX
Quantum computing
ODP
Quantum computers
PPTX
Quantum computers
PPTX
Quantum computer
PDF
Quantum Computers new Generation of Computers part 7 by prof lili saghafi Qua...
PPTX
QuantumComputersPresentation
PPTX
Quantum computing
PDF
Quantum computing
PPT
Quantum Computing
PPTX
Quantum entanglement (1).pptx
PDF
Quantum Computation: What is it and Why?
PPTX
Quantum Computing Explained
PPTX
Quantum Computing: Welcome to the Future
PPTX
Qunatum computing
PPTX
Quantum computers
PPTX
Quantum computing
PPTX
Quantum Computing
PPTX
Quantum Internet By Professor Lili Saghafi

More Related Content

PDF
Quantum Computing: The Why and How
PDF
Quantum Computers New Generation of Computers PART1 by Prof Lili Saghafi
PPTX
Quantum computing
PDF
Quantum computation with superconductors
PPT
Ibm quantum computing
PDF
Quantum Computing and Qiskit
PPT
Quantum Computing Lecture 1: Basic Concepts
PPTX
Shors'algorithm simplified.pptx
Quantum Computing: The Why and How
Quantum Computers New Generation of Computers PART1 by Prof Lili Saghafi
Quantum computing
Quantum computation with superconductors
Ibm quantum computing
Quantum Computing and Qiskit
Quantum Computing Lecture 1: Basic Concepts
Shors'algorithm simplified.pptx

What's hot

PPTX
Quantum computing
PPTX
Quantum computing seminar
PPTX
Quantum computing
ODP
Quantum computers
PPTX
Quantum computers
PPTX
Quantum computer
PDF
Quantum Computers new Generation of Computers part 7 by prof lili saghafi Qua...
PPTX
QuantumComputersPresentation
PPTX
Quantum computing
PDF
Quantum computing
PPT
Quantum Computing
PPTX
Quantum entanglement (1).pptx
PDF
Quantum Computation: What is it and Why?
PPTX
Quantum Computing Explained
PPTX
Quantum Computing: Welcome to the Future
PPTX
Qunatum computing
PPTX
Quantum computers
PPTX
Quantum computing
Quantum computing
Quantum computing seminar
Quantum computing
Quantum computers
Quantum computers
Quantum computer
Quantum Computers new Generation of Computers part 7 by prof lili saghafi Qua...
QuantumComputersPresentation
Quantum computing
Quantum computing
Quantum Computing
Quantum entanglement (1).pptx
Quantum Computation: What is it and Why?
Quantum Computing Explained
Quantum Computing: Welcome to the Future
Qunatum computing
Quantum computers
Quantum computing

Similar to 5 Qubit Modalities Used In Quantum Computing.pptx

PPTX
Quantum Computing
PPTX
Quantum Internet By Professor Lili Saghafi
PDF
Introduction to Quantum Computer
PPTX
Quantum technology
 
PDF
Introduction_to_Quantum_Computers.pdf
PPTX
Qubit_and_Quantum_Gate.pptx
PDF
Introduction to Quantum Computing for Research
PPTX
Unit - II - Theoretical structure of quantum information systems .pptx
PPTX
quantum computing Fundamentals and Applicaiton
PDF
Quantum Computing 101, Part 1 - Hello Quantum World
PPTX
Introduction to Quantum Computers123.pptx
PPTX
Seminar on quatum
PDF
The future is quantum
PPTX
Physics 498 SQD -- Lecture 21---Quantum Information 1 FINAL.pptx
PDF
Superconducting qubits for quantum information an outlook
PDF
This is presentation about quantum computing
PDF
Technological Survey on Quantum Computing
PPTX
Quantum Information FINAL.pptx
PPTX
What is Quantum Computing and Why it is Important
PPTX
Toward a Dependable Quantum Computing Architecture
Quantum Computing
Quantum Internet By Professor Lili Saghafi
Introduction to Quantum Computer
Quantum technology
 
Introduction_to_Quantum_Computers.pdf
Qubit_and_Quantum_Gate.pptx
Introduction to Quantum Computing for Research
Unit - II - Theoretical structure of quantum information systems .pptx
quantum computing Fundamentals and Applicaiton
Quantum Computing 101, Part 1 - Hello Quantum World
Introduction to Quantum Computers123.pptx
Seminar on quatum
The future is quantum
Physics 498 SQD -- Lecture 21---Quantum Information 1 FINAL.pptx
Superconducting qubits for quantum information an outlook
This is presentation about quantum computing
Technological Survey on Quantum Computing
Quantum Information FINAL.pptx
What is Quantum Computing and Why it is Important
Toward a Dependable Quantum Computing Architecture

Recently uploaded

PDF
Overdispersed radio source counts and excess radio dipole detection
PDF
Sujay Rao Mandavilli Knowledge production lifecycle FINAL FINAL FINAL FINAL F...
PPTX
Ontologies for Semantic Interoperability in the Age of AI
PPTX
WORK SIMPLIFICATION IN LABORATORY.pptx DJHJHJH
PDF
CHEM STUDY ( a milestone in science education)
PDF
The Inner Kernel of the Classical Kuiper Belt
PDF
UK National Report and the NBSAP Experience
PPTX
Uses of Metal in drugs:unique properties
PDF
Technical and Scientifical Cooperation and the CHM. History, CBD Decisions, t...
PDF
Genetics & Plant Breeding Question Paper (PYQ + MCQ) for Competitive Plant Sc...
PDF
Extreme properties of a compact and massive accreting black hole host in the ...
PPTX
Correlation and regression analysis.pptx
PDF
Reminder of the Context and UN CBD Decisions on TSCCs
PDF
TSC Knowledge Hub for the UN CBD - Target 11
PDF
Online Reporting Tool and the Belgian Experience
PDF
eTap 2025 Navy Yellow Modern Professional Designer.pdf
PPTX
feedback mechanism for science 10 quarter 3.pptx
PDF
An axisymmetric shock breakout indicated by prompt polarized emission from th...
PDF
ICAR SRF, ASRB NET / SMS & STO Exam – Biotechnology Syllabus | Complete Unit-...
PPTX
VISIT TO SPACE Exploring more about Space
Overdispersed radio source counts and excess radio dipole detection
Sujay Rao Mandavilli Knowledge production lifecycle FINAL FINAL FINAL FINAL F...
Ontologies for Semantic Interoperability in the Age of AI
WORK SIMPLIFICATION IN LABORATORY.pptx DJHJHJH
CHEM STUDY ( a milestone in science education)
The Inner Kernel of the Classical Kuiper Belt
UK National Report and the NBSAP Experience
Uses of Metal in drugs:unique properties
Technical and Scientifical Cooperation and the CHM. History, CBD Decisions, t...
Genetics & Plant Breeding Question Paper (PYQ + MCQ) for Competitive Plant Sc...
Extreme properties of a compact and massive accreting black hole host in the ...
Correlation and regression analysis.pptx
Reminder of the Context and UN CBD Decisions on TSCCs
TSC Knowledge Hub for the UN CBD - Target 11
Online Reporting Tool and the Belgian Experience
eTap 2025 Navy Yellow Modern Professional Designer.pdf
feedback mechanism for science 10 quarter 3.pptx
An axisymmetric shock breakout indicated by prompt polarized emission from th...
ICAR SRF, ASRB NET / SMS & STO Exam – Biotechnology Syllabus | Complete Unit-...
VISIT TO SPACE Exploring more about Space

5 Qubit Modalities Used In Quantum Computing.pptx

  • 1.
    Qubit ModalitiesUsed inQuantumComputingWOMANIUM Quantum Program 2023By Rosa Ayyash 1
  • 2.
    Qubit Modalities• Theclassical bits in traditional computers can represent either a 0 or a1, while qubits can exist in a superposition of 0 and 1.• This property allows quantum computers to perform parallelcomputations on a scale that was previously unattainable.• As the field of quantum computing matures, the development ofrobust and scalable quantum hardware becomes paramount.• This involves creating physical systems that can maintain the delicatequantum states required for computation, while also addressingchallenges like noise, error rates, and decoherence.By Rosa Ayyash 2
  • 3.
    Qubit Modalities• Thisrapid progress in quantum hardware and qubit modalities has ledto a spectrum of applications with far-reaching implications.• Quantum computers hold the potential to revolutionize fields such ascryptography, optimization, material science, drug discovery, andartificial intelligence.• They can potentially solve complex problems exponentially faster thanclassical computers, opening doors to novel solutions that werepreviously unattainable.By Rosa Ayyash 3
  • 4.
    Di Vincenzo’s CriteriaCriteriafor constructing a Quantum Computer:1. A scalable physical system with well-characterized qubit2. The ability to initialize the state of the qubits to a simple fiducial state3. Long relevant decoherence times4. A "universal" set of quantum gates (single and two-qubits gates)5. A qubit-specific readout capabilityBy Rosa Ayyash 4
  • 5.
    1. Scalable CharacterizedQubit•As the number of qubits increase, theybecome less characterized, hence, less usefulfor a computation, until they cross a limitafter which they are not useful.By Rosa Ayyash 5• A qubit is a two-level system with some energy gap.• For a well characterized qubit, we require that the qubit remains inthe subspace of these two states.• Scalability is the problem as the creation and incorporation ofadditional qubits requires an exponential growing experimentalsetup.
  • 6.
    2. Initialization ofQubitsBy Rosa Ayyash 6• All operations and measurements are dependent on the initial stateof the qubit (unitary nature of quantum mechanics).• In most cases, the initialization is realized by letting the systemanneal to its ground state• In quantum annealing, we start with aquantum system in a known configuration( high-energy state) and evolve thesystem's Hamiltonian in such a way that iteventually settles into the ground stateconfiguration (lowest energy state).
  • 7.
    3. Long DecoherenceTimesBy Rosa Ayyash 7• Decoherence describes the loss of quantum coherence and theemergence of classical behavior in a quantum system due to itsinteraction with an external environment.• Superposition and entanglement can belost due to Decoherence.• Long Decoherence times are required,longer than the lifetime of quantumgates, in order to use error correctiontechniques.
  • 8.
    4. Quantum GatesByRosa Ayyash 8• A specific set of elementary quantum logic operationsthat, when combined in various ways, can approximateany unitary transformation on a quantum system.• Quantum gates can be single-qubit gates or mutli-qubitgates (where the state of qubit(s) affect the state of otherqubit(s))• Quantum Gates should conserve unitarity, quantuminformation, probability and most importantly coherence.
  • 9.
    5. Qubit-Specific MeasurementByRosa Ayyash 9• Measurement is projecting the quantum state onto one of its basis.• It is at the foundation of all quantum algorithms.• If our system allows for non-destructive projective measurements,then, in principle, this can be used for state preparation (the qubitcan be re-used all over again).• Measurement techniques that are not 100% efficient are typicallyrepeated to increase the success rate.
  • 10.
  • 11.
    Criteria 1: WellDefined Qubit• Superconducting qubit can be described asHarmonics Oscillators, specifically an LC circuitwith well defined, quantized energy states.• The circuit consists of an inductor and acapacitor connected in series.• The kinetic energy of the system is associatedwith the oscillations of the voltage of thecapacitor.• The potential energy is associated with theflux of the inductor.By Rosa Ayyash 11
  • 12.
    Criteria 1: WellDefined Qubit• The Hamiltonian describing the system:𝐻 =12𝐶𝑉2+12𝐿𝐼2• The flux within the inductor, the charge stored in the capacitor arerespectively written as:𝜑 𝑡 =−∞𝑡𝑉 𝑡′ 𝑑𝑡′ ; 𝑄 𝑡 =−∞𝑡𝐼 𝑡′ 𝑑𝑡′• Hence, the Hamiltonian is rewritten as:𝐻 =12𝐶𝑄2 +12𝐿𝜑2By Rosa Ayyash 12
  • 13.
    Criteria 1: WellDefined Qubit• In the context of dimensionless quantities, charge can be mapped tocooper pair number:𝑛 =𝑄2𝑒• Similarly, the flux can be mapped to the superconducting phase:𝜓 = 𝜑𝑛2𝑒−1• The capacitive and inductive energies can thus be written as:𝐸𝑐 =𝑒22𝐶; 𝐸𝐿 =𝜑02𝐿By Rosa Ayyash 13𝜑0 is the reduced quantum flux
  • 14.
    Criteria 1: WellDefined Qubit• A well defined qubit is characterized by two discrete energy levels.• Josephson Junction is thus added to the circuit to introduce non-linearity, disrupting the equidistance of the energy levels and enablingthe two-state system.By Rosa Ayyash 14This is thesuperconducting qubit
  • 15.
    Criteria 1: WellDefined Qubit• For Charge Qubits: Charge qubits are based on the quantization of electriccharge on a superconducting island.|0⟩ state: No excess Cooper pairs (or electrons) on the superconducting island.|1⟩ state: One excess Cooper pair (or electron) on the island.• For Transmon Qubits: Transmon qubits are a variation of charge qubitsdesigned to have longer coherence times by suppressing the charge noisethat can degrade qubit performance|0⟩ state: Ground state of the anharmonic oscillator.|1⟩ state: First excited states of the anharmonic oscillator• For Phase Qubits: Phase qubits encode quantum information in the phasedifference across a Josephson junction, which is a key component of manysuperconducting qubits.The qubit states |0⟩ and |1⟩ correspond to different values of the phase difference.By Rosa Ayyash 15
  • 16.
    Josephson Junction• Itis superconducting electrodes separated by a thin insulating barrier• The Josephson junction exhibits a quantum mechanical phenomenon (Josephsoneffect) which involves the tunneling of Cooper pairs across the insulating barrier.By Rosa Ayyash 16• When a voltage is applied across aJosephson junction, a supercurrent can flowwithout the need for an applied electricfield. The supercurrent is directlyproportional to the sine of thesuperconducting phase difference ψ acrossthe junction. 𝐼 = 𝐼𝑐𝑠𝑖𝑛𝜓
  • 17.
    Josephson JunctionWhy adda Josephson Junction to an LC circuit?• Nonlinearity for Two-Level System:An LC circuit alone behaves as a linear harmonic oscillator, which means that its energylevels are equidistant, forming a continuous spectrum. The Josephson junctionintroduces nonlinearity, disrupting the equidistant energy levels of the LC circuit andcreating a potential energy landscape with distinct quantum states.• Quantization of Phase Difference:The Josephson junction's function is to quantize the phase difference (𝜓) across it. Bycombining the Josephson effect with the LC circuit, the phase difference becomes aquantized variable.• Energy Levels and Qubit States:The Josephson junction introduces energy levels that depend on the quantized phasedifference. These energy levels can be manipulated using external control parameters,such as magnetic flux or applied voltages.By Rosa Ayyash 17
  • 18.
    Josephson JunctionBy RosaAyyash 18A linear LC circuit /Harmonic Oscillatorwith evenly spacedenergy levels.A non linear LC circuitwith the introduction ofa Josephson junctiondisrupts the evennessthe energy level makingthe circuit operationseasier to implement
  • 19.
    Criteria 2: Initialization•Such systems exhibit quantum behavior only atextremely low temperatures, where interactionswith the environment are extremely low𝑘𝐵𝑇 ≪ ∆𝐸• The superconducting is thus initialized bycooling down the system to low temperatures(≈ 10 𝑚𝐾) where thermal noise is almostnegligible; hence the need of dilutionrefrigerators.By Rosa Ayyash 19
  • 20.
    Criteria 3: LongDecoherenceTimesThe best way to improve the coherence time is by improving on thematerials and design:• Material Selection: Choosing high-quality superconducting materialswith low loss and minimal defects can help improve coherence.Materials with longer coherence times, like certain types of aluminumor niobium, can be used.• Geometry Optimization: Careful design of qubit components, such asthe Josephson junction and resonators, can reduce the susceptibilityof the qubit to noise and interference.By Rosa Ayyash 20
  • 21.
    Criteria 4: QuantumGates• Microwave pulses are applied to the qubits todrive transitions between different energylevels, creating superposition or changing thequantum state of the qubit.• The frequency of the microwave pulses ischosen to match the energy difference betweenthe desired qubit states.• Single-qubit gates, such as the X, Y, and Z gates,correspond to rotations around the Blochsphere.By Rosa Ayyash 21
  • 22.
    Criteria 4: QuantumGates• In superconducting qubit systems, qubits are designed to couple toeach other through capacitive or inductive interactions.• These interactions create a link between the qubits, allowing them toinfluence each other's quantum states.• To implement a two-qubit gate, specific control pulses are applied tothe qubits. These control pulses are carefully designed microwavesignals that induce changes in the qubit states.• When the interactions between the qubits are turned, their quantumstates start to evolve in a correlated manner. The qubits' statesbecome entangled as they exchange information due to theinteraction.By Rosa Ayyash 22
  • 23.
    Criteria 5: Measurement•Measurement, or qubit readout, is achieved through a process thatconverts the quantum state of the qubit into a measurable electricalsignal.• This process typically involves coupling the qubit to a microwaveresonator, allowing the qubit state information to be extracted aschanges in the microwave signal.• A readout pulse (short microwave pulse) is applied to the resonator toprobe the qubit's state. This pulse interacts with the qubit andresonator, causing a symmetric shift in the resonator's frequency basedon the qubit state.By Rosa Ayyash 23
  • 24.
    Advantages & DisadvantagesAdvantagesDisadvantagesStrong Qubit-Qubit Interactions: They can beengineered to have relatively strong interactions,enabling two-qubit gates and multi-qubit operationsOperation at low temperature: Superconducting qubitsrequire extremely low temperature (≈ 10 𝑚𝑘) inorder to execute quantum behaviors.High-fidelity gate: With advances in control techniquesand error correction methods, superconducting qubitshave achieved high fidelity single and two-qubit gatesDecoherence: Superconducting qubits are susceptibleto various sources of decoherence, such as charge andflux noise.Integrated electronics: can be fabricated using standardsemiconductor manufacturing techniques, allowing forthe integration of qubits with classical electronics onthe same chip.Sensitivity to Environmental Factors: Superconductingqubits are sensitive to external electromagnetic fields,temperature variations, and other environmentalfactors, requiring careful shielding and control.Speed: Superconducting qubits can be manipulatedand measured quickly, preserving coherence betweenqubits.By Rosa Ayyash 24
  • 25.
  • 26.
    Criteria 1: WellDefined Qubit• Trapped-ion qubits are a type of qubitrealized using individual ions, usually 𝑌𝑏+that are confined (Pauli Trap) andmanipulated using electromagnetic fields.• Information are encoded in the internalstates of the ion.• The two states are associated with the twolong-lived energy levels (intrinsic); namely,the ground state and an excited state.By Rosa Ayyash 26
  • 27.
    Trapping the IonByRosa Ayyash 27• The ion(s) is trapped in 3D, between six electrodes.• A charged particle will naturally tend to move fromhigher potential to lower potential regions, influencedby the forces exerted by electric fields.• In a static situation where the potentials areunchanging, it is not possible to create a stable trappingenvironment for the ion.• The introduction of dynamic changes in electrode polarities overcomes this limitation.• By altering the potentials applied to the surrounding electrodes, this adjustmentcreates a delicate balance between repulsive and attractive forces, resulting in anequilibrium point where the ion is confined to a specific region, the trap.
  • 28.
    Trapping the IonByRosa Ayyash 28• Another key step is the use of laser cooling to slow downthe motion of ions, reducing their thermal motion andbringing them close to their lowest possible energy state.• Further, It enables precise initialization, enhancescoherence times, improves state manipulation andmeasurement, and facilitates the implementation ofquantum logic gates.
  • 29.
    Criteria 2: InitializationByRosa Ayyash 29• The initialization of trapped-ion qubit involves using externalelectromagnetic fields, often lasers and sometimes microwave radiation, toprepare the ion in a specific quantum state.• Laser beams are directed towards the trapped ion with specific frequenciesmatching the energy difference between the ion's ground state and anauxiliary excited state.• This excited state is chosen such that it has a relatively short lifetime andcan rapidly decay back to the ground state.• As the ion transitions back to the ground state, it emits a photon carryingaway the excess.• The emitted photon can be detected, signaling that the ion has returned toits ground state, and thus initialized.
  • 30.
    Criteria 3: LongDecoherenceTimesStarting with some definitions:• Decoherence-free manifold: Subspace within thelarger Hilbert space of a quantum system wherecertain quantum states are more robust againstcertain types of noise.• Dressed states: Quantum states that emergefrom the interaction between a quantum systemand an external field, such as a laser field. Whena quantum system interacts with a strongexternal field, its energy levels can shift leadingto the creation of new eigenstates, known asdressed states.By Rosa Ayyash 30
  • 31.
    Criteria 3: LongDecoherenceTimes• To improve the decoherence times of trapped-ion qubits, the setup shouldbe moved to a decoherence-free manifold using dressed states.• The idea is to manipulate the qubits' energy levels using appropriately tunedlaser fields so that they become entangled with the environmental degreesof freedom that cause decoherence.• This entanglement can lead to the formation of dressed states, which areeigenstates of the total Hamiltonian, including interactions.• When the qubits are in these dressed states that create a decoherence-freemanifold, the coherence time of the qubits can be significantly extended.• This happens because the dressed states are prone against types ofenvironmental noise.By Rosa Ayyash 31
  • 32.
    Criteria 4: QuantumGates• A single qubit can be controlled using resonant electromagneticradiation to move the ion between the two chosen states.• When the trapped ion is exposed to resonant electromagneticradiation, the interaction allows the qubit to absorb a photon from theradiation field and transition from one state to the other.• By controlling the duration and intensity of the applied radiation,quantum engineers can tailor the qubit's transition probabilities.By Rosa Ayyash 32
  • 33.
    Criteria 4: QuantumGates• To realize two-qubit gates, we need to assure the communicationbetween the ions through a common mode, which is the motional /vibrational mode.• This can be achieved by creating a “quantum bus” which in principle isthe coupling of qubits via their common motion, initiated by theexcitation of one ion.• The momentum is then transferred throughout the line of ions. Thistransfer necessitates the use of short wavelengths, often in the opticalrange.By Rosa Ayyash 33
  • 34.
    Criteria 5: Measurement•Measurement is done using laser light that is resonant with a specificqubit energy transition. This resonance means that the frequency ofthe laser light matches the energy difference between the qubit's twostates.• When the laser light is resonant with one of the qubit states, it caninteract with the qubit in that state, leading to fluorescence.• Fluorescence occurs when the qubit absorbs a photon from the laserand transitions to a higher-energy state.• If the ion is in state | ⟩1 , the fluorescent light can be observed.Inversely, the state | ⟩0 is when the fluorescent light is absent.By Rosa Ayyash 34
  • 35.
    Advantages & DisadvantagesAdvantagesDisadvantagesLong Coherence Times: demonstrated some of thelongest coherence times. Their ability to be isolatedfrom external noise sources and cooled to very lowtemperatures helps maintain quantum coherence.Complex Setup: require sophisticated setups involvingvacuum chambers, lasers, and electromagnetic fields.These setups can be complex and costly to build andmaintain.High Fidelity Gates: manipulated with high precisionusing laser pulses and electromagnetic fields.Limited Qubit Connectivity: the physical arrangement ofions can result in limited qubit connectivity comparedto other platforms.Highly Controllable: The precise control over theinternal and external states allows for the creation ofwell-defined qubits and reliable qubit-qubitinteractions.Qubit Initialization and Measurement Overheads: Theprocess of initializing and measuring trapped-ionqubits can be time-consuming due to the need forlaser cooling, state manipulation, and detection ofemitted photons. This can affect the overall speed ofquantum computations.By Rosa Ayyash 35
  • 36.
  • 37.
    Criteria 1: WellDefined Qubit• Neutral atom qubits are often realized by trapping individual neutralatoms using electromagnetic fields in devices known as atom traps.• Optical traps, such as optical tweezers, are frequently used to confineand manipulate these atoms.By Rosa Ayyash 37
  • 38.
    Criteria 1: WellDefined Qubit• Rydberg atoms, arranged in a lattice are oftenused for this purpose.• The information is encoded within the internalenergy levels of the atom (hyperfine energylevels).• The lowest energy level (state | ⟩0 ) is known asthe ground state, the higher level (state | ⟩1 ) isknown as Rydberg energy level.By Rosa Ayyash 38
  • 39.
    Criteria 2: Initialization•Initialization is done using laser pulses, driving the atom into thedesired initial state.• The atom's temperature should also reduced to nearly absolute zero(≈ 100 𝜇𝐾), which minimizes its motion and thermal excitation andprepares it in a well-defined quantum state.By Rosa Ayyash 39
  • 40.
    Criteria 3: LongDecoherenceTimes• Neutral atom qubits are relatively immune to certain types ofdecoherence, such as electromagnetic interference, which can affectcharged qubit platforms.• Environmental interactions and spontaneous emission, can still degradethe performance of neutral atom qubits.• External sources of noise, like laser phase noise, can also lead todecoherence.• Laser phase noise refers to random fluctuations in the phase of a laserbeam's electromagnetic wave.By Rosa Ayyash 40
  • 41.
    Criteria 4: QuantumGates• By exciting the atoms from one energy stateto another using carefully designed laserpulses, we can perform single-qubit gateoperations.• We use lasers to induce transitions betweenthe chosen energy levels. By carefully tuningthe frequency of the laser, we can cause theatom to absorb a photon and transition fromone state to another.By Rosa Ayyash 41
  • 42.
    Criteria 4: QuantumGates• To realize two-qubit gates, the dipole-dipole interaction between theRydberg atoms is used.• When two Rydberg atoms are brought close together, their electricdipoles can interact with each other, leading to a controlled exchangeof quantum information between the atoms.• By carefully controlling the positions ofthese atoms and the timing of theirinteractions, two-qubit quantum gates can beachieved.By Rosa Ayyash 42
  • 43.
    Criteria 5: Measurement•Measurement is done by detecting the light emitted fromthe atoms when they are probed with a laser beam. Thisprocess is known as fluorescence measurement.• When a neutral atom undergoes a transition between twoenergy states, it absorbs energy and then releases it in theform of light. The frequency and intensity of the emittedlight depend on the specific energy levels involved in thetransition.By Rosa Ayyash 43
  • 44.
    Advantages & DisadvantagesAdvantagesDisadvantagesIdentical: Being natural atoms, neutral-atom qubit areperfectly identical to each other.Thermal Effects: Even with laser cooling, residualthermal motion can lead to qubit errors and reducedcoherence times.Long Coherence Times: Neutral atoms are relativelyisolated from their environment, leading to longercoherence times compared to charged particles likeions or electrons.Limited Interaction Strength: While neutral atoms havestrong dipole-dipole interactions at long distances,these interactions can be relatively weak compared toother qubit platform.Well-Defined Qubit States: The energy levels are well-defined and controllable, which allows for accuratequbit initialization, manipulation, and measurement.Complex Experimental Setup: The construction andoperation of setups for trapping, cooling, andmanipulating neutral atoms can be challenging.Low Crosstalk: Neutral atoms are localized and interactweakly with each other, reducing the chances ofcrosstalk and unwanted interactions between qubits.Slow Gate Operations: The interaction times betweenneutral atoms can be relatively slow, which mightaffect the speed of quantum computations.By Rosa Ayyash 44
  • 45.
  • 46.
    Criteria 1: WellDefined Qubit• The first approach is Discrete Variable encoding.• The photonic mode is represented by a harmonicoscillator with two energy levels.• Any two energy levels consist the two-level system.• The polarization state of a photon is used to encode the qubit. Ahorizontal polarization state |H⟩ corresponds to the qubit |0⟩, and avertical polarization state |V⟩ corresponds to the qubit |1⟩.• This approach requires a large number of photons to create the logicalqubit, which worsens the error correction process.By Rosa Ayyash 46Approach1
  • 47.
    Criteria 1: WellDefined Qubit• The second approach is continuous variableencoding.• The photonic mode is represented by a harmonicoscillator with multiple energy levels.• This is known as multi-level encoding; the photonsare used to access multiple levels of the harmonicoscillator.• Error correction can be done in a single mode whichis easier to implement. However, manufacturing themulti-photon state, the GKP state, is a realchallenge.By Rosa Ayyash 47Approach2
  • 48.
    Criteria 2: Initialization•To initialize a photonic qubit, we use a carefully designed setup ofoptical components, specifically a “beam splitter network” thatincludes beam splitters, wave plates and detectors to generate aspecific quantum state of a photon.By Rosa Ayyash 48
  • 49.
    Criteria 3: LongDecoherenceTimes• To enhance the coherence time, it is imperative to minimize the phasenoise within the system.• Phase noise refers to the random and undesired fluctuations in thephase of a quantum state.• This can involve utilizing precision opticalcomponents, employing error correctionmethods, and applying advanced noisefiltering and suppression protocols.By Rosa Ayyash 49
  • 50.
    Criteria 4: QuantumGates• Implementing single-qubit gates on photonic qubits involves theconcept of measurement-induced teleportation within a cluster state.• A cluster state is a specific type of highly entangled quantum state thatserves as a resource for quantum computation.• These measurements trigger the teleportation of quantuminformation, including the desired single-qubit gate operation, to thetarget qubit.• The specifics of the measurement settings are chosen to correspondto the desired gate operation, allowing for the realization of quantumgates such as rotations.By Rosa Ayyash 50
  • 51.
    Quantum TeleportationBy RosaAyyash 51• Alice and Bob share an entangled quantum state, often referred to as an EPR pair.• Alice possesses a qubit. This qubit is in an unknown quantum state that she wishes totransmit to Bob.• Alice performs a Bell State Measurement, a joint measurement involving her qubit andher portion of the entangled pair.• This measurement projects the joint state of the qubit and the entangled pair onto one ofthe four Bell states.• The Bell State Measurement yields two classical outcomes. These outcomes provideinformation about the correlations between Alice's qubit and her entangled particle.• Alice communicates her measurement outcomes to Bob using classical communicationchannels.• Upon receiving Alice's classical information, Bob applies a series of quantum operations tohis particle.• These operations are designed to transform Bob's particle into a state that approximatesthe original state of Alice's qubit.
  • 52.
  • 53.
    Criteria 4: QuantumGatesBy Rosa Ayyash 53• An optical parametric oscillator is a device that exploits nonlinearinteractions in materials to produce pairs of entangled photons.• Within an OPO, the entangled pair is typically generated through aprocess known as spontaneous parametric down-conversion, where ahigh-energy photon is converted into two lower-energy entangledphotons.• The nonlinearity of the OPO's interactionscan be harnessed to perform two-qubitquantum gate operations on the entangled photonpairs.
  • 54.
    Criteria 5: Measurement•In the context of quantum optics, qubits can berepresented using the properties of light, such as itsamplitude and phase.• These properties can be quadratures of the light, whichencode information about the quantum state of thequbit.• Quadrature measurements refer to measurementsof a pair of complementary quantum observables knownas quadratures. These observables are related to theposition and momentum of the quantum system, and theycan be precisely determined using specific optical techniques.• By measuring one of the quadratures of light associated with the qubit, itbecomes possible to distinguish between different qubit states.By Rosa Ayyash 54
  • 55.
    Advantages & DisadvantagesAdvantagesDisadvantagesScalability: The compatibility of photonic systems withexisting fiber-optic infrastructure provides a promisingpathway for scalability.Difficulty in generating GKP states: GKP states arecharacterized by their narrow Gaussian distribution inthe phase-spaceOperation at room temperature: This significantlysimplifies the experimental setup and reduces thecomplexity and cost of maintaining extremely lowtemperaturesError Correction Complexity: implementing errorcorrection codes can be complex and resource-intensive, requiring additional qubits and operationsthat increase the overall computational overhead.Modularity & Networkability: naturally suited formodular quantum systems. Multiple photonic qubitscan be generated, manipulated, and entangled usingstandard optical components.Low overheads for fault-tolerance: error resilience dueto their weak interaction with the environment.By Rosa Ayyash 55
  • 56.
  • 57.
    Criteria 1: WellDefined Qubit• This approach involves trapping electrons in silicon quantum dots, asemiconductor material, as qubits.• The spin of the electron (up and down) consists our two-level system.By Rosa Ayyash 57Approach1
  • 58.
    Criteria 1: WellDefined Qubit• Another method involves using the nuclearspins of a donor atom embedded in Silicon asqubits.• A single Silicon atom is replaced by a Group Vdonor (P, As, Sb, Bi)• An extra electron is bonded to the donornucleus via the Coulomb potential• These qubits have relatively long coherencetimes, which is important for error correctionin quantum computing.By Rosa Ayyash 58Approach2
  • 59.
    Criteria 2: Initialization•Initialization can be achieved using a single electron transistor (SET)and the energy levels associated with the electron's spin states.• To initialize the qubit, the Fermi level of the single electron transistor isadjusted or tuned to a specific energy level.• By tuning the Fermi level, it's possible toposition it between the energy levels ofthe spin-up and spin-down states of theelectron in the qubit.By Rosa Ayyash 59
  • 60.
    Criteria 3: LongDecoherenceTimes• To improve on the decoherence time, one should use isotopicallypurified Silicon; Natural Silicon is not recommended for this purpose.• Natural Si is composed of approximately:1628𝑆𝑖 𝑏𝑦 92%1629𝑆𝑖 𝑏𝑦 5%1630𝑆𝑖 𝑏𝑦 3%• 1629𝑆𝑖 which has an odd number of nucleons, has a non-zero nuclearspin. This nuclear spin can interact with the spins of electrons, othernuclei in the silicon lattice, or any eternal magnetic field leading todecoherence of the quantum states of qubits.By Rosa Ayyash 60
  • 61.
    Criteria 4: QuantumGates• To execute a single-qubit quantum gate, an oscillating magnetic field isapplied.• This magnetic field is generated using an on-chipmicrowave antenna, which emits microwaves at a specificfrequency.• The frequency of the microwave field is chosen to beresonant with the energy gap between the spin-down andspin-up states of the qubit.• The oscillating magnetic field effectively drives the qubit between itstwo quantum states, implementing a controlled evolution thatcorresponds to a specific quantum gate operation.By Rosa Ayyash 61
  • 62.
    Criteria 4: QuantumGates• Two qubits can be entangled by utilizing flip-flop qubits, which resultfrom the antiparallel spin states of a donor nucleus and an electron.• The interaction between these qubits can be established through theelectric dipole interaction.• This interaction occurs when eachelectron is pulled away from its donornucleus.• The spatial separation of the electronand the nucleus leads to a coupling between their spin states, enablingthe creation of entanglement.By Rosa Ayyash 62Approach1
  • 63.
    Criteria 4: QuantumGates• Entanglement can also be generated between two donor nuclear spinsby exploiting their hyperfine interaction with a shared electron spin.• The hyperfine interaction is a magnetic interaction between a nuclearspin and an electron spin.• By manipulating the shared electron spin,the nuclear spins of the two donors canbecome entangled through their interactionswith this common mediator.By Rosa Ayyash 63Approach2
  • 64.
    Criteria 4: QuantumGates• When particles with antisymmetric wave functions (such as fermions) areexchanged, their spatial and spin coordinates become correlated in a waythat influences their overall behavior. This is known as exchange interaction(SWAP or CROT gates in quantum computing)• Two electron spins can be entangled through the exchange interaction iftheir wavefunctions overlap significantly.• This overlap occurs when the spatial separation between the electronwavefunctions is minimized.• In this scenario, the exchange interaction becomes significant, leading to thecreation of entanglement between the electron spins.By Rosa Ayyash 64Approach3
  • 65.
    Criteria 5: MeasurementInstate |1> In state |0>• The associated electron has sufficient energy totunnel from its current location onto a singleelectron transistor (SET) island.• As the electron tunnels onto the SET island, italters the local charge environment.• This change in the charge state of the SET islandaffects the electrical properties of the singleelectron transistor, leading to a measurablechange in the current passing through thetransistor.• This change in current serves as an indication thatthe qubit is in the |1⟩ state.• The associated electron does not possess enoughenergy to overcome the energy barrier andtunnel onto the SET island.• Consequently, the charge environment of the SETisland remains unchanged, and the currentflowing through the single electron transistorremains unaffected.• This lack of change in current serves as anindicator that the qubit is in the |0⟩ state.By Rosa Ayyash 65
  • 66.
    Advantages & DisadvantagesAdvantagesDisadvantagesIntegrated Electronics: Silicon qubits can be integratedwith classical electronic components on the same chip,enabling hybrid quantum-classical systems and easingqubit control and readout.Fabrication Challenges: The design and fabrication ofsilicon-based qubits with high fidelity can be complexand may require advanced nanofabrication techniques.Potential for Room Temperature Operation: Somesilicon-based qubits show promise for operation athigher temperatures compared to other qubitplatforms, potentially reducing the need for extremecooling.Isotope Enrichment: Enhancing coherence oftenrequires isotopic enrichment of silicon, which can betechnically challenging and increase production costs.Decoherence: Despite relatively long coherence times,silicon qubits still suffer from decoherence due tointeractions with their environment, which can limitthe performance of quantum operations.By Rosa Ayyash 66
  • 67.
  • 68.
    From Womanium YTChannelBy Rosa Ayyash 68• https://youtu.be/qhLSuF_42hE?list=PL_wGNAk5B0pUVk2G7VvjHWA-P_uorDB7X• https://youtu.be/4HqDZ22yWS4?list=PL_wGNAk5B0pUVk2G7VvjHWA-P_uorDB7X• https://youtu.be/TFL-N0hRBkI?list=PL_wGNAk5B0pUVk2G7VvjHWA-P_uorDB7X• https://youtu.be/ieKG8firTOU?list=PL_wGNAk5B0pUVk2G7VvjHWA-P_uorDB7X• https://youtu.be/mBEFGbYMMuU?list=PL_wGNAk5B0pUVk2G7VvjHWA-P_uorDB7X• https://youtu.be/pFP7RvD9HvQ?list=PL_wGNAk5B0pUVk2G7VvjHWA-P_uorDB7X• https://youtu.be/tWdC50pUqus?list=PL_wGNAk5B0pUVk2G7VvjHWA-P_uorDB7X• https://youtu.be/7AQDTM-vw60?list=PL_wGNAk5B0pUVk2G7VvjHWA-P_uorDB7X
  • 69.
    DiVincenzo, David P."The physical implementation of quantum computation." Fortschritte der Physik:Progress of Physics 48.9‐11 (2000): 771-783.• Superconducting qubits:Vool, Uri, and Michel Devoret. "Introduction to quantum electromagnetic circuits." InternationalJournal of Circuit Theory and Applications 45.7 (2017): 897-934.Kjaergaard, Morten, et al. "Superconducting qubits: Current state of play." Annual Review ofCondensed Matter Physics 11 (2020): 369-395.Guo, Shaojun, et al. "Scalable quantum computational chemistry with superconducting qubits." arXivpreprint arXiv:2212.08006 (2022).Hyyppä, Eric, et al. "Unimon qubit." Nature Communications 13.1 (2022): 6895.• Neutral Atom Qubits:Henriet, Loïc, et al. "Quantum computing with neutral atoms." Quantum 4 (2020): 327.Ravets, Sylvain, et al. "Coherent dipole–dipole coupling between two single Rydberg atoms at anelectrically-tuned Förster resonance." Nature Physics 10.12 (2014): 914-917.By Rosa Ayyash 69
  • 70.
    • Si-based Qubits:Kane,B. A silicon-based nuclear spin quantum computer. Nature 393, 133–137 (1998).https://doi.org/10.1038/30156Pla, J., Tan, K., Dehollain, J. et al. A single-atom electron spin qubit in silicon. Nature 489, 541–545(2012). https://doi.org/10.1038/nature11449Morello, A., Pla, J., Zwanenburg, F. et al. Single-shot readout of an electron spin in silicon. Nature 467,687–691 (2010). https://doi.org/10.1038/nature09392• Photonic Qubits:Duan, L-M., and H. J. Kimble. "Scalable photonic quantum computation through cavity-assistedinteractions." Physical review letters 92.12 (2004): 127902.• Trapped-ions Qubits:Bruzewicz, Colin D., et al. "Trapped-ion quantum computing: Progress and challenges." AppliedPhysics Reviews 6.2 (2019).https://www.iqsdirectory.com/articles/chiller/laser-coolers.htmlBy Rosa Ayyash 70

Editor's Notes

  • #14 A Cooper pair is a concept in condensed matter physics that refers to a pair of electrons with opposite spins and momenta that interact in such a way that they form a quantum mechanical bound state. This pairing phenomenon is responsible for the phenomenon of superconductivity, where certain materials at very low temperatures exhibit zero electrical resistance and the expulsion of magnetic fields.The Cooper pair number represents the number of Cooper pairs present in a superconducting material or system. Since each Cooper pair consists of two electrons, the Cooper pair number can also be thought of as twice the number of electrons involved in the pairing.the term "superconducting phase" refers to the macroscopic quantum state that a superconducting material adopts when it transitions into the superconducting state. This phase is characterized by the condensation of Cooper pairs.
  • #29 Laser cooling is a multi-process that includes a number of techniques in which atomic and molecular samples are cooled down to a temperature near absolute zero. These techniques depend on the fact that when an object, which is usually an atom, re-emits a photon its momentum is subject to change.
  • #31 Figure: Quantum states under decoherence; (a) being the strongest (d) with zero decoherence.
  • #47 - Polarization refers to the orientation of the electric field vector of a photon's electromagnetic wave. Photons can be polarized in different ways, such as horizontal (|H⟩) or vertical (|V⟩), which can be thought of as the basis states for a photonic qubit.
  • #48 - Polarization refers to the orientation of the electric field vector of a photon's electromagnetic wave. Photons can be polarized in different ways, such as horizontal (|H⟩) or vertical (|V⟩), which can be thought of as the basis states for a photonic qubit.
  • #49 From left to right: beam splitter / wave plate / photo detector
  • #55 Figure representing quadrature diagram where multiple quantum optical states are living
  • #65 the exchange interaction: a quantum mechanical effect that results from the exchange of particles, arising from the indistinguishability of identical particles
[8]ページ先頭
©2009-2025 Movatter.jp