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Quantum Computing: The Why and How
This document provides an overview of quantum computing, including:- The current state of quantum computing technology, which involves noisy intermediate-scale quantum computers with 10s to 100s of qubits and moderate error rates. - The difference between quantum and classical information, noting that quantum information uses superposition and entanglement, exponentially increasing computational power. - An example quantum algorithm, Bernstein-Vazirani, which can solve a problem in one query that classical computers require n queries to solve, demonstrating quantum computing's potential computational advantages.
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Introduces Quantum Computing and outlines the talk focusing on its significance, challenges, and algorithm applications.
Discusses the fundamental shifts in computability, current limitations, and advantages of quantum over classical computing, highlighting algorithms like Grover’s and Shor’s.
Examines the limitations posed by error rates in quantum operations and how they restrict computational capabilities.
Describes the properties of effective quantum algorithms, including compact problem representation and exploitability with classical systems.
Introduction to the fundamentals of qubits, their behavior, and inherent randomness observed in quantum states.
Discusses why simulating quantum systems is challenging, introducing concepts like superposition and entanglement in quantum information.Description of using vectors, matrices, and projections in quantum information processing, along with the significance of 1-qubit and 2-qubit gates.
Introduction to essential quantum gates, with a focus on the Hadamard and Controlled-NOT gates and their functions in creating superposition.
Detailed exploration of the Bernstein-Vazirani quantum algorithm, illustrating the benefits of quantum oracles over classical methods and the role of phase kickback.
Quantum Computing: The Why and How
- 1.Quantum ComputingThe Whyand HowJonathan BakerArgonne National Lab7-29-2019
- 2.Outline for thisTalk (Pt 1.)1. Why Quantum Computing? What is the current state of quantum computingand what are current challenges? What are algorithms is this paradigm is idealfor?2. What is different between quantum and classical information? What makes aquantum computer that much different than a classical one?3. How can we use a quantum computer to solve concrete problems? Can we dobetter than classical computers at the same tasks?
- 3.Why Quantum Computing?●Fundamentally change what is computable (in a reasonable amount of time)○ The only known means to potentially scale computation exponentially with the number ofdevices○ We can do this by taking advantage of quantum mechanical phenomenon● Solve currently intractable problems in chemistry, simulation, and optimization● Moore’s Law is ending - quantum computing can act as a replacement insome scientific domains to help continue scaling applications● Insights in classical computing○ Many classical algorithms are “quantum-inspired”, e.g. in chemistry physics or cryptography○ Challenges classical algorithms to compete with quantum algorithms3
- 4.Current State ofQuantum Computing: NISQ● Noisy-Intermediate Scale Quantum○ 10s to 100s of qubits○ Moderate error rates○ Limited connectivity○ No error correctionIBM50 SuperconductingQubitsGoogle72 superconductingqubitsRigetti20 SuperconductingQubits
- 5.The Algorithms toMachines GapYear#QubitsGrover’s Algorithm (Database search)Shor’s Algorithm (Integer Factorization)# Qubits Needed# Qubits Buildable
- 6.The Algorithms toMachines GapYear#QubitsGAP!Grover’s Algorithm (Database search)Shor’s Algorithm (Integer Factorization)# Qubits Needed# Qubits Buildable
- 7.The Algorithms toMachines GapYear#QubitsGAP!Grover’s Algorithm (Database search)Shor’s Algorithm (Integer Factorization)# Qubits Needed# Qubits BuildableQ. Sim,Q Chem,QAOA
- 8.Closing the Gap:Software-Enabled VerticalIntegration and Co-DesignYear#QubitsGAP!Grover’s Algorithm (Database search)Shor’s Algorithm (Integer Factorization)# Qubits Needed# Qubits BuildableQ. Sim,Q Chem,QAOACo-Design
- 9.Result: Crossover by2023!Year#QubitsGAP!Grover’s Algorithm (Database search)Shor’s Algorithm (Integer Factorization)# Qubits Needed# Qubits BuildableQ. Sim,Q Chem,QAOADevelop co-designed algorithms, SW, and HW to close the gap betweenalgorithms and devices by 100-1000X, accelerating QC by 10-20 years.
- 10.Space-Time Product LimitsErrorrates of quantum operations limit what we can accomplish
- 11.Space-Time Product LimitsErrorrates of quantum operations limit what we can accomplish
- 12.“Good” Quantum Algorithms●Compact problem representation○ Functions, small molecules, small graphs● High complexity computation● Compact solution● Easily-verifiable solution● Co-processing with classical supercomputers● Can exploit a small number of quantum kernels
- 13.Introduction to theBasics
- 14.
- 15.
- 16.One Qubitwhen wetry to “see” the state, we can onlysee 0 or 1.50% of the time we see 0.50% of the time we see 1.
- 17.One QubitIdentically preparedqubits can stillbehave randomly!This randomness is inherent in nature, andnot a limitation of our observation.
- 18.
- 19.The Power ofQuantum InformationWhy simulating quantum systems becomes intractable quickly
- 20.The Power ofQuantum InformationWhy simulating quantum systems becomes intractable quickly- The state of n qubits isdescribed by 2ncoefficients.- Adding one qubit doublesthe dimension.- This is known assuperposition.
- 21.The Power ofQuantum InformationWhy simulating quantum systems becomes intractable quicklyclassicalprobabilisticbit
- 22.The Power ofQuantum InformationWhy simulating quantum systems becomes intractable quicklyclassicalprobabilisticbit
- 23.The Power ofQuantum InformationWhy simulating quantum systems becomes intractable quicklyclassicalprobabilisticbit
- 24.The Power ofQuantum InformationWhy simulating quantum systems becomes intractable quicklyclassicalprobabilisticbit
- 25.The Power ofQuantum InformationWhy simulating quantum systems becomes intractable quicklyQuantum bit(qubit)
- 26.The Power ofQuantum InformationWhy simulating quantum systems becomes intractable quicklyQuantum bit(qubit)
- 27.The Power ofQuantum InformationWhy simulating quantum systems becomes intractable quicklyQuantum bit(qubit)
- 28.The Power ofQuantum InformationWhy simulating quantum systems becomes intractable quicklyQuantum bit(qubit)
- 29.The Power ofQuantum InformationWhy simulating quantum systems becomes intractable quicklyQuantum bit(qubit)The state of an n-qubit system cannot (ingeneral) be written as the state of itsindividual components.This is known as entanglement.
- 30.Quantum Information ProcessingUsingVectors Matrices and Projections
- 31.Quantum Information ProcessingUsingVectors Matrices and Projections
- 32.Quantum Information ProcessingUsingVectors Matrices and Projections
- 33.Quantum Information ProcessingUsingVectors Matrices and Projections
- 34.Quantum Information ProcessingUsingVectors Matrices and ProjectionsQuantum Circuit Model
- 35.Quantum Information ProcessingUsingVectors Matrices and ProjectionsImportant Result:1-qubit & 2-qubit gates (i.e. local operations)are sufficient for universal computation[Barenco et al. 95].
- 36.Example Quantum Gates:The Hadamard Gate
- 37.Example Quantum Gates:The Hadamard GateH Creates Superposition!
- 38.Example Quantum Gates:The Hadamard GateH Creates Superposition!
- 39.Example Quantum Gates:The Hadamard Gate
- 40.Example Quantum Gates:The Hadamard Gate
- 41.Example Quantum Gates:The Hadamard Gate
- 42.Example Quantum Gates:The Hadamard Gate
- 43.Example Quantum Gates:The Controlled-NOT GateThe Quantum “If” (CNOT)
- 44.Example Quantum Gates:The Controlled-NOT GateThe Quantum “If” (CNOT)A CNOT flips thetarget bit if thecontrol bit is 1
- 45.
- 46.Quantum Algorithm: Bernstein-Vaziranixn-1…x1x0THE ORACLE(sn-1… s1s0)
- 47.Quantum Algorithm: Bernstein-Vaziranixn-1…x1x0THE ORACLE(sn-1… s1s0)
- 48.Quantum Algorithm: Bernstein-VaziraniClassically,we need n tries.Optimalclassicalstrategy:X = 1 0 … 0 0 (2n-1)X = 0 1 … 0 0 (2n-2)..X = 0 0 … 1 0 (2)X = 0 0 … 0 1 (1)n triesQuantumly, we need 1 try.
- 49.Quantum Algorithm: Bernstein-VaziraniClassicalVs. Quantum OracleClassicalDot-ProductOracleTheOracle
- 50.Quantum Algorithm: Bernstein-VaziraniClassicalVs. Quantum OracleClassicalDot-ProductOracleTheOracleQuantumDot-Product OracleDifference? Must be reversible!The Oracle
- 51.Quantum Algorithm: Bernstein-VaziraniImplementingthe OracleThe control pattern for the oracle depends on the hiddenbitstring.
- 52.Quantum Algorithm: Bernstein-VaziraniImplementingthe OracleThe control pattern for the oracle depends on the hiddenbitstring.S = 0101
- 53.Quantum Algorithm: Bernstein-VaziraniImplementingthe OracleThe control pattern for the oracle depends on the hiddenbitstring.S = 1111
- 54.Quantum Algorithm: Bernstein-VaziraniTheKey Trick - Phase Kickback
- 55.Quantum Algorithm: Bernstein-VaziraniTheKey Trick - Phase Kickback
- 56.Quantum Algorithm: Bernstein-VaziraniTheKey Trick - Phase KickbackPhasekickback!
- 57.Quantum Algorithm: Bernstein-VaziraniTheKey Trick - Phase KickbackPhasekickback!
- 58.Quantum Algorithm: Bernstein-VaziraniPuttingit all together
- 59.Quantum Algorithm: Bernstein-VaziraniPuttingit all togetherOracle
- 60.Quantum Algorithm: Bernstein-VaziraniPuttingit all togetherOracle1011
- 61.Quantum Algorithm: Bernstein-VaziraniPuttingit all togetherOracle1011Wherever there’s CNOT, phase kickback puts that control qubit in state |1>.
- 62.Quantum Algorithm: Bernstein-VaziraniWhydid it work?1. Classical oracles can only be queried with a single number at a time.Quantum oracles can be queried in superposition.2. We don’t just “try every answer simultaneously”. The problem had astructure that we could exploit using qubits: encode information inphases