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Quantum ComputingThe Why and HowJonathan BakerArgonne National Lab7-29-2019

Outline for this Talk (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?

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

Current State of Quantum Computing: NISQ● Noisy-Intermediate Scale Quantum○ 10s to 100s of qubits○ Moderate error rates○ Limited connectivity○ No error correctionIBM50 SuperconductingQubitsGoogle72 superconductingqubitsRigetti20 SuperconductingQubits

The Algorithms to Machines GapYear#QubitsGrover’s Algorithm (Database search)Shor’s Algorithm (Integer Factorization)# Qubits Needed# Qubits Buildable

The Algorithms to Machines GapYear#QubitsGAP!Grover’s Algorithm (Database search)Shor’s Algorithm (Integer Factorization)# Qubits Needed# Qubits Buildable

The Algorithms to Machines GapYear#QubitsGAP!Grover’s Algorithm (Database search)Shor’s Algorithm (Integer Factorization)# Qubits Needed# Qubits BuildableQ. Sim,Q Chem,QAOA

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

Result: Crossover by 2023!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.

Space-Time Product LimitsError rates of quantum operations limit what we can accomplish

“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

One Qubitwhen we try to “see” the state, we can onlysee 0 or 1.50% of the time we see 0.50% of the time we see 1.

One QubitIdentically prepared qubits can stillbehave randomly!This randomness is inherent in nature, andnot a limitation of our observation.

The Power of Quantum InformationWhy simulating quantum systems becomes intractable quickly

The Power of Quantum InformationWhy simulating quantum systems becomes intractable quickly- The state of n qubits isdescribed by 2ncoefficients.- Adding one qubit doublesthe dimension.- This is known assuperposition.

The Power of Quantum InformationWhy simulating quantum systems becomes intractable quicklyclassicalprobabilisticbit

The Power of Quantum InformationWhy simulating quantum systems becomes intractable quicklyQuantum bit(qubit)

The Power of Quantum 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.

Quantum Information ProcessingUsing Vectors Matrices and Projections

Quantum Information ProcessingUsing Vectors Matrices and ProjectionsQuantum Circuit Model

Quantum Information ProcessingUsing Vectors Matrices and ProjectionsImportant Result:1-qubit & 2-qubit gates (i.e. local operations)are sufficient for universal computation[Barenco et al. 95].

Example Quantum Gates: The Hadamard Gate

Example Quantum Gates: The Hadamard GateH Creates Superposition!

Example Quantum Gates: The Controlled-NOT GateThe Quantum “If” (CNOT)

Example Quantum Gates: The Controlled-NOT GateThe Quantum “If” (CNOT)A CNOT flips thetarget bit if thecontrol bit is 1

Quantum Algorithm: Bernstein-Vaziranixn-1… x1x0

Quantum Algorithm: Bernstein-Vaziranixn-1… x1x0THE ORACLE(sn-1… s1s0)

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.

Quantum Algorithm: Bernstein-VaziraniClassical Vs. Quantum OracleClassicalDot-ProductOracleTheOracle

Quantum Algorithm: Bernstein-VaziraniClassical Vs. Quantum OracleClassicalDot-ProductOracleTheOracleQuantumDot-Product OracleDifference? Must be reversible!The Oracle

Quantum Algorithm: Bernstein-VaziraniImplementing the OracleThe control pattern for the oracle depends on the hiddenbitstring.

Quantum Algorithm: Bernstein-VaziraniImplementing the OracleThe control pattern for the oracle depends on the hiddenbitstring.S = 0101

Quantum Algorithm: Bernstein-VaziraniImplementing the OracleThe control pattern for the oracle depends on the hiddenbitstring.S = 1111

Quantum Algorithm: Bernstein-VaziraniThe Key Trick - Phase Kickback

Quantum Algorithm: Bernstein-VaziraniThe Key Trick - Phase KickbackPhasekickback!

Quantum Algorithm: Bernstein-VaziraniPutting it all together

Quantum Algorithm: Bernstein-VaziraniPutting it all togetherOracle

Quantum Algorithm: Bernstein-VaziraniPutting it all togetherOracle1011

Quantum Algorithm: Bernstein-VaziraniPutting it all togetherOracle1011Wherever there’s CNOT, phase kickback puts that control qubit in state |1>.

Quantum Algorithm: Bernstein-VaziraniWhy did 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

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Quantum Computing: The Why and How