3.7 Decades of Quantum Computing

Edward (Denny) Dahl D‐Wave Systems April 3, 2019 Simulating Physics with Computers – Richard Feynman

International Journal of Theoretical Physics, Vol. 21, Nos. 6/7, 1982

Superconducting loops Trapped ions Topological matter RF SQUIDS Ytterbium atoms & lasers Majorana fermions

Kamerlingh Onnes Wolfgang Paul Kang Wang Nobel prize ‐ 1913 Hans Dehmelt Shoucheng Zhang Nobel prize – 1989 Nobel prize – ???? Brian Josephson Nobel prize – 1973

gates

This example quantum circuit has nine qubits and so the wavefunction is a complex vector of size 2 512.

Each gate acts on this wavefunction as a unitary matrix of size 512 x 512.

Measurement projects the qubit vector onto a subspace.

time

Peter Shor’s algorithm (1994) relies heavily on number theory and

the Quantum Fourier Transform, which is 3‐qubit QFT: 𝜔𝑒 essentially an FFT 11 111111 (Fast Fourier 1𝜔 𝜔 𝜔 𝜔 𝜔 𝜔 𝜔 Transform) as 1𝜔 𝜔 𝜔 1𝜔 𝜔 𝜔 1 1𝜔 𝜔 𝜔 𝜔 𝜔 𝜔 𝜔 implemented on a 𝑈 2 1𝜔 1𝜔 1𝜔 1𝜔 gate model quantum 1𝜔 𝜔 𝜔 𝜔 𝜔 𝜔 𝜔 computer. 1𝜔 𝜔 𝜔 1𝜔 𝜔 𝜔 1𝜔 𝜔 𝜔 𝜔 𝜔 𝜔 𝜔

• Classical computing has error correction – E.g., SECDED is Single Error Correct Double Error Detect • Peter Shor (1995) showed that certain kinds of errors in a Gate Model Quantum Computer could be corrected: – Shor code: 1 logical qubit requires 9 physical qubits – Steane code: 1 logical qubit requires 7 physical qubits – CSS codes: 1 logical qubit requires 5 physical qubits • General purpose error correcting codes (required for factoring, chemistry, etc.) take many more qubits: – Gottesman: 1 logical qubit requires >100 physical qubits

– Fowler: 𝐹𝑒𝑆with 112 orbitals requires 27,000,000 physical qubits – O’Gorman: 1000‐bit Shor requires 173,000,000 physical qubits

D‐Wave chose Quantum Annealing over Gate Model after an extensive evaluation of both architectures and all implementation technologies

2011 2013 2015 2017 DW‐One DW‐Two DW‐2X DW‐2000Q 128 qubits 512 qubits 1152 qubits 2048 qubits 352 couplers 1472 couplers 3360 couplers 6016 couplers

Lockheed/USC Google/NASA LANL

Quantum Hamiltonian is an operator on Hilbert space:

ℋ 𝑠𝐴𝑠𝜎 𝐵 𝑠 𝑎 𝜎 𝑏 𝜎 𝜎

transverse field

Corresponding classical optimization problem:

Obj𝑎,𝑏;𝑞𝑎𝑞 𝑏𝑞𝑞

D‐Wave Applications

Optimization Machine Learning Material simulation

NASA – Scheduling Google ‐ Qboost Harris ‐ 3D Spin Glass applications

King ‐ 2D XY model Volkswagen – Traffic LANL – Deep learning with Kosterlitz‐ flow optimization vs. quantum inference Thouless phase transition

Recruit – Display ORNL ‐ quantum advertising magnetization plateaus optimization

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The world Quantum of Computing applications

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