3.7 Decades of Quantum Computing



1.3.7 Decades of Quantum Computing Edward (Denny) Dahl D‐Wave Systems April 3, 2019

2.Simulating Physics with Computers – Richard Feynman International Journal of Theoretical Physics, Vol. 21, Nos. 6/7, 1982 Copyright © D‐Wave Systems Inc. 2

3.Q: How do you build a qubit? A: Carefully 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 Copyright © D‐Wave Systems Inc. 3

4.Standard model of quantum computing 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 vector onto a subspace. qubit time Copyright © D‐Wave Systems Inc. 4

5.Shor’s algorithm Peter Shor’s algorithm (1994) relies heavily on number theory and the Quantum Fourier Transform, which is 3‐qubit QFT: 𝜔 𝑒 essentially an FFT 1 1 1 1 1 1 1 1 (Fast Fourier 1 𝜔 𝜔 𝜔 𝜔 𝜔 𝜔 𝜔 Transform) as 1 𝜔 𝜔 𝜔 1 𝜔 𝜔 𝜔 1 1 𝜔 𝜔 𝜔 𝜔 𝜔 𝜔 𝜔 implemented on a 𝑈 gate model quantum 2 1 𝜔 1 𝜔 1 𝜔 1 𝜔 1 𝜔 𝜔 𝜔 𝜔 𝜔 𝜔 𝜔 computer. 1 𝜔 𝜔 𝜔 1 𝜔 𝜔 𝜔 1 𝜔 𝜔 𝜔 𝜔 𝜔 𝜔 𝜔 Copyright © D‐Wave Systems Inc. 5

6.Waves and noise Copyright © D‐Wave Systems Inc. 6

7.Error correction • 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: 𝐹𝑒 𝑆 with 112 orbitals requires 27,000,000 physical qubits – O’Gorman: 1000‐bit Shor requires 173,000,000 physical qubits Copyright © D‐Wave Systems Inc. 7

8.A new model of quantum computing: Annealing Copyright © D‐Wave Systems Inc. 8

9.Quantum annealing finds minima on a landscape Copyright © D‐Wave Systems Inc. 9

10.D‐Wave is born (1999) & goes QA (2004) D‐Wave chose Quantum Annealing over Gate Model after an extensive evaluation of both architectures and all implementation technologies Copyright © D‐Wave Systems Inc. 10

11.D‐Wave product generations 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 Copyright © D‐Wave Systems Inc. 11

12.Quantum & Classical Programming Models Quantum Hamiltonian is an operator on Hilbert space: ℋ 𝑠 𝐴 𝑠 𝜎 𝐵 𝑠 𝑎 𝜎 𝑏 𝜎 𝜎 transverse field Corresponding classical optimization problem: Obj 𝑎 , 𝑏 ; 𝑞 𝑎𝑞 𝑏 𝑞𝑞 s = t/T Copyright © D‐Wave Systems Inc. 12

13.Three paths to programming the D‐Wave 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 Copyright © D‐Wave Systems Inc. 13

14.Applying quantum annealing to databases Copyright © D‐Wave Systems Inc. 14

15.Remote Quantum Computing: LEAP & Ocean FREE quantum computing at https://cloud.dwavesys.com Copyright © D‐Wave Systems Inc. 15

16.The next step The world Quantum of Computing applications Thank you Copyright © D‐Wave Systems Inc. 16