3.7 Decades of Quantum Computing

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自从理查德·费曼在1982年提出用量子积木制造的计算机可能更强大以来，量子计算模型、实现和算法已经有了很多研究。肖尔对量子因子分解算法的发现推动了进一步的活动，尽管仍存在着重大的实际障碍。量子退火已被证明是一种更实用的替代方法，在现实问题的适用性方面也有了进一步的发展。目前，这种方法的原始应用已经存在，并将随着量子比特计数、互连性和控制的短期改进而接近经济可行性。

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1 .3.7 Decades of Quantum Computing Edward (Denny) Dahl D‐Wave Systems April 3, 2019

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

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

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

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