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

3.7 Decades of Quantum Computing

Edward (Denny) Dahl

D‐Wave Systems

April 3, 2019

Copyright © D‐Wave Systems Inc. 2

Simulating Physics with Computers – Richard Feynman

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


Q: How do you build a qubit?A: Carefully

Superconducting loopsRF SQUIDS

Trapped ionsYtterbium atoms & lasers

Topological matterMajorana fermions

Kamerlingh Onnes

Nobel prize ‐ 1913

Brian Josephson

Nobel prize – 1973

Wolfgang PaulHans Dehmelt

Nobel prize – 1989

Kang WangShoucheng Zhang

Nobel prize – ????


Standard model of quantum computing

time

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


Shor’s algorithm

Peter Shor’s algorithm (1994) relies heavily on

number theory and the Quantum Fourier Transform, which is essentially an FFT

(Fast Fourier Transform) as

implemented on a gate model quantum

computer.

3‐qubit QFT: 𝜔 𝑒

𝑈12

1 11 𝜔

1 1𝜔 𝜔

1 𝜔1 𝜔

𝜔 𝜔𝜔 𝜔

1 1𝜔 𝜔

1 1𝜔 𝜔

1 𝜔𝜔 𝜔

𝜔 𝜔𝜔 𝜔

1 𝜔1 𝜔

1 𝜔𝜔 𝜔

1 𝜔1 𝜔

𝜔 𝜔𝜔 𝜔

1 𝜔𝜔 𝜔

1 𝜔𝜔 𝜔

1 𝜔𝜔 𝜔

𝜔 𝜔𝜔 𝜔


Waves and noise


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


A new model of quantum computing: Annealing


Quantum annealing finds minima on a landscape


D‐Wave is born (1999) & goes QA (2004)

D‐Wave chose Quantum Annealing over Gate Model after an extensive evaluation of botharchitectures and allimplementation technologies


D‐Wave product generations

2011DW‐One128 qubits352 couplers

2013DW‐Two512 qubits

1472 couplers

2015DW‐2X

1152 qubits3360 couplers

2017DW‐2000Q2048 qubits6016 couplers

Lockheed/USC Google/NASA LANL


Quantum Hamiltonian is an operator on Hilbert space:

ℋ 𝑠 𝐴 𝑠 𝜎 𝐵 𝑠 𝑎 𝜎 𝑏 𝜎 𝜎

Quantum & Classical Programming Models

s = t/T

Corresponding classical optimization problem:

Obj 𝑎 , 𝑏 ; 𝑞 𝑎 𝑞 𝑏 𝑞 𝑞

transverse field


Three paths to programming the D‐Wave

D‐Wave Applications

Optimization

NASA – Scheduling applications

Volkswagen – Traffic flow optimization

Recruit – Display advertising optimization

Machine Learning

Google ‐ Qboost

LANL – Deep learning vs. quantum inference

Material simulation

Harris ‐ 3D Spin Glass

King ‐ 2D XY model with Kosterlitz‐Thouless phase

transition

ORNL ‐ quantum magnetization plateaus


Applying quantum annealing to databases


Remote Quantum Computing: LEAP & Ocean

FREE quantum computing at https://cloud.dwavesys.com


The next step

The worldof

applications

QuantumComputing

Thank you