Post on 30-May-2020
3.7 Decades of Quantum Computing
Edward (Denny) Dahl
D‐Wave Systems
April 3, 2019
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Simulating Physics with Computers – Richard Feynman
International Journal of Theoretical Physics, Vol. 21, Nos. 6/7, 1982
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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 – ????
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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
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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
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Waves and noise
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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
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A new model of quantum computing: Annealing
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Quantum annealing finds minima on a landscape
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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
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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
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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
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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
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Applying quantum annealing to databases
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Remote Quantum Computing: LEAP & Ocean
FREE quantum computing at https://cloud.dwavesys.com
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The next step
The worldof
applications
QuantumComputing
Thank you