3.7 Decades of Quantum Computing...3.7 Decades of Quantum Computing Edward (Denny) Dahl D‐Wave...
Transcript of 3.7 Decades of Quantum Computing...3.7 Decades of Quantum Computing Edward (Denny) Dahl D‐Wave...
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