Ants Remm Roland Matt Quantum Adiabatic Computation Overview

Ants Remm, Roland Matt Quantum Adiabatic Computation

Overview § The problems solved § The methods § Simulated annealing § Quantum adiabatic computation § Simulated quantum annealing § Results § Comparing SA, QA, SQA § Is there a quantum speedup? D-PHYS first part by Ants second part by Roland Ants Remm, Roland Matt | 29. 04. 2016 | 2

The spin glass system § D-PHYS Ants Remm, Roland Matt | 29. 04. 2016 | 3

Problem equivalence § Many different optimization problems can be reduced to finding the ground state of the spin glass system: § § D-PHYS The knapsack problem Finding Hamiltonian cycles Graph colouring Image restoration, etc. Ants Remm, Roland Matt | 29. 04. 2016 | 4

Problem equivalence: Image restoration D-PHYS Ants Remm, Roland Matt | 29. 04. 2016 | 5

Problem equivalence: Fair partitioning § D-PHYS Ants Remm, Roland Matt | 29. 04. 2016 | 6

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Simulated annealing § D-PHYS Ants Remm, Roland Matt | 29. 04. 2016 | 8

Simulated annealing: Why it works § D-PHYS Ants Remm, Roland Matt | 29. 04. 2016 | 9

Simulated annealing: How it works: The Metropolis algorithm § D-PHYS Ants Remm, Roland Matt | 29. 04. 2016 | 10

Simulated annealing: The shortcomings D-PHYS Thermal jump Energy § The spin glass system has typically many local minima § High probability of having relatively high and narrow potential barriers § For simulated annealing, only the height of the barrier matters § Idea: what if we could tunnel through the barrier Quantum tunnelling Configuration Ants Remm, Roland Matt | 29. 04. 2016 | 11

Quantum adiabatic computation § D-PHYS Ants Remm, Roland Matt | 29. 04. 2016 | 12

Quantum adiabatic computation: The adiabatic theorem § D-PHYS Ants Remm, Roland Matt | 29. 04. 2016 | 13

Quantum adiabatic computation: Motivation for the initial Hamiltonian § D-PHYS Ants Remm, Roland Matt | 29. 04. 2016 | 14

Quantum adiabatic computation: Single qubit example § Let’s consider the simplest example: finding the ground state of a single qubit D-PHYS Ants Remm, Roland Matt | 29. 04. 2016 | 15

Quantum adiabatic computation: Single qubit example D-PHYS Ants Remm, Roland Matt | 29. 04. 2016 | 16

Quantum adiabatic computation: Single qubit example § Commuting Hamiltonians means that energy levels cross D-PHYS Ants Remm, Roland Matt | 29. 04. 2016 | 17

Quantum adiabatic computation: NP-hard example D-PHYS Ants Remm, Roland Matt | 29. 04. 2016 | 18

Quantum adiabatic computation: NP-hard example § D-PHYS Ants Remm, Roland Matt | 29. 04. 2016 | 19

Quantum adiabatic computation: NP-hard example D-PHYS Ants Remm, Roland Matt | 29. 04. 2016 | 20

Quantum adiabatic computation: NP-hard example § D-PHYS Ants Remm, Roland Matt | 29. 04. 2016 | 21

Simulated quantum annealing § Is a quantum Monte Carlo algorithm § Same annealing schedule as the quantum annealer § Start with a strong initial transverse field which goes to zero during simulation § Start ramping up the problem Hamiltonian from zero § Monte Carlo dynamics instead of unitary evolution § Could use discrete or continuous time path integrals D-PHYS Ants Remm, Roland Matt | 29. 04. 2016 | 22

Comparing SA, QA and SQA D-PHYS Ants Remm, Roland Matt | 29. 04. 2016 | 23

One needs to note the difference D-PHYS Ants Remm, Roland Matt | 29. 04. 2016 | 24

How the problem is set up D-PHYS Ants Remm, Roland Matt | 29. 04. 2016 | 25

Similarities between D-Wave and SQA D-PHYS Ants Remm, Roland Matt | 29. 04. 2016 | 26

Correlation plots Another way of comparing algorithms D-PHYS Ants Remm, Roland Matt | 29. 04. 2016 | 27

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Pitfalls of detecting quantum speed-up D-PHYS Ants Remm, Roland Matt | 29. 04. 2016 | 29

Speedup of DW 2 compared to SA • Scaling of the highest quantile is the most informative • High quantiles are hard for DW 2 • Range 7 is harder than Range 1 • Overall positive slope shows that DW is better D-PHYS Ants Remm, Roland Matt | 29. 04. 2016 | 30

We have a quantum device, but is there an universal quantum speedup? D-PHYS Ants Remm, Roland Matt | 29. 04. 2016 | 31

References § http: //people. fas. harvard. edu/~lucas/zurich. CStalk. pdf § Cohen, Eliahu, and Boaz Tamir. "D-Wave and predecessors: From simulated to quantum annealing. " International Journal of Quantum Information 12. 03 (2014): 1430002. § Farhi, Edward, et al. "Quantum computation by adiabatic evolution. " ar. Xiv preprint quant-ph/0001106 (2000). § Farhi, Edward, et al. "A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem. " Science 292. 5516 (2001): 472 -475. § Rønnow, Troels F. , et al. "Defining and detecting quantum speedup. "Science 345. 6195 (2014): 420 -424. § Boixo, Sergio, et al. "Evidence for quantum annealing with more than one hundred qubits. " Nature Physics 10. 3 (2014): 218 -224 D-PHYS Ants Remm, Roland Matt | 29. 04. 2016 | 32

Thank you! D-PHYS Ants Remm | 29. 04. 2016 | 33