Deep learning optimal quantum annealing schedules for random Ising models

Hegde, Pratibha Raghupati; Passarelli, Gianluca; Cantele, Giovanni; Lucignano, P.

doi:10.1088/1367-2630/ace547

Cited by 6 publications

(5 citation statements)

References 89 publications

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“…Thus, finding the maximum cut is equivalent to finding the ground state of the corresponding Ising Hamiltonian. This problem can be tackled using techniques from statistical and quantum physics, such as quantum and simulated annealing [16,27,30,[73][74][75][76][77][78][79][80][81], or QAOA. In what follows, we will focus on the latter.…”

Section: Maxcut Modelmentioning

confidence: 99%

“…readily generalizes equation (16). Notice that in this case we consider five variational parameters per QAOA-2CD step, hence the total number of free angles in this variant of the algorithm is 5p.…”

Section: Qaoa-2cdmentioning

confidence: 99%

“…In the last decade, variational quantum eigensolvers such as the quantum approximate optimization algorithm (QAOA) [1] have sparked the interest of the scientific community [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16], proving to be valuable tools in tackling the Hamiltonian-to-ground-state problem [1,[17][18][19].…”

Section: Introductionmentioning

confidence: 99%

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Convergence of digitized-counterdiabatic QAOA: circuit depth versus free parameters

Vizzuso,

Passarelli,

Cantele

et al. 2024

New J. Phys.

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Recently, Digitized-Counterdiabatic (CD) Quantum Approximate Optimization Algorithm (QAOA) has been proposed to make QAOA converge to the solution of an optimization problem in fewer steps, inspired by Trotterized counterdiabatic driving in continuous-time quantum annealing. In this paper, we critically revisit this approach by focusing on the paradigmatic weighted and unweighted one-dimensional MaxCut problem. We study two variants of QAOA with first and second-order CD corrections. Our results show that, indeed, higher order CD corrections allow for a quicker convergence to the exact solution of the problem at hand by increasing the complexity of the variational cost function. Remarkably, however, the total number of free parameters needed to achieve this result is independent of the particular QAOA variant analyzed for the problems considered.

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Section: Maxcut Modelmentioning

confidence: 99%

Section: Qaoa-2cdmentioning

confidence: 99%

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Convergence of digitized-counterdiabatic QAOA: circuit depth versus free parameters

Vizzuso,

Passarelli,

Cantele

et al. 2024

New J. Phys.

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“…The shape of an annealing schedule influences the performance of a QA device and optimizing the annealing schedule is an active field of research (Farhi et al, 2002;Morita, 2007;Zeng et al, 2016;Brady et al, 2021;Mehta et al, 2021;Susa and Nishimori, 2021;Venuti et al, 2021;Chen et al, 2022;Hegde et al, 2022Hegde et al, , 2023. The D-Wave annealing schedules are partly dictated by the hardware as the functions A and B cannot be chosen completely independently (Harris et al, 2010).…”

Section: (Ideal) Quantum Annealing Simulation Influence Of the Anne...mentioning

confidence: 99%

Benchmarking quantum annealing with maximum cardinality matching problems

Vert,

Willsch,

Yenilen

et al. 2024

Front. Comput. Sci.

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We benchmark Quantum Annealing (QA) vs. Simulated Annealing (SA) with a focus on the impact of the embedding of problems onto the different topologies of the D-Wave quantum annealers. The series of problems we study are especially designed instances of the maximum cardinality matching problem that are easy to solve classically but difficult for SA and, as found experimentally, not easy for QA either. In addition to using several D-Wave processors, we simulate the QA process by numerically solving the time-dependent Schrödinger equation. We find that the embedded problems can be significantly more difficult than the unembedded problems, and some parameters, such as the chain strength, can be very impactful for finding the optimal solution. Thus, finding a good embedding and optimal parameter values can improve the results considerably. Interestingly, we find that although SA succeeds for the unembedded problems, the SA results obtained for the embedded version scale quite poorly in comparison with what we can achieve on the D-Wave quantum annealers.

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“…We parameterize the schedule A(t) in terms of a finite number of continuous parameters corresponding to weights over a predefined set of functions. For instance, these functions could be a basis of trigonometric functions [31], a basis of polynomials [32,33], 'bang-bang' or on-off pulses (standard in the quantum approximate optimization algorithm (QAOA) [34,35]), or others [36,37]. In our case, we opt for a linear piecewise decomposition [38], which we iteratively refine and now describe.…”

Section: Optimizing the Schedulementioning

confidence: 99%

Diabatic quantum annealing for the frustrated ring model

Côté,

Sauvage,

Larocca

et al. 2023

Quantum Sci. Technol.

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Quantum annealing is a continuous-time heuristic quantum algorithm for solving or approximately solving classical optimization problems. The algorithm uses a schedule to interpolate between a driver Hamiltonian with an easy-to-prepare ground state and a problem Hamiltonian whose ground state encodes solutions to an optimization problem. The standard implementation relies on the evolution being adiabatic: keeping the system in the instantaneous ground state with high probability and requiring a time scale inversely related to the minimum energy gap between the instantaneous ground and excited states. However, adiabatic evolution can lead to evolution times that scale exponentially with the system size, even for computationally simple problems. Here, we study whether non-adiabatic evolutions with optimized annealing schedules can bypass this exponential slowdown for one such class of problems called the frustrated ring model. For suﬃciently optimized annealing schedules and system sizes of up to 39 qubits, we provide numerical evidence that we can avoid the exponential slowdown. Our work highlights the potential of highly-controllable quantum annealing to circumvent bottlenecks associated with the standard implementation of quantum annealing.

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Deep learning optimal quantum annealing schedules for random Ising models

Cited by 6 publications

References 89 publications

Convergence of digitized-counterdiabatic QAOA: circuit depth versus free parameters

Convergence of digitized-counterdiabatic QAOA: circuit depth versus free parameters

Benchmarking quantum annealing with maximum cardinality matching problems

Diabatic quantum annealing for the frustrated ring model

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