Optimal Protocols in Quantum Annealing and Quantum Approximate Optimization Algorithm Problems

Brady, Lucas T.; Baldwin, Christopher L.; Bapat, Aniruddha; Kharkov, Yaroslav A.; Gorshkov, Alexey V.

doi:10.1103/physrevlett.126.070505

Cited by 87 publications

(88 citation statements)

References 29 publications

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“…Conversely, in quantum annealing architectures mapping the logical problem qubits to a graph of physical hardware qubits can be a significant challenge in the general case [79,80]. Our work is certainly not the first in applying QAOA to various relevant computational problems, and we refer the reader to a small list of examples [81][82][83]; in this work, we make an attempt to highlight some of the salient features and challenges of QAOA in the context of problems applicable to linear algebra and numerical analysis.…”

Section: Related Workmentioning

confidence: 99%

Quantum approximate optimization for hard problems in linear algebra

Borle

Elfving²,

Lomonaco

2021

SciPost Phys. Core

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The quantum approximate optimization algorithm (QAOA) by Farhi et al. is a quantum computational framework for solving quantum or classical optimization tasks. Here, we explore using QAOA for binary linear least squares (BLLS); a problem that can serve as a building block of several other hard problems in linear algebra, such as the non-negative binary matrix factorization (NBMF) and other variants of the non-negative matrix factorization (NMF) problem. Most of the previous efforts in quantum computing for solving these problems were done using the quantum annealing paradigm. For the scope of this work, our experiments were done on noiseless quantum simulators, a simulator including a device-realistic noise-model, and two IBM Q 5-qubit machines. We highlight the possibilities of using QAOA and QAOA-like variational algorithms for solving such problems, where trial solutions can be obtained directly as samples, rather than being amplitude-encoded in the quantum wavefunction. Our numerics show that even for a small number of steps, simulated annealing can outperform QAOA for BLLS at a QAOA depth of p\leq3p≤3 for the probability of sampling the ground state. Finally, we point out some of the challenges involved in current-day experimental implementations of this technique on cloud-based quantum computers.

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Section: Related Workmentioning

confidence: 99%

Quantum approximate optimization for hard problems in linear algebra

Borle

Elfving²,

Lomonaco

2021

SciPost Phys. Core

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“…The necessary conditions for an optimal solution evidence that when the final time T is long enough, there are optimal solutions such that the control Hamiltonian H * is null and the maximum possible value of the functional (2), J * max , can be reached [28]. On the other hand, below a certain critical value T c of the final time, J * max cannot be reached.…”

Section: Setup Of the Control Problemmentioning

confidence: 99%

“…However, from the standard form of QA involving a single control function, Ref. [28] has shown that a more general form of the optimal solution is of "bang-annealing-bang" type, meaning that an hybrid time-dependent control starting at the minimum allowed value and ending at the maximum possible value, with an smooth annealing segment in between is usually optimal.…”

Section: Introductionmentioning

confidence: 99%

Optimal solutions to quantum annealing using two independent control functions

Fernandes,

de Lima,

Castelano

2021

Preprint

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We investigate the quantum computing paradigm consisted of obtaining a target state that encodes the solution of a certain computational task by evolving the system with a combination of the problem-Hamiltonian and the driving-Hamiltonian.We analyze this paradigm in the light of Optimal Control Theory considering each Hamiltonian modulated by an independent control function. In the case of short evolution times and bounded controls, we analytically demonstrate that an optimal solution consists of both controls tuned at their upper bound for the whole evolution time. This optimal solution is appealing because of its simplicity and experimental feasibility. To numerically solve the control problem, we propose the use of a quantum optimal control technique adapted to limit the amplitude of the controls.As an application, we consider a teleportation protocol and compare the fidelity of the teleported state obtained for the two-control functions with the usual singlecontrol function scheme and with the quantum approximate optimization algorithm (QAOA). We also investigate the energetic cost and the robustness against systematic errors in the teleportation protocol, considering different time evolution schemes.We show that the scheme with two-control functions yields a higher fidelity than the other schemes for the same evolution time.

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“…Although adiabatic evolution and quenching are two opposite extremes with a clear discrepancy in the time-dependence of the field, relations between the two approaches have been studied [44,45]. A physical phenomenon which can occur after a quantum quench is the so-called dynamical quantum phase transition, which may be manifested from the behavior of an order parameter after the quench [46,47].…”

Section: Introductionmentioning

confidence: 99%

The quantum annealing gap and quench dynamics in the exact cover problem

Irsigler

Graß

2022

Quantum

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Quenching and annealing are extreme opposites in the time evolution of a quantum system: Annealing explores equilibrium phases of a Hamiltonian with slowly changing parameters and can be exploited as a tool for solving complex optimization problems. In contrast, quenches are sudden changes of the Hamiltonian, producing a non-equilibrium situation. Here, we investigate the relation between the two cases. Specifically, we show that the minimum of the annealing gap, which is an important bottleneck of quantum annealing algorithms, can be revealed from a dynamical quench parameter which describes the dynamical quantum state after the quench. Combined with statistical tools including the training of a neural network, the relation between quench and annealing dynamics can be exploited to reproduce the full functional behavior of the annealing gap from the quench data. We show that the partial or full knowledge about the annealing gap which can be gained in this way can be used to design optimized quantum annealing protocols with a practical time-to-solution benefit. Our results are obtained from simulating random Ising Hamiltonians, representing hard-to-solve instances of the exact cover problem.

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Optimal Protocols in Quantum Annealing and Quantum Approximate Optimization Algorithm Problems

Cited by 87 publications

References 29 publications

Quantum approximate optimization for hard problems in linear algebra

Quantum approximate optimization for hard problems in linear algebra

Optimal solutions to quantum annealing using two independent control functions

The quantum annealing gap and quench dynamics in the exact cover problem

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