Reinforcement-learning-assisted quantum optimization

Wauters, Matteo M.; Panizon, Emanuele; Mbeng, Glen Bigan; Santoro, Giuseppe E.

doi:10.1103/physrevresearch.2.033446

Cited by 65 publications

(43 citation statements)

References 31 publications

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“…Recent work has improved the original QAOA, for instance, by aggregating only the best sampled candidate solutions [15] and carefully choosing the mixer operator to improve convergence [26][27][28][29], empirically. Reinforcement learning [30,31], multi-start methods [32], and local optimization [33] help navigate the QAOA optimization landscape. Algorithms such as the Hamiltonian Variational Ansatz produce optimization landscapes that are easier to navigate [34].…”

Section: Introductionmentioning

confidence: 99%

Warm-starting quantum optimization

Egger

Mareček

Woerner

2021

Quantum

148

111

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There is an increasing interest in quantum algorithms for problems of integer programming and combinatorial optimization. Classical solvers for such problems employ relaxations, which replace binary variables with continuous ones, for instance in the form of higher-dimensional matrix-valued problems (semidefinite programming). Under the Unique Games Conjecture, these relaxations often provide the best performance ratios available classically in polynomial time. Here, we discuss how to warm-start quantum optimization with an initial state corresponding to the solution of a relaxation of a combinatorial optimization problem and how to analyze properties of the associated quantum algorithms. In particular, this allows the quantum algorithm to inherit the performance guarantees of the classical algorithm. We illustrate this in the context of portfolio optimization, where our results indicate that warm-starting the Quantum Approximate Optimization Algorithm (QAOA) is particularly beneficial at low depth. Likewise, Recursive QAOA for MAXCUT problems shows a systematic increase in the size of the obtained cut for fully connected graphs with random weights, when Goemans-Williamson randomized rounding is utilized in a warm start. It is straightforward to apply the same ideas to other randomized-rounding schemes and optimization problems.

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Section: Introductionmentioning

confidence: 99%

Warm-starting quantum optimization

Egger

Mareček

Woerner

2021

Quantum

148

111

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“…In the learning process, we use a reward setting that reflects the AQC performance on the most difficult factorization instances. Using a soft-actor-critic RL method, we find the learning process has an astonishing convergence speed-it converges within only a few hundred measurement steps, significantly faster as compared to previous studies using RL for quantum state preparation [22], for parameter configuration in quantum approximate optimization [23], and for adiabatic quantum algorithm design [24], which takes about 10 4 to 10 6 measurement steps. The configured AQC algorithm produces an improved success probability, more evenly distributed over different factorization instances as compared with the un-configured algorithm.…”

mentioning

confidence: 77%

Hard instance learning for quantum adiabatic prime factorization

Lin,

Zhang,

Zhang

et al. 2021

Preprint

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Prime factorization is a difficult problem with classical computing, whose exponential hardness is the foundation of Rivest-Shamir-Adleman (RSA) cryptography. With programmable quantum devices, adiabatic quantum computing has been proposed as a plausible approach to solve prime factorization, having promising advantage over classical computing. Here, we find there are certain hard instances that are consistently intractable for both classical simulated annealing and un-configured adiabatic quantum computing (AQC). Aiming at an automated architecture for optimal configuration of quantum adiabatic factorization, we apply a deep reinforcement learning (RL) method to configure the AQC algorithm. By setting the success probability of the worst-case problem instances as the reward to RL, we show the AQC performance on the hard instances is dramatically improved by RL configuration. The success probability also becomes more evenly distributed over different problem instances, meaning the configured AQC is more stable as compared to the un-configured case. Through a technique of transfer learning, we find prominent evidence that the framework of AQC configuration is scalable-the configured AQC as trained on five qubits remains working efficiently on nine qubits with a minimal amount of additional training cost.

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“…The variational parameters are optimized using a classical optimization routine. While there are many options for this procedure [34][35][36][37], all of them seek to obtain an approximate solution to the optimization problem by maximizing…”

Section: Quantum Approximate Optimization Algorithmmentioning

confidence: 99%