Training Saturation in Layerwise Quantum Approximate Optimisation

Campos, E.; Rabinovich, D.; Akshay, V.; Biamonte, J.

doi:10.48550/arxiv.2106.13814

Cited by 3 publications

(3 citation statements)

References 26 publications

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“…The underlying layer-wise trainability conjecture is proved to not be true in all cases [40], i.e., the optimization can be predestined to saturate prematurely without finding the global optimum. However, very recent work shows that, for QAOA, this saturation occurs only as p reaches closer to the number of qubits [41]. Thus, layer-wise optimization can outperform standard optimization for low-depth QAOA.…”

Section: Layer-wise Trainingmentioning

confidence: 99%

Selection and Optimization of Hyperparameters in Warm-Started Quantum Optimization for the MaxCut Problem

et al. 2022

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Today’s quantum computers are limited in their capabilities, e.g., the size of executable quantum circuits. The Quantum Approximate Optimization Algorithm (QAOA) addresses these limitations and is, therefore, a promising candidate for achieving a near-term quantum advantage. Warm-starting can further improve QAOA by utilizing classically pre-computed approximations to achieve better solutions at a small circuit depth. However, warm-starting requirements often depend on the quantum algorithm and problem at hand. Warm-started QAOA (WS-QAOA) requires developers to understand how to select approach-specific hyperparameter values that tune the embedding of classically pre-computed approximations. In this paper, we address the problem of hyperparameter selection in WS-QAOA for the maximum cut problem using the classical Goemans–Williamson algorithm for pre-computations. The contributions of this work are as follows: We implement and run a set of experiments to determine how different hyperparameter settings influence the solution quality. In particular, we (i) analyze how the regularization parameter that tunes the bias of the warm-started quantum algorithm towards the pre-computed solution can be selected and optimized, (ii) compare three distinct optimization strategies, and (iii) evaluate five objective functions for the classical optimization, two of which we introduce specifically for our scenario. The experimental results provide insights on efficient selection of the regularization parameter, optimization strategy, and objective function and, thus, support developers in setting up one of the central algorithms of contemporary and near-term quantum computing.

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Section: Layer-wise Trainingmentioning

confidence: 99%

Selection and Optimization of Hyperparameters in Warm-Started Quantum Optimization for the MaxCut Problem

et al. 2022

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“…After collecting a set of samples, the bit string associated with the best solution to the combinatorial optimization problem, i.e., the bit string z that returns the minimum value of the associated cost function C(z), should be saved as the best approximate solution to the combinatorial optimization problem of interest. We note that FALQON has similarities to other quantum circuit parameter-setting protocols that involve "greedy", layer-by-layer optimization, e.g., where a classical optimization routine is used to sequentially optimize quantum circuit parameters in order to minimize a cost function in a layer-wise manner [64][65][66][67]. In fact, the parameter-setting rule given in Eq.…”

Section: Feedback-based Algorithm For Quantum Optimizationmentioning

confidence: 99%

Lyapunov control-inspired strategies for quantum combinatorial optimization

Magann¹,

Rudinger²,

Grace³

et al. 2021

Preprint

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“…In parallel to explore the initialization strategy, another crucial topic is designing advanced training strategies of QAOA to avoid local optima and accelerate optimization. Concrete examples include modifying the objective functions [35], applying the iterative training strategy [36,37] using adaptive mixing operators [34,[38][39][40]. Despite the remarkable achievements, little progress has been made in overcoming the scalability issue of QAOAs, whereas the ultimate goal of the most advanced QAOA is solving a problem with hundreds of vertices [41].…”

Section: Introductionmentioning

confidence: 99%