Bridging Classical and Quantum with SDP initialized warm-starts for QAOA

Tate, Reuben; Farhadi, Majid; Herold, Creston; Mohler, Greg; Gupta, Swati

doi:10.1145/3549554

Cited by 19 publications

(8 citation statements)

References 32 publications

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“…It is proved that the hyperparameter optimisation of classical algorithms can effectively improve the probability of achieving the Max-Cut. Meanwhile, Swati Gupta et al conducted an in-depth study to explore the effects of preprocessing of classical algorithms and max-cut relaxation solutions of low-rank local optima on the initial state of QAOA [50], and proposed an efficient QAOA-warm scheme and ensured that its initialisation generates a flatter energy landscape. The scheme is demonstrated experimentally and theoretically to outperform standard QAOA on low depth quantum circuits.…”

Section: Discussionmentioning

confidence: 99%

Artificial intelligence warm-start approach: optimizing the generalization capability of QAOA in complex energy landscapes

Zhao,

Cheng,

Wang

et al. 2024

New J. Phys.

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To address the issue of the Quantum Approximate Optimization Algorithm (QAOA) frequently encountering local minima and the cost of parameter optimization within complex non-convex optimization energy landscapes, we consider a warm-start method. This approach leverages the characteristics of transition states (TS) in the enhanced optimizer, specifically descending along unique negative curvature directions, to find smaller local minima. Our research results indicate that with the assistance of an enhanced pre-training structure of the AlphaZero AI model, the initialization generalization ability of the new optimizer is significantly enhanced across various test sets. We train on 2-SAT training sets with clause densities between α≅ 2.6 and α≅ 2.89, and transfer to more complex test sets. Additionally, the average residual energy density in transfer learning consistently remains below 0.01, even achieving a high transfer success probability of 98% in hard instances with α≅ 3.7. The search efficiency, pre-trained by ensemble learning, was significantly enhanced, while only requiring simple interpolation of a few transition points to transfer on the global optimal solutions at higher sample clause densities.

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Section: Discussionmentioning

confidence: 99%

Artificial intelligence warm-start approach: optimizing the generalization capability of QAOA in complex energy landscapes

Zhao,

Cheng,

Wang

et al. 2024

New J. Phys.

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“…In this work we study unconstrained problems involving n binary variables, and we use the stan-dard initial state |ψ 0 = |+ ⊗n . Recent work has argued in favor of using classical algorithms to generate initial states which are weighted in favor of likely good solutions [6,7], and the effect of this "warm-start" approach in conjunction with different mixers and phase separators, particularly for small number of rounds, is worth future study.…”

Section: Qaoa Reviewmentioning

confidence: 99%

The Quantum Alternating Operator Ansatz for Satisfiability Problems

Golden¹,

Bärtschi²,

O’Malley³

et al. 2023

Preprint

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We comparatively study, through largescale numerical simulation, the performance across a large set of Quantum Alternating Operator Ansatz (QAOA) implementations for finding approximate and optimum solutions to unconstrained combinatorial optimization problems. Our survey includes over 100 different mixing unitaries, and we combine each mixer with both the standard phase separator unitary representing the objective function and a thresholded version. Our numerical tests for randomly chosen instances of the unconstrained optimization problems Max 2-SAT and Max 3-SAT reveal that the traditional transverse-field mixer with the standard phase separator performs best for problem sizes of 8 through 14 variables, while the recently introduced Grover mixer with thresholding wins at problems of size 6. This result (i) corrects earlier work suggesting that the Grover mixer is a superior mixer based only on results from problems of size 6, thus illustrating the need to push numerical simulation to larger problem sizes to more accurately predict performance; and (ii) it suggests that more complicated mixers and phase separators may not improve QAOA performance.

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“…Their results are promising on simulators but are limited to relatively small graphs of up to 14 nodes (with edge probability between 20% and 80%) due to lack of computational resources. Note that there is a large literature on warm starting quantum optimisation algorithms that is not covered in detail here [93][94][95].…”

Section: Constrained Optimisation and The Quantum Alternating Operato...mentioning

confidence: 99%

A practitioner’s guide to quantum algorithms for optimisation problems

Symons,

Galvin,

Sahin

et al. 2023

J. Phys. A: Math. Theor.

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Quantum computing is gaining popularity across a wide range of scientific disciplines due to its potential to solve long-standing computational problems that are considered intractable with classical computers. One promising area where quantum computing has potential is in the speed-up of NP-hard optimisation problems that are common in industrial areas such as logistics and finance. Newcomers to the field of quantum computing who are interested in using this technology to solve optimisation problems do not have an easily accessible source of information on the current capabilities of quantum computers and algorithms. This paper aims to provide a comprehensive overview of the theory of quantum optimisation techniques and their practical application, focusing on their near-term potential for NISQ devices.The paper starts by drawing parallels between classical and quantum optimisation problems, highlighting their conceptual similarities and differences. Two main paradigms for quantum hardware are then discussed: quantum annealing and gate-based quantum computing. While quantum annealers are effective for some optimisation problems, they have limitations and cannot be used for universal quantum computation. In contrast, gate-based quantum computers offer the potential for universal quantum computation, but they face challenges with hardware limitations and accurate gate implementation. The paper provides a detailed mathematical discussion with references to key works in the field, as well as a more practical discussion with relevant examples.The most popular techniques for quantum optimisation on gate-based quantum computers, the quantum approximate optimisation (QAO) algorithm and the quantum alternating operator ansatz (QAOA) framework, are discussed in detail. However, it is still unclear whether these techniques will yield quantum advantage, even with advancements in hardware and noise reduction. The paper concludes with a discussion of the challenges facing quantum optimisation techniques and the need for further research and development to identify new, effective methods for achieving quantum advantage.

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Bridging Classical and Quantum with SDP initialized warm-starts for QAOA

Cited by 19 publications

References 32 publications

Artificial intelligence warm-start approach: optimizing the generalization capability of QAOA in complex energy landscapes

Artificial intelligence warm-start approach: optimizing the generalization capability of QAOA in complex energy landscapes

The Quantum Alternating Operator Ansatz for Satisfiability Problems

A practitioner’s guide to quantum algorithms for optimisation problems

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