arXiv subjects

Puya Mirkarimi

Publications and source records attributed to Puya Mirkarimi.

3 recordsLinked to original sources

arXiv2024

Experimental demonstration of improved quantum optimization with linear Ising penalties

The standard approach to encoding constraints in quantum optimization is the quadratic penalty method. Quadratic penalties introduce additional couplings and energy scales, which can be detrimental to the performance of a quantum optimizer. In quantum annealing experiments performed on a D-Wave Advantage, we explore an alternative penalty method that only involves linear Ising terms and apply it to a customer data science problem. Our findings support our hypothesis that the linear Ising penalty method should improve the performance of quantum optimization compared to using the quadratic penalty method due to its more efficient use of physical resources. Although the linear Ising penalty method is not guaranteed to exactly implement the desired constraint in all cases, it is able to do so for the majority of problem instances we consider. For problems with many constraints, where making all penalties linear is unlikely to be feasible, we investigate strategies for combining linear Ising penalties with quadratic penalties to satisfy constraints for which the linear method is not well-suited. We find that this strategy is most effective when the penalties that contribute most to limiting the dynamic range are removed.

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arXiv2024

Quantum optimization with linear Ising penalty functions for customer data science

Constrained combinatorial optimization problems, which are ubiquitous in industry, can be solved by quantum algorithms such as quantum annealing (QA) and the quantum approximate optimization algorithm (QAOA). In these quantum algorithms, constraints are typically implemented with quadratic penalty functions. This penalty method can introduce large energy scales and make interaction graphs much more dense. These effects can result in worse performance of quantum optimization, particularly on near-term devices that have sparse hardware graphs and other physical limitations. In this work, we consider linear Ising penalty functions, which are applied with local fields in the Ising model, as an alternative method for implementing constraints that makes more efficient use of physical resources. We study the behaviour of the penalty method in the context of quantum optimization for customer data science problems. Our theoretical analysis and numerical simulations of QA and the QAOA indicate that this penalty method can lead to better performance in quantum optimization than the quadratic method. However, the linear Ising penalty method is not suitable for all problems as it cannot always exactly implement the desired constraint. In cases where the linear method is not successful in implementing all constraints, we propose that schemes involving both quadratic and linear Ising penalties can be effective.

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arXiv2023

Comparing the hardness of MAX 2-SAT problem instances for quantum and classical algorithms

An algorithm for a particular problem may find some instances of the problem easier and others harder to solve, even for a fixed input size. We numerically analyse the relative hardness of MAX 2-SAT problem instances for various continuous-time quantum algorithms and a comparable classical algorithm. This has two motivations: to investigate whether small-sized problem instances, which are commonly used in numerical simulations of quantum algorithms for benchmarking purposes, are a good representation of larger instances in terms of their hardness to solve, and to determine the applicability of continuous-time quantum algorithms in a portfolio approach, where we take advantage of the variation in the hardness of instances between different algorithms by running them in parallel. We find that, while there are correlations in instance hardness between all of the algorithms considered, they appear weak enough that a portfolio approach would likely be desirable in practice. Our results also show a widening range of hardness of randomly generated instances as the problem size is increased, which demonstrates both the difference in the distribution of hardness at small sizes and the value of a portfolio approach that can reduce the number of extremely hard instances. We identify specific weaknesses of these quantum algorithms that can be overcome with a portfolio approach, such their inability to efficiently solve satisfiable instances (which is easy classically).

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