Evaluation of QAOA based on the approximation ratio of individual samples

Larkin, Jason M.; Jonsson, Matías; Justice, Daniel; Guerreschi, Gian Giacomo

doi:10.1088/2058-9565/ac6973

Cited by 18 publications

(9 citation statements)

References 71 publications

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“…By extension, with probability ∼ 50%, any single measurement will yield a bitstring with a cut value greater than the average. These results of cut distributions have been found heuristically in [33].…”

Section: Single-shot Samplingsupporting

confidence: 66%

Sampling Frequency Thresholds for Quantum Advantage of Quantum Approximate Optimization Algorithm

Lykov

Wurtz

Poole

et al. 2022

Preprint

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In this work, we compare the performance of the Quantum Approximate Optimization Algorithm (QAOA) with state-of-the-art classical solvers such as Gurobi and MQLib to solve the combinatorial optimization problem MaxCut on 3-regular graphs. The goal is to identify under which conditions QAOA can achieve “quantum advantage” over classical algorithms, in terms of both solution quality and time to solution. One might be able to achieve quantum advantage on hundreds of qubits and moderate depth p by sampling the QAOA state at a frequency of order 10 kHz. We observe, however, that classical heuristic solvers are capable of producing high-quality approximate solutions in linear time complexity. In order to match this quality for large graph sizes N, a quantum device must support depth p > 11. Otherwise, we demonstrate that the number of required samples grows exponentially with N, hindering the scalability of QAOA with p ≤ 11. These results put challenging bounds on achieving quantum advantage for QAOA MaxCut on 3-regular graphs. Other problems, such as different graphs, weighted MaxCut, maximum independent set, and 3-SAT, may be better suited for achieving quantum advantage on near-term quantum devices.

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Section: Single-shot Samplingsupporting

confidence: 66%

Sampling Frequency Thresholds for Quantum Advantage of Quantum Approximate Optimization Algorithm

Lykov

Wurtz

Poole

et al. 2022

Preprint

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“…When executed under control of the optimizer, sampling a completely random distribution will yield an approximation ratio greater than 0.5 (see Figure 22). The optimizer may or may not converge to a better ratio, depending on the level of noise in the quantum system [66,[83][84][85][86].…”

Section: Results Quality and Time Of Executionmentioning

confidence: 99%

Optimization Applications as Quantum Performance Benchmarks

Lubinski¹,

Coffrin²,

McGeoch³

et al. 2023

Preprint

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Combinatorial optimization is anticipated to be one of the primary use cases for quantum computation in the coming years. The Quantum Approximate Optimization Algorithm (QAOA) and Quantum Annealing (QA) have the potential to demonstrate significant run-time performance benefits over current state-of-the-art solutions. Using existing methods for characterizing classical optimization algorithms, we analyze solution quality obtained by solving Max-Cut problems using a quantum annealing device and gate-model quantum simulators and devices. This is used to guide the development of an advanced benchmarking framework for quantum computers designed to evaluate the trade-off between run-time execution performance and the solution quality for iterative hybrid quantum-classical applications. The framework generates performance profiles through effective visualizations that show performance progression as a function of time for various problem sizes and illustrates algorithm limitations uncovered by the benchmarking approach. The framework is an enhancement to the existing opensource QED-C Application-Oriented Benchmark suite and can connect to the open-source analysis libraries. The suite can be executed on various quantum simulators and quantum hardware systems.CONTENTS * This work was sponsored by the Quantum Economic Development Consortium (QED-C) and was performed under the auspices of the QED-C Technical Advisory Committee on Standards and Performance Benchmarks. The authors acknowledge many committee members for their input to and feedback on the project and this manuscript.

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“…Hence, the actual solutions obtained from QAOA, QAOA * , and MA-QAOA may differ from the expected approximation ratios shown in the boxplots, and could be either higher or lower. For an extended discussion of the distinction between using expected approximation ratios and approximation ratios of individual samples, we refer the reader to Larkin et al [124].…”

Section: Data Availabilitymentioning

confidence: 99%

An Expressive Ansatz for Low-Depth Quantum Optimisation

Vijendran¹,

Das²,

Koh³

et al. 2023

Preprint

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The Quantum Approximate Optimisation Algorithm (QAOA) is a hybrid quantum-classical algorithm used to approximately solve combinatorial optimisation problems. It involves multiple iterations of a parameterised ansatz that consists of a problem and mixer Hamiltonian, with the parameters being classically optimised. While QAOA can be implemented on near-term quantum hardware, physical limitations such as gate noise, restricted qubit connectivity, and statepreparation-and-measurement (SPAM) errors can limit circuit depth and decrease performance. To address these limitations, this work introduces the eXpressive QAOA (XQAOA), a modified version of QAOA that assigns more classical parameters to the ansatz to improve the performance of low-depth quantum circuits. XQAOA includes an additional Pauli-Y component in the mixer Hamiltonian, thereby allowing the mixer to effectively implement arbitrary unitary transformations on each qubit. To benchmark the performance of the XQAOA ansatz at low depth, we derive its closed-form expression for the MaxCut problem and compare it to QAOA, MA-QAOA [Sci Rep 12, 6781 (2022)], a Classical-Relaxed algorithm, and the state-of-the-art Goemans-Williamson algorithm on a set of unweighted regular graphs with 128 and 256 nodes and degrees ranging from 3 to 10. Our results show that XQAOA performs better than QAOA, MA-QAOA, and the Classical-Relaxed algorithm on all graph instances and outperforms the Goemans-Williamson algorithm on unweighted regular graphs with degrees greater than 4. Additionally, we find an infinite family of graphs for which XQAOA solves MaxCut exactly and show analytically that for some graphs in this family, special cases of XQAOA are capable of achieving a much larger approximation ratio than QAOA. Overall, XQAOA is a more viable choice for implementing quantum combinatorial optimisation on near-term quantum devices, as it can achieve better results with a single iteration, despite requiring additional classical resources.

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Evaluation of QAOA based on the approximation ratio of individual samples

Cited by 18 publications

References 71 publications

Sampling Frequency Thresholds for Quantum Advantage of Quantum Approximate Optimization Algorithm

Sampling Frequency Thresholds for Quantum Advantage of Quantum Approximate Optimization Algorithm

Optimization Applications as Quantum Performance Benchmarks

An Expressive Ansatz for Low-Depth Quantum Optimisation

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