The Quantum Alternating Operator Ansatz for Satisfiability Problems

Golden, John M.; Bärtschi, Andreas; O’Malley, Daniel; Eidenbenz, Stephan

doi:10.48550/arxiv.2301.11292

Cited by 2 publications

(3 citation statements)

References 11 publications

(25 reference statements)

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“…JuliQAOA enables quick, low-overhead QAOA simulation on personal computers, while also scaling well to HPC-level resources. JuliQAOA has already enabled robust numerical studies in several publications [17][18][19]29], and will be released as an open source package later this year to facilitate further development.…”

Section: Pre-computationmentioning

confidence: 99%

“…For unconstrained problems, JuliQAOA is specifically optimized to use mixer Hamiltonians written as sums of products Pauli 𝑋 operators. This choice covers a broad array of mixers [19], including the original transverse-field mixer [13,20] and Grover mixer [8]. Time evolution of such a mixer Hamiltonian, which we generically denote 𝑓 (𝑋 𝑖 ) can be diagonalized by exploiting 𝐻𝑍𝐻 = 𝑋 :…”

Section: Pre-computationmentioning

confidence: 99%

See 1 more Smart Citation

JuliQAOA: Fast, Flexible QAOA Simulation

Golden,

Baertschi,

O'Malley

et al. 2023

Proceedings of the SC '23 Workshops of the International Conference on High Performance Computing, Network, Storage, and Analys

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We introduce JuliQAOA, a simulation package specifically built for the Quantum Alternating Operator Ansatz (QAOA). JuliQAOA does not require a circuit-level description of QAOA problems, or another package to simulate such circuits, instead relying on a more direct linear algebra implementation. This allows for increased QAOAspecific performance improvements, as well as improved flexibility and generality. JuliQAOA is the first QAOA package designed to aid in the study of both constrained and unconstrained combinatorial optimization problems, and can easily include novel cost functions, mixer Hamiltonians, and other variations. JuliQAOA also includes robust and extensible methods for learning optimal angles. Written in the Julia language, JuliQAOA outperforms existing QAOA software packages and scales well to HPC-level resources.JuliQAOA is available at https://github.com/lanl/JuliQAOA.jl.

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Section: Pre-computationmentioning

confidence: 99%

Section: Pre-computationmentioning

confidence: 99%

JuliQAOA: Fast, Flexible QAOA Simulation

Golden,

Baertschi,

O'Malley

et al. 2023

Proceedings of the SC '23 Workshops of the International Conference on High Performance Computing, Network, Storage, and Analys

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show abstract

“…Several variants of the original QAOA algorithm have been developed, each with different operators and initial states [14][15][16][17][18][19][20][21][22][23][24][25] or different objective functions for tuning the variational parameters [26,27]. Depth-reduction techniques [28,29] or methods like circuit cutting [30,31] that optimise QAOA circuits while taking into account quantum hardware limitations; as well as classical aspects such as hyper-parameter optimisation and exploitation of problem structure, have been studied as well [18,19,[32][33][34][35][36][37][38][39].…”

Section: Introductionmentioning

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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The Quantum Alternating Operator Ansatz for Satisfiability Problems

Cited by 2 publications

References 11 publications

JuliQAOA: Fast, Flexible QAOA Simulation

JuliQAOA: Fast, Flexible QAOA Simulation

An Expressive Ansatz for Low-Depth Quantum Optimisation

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