MaxCut quantum approximate optimization algorithm performance guarantees for 
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Wurtz, Jonathan; Love, Peter J.

doi:10.1103/physreva.103.042612

Cited by 63 publications

(44 citation statements)

References 15 publications

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“…In the original introduction of Farhi et. al [4], the performance was guaranteed to be at least 0.693 for p = 1 and 3 regular graphs, and in a later work [1], the performance was guaranteed to be at least 0.7559 for p = 2 and 3 regular graphs. The same work observed that worst-case graphs have no small cycles, and conjectured that the same holds for larger p.…”

Section: Introductionmentioning

confidence: 91%

“…However, little is known about performance guarantees for p > 2. A recent work [1] computing MaxCut performance guarantees for 3-regular graphs conjectures that any d-regular graph evaluated at particular fixed angles has an approximation ratio greater than some worst-case guarantee. In this work, we provide numerical evidence for this fixed angle conjecture for p < 12.…”

mentioning

confidence: 99%

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The fixed angle conjecture for QAOA on regular MaxCut graphs

Wurtz¹,

Lykov²

2021

Preprint

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The quantum approximate optimization algorithm (QAOA) is a near-term combinatorial optimization algorithm suitable for noisy quantum devices. However, little is known about performance guarantees for p > 2. A recent work [1] computing MaxCut performance guarantees for 3-regular graphs conjectures that any d-regular graph evaluated at particular fixed angles has an approximation ratio greater than some worst-case guarantee. In this work, we provide numerical evidence for this fixed angle conjecture for p < 12. We compute and provide these angles via numerical optimization and tensor networks. These fixed angles serve for an optimization-free version of QAOA, and have universally good performance on any 3 regular graph. Heuristic evidence is presented for the fixed angle conjecture on graph ensembles, which suggests that these fixed angles are "close" to global optimum. Under the fixed angle conjecture, QAOA has a larger performance guarantee than the Goemans Williamson algorithm on 3-regular graphs for p ≥ 11.

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Section: Introductionmentioning

confidence: 91%

mentioning

confidence: 99%

The fixed angle conjecture for QAOA on regular MaxCut graphs

Wurtz¹,

Lykov²

2021

Preprint

Self Cite

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“…Simulated annealing on BLLS however, yields a higher success probability than QAOA at depth p = 3 when n > 8 (for 10 steps). This empirical result is supported by the theoretical work on QAOA for MAXCUT [89] which indicates that there exists classes of graphs for which quantum advantage is not possible for p < 6. Another work focusing on numerical simulations on MAXCUT problems suggests any QAOA advantage would need quantum computers to have in the order of hundreds of qubits at the very least [90].…”

Section: Probability Of Sampling the Ground Statementioning

confidence: 57%

Quantum approximate optimization for hard problems in linear algebra

Borle

Elfving²,

Lomonaco

2021

SciPost Phys. Core

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The quantum approximate optimization algorithm (QAOA) by Farhi et al. is a quantum computational framework for solving quantum or classical optimization tasks. Here, we explore using QAOA for binary linear least squares (BLLS); a problem that can serve as a building block of several other hard problems in linear algebra, such as the non-negative binary matrix factorization (NBMF) and other variants of the non-negative matrix factorization (NMF) problem. Most of the previous efforts in quantum computing for solving these problems were done using the quantum annealing paradigm. For the scope of this work, our experiments were done on noiseless quantum simulators, a simulator including a device-realistic noise-model, and two IBM Q 5-qubit machines. We highlight the possibilities of using QAOA and QAOA-like variational algorithms for solving such problems, where trial solutions can be obtained directly as samples, rather than being amplitude-encoded in the quantum wavefunction. Our numerics show that even for a small number of steps, simulated annealing can outperform QAOA for BLLS at a QAOA depth of p\leq3p≤3 for the probability of sampling the ground state. Finally, we point out some of the challenges involved in current-day experimental implementations of this technique on cloud-based quantum computers.

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“…For a complete proof, see [4]. Impact of noise: While the original based Quantum Approximate Optimization Algorithm ofers non-trivial provable performance guarantees already for a single for certain problems such as MaxCut on (d=3)-regular graphs [8], a higher number of rounds ś p ≥ 6 [33] or even p ∈ Ω(log(n)/d ) [3] ś might be necessary to outperform the best-known classical approximation ratios.…”

Section: Fair Sampling In the Uantum Alternating Operator Ansatzmentioning

confidence: 99%

Fair Sampling Error Analysis on NISQ Devices

Golden

Bärtschi

O’Malley

et al. 2022

ACM Transactions on Quantum Computing

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We study the status of fair sampling on Noisy Intermediate Scale Quantum (NISQ) devices, in particular the IBM Q family of backends. Using the recently introduced Grover Mixer-QAOA algorithm for discrete optimization, we generate fair sampling circuits to solve six problems of varying difficulty, each with several optimal solutions, which we then run on twenty backends across the IBM Q system. For a given circuit evaluated on a specific set of qubits, we evaluate: how frequently the qubits return an optimal solution to the problem, the fairness with which the qubits sample from all optimal solutions, and the reported hardware error rate of the qubits. To quantify fairness, we define a novel metric based on Pearson’s χ 2 test. We find that fairness is relatively high for circuits with small and large error rates, but drops for circuits with medium error rates. This indicates that structured errors dominate in this regime, while unstructured errors, which are random and thus inherently fair, dominate in noisier qubits and longer circuits. Our results show that fairness can be a powerful tool for understanding the intricate web of errors affecting current NISQ hardware.

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MaxCut quantum approximate optimization algorithm performance guarantees for p>1

Cited by 63 publications

References 15 publications

The fixed angle conjecture for QAOA on regular MaxCut graphs

The fixed angle conjecture for QAOA on regular MaxCut graphs

Quantum approximate optimization for hard problems in linear algebra

Fair Sampling Error Analysis on NISQ Devices

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