Applying the Quantum Approximate Optimization Algorithm to the Tail-Assignment Problem

Vikstål, Pontus; Grönkvist, Mattias; Svensson, Marika; Andersson, Martin; Johansson, Göran; Ferrini, Giulia

doi:10.1103/physrevapplied.14.034009

Cited by 72 publications

(47 citation statements)

References 20 publications

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“…We use this probability inequality to bound the number of measurements M = log(1 − P)/ log(1 − P ) that are needed to obtain a single sample from the distribution of the intended state with probability P [16,20],…”

Section: Noisy Architecture Model and Measurement Count Scalingmentioning

confidence: 99%

“…Farhi et al have argued that QAOA recovers the ground state of C as p → ∞ [2], but the primary interest in QAOA is in reaching high performance with a modest number of layers p that could realistically be implemented on a quantum computer. A significant body of theoretical [4][5][6][7][8], computational [9][10][11][12][13], and experimental [14,15] research has focused on understanding QAOA performance at p ≈ 1, mostly on the MaxCut problem with a small number of qubits n, but also for other types of problems [16][17][18]. These studies have shown some promising results, for example, with QAOA outperforming the conventional lower bound of the GW algorithm for MaxCut on some small instances [19,20].…”

Section: Introductionmentioning

confidence: 99%

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Scaling Quantum Approximate Optimization on Near-term Hardware

Lotshaw,

Nguyen,

Santana

et al. 2022

Preprint

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The quantum approximate optimization algorithm (QAOA) is an approach for near-term quantum computers to potentially demonstrate computational advantage in solving combinatorial optimization problems. However, the viability of the QAOA depends on how its performance and resource requirements scale with problem size and complexity for realistic hardware implementations. Here, we quantify scaling of the expected resource requirements by synthesizing optimized circuits for hardware architectures with varying levels of connectivity. Assuming noisy gate operations, we estimate the number of measurements needed to sample the output of the idealized QAOA circuit with high probability. We show the number of measurements, and hence total time to solution, grows exponentially in problem size and problem graph degree as well as depth of the QAOA ansatz, gate infidelities, and inverse hardware graph degree. These problems may be alleviated by increasing hardware connectivity or by recently proposed modifications to the QAOA that achieve higher performance with fewer circuit layers.

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Section: Noisy Architecture Model and Measurement Count Scalingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Scaling Quantum Approximate Optimization on Near-term Hardware

Lotshaw,

Nguyen,

Santana

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…In the seminal paper of Farhi, Goldstone, and Gutmann, the QAOA is proposed as a variational quantum algorithm to produce approximate solutions for combinatorial optimization (CO) problems [14]. Since then numerous research works on QAOA have been shown both theoretically [22][23][24][25][26][27][28][29][30][31]and experimentally [16,[32][33][34][35][36]. Similar to quantum annealing (QA), in which CO problems are modeled as the form of Ising Hamiltonian, the QAOA also starts with Ising form as cost function.…”

Section: The Quantum Approximate Optimization Algorithmmentioning

confidence: 99%

Efficient Classical Computation of Quantum Mean Values for Shallow QAOA Circuits

Zhuang¹,

Pu²,

Xu³

et al. 2021

Preprint

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The Quantum Approximate Optimization Algorithm (QAOA), which is a variational quantum algorithm, aims to give sub-optimal solutions of combinatorial optimization problems. It is widely believed that QAOA has the potential to demonstrate application-level quantum advantages in the noisy intermediate-scale quantum(NISQ) processors with shallow circuit depth. Since the core of QAOA is the computation of expectation values of the problem Hamiltonian, an important practical question is whether we can find an efficient classical algorithm to solve quantum mean value in the case of general shallow quantum circuits. Here, we present a novel graph decomposition based classical algorithm that scales linearly with the number of qubits for the shallow QAOA circuits in most optimization problems except for complete graph case. Numerical tests in Max-cut, graph coloring and Sherrington-Kirkpatrick model problems, compared to the state-of-the-art method, shows orders of magnitude performance improvement. Our results are not only important for the exploration of quantum advantages with QAOA, but also useful for the benchmarking of NISQ processors.

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“…Applications of optimization problems are very diverse and include, among others, scheduling chemotherapy for cancer patients [1,2] and aircraft assignment problems [3,4]. Modeling these problems to fit real-life applications requires a large number of variables.…”

Section: Introductionmentioning

confidence: 99%