Analyzing the Performance of Variational Quantum Factoring on a Superconducting Quantum Processor

Abstract

Quantum computers hold promise as accelerators onto which some classically-intractable problems may be offloaded, necessitating hybrid quantum-classical workflows. Understanding how these two computing paradigms can work in tandem is critical for identifying where such workflows could provide an advantage over strictly classical ones. In this work, we study such workflows in the context of quantum optimization, using an implementation of the Variational Quantum Factoring (VQF) algorithm as a prototypical example of QAOA-based quantum optimization algorithms. We execute experimental demonstrations using a superconducting quantum processor, and investigate the trade off between quantum resources (number of qubits and circuit depth) and the probability that a given integer is successfully factored. In our experiments, the integers 1,099,551,473,989 and 6,557 are factored with 3 and 5 qubits, respectively, using a QAOA ansatz with up to 8 layers. Our results empirically demonstrate the impact of different noise sources, and reveal a residual ZZcoupling between qubits as a dominant source of error. Additionally, we are able to identify the optimal number of circuit layers for a given instance to maximize success probability.

Noisy intermediate-scale quantum algorithms

“…Numerical simulations were provided for numbers as high as 291311. For a recent experimental realization and detailed analysis of VQF, refer to (Karamlou et al, 2020).…”

The Variational Quantum Eigensolver: a review of methods and best practices

“…Also, errors on the hardware affect the landscape of the cost function, potentially creating more local minima and therefore jeopardizing the optimization procedure. This has been experimentally investigated for the variational quantum factoring algorithm [573] (See Sec. 6.1 for relevant discussions) which is a close relative to VQE algorithm discussed here.…”

Neural Predictor based Quantum Architecture Search

“…Various VQA have been designed for problems in a vast array of fields. Some typical examples include determining the ground and low excited states of a quantum Hamiltonian [4,[6][7][8][94][95][96][97], simulating quantum dynamics [98][99][100][101][102][103][104][105][106][107], preparing Gibbs thermal states [108][109][110], supervised and unsupervised machine learning [15][16][17][18][19][20][21][22][23][24][25][26][27], compiling quantum circuits [111][112][113], solving classical combinatorial optimizations [10][11][12][13][14], factoring integers [114][115][116], and solving linear or differential equations [117][118]…”