Analyzing the performance of variational quantum factoring on a superconducting quantum processor

Abstract

In the near-term, hybrid quantum-classical algorithms hold great potential for outperforming classical approaches. Understanding how these two computing paradigms work in tandem is critical for identifying areas where such hybrid algorithms could provide a quantum advantage. In this work, we study a QAOA-based quantum optimization approach by implementing the Variational Quantum Factoring (VQF) algorithm. 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 biprime is successfully factored. In our experiments, the integers 1099551473989, 3127, and 6557 are factored with 3, 4, and 5 qubits, respectively, using a QAOA ansatz with up to 8 layers and we are able to identify the optimal number of circuit layers for a given instance to maximize success probability. Furthermore, we demonstrate the impact of different noise sources on the performance of QAOA, and reveal the coherent error caused by the residual ZZ-coupling between qubits as a dominant source of error in a near-term superconducting quantum processor.

Deploying hybrid quantum-secured infrastructure for applications: When quantum and post-quantum can work together

“…No fundamental obstacles preventing the further scaling of quantum computers have yet been identified. However, there is an increasing interest in alternative schemes for solving the prime factorization problem using quantum tools, such as variational quantum factoring (Anschuetz et al, 2019;Karamlou et al, 2021). A very recent proposal demonstrated the possibility of accelerating factoring using quantum computers with sublinear scaling in the number of qubits (Yan et al, 2022) (however, this proposal is not yet fully verified).…”

SoK: Benchmarking the Performance of a Quantum Computer

“…Zapata tries to investigate what can be done with NISQ devices. Thus, Zapata proposed to benchmark quantum devices with variational quantum factoring (VQF) and fermionic simulation [ 29 , 36 ]. The VQF solves the integer factoring problem with variational quantum solutions, such as VQE and QAOA.…”

Trainability Enhancement of Parameterized Quantum Circuits via Reduced-Domain Parameter Initialization

“…The core idea is exploiting PQCs to delegate classically difficult computation and variationally updating the parameters in PQCs with a powerful classical optimizer [28,29,30,31,32]. With error mitigation techniques [33,34,35,36,37,38,39,40], VQAs have been applied to various fields and the corresponding specific algorithms have been developed, including variational quantum eigensolver (VQE) [41,42,43,44,45], quantum approximate optimization algorithm [46,47,48,15,49], variational quantum simulator [50,51,52,53], quantum neural network (QNN) [54,55,56,57,58,59,60,61,62,63], and others [64,65,66,67,68,69,70,71,72,...…”