Survey on Quantum Circuit Compilation for Noisy Intermediate-Scale Quantum Computers: Artificial Intelligence to Heuristics

Abstract

Computationally expensive applications, including machine learning, chemical simulations and financial modeling, are promising candidates for noisy intermediate scale quantum (NISQ) computers. In these problems, one important challenge is mapping a quantum circuit onto NISQ hardware while satisfying physical constraints of an underlying quantum architecture. Quantum circuit compilation (QCC) aims to generate feasible mappings such that a quantum circuit can be executed in a given hardware platform with acceptable confidence in outcomes. Physical constraints of a NISQ computer change frequently, requiring QCC process to be repeated often. When a circuit cannot directly be executed on a quantum hardware due to its physical limitations, it is necessary to modify the circuit by adding new quantum gates and auxiliary qubits, increasing its space and time complexity. An inefficient QCC may significantly increase error rate and circuit latency for even the simplest algorithms. In this survey, we present AI and heuristic based methods recently reported in the literature that attempt to address these QCC challenges. We group them based on underlying techniques that they implement, such as AI algorithms including genetic algorithms, genetic programming, ant colony optimization and AI planning, and heuristics methods employing greedy algorithms, satisfiability problem solvers, dynamic and graph optimization techniques. We discuss performance of each QCC technique and evaluate its potential limitations.

Pauli Error Propagation-Based Gate Reschedulingfor Quantum Circuit Error Mitigation

“…Since quantum circuit mapping is an NP-Complete problem [13], traversing the search space is speculative for quantum architectures with a large number of qubits. Various heuristics-based techniques have been proposed to address this problem [14]. Some of these techniques target minimizing the number of circuit SWAP operations [15]- [19], while others focus on minimizing the circuit error rates [10], [20].…”

Pauli Error Propagation-Based Gate Rescheduling for Quantum Circuit Error Mitigation

“…Since quantum circuit mapping is an NP-complete problem [13], traversing the search space is speculative for quantum architectures with a large number of qubits. Various VOLUME 3, 2022 heuristics-based techniques have been proposed to address this problem [14]. Some of these techniques target minimizing the number of circuit SWAP operations [15]- [19], while others focus on minimizing the circuit error rates [10], [20].…”

Quantum Circuit Transformation: A Monte Carlo Tree Search Framework

“…To reduce the gate overheads in the qubit routing step, many algorithms have been proposed aiming at minimising gate counts Lye et al 2015;Zhou et al 2020b;Zulehner et al 2018], circuit depths [Booth et al 2018;Lao et al 2019;Venturelli et al 2017;Zhang et al 2020] or circuit error [Murali et al 2019;Nishio et al 2020]. These algorithms can be roughly classiied into two broad categories (see also [Kusyk et al 2021] for a similar classiication). The irst category consists of algorithms that try to reformulate QCT as a planning or optimisation problem and solve it by applying of-the-shelf tools [Booth et al 2018;de Almeida et al 2019;Murali et al 2019;Rasconi and Oddi 2019;Saeedi et al 2011;Siraichi et al 2018;Venturelli et al , 2017Wille et al 2019;Zhang et al 2021;Zhu et al 2020].…”