Noisy intermediate-scale quantum (NISQ) algorithms

A universal fault-tolerant quantum computer that can efficiently solve problems such as integer factorization and unstructured database search requires millions of qubits with low error rates and long coherence times. While the experimental advancement toward realizing such devices will potentially take decades of research, noisy intermediate-scale quantum (NISQ) computers already exist. These computers are composed of hundreds of noisy qubits, i.e., qubits that are not error corrected, and therefore perform imperfect operations within a limited coherence time. In the search for achieving quantum advantage with these devices, algorithms have been proposed for applications in various disciplines spanning physics, machine learning, quantum chemistry, and combinatorial optimization. The overarching goal of such algorithms is to leverage the limited available resources to perform classically challenging tasks. In this review, a thorough summary of NISQ computational paradigms and algorithms is provided. The key structure of these algorithms and their limitations and advantages are discussed. A comprehensive overview of various benchmarking and software tools useful for programming and testing NISQ devices is additionally provided.Ministry of Education (MOE)National Research Foundation (NRF)Published versionA. A.-G. acknowledges the generous support of Google, Inc., in the form of a Google Focused Award. This work was supported by the U.S. Department of Energy under Award No. DESC0019374 and the U.S. Office of Naval Research (Grant No. ONS506661). A. A.-G. also acknowledges support from the Canada Industrial Research Chairs Program and the Canada 150 Research Chairs Program. T. H. is supported by a Samsung GRC project and the UK Hub in Quantum Computing and Simulation, part of the UK National Quantum Technologies Programme, with funding from UKRI EPSRC Grant No. EP/T001062/1. L.-C. K and K. B acknowledge the financial support from the National Research Foundation and the Ministry of Education, Singapore