Constructing a virtual two-qubit gate by sampling single-qubit operations

Abstract

Abstract We show a certain kind of non-local operations can be simulated by sampling a set of local operations with a quasi-probability distribution when the task of a quantum circuit is to evaluate an expectation value of observables. Utilizing the result, we describe a strategy to decompose a two-qubit gate to a sequence of single-qubit operations. Required operations are projective measurement of a qubit in Pauli basis, and π/2 rotation around x, y, and z axes. The required number of sampling to get an expectation value of a target observable within an error of ϵ is roughly O(9 k /ϵ 2), where k is the number of ‘cuts’ performed. The proposed technique enables to perform ‘virtual’ gates between a distant pair of qubits, where there is no direct interaction and thus a number of swap gates are inevitable otherwise. It can also be utilized to improve the simulation of a large quantum computer with a small-sized quantum device, which is an idea put forward by Peng et al (2019 arXiv:1904.00102). This work can enhance the connectivity of qubits on near-term, noisy quantum computers.