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

TL;DR

This paper introduces a method to simulate non-local two-qubit gates using local operations and sampling, enabling virtual gates and improved connectivity in near-term quantum computers.

Contribution

The authors propose a sampling-based decomposition of two-qubit gates into single-qubit operations, facilitating virtual interactions without direct coupling.

Findings

Sampling complexity is roughly O(9^k/ε^2) for expectation value accuracy.

Enables virtual two-qubit gates between distant qubits without direct interaction.

Improves qubit connectivity and simulation capabilities on noisy, small-scale quantum devices.

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 $\pi/2$ 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 $\epsilon$ is roughly $O(9^k/\epsilon^2)$, 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., arXiv:1904.00102]. This work can enhance the connectivity of qubits on near-term, noisy quantum computers.