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

TLDR

The approach can improve simulation of large quantum computers using smaller devices, following the idea of Peng et al. The paper proposes a strategy to decompose a two‑qubit gate into a sequence of single‑qubit operations. The method uses projective Pauli measurements and π/2 rotations about the x, y, and z axes to implement the decomposition. The authors demonstrate that non‑local two‑qubit gates can be simulated via sampling local operations, achieving an expectation‑value error ε with O(9^k/ε^2) samples, enabling virtual gates between distant qubits and improving connectivity on near‑term noisy 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 $π/2$ 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., arXiv:1904.00102]. This work can enhance the connectivity of qubits on near-term, noisy quantum computers.