Experimental implementation and characterization of a virtual two-qubit gate

Quantum computers seem to be on a promising path to realize the capabilities which could prove to be more fast, secure, and efficient than their classical counterparts. However, the size of current quantum devices, termed as Noisy intermediate-scale quantum (NISQ) devices, is strictly limited. The other major challenges faced by NISQ devices are finite noise and limited coherence times. In relation to the limited size issue, several techniques have been proposed to increase the effective size of the devices with additional classical processing costs. One such technique was proposed by K. Mitarai and K. Fujii [New J. Phys. 23 023021 (2021)], which constructs a general two-qubit gate from only single-qubit operations or referred here as a "virtual two-qubit" gate. This virtual two-qubit gate allows us to, for example, simulate the quantum circuit of 2N qubits by using only N physical qubits with sampling overhead when the goal of the quantum circuit is expectation value estimation. Hence, it enables us to expand the computing capabilities of NISQ devices in certain algorithms. In this work, we present the experimental demonstration and characterization of the "virtual CZ" gate. While local operations on each qubit involved in a virtual gate consist of single-qubit gates and measurements, measurement errors are usually much larger than single-qubit gate errors in experiments. Thus, we have also implemented measurement error mitigation to improve virtual gate fidelity. As a result, we experimentally achieved virtual CZ gate with average gate fidelity of 0.9975±0.0028. This technique helps us to obtain expectation values in "scaled-up" quantum circuits, which are used in many quantum algorithms such as variational quantum eigensolver and others.