Optimization of a virtual two-qubit gate

Noisy intermediate scale quantum (NISQ) devices seem to be on a promising path to realize the capabilities of quantum computers which could prove to be more fast, secure, and efficient than their classical counterparts. However, presently NISQ devices are with their two biggest challenges: scalability and limited coherence times, still proving to be the testbeds of many promising quantum algorithms. One of the techniques addressing the former challenge in certain situations was proposed by [1], 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 a 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. Here, we present the construction of a "virtual" controlled-NOT (CNOT) gate, an essential component in the construction of gate-based quantum computers. We construct the process matrix for the "virtual CNOT" gate and compare it with the ideal matrix. Further, we also optimize the proposed theoretical decomposition of the virtual two-qubit gates taking into account the imperfections of local operations arising from the real implementation. 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.

[1] Kosuke Mitarai and Keisuke Fujii 2021 New J. Phys. 23 023021.