A Computation-Enhanced High-Dimensional Quantum Gate for Silicon-Vacancy Spins

TL;DR

This paper introduces a high-dimensional, deterministic 2-qudit CNOT gate for silicon-vacancy spins, leveraging an ancillary photon in optical nanocavities to enable efficient quantum logic operations in solid-state systems.

Contribution

It proposes a novel 2-qudit CNOT gate protocol for silicon-vacancy spins using an ancillary photon, enhancing quantum computing capabilities in solid-state platforms.

Findings

High efficiency and fidelity under current technology

Deterministic operation with relational feed-forward control

Potential for generalization to other solid-state systems

Abstract

Qudit-based quantum gates in high-dimensional Hilbert space can provide a viable route towards effectively accelerating the speed of quantum computing and performing complex quantum logic operations. In the paper, we propose a 2-qudit $4\times4$-dimensional controlled-not (CNOT) gate for four silicon-vacancy spins, in which the first two electron-spin states in silicon-vacancy centers are encoded as the control qudits, and the other ones as the target qudits. The proposed protocol is implemented with assistance of an ancillary photon that serves as a common-data bus linking four motionless silicon-vacancy spins placed in four independent single-sided optical nanocavities. Moreover, the CNOT gate works in a deterministic manner by performing the relational feed-forward operations corresponding to the diverse outcomes of the single-photon detectors to be directed against the ancillary photon. Further, it can be potentially generalized to other solid-state quantum system. Under current technological conditions, both the efficiency and fidelity of the 2-qudit CNOT gate are high.