Procedures for realizing an approximate universal NOT gate

TL;DR

This paper explores procedures to implement an approximate universal NOT gate, analyzing the trade-offs between fidelity and universality for different qubit operations, and proposes a feedback method to recover from operational noise.

Contribution

It introduces a detailed analysis of fidelity trade-offs in universal NOT gate implementations and presents a feedback scheme to optimize and recover quantum operations under noise.

Findings

One-qubit operations have a sharp trade-off between fidelity and universality.

Two-qubit operations show a looser trade-off relation.

Feedback via differential evolution can recover from operational noise.

Abstract

We consider procedures to realize an approximate universal NOT gate in terms of average fidelity and fidelity deviation. The average fidelity indicates the optimality of operation on average, while the fidelity deviation does the universality of operation. We show that one-qubit operations have a sharp trade-off relation between average fidelity and fidelity deviation, and two-qubit operations show a looser trade-off relation. The genuine universality holds for operations of more than two qubits, and those of even more qubits are beneficial to compensating imperfection of control. In addition, we take into account operational noises which contaminate quantum operation in realistic circumstances. We show that the operation recovers from the contamination by a feedback procedure of differential evolution. Our feedback scheme is also applicable to finding an optimal and universal operation of NOT.