Quantum error pre-compensation for quantum noisy channels

TL;DR

This paper introduces a method for designing pre-compensated input states to mitigate errors in quantum noisy channels, providing analytical solutions and semidefinite programming techniques for optimal fidelity.

Contribution

It presents a novel approach to quantum error pre-compensation, including analytical solutions for single-partite systems and numerical methods for general cases.

Findings

Analytical solutions for pre-compensated states in single-partite systems.

Semidefinite programs effectively find optimal pre-compensated states.

Numerical results match analytical solutions, validating the approach.

Abstract

Most previous efforts of quantum error correction focused on either extending classical error correction schemes to the quantum regime by performing a perfect correction on a subset of errors, or seeking a recovery operation to maximize the fidelity between a input state and its corresponding output state of a noisy channel. There are few results concerning quantum error pre-compensation. Here we design an error pre-compensated input state for an arbitrary quantum noisy channel and a given target output state. By following a procedure, the required input state, if it exists, can be analytically obtained in single-partite systems. Furthermore, we also present semidefinite programs to numerically obtain the error pre-compensated input states with maximal fidelities between the target state and the output state. The numerical results coincide with the analytical results.