# Protecting quantum systems from decoherence with unitary operations

## TL;DR

This paper introduces a novel method for protecting quantum states from decoherence using pre- and post-processing unitary operations, avoiding the need for ancillary qubits or measurements, and analyzes its effectiveness across common decoherence models.

## Contribution

The work proposes a decoherence suppression technique based on tailored unitary operations, providing a classification, optimal strategies, and demonstrating its application to key quantum noise channels.

## Key findings

- Optimal unitary operators maximize fidelity between initial and final states.
- Protection schemes can be implemented with either individual or collective unitaries.
- Decoherence robustness relates to the entropy of the reduced state of the affected qubit.

## Abstract

Decoherence is a fundamental obstacle to the implementation of large-scale and low-noise quantum information processing devices. In this work, we suggest an approach for suppressing errors by employing pre-processing and post-processing unitary operations, which precede and follow the action of a decoherence channel. In contrast to quantum error correction and measurement-based methods, the suggested approach relies on specifically designed unitary operators for a particular state without the need in ancillary qubits or post-selection procedures. We consider the case of decoherence channels acting on a single qubit belonging to a many-qubit state. Pre-processing and post-processing operators can be either individual, that is acting on the qubit effected by the decoherence channel only, or collective, that is acting on the whole multi-qubit state. We give a classification of possible strategies for the protection scheme, analyze them, and derive expressions for the optimal unitary operators providing the maximal value of the fidelity regarding initial and final states. Specifically, we demonstrate the equivalence of the schemes where one of the unitary operations is individual while the other is collective. We then consider the realization of our approach for the basic decoherence models, which include single-qubit depolarizing, dephasing, and amplitude damping channels. We also demonstrate that the decoherence robustness of multi-qubit states for these decoherence models is determined by the entropy of the reduced state of the qubit undergoing the decoherence channel.