Stabilization of cat-state manifolds using nonlinear reservoir engineering

TL;DR

This paper presents a new reservoir engineering method to stabilize multi-component Schrödinger cat manifolds using nonlinear interactions, enabling improved quantum error correction and state stabilization across various physical platforms.

Contribution

The authors introduce a nonlinear reservoir engineering framework for stabilizing cat-state manifolds, offering new insights and methods for quantum state control and error correction.

Findings

Stabilization of multi-component cat states via nonlinear gain and loss terms.

Analysis of error correction properties for bosonic codes.

Implementation examples in trapped ions and superconducting circuits.

Abstract

We introduce a novel reservoir engineering approach for stabilizing multi-component Schr\"odinger's cat manifolds. The fundamental principle of the method lies in the destructive interference at crossings of gain and loss Hamiltonian terms in the coupling of an oscillator to a zero-temperature auxiliary system, which are nonlinear with respect to the oscillator's energy. The nature of these gain and loss terms is found to determine the rotational symmetry, energy distributions, and degeneracy of the resulting stabilized manifolds. Considering these systems as bosonic error-correction codes, we analyze their properties with respect to a variety of errors, including both autonomous and passive error correction, where we find that our formalism gives straightforward insights into the nature of the correction. We give example implementations using the anharmonic laser-ion coupling of a trapped ion outside the Lamb-Dicke regime as well as nonlinear superconducting circuits. Beyond the dissipative stabilization of standard cat manifolds and novel rotation symmetric codes, we demonstrate that our formalism allows for the stabilization of bosonic codes linked to cat states through unitary transformations, such as quadrature-squeezed cats. Our work establishes a design approach for creating and utilizing codes using nonlinearity, providing access to novel quantum states and processes across a range of physical systems.