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Stabilization of Cat-State Manifolds Using Nonlinear Reservoir Engineering

Ivan Rojkov1,2,*,†, Matteo Simoni1,2,*,‡, Elias Zapusek1,2, Florentin Reiter1,2,3, and Jonathan Home1,2,§

  • *These authors contributed equally to this work.
  • †Contact author: irojkov@phys.ethz.ch
  • ‡Contact author: masimoni@phys.ethz.ch
  • §Contact author: jhome@phys.ethz.ch
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Phys. Rev. X 16, 011056 – Published 13 March, 2026

DOI: https://doi.org/10.1103/d557-9lr4

Abstract

We introduce a novel reservoir engineering approach for stabilizing multicomponent Schrödinger’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.

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Popular Summary

The competition of nonlinear energy gain and loss processes stabilizes the energy of various physical systems, with the laser being a prime example. Here, we introduce a general approach for stabilizing quantum states through the interference of different nonlinear processes. The key idea is to identify crossing points where gain and loss terms in an engineered dissipation mechanism destructively interfere. We demonstrate that the resulting stable sets of states include squeezed and multicomponent generalizations of Schrödinger cat states, providing specific insights into their capacity for autonomous quantum error correction. In particular, we demonstrate that nonlinearities can significantly enhance stabilization strength, corrective capability, and robustness against new classes of errors. By applying this design to trapped ions and superconducting circuits, we provide techniques for moving beyond standard operating approximations to access the nonlinear regime necessary for advanced quantum control.

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Phys. Rev. X 16, 011056– Published 13 March, 2026
  • Received 16 September 2024
  • Accepted 27 January 2026
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