Stabilizing a Bosonic Qubit using Colored Dissipation

TL;DR

This paper introduces a novel dissipative stabilization method using frequency-selective (colored) dissipation to enhance the robustness of energy-gap-protected bosonic qubits, notably Kerr cat qubits, by suppressing leakage errors without inducing additional errors.

Contribution

The authors propose a new colored dissipation scheme for stabilizing protected qubits, improving error suppression while maintaining linear interactions, applicable to various bosonic qubits.

Findings

Significantly reduces leakage-induced bit-flip errors in Kerr cat qubits.

Demonstrates the effectiveness of frequency-selective loss in protecting energy-gap qubits.

Applicable to a broader class of protected qubits beyond Kerr cats.

Abstract

Protected qubits such as the 0-$\pi$ qubit, and bosonic qubits including cat qubits and GKP qubits offer advantages for fault-tolerance. Some of these protected qubits (e.g., 0-$\pi$ qubit and Kerr cat qubit) are stabilized by Hamiltonians which have (near-)degenerate ground state manifolds with large energy-gaps to the excited state manifolds. Without dissipative stabilization mechanisms the performance of such energy-gap-protected qubits can be limited by leakage to excited states. Here, we propose a scheme for dissipatively stabilizing an energy-gap-protected qubit using colored (i.e., frequency-selective) dissipation without inducing errors in the ground state manifold. Concretely we apply our colored dissipation technique to Kerr cat qubits and propose colored Kerr cat qubits which are protected by an engineered colored single-photon loss. When applied to the Kerr cat qubits our scheme significantly suppresses leakage-induced bit-flip errors (which we show are a limiting error mechanism) while only using linear interactions. Beyond the benefits to the Kerr cat qubit we also show that our frequency-selective loss technique can be applied to a broader class of protected qubits.