Approximate Autonomous Quantum Error Correction with Reinforcement Learning

• URL: http://arxiv.org/abs/2212.11651v2
• Date: Tue, 12 Sep 2023 16:57:14 GMT
• Title: Approximate Autonomous Quantum Error Correction with Reinforcement Learning
• Authors: Yexiong Zeng, Zheng-Yang Zhou, Enrico Rinaldi, Clemens Gneiting, Franco Nori
• Abstract summary: Autonomous quantum error correction (AQEC) protects logical qubits by engineered dissipation. Bosonic code spaces, where single-photon loss represents the dominant source of error, are promising candidates for AQEC. We propose a bosonic code for approximate AQEC by relaxing the Knill-Laflamme conditions.
• Score: 4.015029887580199
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Autonomous quantum error correction (AQEC) protects logical qubits by engineered dissipation and thus circumvents the necessity of frequent, error-prone measurement-feedback loops. Bosonic code spaces, where single-photon loss represents the dominant source of error, are promising candidates for AQEC due to their flexibility and controllability. While existing proposals have demonstrated the in-principle feasibility of AQEC with bosonic code spaces, these schemes are typically based on the exact implementation of the Knill-Laflamme conditions and thus require the realization of Hamiltonian distances $d\geq 2$. Implementing such Hamiltonian distances requires multiple nonlinear interactions and control fields, rendering these schemes experimentally challenging. Here, we propose a bosonic code for approximate AQEC by relaxing the Knill-Laflamme conditions. Using reinforcement learning (RL), we identify the optimal bosonic set of codewords (denoted here by RL code), which, surprisingly, is composed of the Fock states $\vert 2\rangle$ and $\vert 4\rangle$. As we show, the RL code, despite its approximate nature, successfully suppresses single-photon loss, reducing it to an effective dephasing process that well surpasses the break-even threshold. It may thus provide a valuable building block toward full error protection. The error-correcting Hamiltonian, which includes ancilla systems that emulate the engineered dissipation, is entirely based on the Hamiltonian distance $d=1$, significantly reducing model complexity. Single-qubit gates are implemented in the RL code with a maximum distance $d_g=2$.

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