Approximate Dynamical Quantum Error-Correcting Codes

TL;DR

This paper introduces approximate dynamical quantum error-correcting codes that combine time-dependent stabilization techniques with tailored noise mitigation, aiming to reduce resource requirements for near-term quantum devices.

Contribution

It develops a new class of approximate dynamical codes, integrating dynamical and approximate error correction, with analysis via semidefinite programming and a specialized recovery map.

Findings

Constructed several approximate dynamical codes using strategic code framework.

Proved the uniqueness and robustness of optimal encoding and decoding.

Recovered known static codes as a special case.

Abstract

Quantum error correction plays a critical role in enabling fault-tolerant quantum computing by protecting fragile quantum information from noise. While general-purpose quantum error correction codes are designed to address a wide range of noise types, they often require substantial resources, making them impractical for near-term quantum devices. Approximate quantum error correction provides an alternative by tailoring codes to specific noise environments, reducing resource demands while still maintaining noise-robustness. Dynamical codes, including Floquet codes, introduce a dynamic approach to quantum error correction, employing time-dependent operations to stabilize logical qubits. In this work, we combine the flexibility of dynamical codes with the versatility of approximate quantum error correction to offer a promising avenue for addressing dominant noise in quantum systems. We construct several approximate dynamical codes using the recently developed strategic code framework. As a special case, we recover the approximate static codes widely studied in the existing literature. By analyzing these approximate dynamical codes through semidefinite programming, we establish the uniqueness and robustness of the optimal encoding, decoding, and check measurements. We also develop a temporal Petz recovery map suited to approximate dynamical codes.