Spacetime Spins: Statistical Mechanics for Quantum Error Correction
Analysis
This paper introduces a novel framework for analyzing quantum error-correcting codes by mapping them to classical statistical mechanics models, specifically focusing on stabilizer circuits in spacetime. This approach allows for the analysis, simulation, and comparison of different decoding properties of stabilizer circuits, including those with dynamic syndrome extraction. The paper's significance lies in its ability to unify various quantum error correction paradigms and reveal connections between dynamical quantum systems and noise-resilient phases of matter. It provides a universal prescription for analyzing stabilizer circuits and offers insights into logical error rates and thresholds.
Key Takeaways
- •Introduces a statistical mechanics framework for analyzing stabilizer circuits in quantum error correction.
- •Provides a modular language of spin diagrams for constructing spin Hamiltonians.
- •Enables the analysis and comparison of different decoding properties of stabilizer circuits.
- •Reveals connections between dynamical quantum systems and noise-resilient phases of matter.
“The paper shows how to construct statistical mechanical models for stabilizer circuits subject to independent Pauli errors, by mapping logical equivalence class probabilities of errors to partition functions using the spacetime subsystem code formalism.”