[Paper Review] Error correction for a proposed quantum annealing architecture

Fernando Pastawski, John Preskill|arXiv (Cornell University)|Oct 30, 2015

Theoretical and Computational Physics3 citations

TL;DR

This paper proposes a quantum annealing architecture based on a classical error-correcting code that maps all-to-all spin glass interactions onto a geometrically local lattice. By interpreting the Lechner-Hauke-Zoller architecture as a code, the study demonstrates robustness against weakly correlated bit-flip noise, offering a fault-tolerant design for quantum annealing systems.

ABSTRACT

Recently, Lechner, Hauke and Zoller [Science Advances, 1(9)e1500838, (2015)] have proposed a quantum annealing architecture, in which a classical spin glass with all-to-all connectivity is simulated by a spin glass with geometrically local interactions. We interpret this architecture as a classical error-correcting code, which is highly robust against weakly correlated bit-flip noise.

Motivation & Objective

• To investigate whether the Lechner-Hauke-Zoller quantum annealing architecture can be interpreted as a classical error-correcting code.
• To analyze the resilience of this architecture against weakly correlated bit-flip noise.
• To establish a theoretical foundation for fault tolerance in quantum annealing using classical coding principles.

Proposed method

• The architecture is reinterpreted as a classical error-correcting code that encodes all-to-all spin glass interactions into a geometrically local spin glass.
• The code maps a fully connected spin glass onto a lattice with only local interactions, preserving the computational structure.
• Noise robustness is analyzed under weakly correlated bit-flip noise, modeling realistic error sources.
• The error-correcting properties are derived from the code's structure, leveraging known results from classical coding theory.
• The analysis focuses on the logical error rate under noise, showing suppression due to code distance.

Experimental results

Research questions

• RQ1 Can the Lechner-Hauke-Zoller architecture be understood as a classical error-correcting code?
• RQ2 How does the architecture perform under weakly correlated bit-flip noise?
• RQ3 What is the relationship between code structure and noise resilience in this quantum annealing model?

Key findings

• The Lechner-Hauke-Zoller architecture functions as a classical error-correcting code that maps all-to-all interactions to local ones.
• The code structure provides robustness against weakly correlated bit-flip noise, suppressing logical errors.
• The error-correcting capability arises from the code's geometric and topological design, enabling fault-tolerant quantum annealing.
• The study establishes a direct link between quantum annealing architecture and classical coding theory, enabling new fault-tolerance strategies.