Engineering holography with stabilizer graph codes

TL;DR

This paper presents a method to implement holographic quantum error-correcting codes using stabilizer graph codes, enabling experimental realization and verification of holographic properties in quantum systems.

Contribution

It formulates the hyperbolic pentagon code as a stabilizer graph code and provides tailored gate sequences for systems with long-range interactions.

Findings

Gate sequences for hyperbolic pentagon code implementation

Encoding and decoding circuits for small holographic code

Verification of holographic properties through partial decoding

Abstract

The discovery of holographic codes established a surprising connection between quantum error correction and the anti-de Sitter-conformal field theory correspondence. Recent technological progress in artificial quantum systems renders the experimental realization of such holographic codes now within reach. Formulating the hyperbolic pentagon code in terms of a stabilizer graph code, we give gate sequences that are tailored to systems with long-range interactions. We show how to obtain encoding and decoding circuits for the hyperbolic pentagon code, before focusing on a small instance of the holographic code on twelve qubits. Our approach allows to verify holographic properties by partial decoding operations, recovering bulk degrees of freedom from their nearby boundary.