Engineering holography with stabilizer graph codes

Abstract

The discovery of holographic codes established a surprising connection between quantum error correction and the AdS/CFT 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 propose an experimental implementation that is tailored to systems with long-range interactions. We show how to obtain encoding and decoding circuits for the hyperbolic pentagon code [Pastawski et al., JHEP 2015:149 (2015], 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.