The Stability of Quantum Concatenated Code Hamiltonians

TL;DR

This paper introduces a class of Hamiltonians whose ground states are concatenated quantum error-correcting codes, enabling natural quantum error correction through system dynamics, potentially reducing the need for active error correction.

Contribution

It proposes a novel Hamiltonian design that encodes concatenated quantum codes in ground states, providing a new approach to protecting quantum information.

Findings

Hamiltonians with ground states as concatenated quantum codes

Analysis of robustness of these Hamiltonians

Proposed methods for implementing these Hamiltonians

Abstract

Protecting quantum information from the detrimental effects of decoherence and lack of precise quantum control is a central challenge that must be overcome if a large robust quantum computer is to be constructed. The traditional approach to achieving this is via active quantum error correction using fault-tolerant techniques. An alternative to this approach is to engineer strongly interacting many-body quantum systems that enact the quantum error correction via the natural dynamics of these systems. Here we present a method for achieving this based on the concept of concatenated quantum error correcting codes. We define a class of Hamiltonians whose ground states are concatenated quantum codes and whose energy landscape naturally causes quantum error correction. We analyze these Hamiltonians for robustness and suggest methods for implementing these highly unnatural Hamiltonians.