Nonlocal quantum information in bipartite quantum error correction

TL;DR

This paper introduces a method to convert stabilizer codes into bipartite quantum codes involving two senders and one receiver, utilizing nonlocal resources for efficient quantum information encoding and decoding, with applications in quantum communication and fault-tolerant quantum computing.

Contribution

It presents a novel technique for bipartite quantum error correction, including a local encoding circuit for a bipartite Steane code with nearest-neighbor interactions, improving fault-tolerance.

Findings

Improved pseudothreshold in fault-tolerant simulation

Local encoding circuit for bipartite Steane code

Effective use of nonlocal resources in quantum error correction

Abstract

We show how to convert an arbitrary stabilizer code into a bipartite quantum code. A bipartite quantum code is one that involves two senders and one receiver. The two senders exploit both nonlocal and local quantum resources to encode quantum information with local encoding circuits. They transmit their encoded quantum data to a single receiver who then decodes the transmitted quantum information. The nonlocal resources in a bipartite code are ebits and nonlocal information qubits and the local resources are ancillas and local information qubits. The technique of bipartite quantum error correction is useful in both the quantum communication scenario described above and in fault-tolerant quantum computation. It has application in fault-tolerant quantum computation because we can prepare nonlocal resources offline and exploit local encoding circuits. In particular, we derive an encoding circuit for a bipartite version of the Steane code that is local and additionally requires only nearest-neighbor interactions. We have simulated this encoding in the CNOT extended rectangle with a publicly available fault-tolerant simulation software. The result is that there is an improvement in the "pseudothreshold" with respect to the baseline Steane code, under the assumption that quantum memory errors occur less frequently than quantum gate errors.