Detecting Errors in a Quantum Network with Pauli Checks

TL;DR

This paper extends the Pauli check sandwiching (PCS) error detection scheme to quantum networks, providing analytical fidelity equations, a recursive family of quantum codes, and demonstrating fidelity improvements through simulations.

Contribution

It introduces a distributed multiparty PCS protocol, a recursive PCS version for distance 2 codes, and benchmarks analytical results against existing protocols.

Findings

Analytical equations for fidelity and postselection rate.

Recursive PCS generates a family of CSS-like quantum codes.

Simulations show fidelity improvements with noisy gates.

Abstract

We apply the quantum error detection scheme Pauli check sandwiching (PCS) to quantum networks by turning it into a distributed multiparty protocol. PCS provides protection on the targeted qubits and generally requires less resource overhead than standard quantum error correction and detection codes. We provide analytical equations for the final fidelity and postselection rate for different PCS checks. We also introduce a recursive version of PCS that generates a family of distance 2 quantum codes that are locally equivalent to Calderbank-Shor-Steane (CSS) codes. Our analytical results are benchmarked against the Bennet-Brassard-Popescu-Schumacher-Smolin-Wooters (BBPSSW) protocol in comparable scenarios. We also perform simulations with noisy gates for entanglement swapping and attain fidelity improvements. Lastly, we discuss various setups and graph state properties of PCS.