GHZ-Preserving Gates and Optimized Distillation Circuits

TL;DR

This paper presents a novel, highly efficient method for simulating and optimizing circuits that preserve and distill GHZ states, significantly reducing computational complexity and enabling advanced quantum network design.

Contribution

The work introduces a new simulation technique reducing complexity to constant time for GHZ-preserving circuits and demonstrates optimized distillation circuits surpassing existing methods.

Findings

Simulation complexity reduced to O(1) for GHZ-preserving circuits.

Discovered GHZ distillation circuits outperform previous approaches.

Method extends naturally to graph states related to GHZ states.

Abstract

Greenberger-Horne-Zeilinger (GHZ) states play a central role in quantum computing and communication protocols, as a typical multipartite entanglement resource. This work introduces an efficient enumeration and simulation method for circuits that preserve and distill noisy GHZ states, significantly reducing the simulation complexity of a gate on $n$ qubits, from exponential $O(2^n)$ for standard state-vector methods or $O(n)$ for Clifford circuits, to a constant $O(1)$ for the method presented here. This method has profound implications for the design of quantum networks, where preservation and purification of entanglement with minimal resource overhead is critical. In particular, we demonstrate the use of the new method in an optimization procedure enabled by the fast simulation, that discovers GHZ distillation circuits far outperforming the state of the art. Fine-tuning to arbitrary noise models is possible as well. We also show that the method naturally extends to graph states that are local Clifford equivalent to GHZ states.