Optimal Fusion Transformations for Linear Optical Cluster State Generation

TL;DR

This paper investigates optimal methods for generating linear optical cluster states, revealing more efficient fusion schemes than the standard CZ gate with success rates exponentially higher, and provides explicit designs for these operations.

Contribution

It introduces alternative fusion schemes that outperform the traditional CZ gate, demonstrating their optimality and providing explicit optical designs for implementation.

Findings

Maximal success rate for fusing n qubits is 1/2^{n-1}.

Maximal success rate for fusing m Bell pairs is 1/4^{m-1}.

Sequential growth of LOCS is globally optimal.

Abstract

We analyze the generation of linear optical cluster states (LOCS) via addition of one and two qubits. Existing approaches employ the stochastic linear optical two-qubit CZ gate with success rate of 1/9 per fusion operation. The question of optimality of the CZ gate with respect to LOCS generation remains open. We report that there are alternative schemes to the CZ gate that are exponentially more efficient and show that sequential LOCS growth is globally optimal. We find that the optimal cluster growth operation is a state transformation on a subspace of the full Hilbert space. We show that the maximal success rate of fusing n photonic qubits or m Bell pairs is 1/2^n-1 and 1/4^m-1 respectively and give an explicit optical design.