Generalized Type II Fusion of Cluster States

TL;DR

This paper generalizes the type-II fusion process in measurement-based quantum computation, classifies the resulting states, and analyzes success probabilities, revealing that perfect success is only achievable with product states.

Contribution

It introduces a generalized measurement setup for type-II fusion, classifies the resulting states, and establishes bounds on success probabilities in quantum cluster state fusion.

Findings

Success probability is bounded by 50%.

States with 100% success are only product states.

Reduction of entanglement entropy can improve fusion success.

Abstract

Measurement based quantum computation is a quantum computing paradigm that employs single-qubit measurements performed on an entangled resource state in the form of a cluster state. A basic ingredient in the construction of the resource state is the type-II fusion procedure, which probabilistically merges two separate photonic cluster states by a quantum measurement. We generalize the type-II fusion procedure by generalizing the measurement setup, and classify the resulting final states, which also include cluster states up to single-qubit rotations. We prove that the probability for the success of the generalized type-II fusion is bounded by fifty percent, and classify all the possibilities to saturate the bound. We analyze the enhancement of the fusion success probability above the fifty percent bound, by the reduction of the entanglement entropy of the resulting state. We prove that the only states that can be obtained with a hundred percent probability of success, are product states.