Fermionic Measurement-based Quantum Computation

TL;DR

This paper extends measurement-based quantum computation to fermionic systems, providing a formalism for constructing resource states and demonstrating a universal fermionic state, thus broadening experimental possibilities.

Contribution

It introduces a general framework for fermionic MBQC, including a method to construct resource states and a specific universal fermionic state, advancing the understanding of fermionic quantum computation.

Findings

Developed a formalism for fermionic resource states in MBQC

Constructed a specific fermionic state enabling universal MBQC

Addressed non-locality issues with suitable measurement schemes

Abstract

Fermions, as a major class of quantum particles, provide platforms for quantum information processing beyond the possibilities of spins or bosons which have been studied more extensively. One particularly interesting model to study, in view of recent progress in manipulating ultracold fermion gases, is the fermionic version of measurement-based quantum computation (MBQC), which implements full quantum computation with only single site measurements on a proper fermionic many-body resource state. However, it is not known which fermionic states can be used as the resource states for MBQC and how to find them. In this paper, we generalize the framework of spin MBQC to fermions. In particular, we provide a general formalism to construct many-body entangled fermion resource states for MBQC based on the fermionic projected entangled pair state representation. We give a specific fermionic state which enables universal MBQC and demonstrate that the non-locality inherent in fermion systems can be properly taken care of with suitable measurement schemes. Such a framework opens up possibilities of finding MBQC resource states which can be more readily realized in the lab.