Exterior calculus and fermionic quantum computation

TL;DR

This paper explores the use of exterior calculus to represent fermionic systems and proposes two schemes for implementing fermionic quantum computation, including novel electronic devices and simulation methods within multi-qubit systems.

Contribution

It introduces two new schemes for fermionic quantum computation, leveraging exterior calculus and mappings to multi-qubit systems, advancing quantum simulation techniques.

Findings

Proposes fermionic gate implementations with exterior calculus

Develops electronic devices simulating fermionic gates

Demonstrates fermionic gate simulation within multi-qubit systems

Abstract

Exterior calculus with its three operations meet, join and hodge star complement, is used for the representation of fermion-hole systems and for fermionic analogues of logical gates. Two different schemes that implement fermionic quantum computation, are proposed. The first scheme compares fermionic gates with Boolean gates, and leads to novel electronic devices that simulate fermionic gates. The second scheme usesa well known map between fermionic and multi-qubit systems, to simulate fermionic gates within multi-qubit systems.