Exterior calculus and fermionic quantum computation

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.

References in corpus (2)

• Digital quantum simulation of fermionic models with a superconducting circuit
• Fermionic mode entanglement in quantum information

Cited by in corpus (3)

• Calculating the distance from an electronic wave function to the manifold of Slater determinants through the geometry of Grassmannians
• Accelerating Dissipative State Preparation with Adaptive Open Quantum Dynamics
• Shallow quantum circuits for efficient preparation of Slater determinants and correlated states on a quantum computer