Quantum operation of fermionic systems and process tomography using Majorana fermion gates

TL;DR

This paper develops a quantum tomography framework for fermionic systems, highlighting the unique constraints due to superselection rules and proposing a protocol using Majorana fermion gates for full process reconstruction.

Contribution

It introduces a fermionic quantum tomography framework and a protocol leveraging Majorana fermion gates for complete process characterization.

Findings

Partial reconstruction of fermionic operations under superselection rules

Full reconstruction requires at least one ancillary fermion mode

Protocol for informationally-complete state preparation and measurement using Majorana gates

Abstract

Quantum tomography is an important tool for the characterisation of quantum operations. In this paper, we present a framework of quantum tomography in fermionic systems. Compared with qubit systems, fermions obey the superselection rule, which sets constraints on states, processes and measurements in a fermionic system. As a result, we can only partly reconstruct an operation that acts on a subset of fermion modes, and the full reconstruction always requires at least one ancillary fermion mode in addition to the subset. We also report a protocol for the full reconstruction based on gates in Majorana fermion quantum computer, including a set of circuits for realising the informationally-complete state preparation and measurement.