Gate-set tomography of fermionic systems using Majorana-fermion operations

Quantum tomography is an important tool for the characterization 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 a Majorana-fermion quantum computer, including a set of circuits for realizing the informationally complete state preparation and measurement.

Automated summary

This paper presents a framework of quantum tomography in fermionic systems, where the superselection rule for fermions imposes constraints on states, processes, and measurements. Due to these constraints, only partial reconstruction of operations acting on a subset of fermion modes is possible, with full reconstruction requiring at least one additional ancillary fermion mode.