Abstract

We introduce a fermion-to-qubit mapping defined on ternary trees, where any single Majorana operator on an -mode fermionic system is mapped to a multi-qubit Pauli operator acting nontrivially on qubits. The mapping has a simple structure and is optimal in the sense that it is impossible to construct Pauli operators in any fermion-to-qubit mapping acting nontrivially on less than qubits on average. We apply it to the problem of learning -fermion reduced density matrix (RDM), a problem relevant in various quantum simulation applications. We show that one can determine individual elements of all -fermion RDMs in parallel, to precision , by repeating a single quantum circuit for times. This result is based on a method we develop here that allows one to determine individual elements of all -qubit RDMs in parallel, to precision , by repeating a single quantum circuit for times, independent of the system size. This improves over existing schemes for determining qubit RDMs.

Date

2020

Authors

Zhang Jiang, Amir Kalev, Wojciech Mruczkiewicz, Hartmut Neven

Journal

Quantum

Volume

4

Pages

276

Publisher

Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften