Optimal fermion-to-qubit mapping via ternary trees with applications to reduced quantum states learning

2019/10/31 by Zhang Jiang, Amir Kalev, Wojciech Mruczkiewicz +1 · 4 citations
Physics and Astronomy · #quant-ph

paper · pdf · doi:10.22331/q-2020-06-04-276

published as Quantum 4, 276 (2020) · 10 pages, 3 figures

arxiv created 2020/05/26 · arxiv updated 2020/07/01

Abstract

We introduce a fermion-to-qubit mapping defined on ternary trees, where any single Majorana operator on an n-mode fermionic system is mapped to a multi-qubit Pauli operator acting nontrivially on \lceil log₃(2n+1)\rceil 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 log₃(2n) qubits on average. We apply it to the problem of learning k-fermion reduced density matrix (RDM), a problem relevant in various quantum simulation applications. We show that using the ternary-tree mapping one can determine the elements of all k-fermion RDMs, to precision ε, by repeating a single quantum circuit for \lesssim (2n+1)^k ε^-2 times. This result is based on a method we develop here that allows one to determine the elements of all k-qubit RDMs, to precision ε, by repeating a single quantum circuit for \lesssim 3^k ε^-2 times, independent of the system size. This improves over existing schemes for determining qubit RDMs.

Cited by

• Scalable quantum circuit generation for iterative ground state approximation using Majorana Propagation
• On the stability to noise of fermion-to-qubit mappings
• Tightness of and counterexamples to several quantum estimates
• Digital quantum simulation of the Su-Schrieffer-Heeger model using a parameterized quantum circuit