



01576nas a2200157   4500008004100000245010800041210006900149260001400218490000600232520106400238100001701302700001601319700002701335700001901362856003701381       2020                        eng d00aOptimal fermion-to-qubit mapping via ternary trees with applications to reduced quantum states learning0 aOptimal fermiontoqubit mapping via ternary trees with applicatio  c5/26/20200 v43 a<p>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 ≲(2n+1)kϵ&minus;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 ≲3kϵ&minus;2 times, independent of the system size. This improves over existing schemes for determining qubit RDMs.</p>1 aJiang, Zhang1 aKalev, Amir1 aMruczkiewicz, Wojciech1 aNeven, Hartmut  uhttps://arxiv.org/abs/1910.10746