Fermion-to-qubit mappings with varying resource requirements for quantum simulation

Abstract

The mapping of fermionic states onto qubit states, as well as the mapping of fermionic Hamiltonian into quantum gates enables us to simulate electronic systems with a quantum computer. Benefiting the understanding of many-body systems in chemistry and physics, quantum simulation is one of the great promises of the coming age of quantum computers. Interestingly, the minimal requirement of qubits for simulating Fermions seems to be agnostic of the actual number of particles as well as other symmetries. This leads to qubit requirements that are well above the minimal requirements as suggested by combinatorial considerations. In this work, we develop methods that allow us to tradeoff qubit requirements against the complexity of the resulting quantum circuit. We first show that any classical code used to map the state of a fermionic Fock space to qubits gives rise to a mapping of fermionic models to quantum gates. As an illustrative example, we present a mapping based on a nonlinear classical error correcting code, which leads to significant qubit savings albeit at the expense of additional quantum gates. We proceed to use this framework to present a number of simpler mappings that lead to qubit savings with a more modest increase in gate difficulty. We discuss the role of symmetries such as particle conservation, and savings that could be obtained if an experimental platform could easily realize multi-controlled gates.

Resource-efficient digital quantum simulation of d-level systems for photonic, vibrational, and spin-s Hamiltonians

“…1. Similar considerations have been studied for fermionic mappings 26 . For near-and intermediate-term hardware, one will often have stringent resource constraints in terms of both qubit count and gate count.…”

Secure multiparty quantum computation with few qubits

“…Since near-term quantum networks will be able to support only a small number of qubits, it would be preferable to implement an MPQC protocol with as few qubits as possible. So far, reducing quantum resources has received a lot of attention in the domain of nondistributed quantum computation and simulation (see, for example, [15][16][17][18][19]). Recently, in [20] we considered a problem of reducing quantum resources for a distributed protocol, namely, verifiable secret sharing of a quantum state.…”

Quantum codes for quantum simulation of fermions on a square lattice of qubits

“…We will now show how this transform translates the Hamiltonian (2). Mimicking the effect of the Fermion operators c † j , c j on the basis states, we find [42]…”