Symbolic Hamiltonian Compiler for Hybrid Qubit-Boson Processors

Abstract

Quantum simulation of the interactions of fermions and bosons -- the fundamental particles of nature -- is essential for modeling complex quantum systems in material science, chemistry and high-energy physics and has been proposed as a promising application of fermion-boson quantum computers, which overcome the overhead encountered in mapping fermions and bosons to qubits. However, compiling the simulation of specific fermion-boson Hamiltonians into the natively available fermion-boson gate set is challenging. In particular, the large local dimension of bosons renders matrix-based compilation methods, as used for qubits and in existing tools such as Bosonic Qiskit or OpenFermion, challenging. We overcome this issue by introducing a novel symbolic compiler based on matrix-free symbolic manipulation of second quantised Hamiltonians, which automates the decomposition of fermion-boson second quantized problems into qubit-boson instruction set architectures. This integration establishes a comprehensive pipeline for simulating quantum systems on emerging qubit-boson and fermion-boson hardware, paving the way for their large-scale usage.