Symbolic Hamiltonian Compiler for Hybrid Qubit-Boson Processors

Ethan Decker; Erik Gustafson; Evan McKinney; Alex K. Jones; Lucas Goetz; Ang Li; Alexander Schuckert; Samuel Stein; Gushu Li; Eleanor Crane

arXiv · 2506.00215

Symbolic Hamiltonian Compiler for Hybrid Qubit-Boson Processors

Ethan Decker·Erik Gustafson·Evan McKinney·Alex K. Jones·Lucas Goetz·Ang Li·Alexander Schuckert·Samuel Stein·Gushu Li·Eleanor Crane

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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.

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Ethan Decker, Erik Gustafson, Evan McKinney, Alex K. Jones, Lucas Goetz, Ang Li, Alexander Schuckert, Samuel Stein, Gushu Li, Eleanor Crane. 2025-05-30. Symbolic Hamiltonian Compiler for Hybrid Qubit-Boson Processors. https://arxiv.org/abs/2506.00215

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