Coordinate space representation for quantum simulation of scalar field theory

Abstract:Quantum computing provides a promising framework for the simulation of quantum field theories, where the computational cost depends both on the quantum algorithm employed and on the representation of the Hamiltonian. We investigate a formulation of the $\phi^4$ model based on the harmonic-oscillator basis in coordinate space. We derive the lattice $\phi^4$ Hamiltonian in this representation and analyze the structure of the resulting one-body matrix and interaction tensor. We show that both exhibit an effective band-diagonal structure, allowing controlled truncations of the Hamiltonian while preserving the low-energy spectrum. We validate this formulation by comparing low-energy observables obtained from numerical diagonalization with those computed in the standard harmonic-oscillator momentum-space representation. Finally, we estimate the resources required to encode the Hamiltonian on a quantum computer using both binary and unary boson-to-qubit mappings. By exploiting effective locality, the coordinate-space representation reduces the resources required for quantum simulation over a broad range of parameters.

arXiv:2608.00670 [quant-ph]

(or arXiv:2608.00670v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.00670 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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