Coordinate space representation for quantum simulation of scalar field theory

• URL: http://arxiv.org/abs/2608.00670v1
• Date: Sat, 01 Aug 2026 13:44:37 GMT
• Title: Coordinate space representation for quantum simulation of scalar field theory
• Abstract summary: We investigate a formulation of the $4$ model based on the harmonic-oscillator basis in coordinate space.<n>We show that both exhibit an effective band-diagonal structure, allowing controlled truncations of the Hamiltonian.<n>We estimate the resources required to encode the Hamiltonian on a quantum computer using both binary and unary boson-to-qubit mappings.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $φ^4$ model based on the harmonic-oscillator basis in coordinate space. We derive the lattice $φ^4$ 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.

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