Efficient Hamiltonian Truncation: Fast Matrix Construction and Quantum Krylov Diagonalization

• URL: http://arxiv.org/abs/2608.13691v1
• Date: Thu, 13 Aug 2026 18:37:19 GMT
• Title: Efficient Hamiltonian Truncation: Fast Matrix Construction and Quantum Krylov Diagonalization
• Abstract summary: Hamiltonian truncation offers a nonperturbative route to quantum field theory.<n>We develop an efficient basis-generation scheme built on integer partitions.<n>We speed up the construction of the sparse Hamiltonian matrix using symmetry-aware algorithms.
• Score: 36.99783938253534
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Hamiltonian truncation offers a nonperturbative route to quantum field theory, yet its accuracy is limited by the rapid expansion of the truncated Hilbert space, which drives up computational cost. We tackle this bottleneck with a hybrid strategy that pairs classical and quantum algorithms: 1) we develop an efficient basis-generation scheme built on integer partitions; 2) we speed up the construction of the sparse Hamiltonian matrix using symmetry-aware algorithms; and 3) we explore quantum Krylov diagonalization as a route to the low-lying spectrum. Benchmarking against the free massive scalar and $φ^4$ theories in two spacetime dimensions, we achieve substantial gains in the computational efficiency of Hamiltonian truncation and chart a path toward future quantum implementations.

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