Efficient Hamiltonian Truncation: Fast Matrix Construction and Quantum Krylov Diagonalization

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 $\phi^4$ theories in two spacetime dimensions, we achieve substantial gains in the computational efficiency of Hamiltonian truncation and chart a path toward future quantum implementations.

arXiv:2608.13691 [quant-ph]

(or arXiv:2608.13691v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.13691 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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