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This paper proposes a novel quantum algorithm that leverages thermalization and the eigenstate thermalization hypothesis to solve linear algebra problems without requiring complex wavefunction preparation. By utilizing full ergodicity in quantum systems, the method achieves poly-logarithmic time complexity for computing functions of input operators via quantum phase estimation. This approach represents a significant theoretical advancement in reducing resource overhead for quantum linear algebra applications.
Quantum computation with the eigenstate thermalization hypothesis instead of wavefunction preparation
arXiv:2504.19185v3 Announce Type: replace Abstract: It is proposed that the ability for a quantum circuit to thermalize under time evolution is a valid way to compute linear algebra problems. The algorithm makes use of the eigenstate thermalization hypothesis and full ergodicity in quantum systems to produce an equal superposition of eigenstates. The quantum phase estimation subroutine then allows for the computations of functions of the input operator, leading to a variety of methods in linear algebra. The algorithm circumvents the need for elaborate wavefunction preparation on the quantum computer to find the solution of the linear algebra problem in poly-logarithmic time.
Abstract:It is proposed that the ability for a quantum circuit to thermalize under time evolution is a valid way to compute linear algebra problems. The algorithm makes use of the eigenstate thermalization hypothesis and full ergodicity in quantum systems to produce an equal superposition of eigenstates. The quantum phase estimation subroutine then allows for the computations of functions of the input operator, leading to a variety of methods in linear algebra. The algorithm circumvents the need for elaborate wavefunction preparation on the quantum computer to find the solution of the linear algebra problem in poly-logarithmic time.
arXiv:2504.19185 [quant-ph]
(or arXiv:2504.19185v3 [quant-ph] for this version)
From: Thomas E. Baker [view email] [v1] Sun, 27 Apr 2025 10:20:07 UTC (16 KB) [v2] Tue, 26 May 2026 17:41:31 UTC (55 KB) [v3] Tue, 6 Oct 2026 22:50:35 UTC (43 KB)
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