aiqbench analysis
This paper establishes that von Neumann measurement procedures remain practically viable for fault-tolerant quantum algorithms by deriving competitive Clifford + T complexity bounds for quantum phase estimation and energy estimation. By accounting for Hamiltonian simulation costs, the work validates the efficiency of these long-standing ideas when applied to block-encoded Hamiltonians and linear combinations of Pauli strings. The analysis provides a rigorous foundation for near-term fault-tolerant implementations of quantum energy estimation protocols.
von Neumann measurement and quantum phase estimation of block-encoded Hamiltonians
arXiv:2509.04246v2 Announce Type: replace Abstract: We review how to use von Neumann's measurement procedure to estimate a phase, using an efficient Hamiltonian simulation subroutine acts on a block-encoded Hamiltonian. We show that the resulting algorithm can be used to solve quantum phase estimation (QPE) or quantum energy estimation (QEE) {with competitive complexity scaling.} We then use recent results for block-encoding implementations to derive the Clifford + T complexity bound for QPE with respect to model-relevant parameters of the Hamiltonian and the desired precision. With this result, we demonstrate an efficient algorithm for QEE beginning from any linear combinations of Pauli strings. In this way, we argue that a well-understood and long-standing idea retains practical legitimacy for fault-tolerant era algorithms, once the costs of Hamiltonian simulation are accounted for.
Abstract:We review how to use von Neumann's measurement procedure to estimate a phase, using an efficient Hamiltonian simulation subroutine acts on a block-encoded Hamiltonian. We show that the resulting algorithm can be used to solve quantum phase estimation (QPE) or quantum energy estimation (QEE) {with competitive complexity scaling.} We then use recent results for block-encoding implementations to derive the Clifford + T complexity bound for QPE with respect to model-relevant parameters of the Hamiltonian and the desired precision. With this result, we demonstrate an efficient algorithm for QEE beginning from any linear combinations of Pauli strings. In this way, we argue that a well-understood and long-standing idea retains practical legitimacy for fault-tolerant era algorithms, once the costs of Hamiltonian simulation are accounted for.
arXiv:2509.04246 [quant-ph]
(or arXiv:2509.04246v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2509.04246 Focus to learn more arXiv-issued DOI via DataCite
https://doi.org/10.1088/2058-9565/ae7752 Focus to learn more DOI(s) linking to related resources
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