Gate-Efficient Implementation of the Query-Optimal Time-Dependent Hamiltonian Simulation

Abstract:The query-optimal algorithm of [CGWZ26] for general time-dependent Hamiltonian simulation uses $$ q = O\left( \alpha T + \frac{\log(1/\varepsilon)}{\log\left(e + \log(1/\varepsilon)/(\alpha T) \right)} \right) $$ queries to $\mathrm{HAM\mbox{-}T}$ within $\varepsilon$ error for a Lipschitz-continuous time-dependent Hamiltonian $H(t)$ on $[0,T]$ satisfying $\left\lVert H(t)\right\rVert\leq\alpha$. However, its direct circuit implementation incurs a substantially larger gate overhead. In this note, we give an implementation of the same algorithm that retains its optimal query complexity and uses $$ O\left[ q \left( a + \log\left(1 + \frac{T(\alpha + \beta T)}{\varepsilon} \right) \right) \right] $$ one- and two-qubit gates, where $a$ is the number of block-encoding ancilla qubits and $\beta$ is the Lipschitz constant of $H$. The main ingredient is an exact dyadic factorization of the ordered update product in the underlying one-query transducer.

Quantum Physics (quant-ph); Data Structures and Algorithms (cs.DS)

arXiv:2608.30629 [quant-ph]

(or arXiv:2608.30629v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.30629 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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