We develop a quantum algorithm for slow analytic Hamiltonians $\widetilde H(t)=H(t/T)$ with $\|H(s)\|\leq\alpha$ that achieves nearly additive query complexity and low gate overhead. Our main technical contribution is a periodic Gevrey extension of $H(s)$, together with Fourier component decay and truncation bounds that enable an efficient finite-dimensional simulation. Combined with Floquet embedding and optimal time-independent Hamiltonian simulation technique, this gives query complexity $\widetilde{\mathcal O}\!\left(\alpha T+\log(1/\varepsilon)\right)$ and additional gate complexity $\widetilde{\mathcal O}\!\left((\alpha T+\log(1/\varepsilon))^2\log(1/\varepsilon)\right)$, assuming coherent access to $H'(s)$ and endpoint derivatives. For slow analytic control Hamiltonians, only block encodings of the time-independent control operators are required, with the same query complexity and lower gate overhead. Our method also extends to Gevrey Hamiltonians and improves the precision dependence for simulating slow analytic semi-dissipative linear differential equations.
We give a quantum algorithm for Lindbladian simulation given a block encoding of the Hamiltonian $H$ and a projected unitary encoding of the stacked jump operator $B=\sum_{k=1}^m \lvert k\rangle\otimes L_k$, with normalization factors $\alpha_H$ and $\alpha_B$, respectively. For evolution time $t$, set $\tau=(\alpha_H+...
Bo-Yang Chen, Min-Bo Gao, Xin-Zhao Wang et al.· 5 citations
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 Ham...
Bo-Yang Chen, Min-Bo Gao, Zheng-Feng Ji et al.· 7 citations
We give a quantum algorithm for simulating a $d$-sparse Hermitian Hamiltonian $H$, assuming a known upper bound $\Lambda$ on its maximum column Euclidean norm $\|H\|_{1\to2}$. For $t\Lambda\ge1/2$, simulation with operator-norm error $\epsilon$ uses \[ O\!\left(t\Lambda\sqrt d+\sqrt d\log(2/\epsilon)\right) \] sparse-o...
We prove the first quantum-classical separation for a sampling problem over a continuous domain. For a class of Gibbs states $p\propto e^{-\beta E}$ on the torus $\mathbb{T}^d$ with smooth ($s$-Gevrey) potential and barrier amplitude $\alpha=e^{\beta\Delta}$, where $\Delta = \max E-\min E$, every classical algorithm qu...
Enrico Olivucci, Mariia Sobchuk, Sehmimul Hoque et al.· 1 citation
Dissipation has been recently demonstrated as a powerful primitive for designing quantum algorithms. We apply this viewpoint directly to linear-system solving, $Ax=b$. We construct a simple purely dissipative Lindbladian whose unique fixed point encodes the linear-system solution. We prove dimension-independent trace-d...
At what rate does the von Neumann entropy of an ensemble of quantum states change under Hamiltonian evolution of its constituents? Bravyi proposed the small incremental mixing conjecture controlling the mixing rate of a binary ensemble $\{(1\!-\!p,\rho_1),(p,\rho_2)\}$ by $c\,\|{H}\|h_{2}(p)$ (with the binary entropy $...
Alexander Stottmeister· 0 citations
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