Deterministic exact inversion of an arbitrary $d$-dimensional unitary requires {$\Theta(d^2)$} coherent forward calls in the worst case. We ask how this cost changes for Hamiltonian evolution $U(x)=\exp(i\sum_j x_jH_j)$ when the generators are known but the parameters are hidden. For one-parameter families with a fixed eigenbasis, we show that additive relations among the distinct eigenvalues determine the optimal query number exactly, and we construct the corresponding inversion protocol. For general families, we prove that repeated symmetry sectors do not affect the exact query complexity and give an automatic construction for combining inverses from inequivalent active sectors. We also give a sufficient phase-alignment condition under which family-specific structure can reduce the query number. These results establish structure-dependent bounds for reversing the unknown dynamics arising in Tavis-Cummings out-of-time-order correlator protocols, collective-spin echo verification, and passive multimode links, without requiring prior knowledge or explicit estimation of the underlying coupling strengths.
This work introduces Pathwise Random Hamiltonian Simulation (PRHS), which extends qDrift to arbitrary order by subdividing each time step into correlated slices, each evolving under a term sampled from a quasi-probability distribution that is constructed in closed form and proves unique.
Unitary $k$-designs provide a resource-efficient framework for emulating Haar randomness up to the $k$-th order. Quench-based protocols have recently been shown to generate such designs, but achieving this typically requires multiple Hamiltonian realizations, even when using temporal ensembles. Here, we show that no in...
We consider the classical analytic linearization problem for vector fields on the torus $\mathbb{T}^d$ close to a constant vector field $\omega$. Our goals are twofold. First, we provide a geometric framework in which the arithmetic condition governing analytic linearization arises naturally from the orbit of a unimodu...
N. Chevallier, J. Dias, Jose Gaivao et al.· 0 citations
This work suggests that for many physical systems, gate count must scale polynomially in $1/\epsilon$, contrary to the complexity suggested by counting coherent oracle queries such as those in the block-encoding model.
Alexander Zlokapa, Richard R. Allen, A. Harrow· 3 citations
This work gives an unconditional exact quantum implementation in a circuit model permitting single-qubit rotations through efficiently computable angles and combines R'onyai's classical structure theory with R'onyai's classical structure theory to yield the radical and the Wedderburn decomposition.
We study online search for an unknown affine hyperplane in $\mathbb{R}^D$, for arbitrary fixed finite dimension. Building on a companion self-similar cell reduction and support-function formulation, we ask how the mechanism changes as the normal space grows from $\mathbb{S}^0$ to $\mathbb{S}^{D-1}$. In $D=1$, alternati...
Florentin Koch· 0 citations
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