For the problem of simulating Lindblad evolution for time $t$ to precision $\epsilon$, Hamiltonian simulation provides an additive query lower bound, informally, $\Omega(t + \mathrm{polylog}(1/\epsilon))$. However, the best previously known algorithms for general Lindblad simulation achieve a multiplicative upper bound...
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...
This framework accelerates classical stochastic Langevin Monte Carlo and Hamiltonian Monte Carlo algorithms by replacing stochastic gradient estimators with variance-controlled quantum mean estimation and gradient estimation subroutines, and develops gradient estimators robust to noisy function evaluations, yielding im...
Guneykan Ozgul, Xian-Tao Li, Mehrdad Mahdavi et al.· Theory of Quantum Computatio...· 6 citations· ⚡1
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