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We introduce an algorithm to compute Hamiltonian dynamics on digital quantumcomputers that requires only a finite circuit depth to reach an arbitraryprecision, i.e. achieves zero discretization error with finite depth. Thisfinite number of gates comes at the cost of an attenuation of the measuredexpectation value by a known amplitude, requiring more shots per circuit. Thegate count for simulation up to time $t$ is $O(t^2\mu^2)$ with $\mu$ the$1$-norm of the Hamiltonian, without dependence on the precision desired on theresult, providing a significant improvement over previous algorithms. The onlydependence in the norm makes it particularly adapted to non-sparseHamiltonians. The algorithm generalizes to time-dependent Hamiltonians,appearing for example in adiabatic state preparation. These properties make itparticularly suitable for present-day relatively noisy hardware that supportsonly circuits with moderate depth.

Continuous Hamiltonian dynamics on digital quantum computers without discretization error