Parallel Quantum Algorithm for Hamiltonian Simulation

Understand

We study how parallelism can speed up quantum simulation.

• A parallel quantum algorithm is proposed for simulating the dynamics of a large class of Hamiltonians with good sparse structures, called uniform-structured Hamiltonians, including various Hamiltonians of practical interest like local Hamiltonians and Pauli sums.
• Given the oracle access to the target sparse Hamiltonian, in both query and gate complexity, the running time of our parallel quantum simulation algorithm measured by the quantum circuit depth has a doubly (poly-)logarithmic dependence $\operatorname{polylog}\log(1/\epsilon)$ on the simulation precision $\epsilon$.
• This presents an exponential improvement over the dependence $\operatorname{polylog}(1/\epsilon)$ of previous optimal sparse Hamiltonian simulation algorithm without parallelism.