This concept, drawn from the intersection of quantum computing and physics, addresses the quantum simulation of local Hamiltonians: how a quantum computer can efficiently approximate the time evolution and energy spectra of quantum systems whose Hamiltonians decompose into a sum of bounded-norm terms each acting on a constant number of qubits. The core theoretical results are that Schrodinger time evolution under a (geometrically) local Hamiltonian can be simulated by a quantum circuit of size polynomial (indeed near-linear) in the simulated spacetime volume via Trotter/Suzuki product-formula approximations, and that energy eigenvalues can be estimated to inverse-polynomial accuracy via quantum phase estimation, contingent on preparing an initial state with non-negligible overlap with the target eigenstate. The material situates quantum simulation within complexity theory and physics, connecting the tractability of state preparation to the adiabatic theorem, the energy gap, and the QMA-hardness of ground-state energy estimation.
This concept, drawn from the intersection of quantum computing and physics, addresses the quantum simulation of local Hamiltonians: how a quantum computer can efficiently approximate the time evoluti…