CQuIC Seminars
A simple method for optimal hamiltonian simulation
Presented by Rolando Somma, Los Alamos National Laboratory
I will provide a simple quantum algorithm for simulating the dynamics of sparse Hamiltonians with complexity sublogarithmic in the inverse error, an exponential improvement over previous methods.
Unlike previous approaches based on product formulas, the query complexity is independent of the number of qubits acted on, and for time-varying Hamiltonians, the gate complexity is only logarithmic in the norm of the derivative of the Hamiltonian. The algorithm is based on a quantum circuit designed to simulate the series of the exponential operator, thus not requiring the notion of a "fractional query", as in our recent result [1].
A new form of "oblivious amplitude amplification" then is applied, even though the reflection about the input state is unavailable. We also show how this simple method can be extended to the simulation of quantum query models in continuous time.
[1] D.W. Berry, et.al., arXiv:1312.1414
3:30 pm, Thursday, April 10, 2014
PAIS-2540, PAIS
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