Is the Hamiltonian simulation problem a classical problem?
“… nature isn’t classical, dammit, and if you want to make a simulation of nature, you’d better make it quantum mechanical, and by golly it’s a wonderful problem, because it doesn’t look so easy.”! Richard Feynman! Simulating physics with computers(1981) Outline •The Hamiltonian simulation problem! •Three approaches to simulation!
How to simulate Hamiltonian dynamics on a quantum computer?
Sparse Hamiltonians and coloring Strategy [Childs, Cleve, Deotto, Farhi, Gutmann, Spielman 03; Aharonov, Ta-Shma 03]: Color the edges of the graph of H. Then the simulation breaks into small pieces that are easy to handle. = + + A sparse graph can be efficiently colored using only local information [Linial 87], so this gives efficient simulations.
Is the Hamiltonian of a quantum circuit time dependent?
Problem: Given* a Hamiltonian H, a time t, and an error tolerance ² (say, with respect to trace distance), find a quantum circuit that performs the unitary operation e—iHt(on an unknown quantum state) with error at most ². More generally, H can be time-dependent. Local and sparse Hamiltonians
How is Hamiltonian parameter estimation using deep learning techniques?
The errors from the estimations was analyzed with statistical methods and confirmed the network was successfully trained to relate the Hamiltonian parameters with magnetic structure characteristics. The network was applied to estimate experimentally observed domain images.
How to calculate the Hamiltonian of time evolution?
Scite or leave a comment on SciRate. We present the problem of approximating the time-evolution operator e−i^Ht e − i H ^ t to error ϵ ϵ, where the Hamiltonian ^H= (⟨G|⊗ ^I)^U (|G⟩⊗ ^I) H ^ = ( ⟨ G | ⊗ I ^) U ^ ( | G ⟩ ⊗ I ^) is the projection of a unitary oracle ^U U ^ onto the state |G⟩ | G ⟩ created by another unitary oracle.