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Optimisation of Quantum Evolution Algorithms | | Apoorva Patel
; | | Date: |
4 Mar 2015 | | Abstract: | Given a quantum Hamiltonian and its evolution time, the corresponding unitary
evolution operator can be constructed in many different ways, corresponding to
different trajectories between the desired end-points. A choice among these
trajectories can then be made to obtain the best computational complexity and
control over errors. As an explicit example, Grover’s quantum search algorithm
is described as a Hamiltonian evolution problem. It is shown that the
computational complexity has a power-law dependence on error when a
straightforward Lie-Trotter discretisation formula is used, and it becomes
logarithmic in error when reflection operators are used. The exponential change
in error control is striking, and can be used to improve many importance
sampling methods. The key concept is to make the evolution steps as large as
possible while obeying the constraints of the problem. In particular, we can
understand why overrelaxation algorithms are superior to small step size
algorithms. | | Source: | arXiv, 1503.1429 | | Services: | Forum | Review | PDF | Favorites | |
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