Optimal solutions to quantum annealing using two independent control
functions
- URL: http://arxiv.org/abs/2110.13852v1
- Date: Tue, 26 Oct 2021 16:54:17 GMT
- Title: Optimal solutions to quantum annealing using two independent control
functions
- Authors: Marllos E. F. Fernandes, Emanuel F. de Lima, and Leonardo K. Castelano
- Abstract summary: We show that an optimal solution consists of both controls tuned at their upper bound for the whole evolution time.
We propose the use of a quantum optimal control technique adapted to limit the amplitude of the controls.
We show that the scheme with two-control functions yields a higher fidelity than the other schemes for the same evolution time.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We investigate the quantum computing paradigm consisted of obtaining a target
state that encodes the solution of a certain computational task by evolving the
system with a combination of the problem-Hamiltonian and the
driving-Hamiltonian. We analyze this paradigm in the light of Optimal Control
Theory considering each Hamiltonian modulated by an independent control
function. In the case of short evolution times and bounded controls, we
analytically demonstrate that an optimal solution consists of both controls
tuned at their upper bound for the whole evolution time. This optimal solution
is appealing because of its simplicity and experimental feasibility. To
numerically solve the control problem, we propose the use of a quantum optimal
control technique adapted to limit the amplitude of the controls. As an
application, we consider a teleportation protocol and compare the fidelity of
the teleported state obtained for the two-control functions with the usual
single-control function scheme and with the quantum approximate optimization
algorithm (QAOA). We also investigate the energetic cost and the robustness
against systematic errors in the teleportation protocol, considering different
time evolution schemes. We show that the scheme with two-control functions
yields a higher fidelity than the other schemes for the same evolution time.
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