Abstract
Adiabatic quantum computation employs a slow change of a time-dependent control function (or functions) to interpolate between an initial and final Hamiltonian, which helps to keep the system in the instantaneous ground state. When the evolution time is finite, the degree of adiabaticity (quantified in this work as the average ground-state population during evolution) depends on the particulars of a dynamic trajectory associated with a given set of control functions. We use quantum optimal control theory with a composite objective functional to numerically search for controls that achieve the target final state with a high fidelity while simultaneously maximizing the degree of adiabaticity. Exploring the properties of optimal adiabatic trajectories in model systems elucidates the dynamic mechanisms that suppress unwanted excitations from the ground state. Specifically, we discover that the use of multiple control functions makes it possible to access a rich set of dynamic trajectories, some of which attain a significantly improved performance (in terms of both fidelity and adiabaticity) through the increase of the energy gap during most of the evolution time.
Highlights
Many important, computationally challenging problems in combinatorial optimization can be solved by determining the ground state of some quantum Hamiltonian
Adiabatic quantum computation (AQC) [2, 3], on the other hand, offers a route to producing the target ground state by slowly changing the system’s Hamiltonian H(t) from some initial one, whose ground state is prepared at t = 0, to the final one, whose ground state encodes the solution to the problem
In order to numerically investigate the performance of the quantum optimal control theory (QOCT) formalism presented in section 3, we consider two simple AQC problems, which both correspond to the one-qubit Hamiltonian (28)
Summary
Computationally challenging problems in combinatorial optimization can be solved by determining the ground state of some quantum Hamiltonian. By virtue of keeping the system in the instantaneous ground state of a slowly varying Hamiltonian, AQC acquires an inherent robustness to several sources of noise, such as dephasing and relaxation in the energy eigenbasis [6], which are known to plague the standard circuit model of quantum computation [7]. A numerical search is required to find a control set, which implements the desired Hamiltonian interpolation in a limited time while simultaneously maximizing the degree of adiabaticity We perform these searches, using a gradient-based optimization algorithm, for two AQC problems with a Landau–Zener type Hamiltonian. We couch our discussion in the context of AQC, our main result — that increasing the number of control handles in the Hamiltonian enables to preserve larger ground state populations in shorter evolution times — is more widely applicable to all situations that employ adiabatic evolution to produce transformations of the ground state
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