Adiabatic quantum computation along quasienergies
Atushi Tanaka, Kae Nemoto · Physical Review A · 2010
The parametric deformations of quasienergies and eigenvectors of unitary operators are applied to the design of quantum adiabatic algorithms. The conventional, standard adiabatic quantum computation proceeds along eigenenergies of parameter-dependent Hamiltonians. By contrast, discrete adiabatic computation utilizes adiabatic passage along the quasienergies of parameter-dependent unitary operators. For example, such computation can be realized by a concatenation of parameterized quantum circuits, with an adiabatic though inevitably discrete change of the parameter. A design principle of adiabatic passage along quasienergy was recently proposed: Cheon's quasienergy and eigenspace anholonomies on unitary operators is available to realize anholonomic adiabatic algorithms [A. Tanaka and M. Miyamoto, Phys. Rev. Lett. 98, 160407 (2007)], which compose a nontrivial family of discrete adiabatic algorithms. It is straightforward to port a standard adiabatic algorithm to an anholonomic adiabatic one, except an introduction of a parameter $|v\ensuremath{\rangle}$, which is available to adjust the gaps of the quasienergies to control the running time steps. In Grover's database search problem, the costs to prepare $|v\ensuremath{\rangle}$ for the qualitatively different (i.e., power or exponential) running time steps are shown to be qualitatively different.