Adiabatic quantum computation along quasienergies

Abstract

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 is recently proposed: Cheon's quasienergy and eigenspace anholonomies on unitary operators is available to realize anholonomic adiabatic algorithms [Tanaka and 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>, 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> for the qualitatively different, i.e., power or exponential, running time steps are shown to be qualitatively different. Curiously, in establishing the equivalence between the standard quantum computation based on the circuit model and the anholonomic adiabatic quantum computation model, it is shown that the cost for |v> to enlarge the gaps of the eigenvalue is qualitatively negligible.

11 pages, 2 figures

References in corpus (4)

• Experimental implementation of an adiabatic quantum optimization algorithm
• Adiabatic quantum search with atoms in a cavity driven by lasers
• Quasienergy anholonomy and its application to adiabatic quantum state manipulation
• Cheon's anholonomies in Floquet operators

Cited by in corpus (9)

• A general approximation of quantum graph vertex couplings by scaled Schroedinger operators on thin branched manifolds
• Schrödinger-Koopman quasienergy states of quantum systems driven by a classical flow
• Quantum anholonomies in time-dependent Aharonov-Bohm rings
• Bloch vector, disclination and exotic quantum holonomy
• Fully-programmable universal quantum simulator with a one-dimensional quantum processor
• Gauge invariants of eigenspace and eigenvalue anholonomies: Examples in hierarchical quantum circuits
• Exotic quantum holonomy and higher-order exceptional points in quantum kicked tops
• Quantum controllability on graph-like manifolds through magnetic potentials and boundary conditions
• Eigenvalue and eigenspace anholonomies in hierarchical systems