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In this paper, we present a U(1)-invariant expansion theory of the adiabatic process. As its application, we propose and discuss new sufficient adiabatic approximation conditions. In the new conditions, we find a new invariant quantity referred as quantum geometric potential (QGP) contained in all time-dependent processes. Furthermore, we also give detailed discussion and analysis on the properties and effects of QGP.
We present a formal geometric framework for the study of adiabatic quantum mechanics for arbitrary finite-dimensional non-degenerate Hamiltonians. This framework generalizes earlier holonomy interpretations of the geometric phase to non-cyclic states
The asymmetric quantum Rabi model (AQRM), which describes the interaction between a quantum harmonic oscillator and a biased qubit, arises naturally in circuit quantum electrodynamic circuits and devices. The existence of hidden symmetry in the AQRM
Steering a quantum harmonic oscillator state along cyclic trajectories leads to a path-dependent geometric phase. Here we describe an experiment observing this geometric phase in an electronic harmonic oscillator. We use a superconducting qubit as a
We formulate a time-optimal approach to adiabatic quantum computation (AQC). A corresponding natural Riemannian metric is also derived, through which AQC can be understood as the problem of finding a geodesic on the manifold of control parameters. Th
The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers $R(m,n)$ with $m,ngeq 3$, only nine are currently known. We present a quantum algorithm for the computation of the Ramsey numbers $R(