Related papers: Fast forward to the classical adiabatic invariant
Invariants at arbitrary and fixed energy (strongly and weakly conserved quantities) for 2-dimensional Hamiltonian systems are treated in a unified way. This is achieved by utilizing the Jacobi metric geometrization of the dynamics. Using…
The time-evolution operator for an explicitly time-dependent Hamiltonian is expressed as the product of a sequence of unitary operators. These are obtained by successive time-dependent unitary transformations of the Hilbert space followed…
Adiabatic limit is the presumption of the adiabatic geometric quantum computation and of the adiabatic quantum algorithm. But in reality, the variation speed of the Hamiltonian is finite. Here we develop a general formulation of adiabatic…
We provide a theoretical study of the quantum adiabatic evolution algorithm with different evolution paths proposed in [E. Farhi, et al., arXiv:quant-ph/0208135]. The algorithm is applied to a random binary optimization problem (a version…
A universal scheme is introduced to speed up the dynamics of a driven open quantum system along a prescribed trajectory of interest. This framework generalizes counterdiabatic driving to open quantum processes. Shortcuts to adiabaticity…
The theory of adiabatic invariants has a long history, and very important implications and applications in many different branches of physics, classically and quantally, but is rarely founded on rigorous results. Here we treat the general…
The nonadiabatic dynamic of the electromagnetic field triggers photons generation from the quantum vacuum. Shortcuts to adiabaticity, instead, are protocols that mimic the field's adiabatic dynamic in a finite time. Here, we show how the…
We discover that the energy-integral of time-delay is an adiabatic invariant in quantum scattering theory and corresponds classically to the phase space volume. The integral thus found provides a quantization condition for resonances,…
Adiabatic gauge potential is the origin of nonadiabatic transitions. In counterdiabatic driving, which is a method of shortcuts to adiabaticity, adiabatic gauge potential can be used to realize identical dynamics to adiabatic time evolution…
We present a general method for studying coupled qubits driven by adiabatically changing external parameters. Extended calculations are provided for a two-bit Hamiltonian whose eigenstates can be used as logical states for a quantum CNOT…
A conceptually simple physical interpretation of a conserved Hamiltonian $\mathcal{H}$ for a mechanical system with a time-dependent constraint is given. For the case of a bead on a vertical hoop forced to rotate with constant angular…
A shortcut to adiabaticity (STA) is concerned with the fast and robust manipulation of the dynamics of a quantum system that reproduces the effect of an adiabatic process. A recently proposed method enables the generation of shortcuts from…
In this paper we present an invariant perturbation theory to adiabatic process according to the concepts of adiabatic orbits, adiabatic evolution orbit and U(1)-invariant adiabatic orbit. The probabilities of keeping the adiabatic orbit in…
We study the most general form of a three dimensional classical integrable system with axial symmetry and invariant under the axis reflection. We assume that the three constants of motion are the Hamiltonian, $H$, with the standard form of…
Counterdiabatic (CD) driving has the potential to speed up adiabatic quantum state preparation by suppressing unwanted excitations. However, existing approaches either require intractable classical computations or are based on…
The adiabatic theorem addresses the dynamics of a target instantaneous eigenstate of a time-dependent Hamiltonian. We use a Feshbach P-Q partitioning technique to derive a closed one-component integro-differential equation. The resultant…
Shortcuts to adiabaticity are alternative fast processes which reproduce the same final state as the adiabatic process in a finite or even shorter time, which have been extended from Hermitian systems to non-Hermitian systems in recent…
Time evolution of quantum systems is accelerated by the fast-forward scaling. We reformulate the method to study systems in a finite-dimensional Hilbert space. For several simple systems, we explicitly construct the acceleration potential.…
We introduce an operational framework to analyze non-adiabatic Abelian and non-Abelian, cyclic and non-cyclic, geometric phases in open quantum systems. In order to remove the adiabaticity condition, we generalize the theory of dynamical…
Different methods have been recently put forward and implemented experimentally to inverse engineer the time dependent Hamiltonian of a quantum system and accelerate slow adiabatic processes via non-adiabatic shortcuts. In the…