Related papers: Adiabatic Error Cancellation in Berry Phase Estima…
Systematic effects caused by the Berry (geometric) phases in an electric-dipole-moment experiment in an all-electric storage ring are considered. We analyze the experimental setup when the spin is frozen and local longitudinal and vertical…
We show that in a quantum adiabatic evolution, even though the adiabatic approximation is valid, the total phase of the final state indicated by the adiabatic theorem may evidently differ from the actual total phase. This invalidates the…
The simulation of adiabatic evolution has deep connections with Adiabatic Quantum Computation, the Quantum Approximate Optimization Algorithm and adiabatic state preparation. Here we address the error analysis problem in quantum simulation…
Quantum systems with adiabatic classical parameters are widely studied, e.g., in the modern holonomic quantum computation. We here provide complete geometric quantization of a Hamiltonian system with time-dependent parameters, without the…
We study QED$_4$ in the adiabatic approximation, incorporating global topological effects associated with the $U(1)$ Berry connection. The Berry phase accumulated by the fermionic vacuum is given by $\Delta \alpha = \oint_{\mathcal{C}}…
We analyse the Kitaev honeycomb model, by means of the Berry curvature with respect to Hamiltonian parameters. We concentrate on the ground-state vortex-free sector, which allows us to exploit an appropriate Fermionisation technique. The…
A countable set of asymptotic space -- localized solutions is constructed by the complex germ method in the adiabatic approximation for 3D Hartree type equations with a quadratic potential. The asymptotic parameter is 1/T, where $T\gg1$ is…
Adiabatic evolution is a central paradigm in quantum physics. Digital simulations of adiabatic processes are generally viewed as costly, since algorithmic errors typically accumulate over the long evolution time, requiring exceptionally…
The adiabatic quantum algorithm has drawn intense interest as a potential approach to accelerating optimization tasks using quantum computation. The algorithm is most naturally realised in systems which support Hamiltonian evolution, rather…
Nonadiabatic holonomic quantum computation has been attracting continuous attention since it was proposed. Until now, various schemes of nonadiabatic holonomic quantum computation have been developed and many of them have been…
A major challenge facing adiabatic quantum computing is that algorithm design and error correction can be difficult for adiabatic quantum computing. Recent work has considered addressing his challenge by using coherently controlled…
Adiabatic approximation for quantum evolution is investigated quantitatively with addressing its dependence on the Berry connections. We find that, in the adiabatic limit, the adiabatic fidelity may uniformly converge to unit or diverge…
We consider a two-level system coupled to a highly non-Markovian environment when the coupling axis rotates with time. The environment may be quantum (for example a bosonic bath or a spin bath) or classical (such as classical noise). We…
Adiabatic quantum algorithms are characterized by their run time and accuracy. The relation between the two is essential for quantifying adiabatic algorithmic performance, yet is often poorly understood. We study the dynamics of a…
The viability of adiabatic quantum computation depends on the slow evolution of the Hamiltonian. The adiabatic switching theorem provides an asymptotic series for error estimates in $1/T$, based on the lowest non-zero derivative of the…
A Berry phase can be added to the wavefunction of an isolated quantum dot by adiabatically modulating a nonuniform electric field along a time-cycle. The dot is tuned close to a three-level degeneracy, which provides a wide range of…
In 1984 Michael Berry discovered that an isolated eigenstate of an adiabatically changing periodic Hamiltonian $H(t)$ acquires a phase, called the Berry phase. We show that under very general assumptions the adiabatic approximation of the…
Many physically interesting models show a quantum phase transition when a single parameter is varied through a critical point, where the ground state and the first excited state become degenerate. When this parameter appears as a coupling…
The recent discovery of inconsistency (MS inconsistency) in the adiabatic approximation is discussed. In particular, the so-called, inconsistency in Berry phase is analyzed. On the contrary to some authors, we found that the MS…
We introduce the non-adiabatic, or Aharonov-Anandan, geometric phase as a tool for quantum computation and show how it could be implemented with superconducting charge qubits. While it may circumvent many of the drawbacks related to the…