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In this work we generalize some of the previously known adiabatic theorems to situations with non-unitary evolutions in Banach spaces. We prove adiabatic theorems with uniform gap condition (generalizing a theorem of Abou Salem), adiabatic…
Adiabaticity occurs when, during its evolution, a physical system remains in the instantaneous eigenstate of the hamiltonian. Unfortunately, existing results, such as the quantum adiabatic theorem based on a slow down evolution (H(epsilon…
Shortcuts to adiabaticity (STA) are fast methods to realize the same final state evolution of quantum adiabatic process. We develop a general theory to construct a new kind of STA by solely sampling the points of the adiabatic path of the…
Adiabatic quantum algorithms must evolve slowly enough to suppress non-adiabatic transitions while remaining fast enough to be practical. In open systems, this trade-off is reshaped by decoherence. For Hamiltonians subject to dephasing…
The smallness of the variation rate of the hamiltonian matrix elements compared to the (square of the) energy spectrum gap is usually believed to be the key parameter for a quantum adiabatic evolution. However it is only perturbatively…
A geometric phase is found for a general quantum state that undergoes adiabatic evolution. For the case of eigenstates, it reduces to the original Berry's phase. Such a phase is applicable in both linear and nonlinear quantum systems.…
Towards better understanding of how to design efficient adiabatic quantum algorithms, we study how the adiabatic gap depends on the spectra of the initial and final Hamiltonians in a natural family of test-bed examples. We show that perhaps…
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…
We prove an adiabatic theorem for the evolution of spectral data under a weak additive perturbation in the context of a system without an intrinsic time scale. For continuous functions of the unperturbed Hamiltonian the convergence is in…
We present a variational quantum adiabatic theorem, which states that, under certain assumptions, the adiabatic dynamics projected onto a variational manifold follow the instantaneous variational ground state. We focus on low-entanglement…
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…
We shall revisit the conventional adiabatic or Markov approximation, which --contrary to the semiclassical case-- does not preserve the positive-definite character of the corresponding density matrix, thus leading to highly non-physical…
We map adiabatic quantum evolution on the classical Hamiltonian dynamics of a 1D gas (Pechukas gas) and simulate the latter numerically. This approach turns out to be both insightful and numerically efficient, as seen from our example of a…
In this paper,we present a rigorous demonstration and discussion of the quantum adiabatic theorem for systems having a non degenerate continuous spectrum. A new strategy is initiated by defining a kind of gap, "a virtual gap", for the…
We present an analysis of the adiabatic approximation to understand when it applies, in view of the recent criticisms and studies for the validity of the adiabatic theorem. We point out that this approximation is just the leading order of a…
The propagation of errors severely compromises the reliability of quantum computations. The quantum adiabatic algorithm is a physically motivated method to prepare ground states of classical and quantum Hamiltonians. Here, we analyze the…
We develop a robust functional analytic framework for adiabatic limits. This framework consist of a notion of adiabatic Fredholm family, several possible regularity properties, and an explicit construction that provides finite dimensional…
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…
We give an example of a simple mechanical system described by the generalized harmonic oscillator equation, which is a basic model in discussion of the adiabatic dynamics and geometric phase. This system is a linearized plane pendulum with…
We expand upon the standard quantum adiabatic theorem, examining the time-dependence of quantum evolution in the near-adiabatic limit. We examine a Hamiltonian that evolves along some fixed trajectory from $\hat{H}_0$ to $\hat{H}_1$ in a…