Related papers: The adiabatic theorem in a quantum many-body setti…
Quantum computation has emerged as a powerful computational medium of our time, having demonstrated the remarkable efficiency in factoring a positive integer and searching databases faster than any currently known classical computing…
Quantum adiabatic transfer is widely used in quantum computation and quantum simulation. However, the transfer speed is limited by the quantum adiabatic approximation condition, which hinders its application in quantum systems with a short…
This paper explores several aspects of the adiabatic quantum computation model. We first show a way that directly maps any arbitrary circuit in the standard quantum computing model to an adiabatic algorithm of the same depth. Specifically,…
We present a possible definition of a mobility gap for a many-body quantum system, in analogy to definitions of dynamical localization for single particle systems. Using this definition, we construct "corrected" quasi-adiabatic continuation…
We concentrate on the geometric potential in the invariant perturbation theory of quantum adiabatic process which is presented in our recent papers. It is found out to be related to the geodesic curvature of the spherical curve in…
Recent theoretical and numerical evidence suggests that localization can survive in disordered many-body systems with very high energy density, provided that interactions are sufficiently weak. Stronger interactions can destroy…
A quantum system will stay near its instantaneous ground state if the Hamiltonian that governs its evolution varies slowly enough. This quantum adiabatic behavior is the basis of a new class of algorithms for quantum computing. We test one…
In adiabatic quantum computing the aim is to track an eigenstate as the Hamiltonian changes. In the usual setup this is achieved using the natural time-dependent Hamiltonian evolution of the system and the main technical tool is the…
The adiabatic charge pumping of a non-equilibrium state of spinless fermions in a one-dimensional lattice is investigated, with an emphasis placed on its usefulness in revealing many-body interaction effects on interband coherence. For a…
We introduce an adiabatic perturbation theory for quantum systems with degenerate energy spectra. This perturbative series enables one to rigorously establish conditions for the validity of the adiabatic theorem of quantum mechanics for…
We present generalized adiabatic theorems for closed and open quantum systems that can be applied to slow modulations of rapidly varying fields, such as oscillatory fields that occur in optical experiments and light induced processes. The…
An alternative interpretation of the quantum adiabatic approximation is presented. This interpretation is based on the ideas originally advocated by David Bohm in his quest for establishing a hidden variable alternative to quantum…
We present straightforward proofs of estimates used in the adiabatic approximation. The gap dependence is analyzed explicitly. We apply the result to interpolating Hamiltonians of interest in quantum computing.
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…
These Lecture Notes discuss the recent theoretical advances in the understanding of open quantum many-body physics in platforms where both dissipative and coherent processes can be tuned and controlled to a high degree. We start by…
We define for quantum many-body systems a quasi-adiabatic continuation of quantum states. The continuation is valid when the Hamiltonian has a gap, or else has a sufficiently small low-energy density of states, and thus is away from a…
In this paper, we attempt to give a sufficient condition of guaranteeing the validity of the proof of the quantum adiabatic theorem. The new sufficient condition can clearly remove the inconsistency and the counterexample of the quantum…
The quantum speed limit specifies a universal bound of the fidelity between the initial state and the time-evolved state. We apply this method to find a bound of the fidelity between the adiabatic state and the time-evolved state. The bound…
In this paper, decoherence is studied for quantum systems undergoing adiabatic processes, which are coupled to huge quantum environments. It is shown that decoherence can happen with respect to a preferred basis given by transient…
Recently, some quantum algorithms have been implemented by quantum adiabatic evolutions. In this paper, we discuss the accurate relation between the running time and the distance of the initial state and the final state of a kind of quantum…