Related papers: Geometric tools of the adiabatic complex WKB metho…

This paper shows that WKB wave function can be expressed in the form of an adiabatic expansion. To build a bridge between two widely invoked approximation schemes seems pedagogically instructive. Further "cubic-WKB" method that has been…

Adiabatic vacua play a central role in quantum fields in cosmological spacetimes, where they serve as distinguished initial conditions and as reference states for the renormalization of observables. In this paper we introduce new methods…

The dynamics of quantum systems under the adiabatic Hamiltonian has attracted attention not only in quantum control but also in a wide range of fields from condensed matter physics to high-energy physics because of its non-perturbative…

In various applications one is interested in quantum dynamics at intermediate evolution times, for which the adiabatic approximation is inadequate. Here we develop a quasi-adiabatic approximation based on the WKB method, designed to work…

We discuss in this chapter the basics of adiabatic computation, as well as some physical implementations. After a short introduction of the quantum circuit model, we describe quantum adiabatic computation, quantum annealing, and the strong…

A common strategy for inference in complex models is the relaxation of a simple model into the more complex target model, for example the prior into the posterior in Bayesian inference. Existing approaches that attempt to generate such…

A convenient framework is developed to generalize Berry's investigation of the adiabatic geometrical phase for a classical relativistic charged scalar field in a curved background spacetime which is minimally coupled to electromagnetism and…

Adiabatic Quantum Computing (AQC) is an attractive paradigm for solving hard integer polynomial optimization problems. Available hardware restricts the Hamiltonians to be of a structure that allows only pairwise interactions. This requires…

Treating a many-body Fermi system in terms of a single particle in a deforming mean field. We relate adiabatic geometric phase to susceptibility for the noncyclic case, and to its derivative for the cyclic case. Employing the semiclassical…

The geometric (Berry) phase of a two-level system in a dissipative environment is analyzed by using the second-quantized formulation, which provides a unified and gauge-invariant treatment of adiabatic and nonadiabatic phases and is thus…

Adiabatic quantum computers can solve difficult optimization problems (e.g., the quadratic unconstrained binary optimization problem), and they seem well suited to train machine learning models. In this paper, we describe an adiabatic…

Adiabatic quantum computing (AQC) started as an approach to solving optimization problems, and has evolved into an important universal alternative to the standard circuit model of quantum computing, with deep connections to both classical…

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…

Adiabatic elimination is a perturbative model reduction technique based on timescale separation and often used to simplify the description of composite quantum systems. We here analyze a quantum experiment where the perturbative expansion…

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…

This article is a brief introduction to quantum algorithms for the eigenvalue problem in quantum many-body systems. Rather than a broad survey of topics, we focus on providing a conceptual understanding of several quantum algorithms that…

We adopt a geometric approach to describe the performance of adiabatic quantum machines, operating under slow time-dependent driving and in contact to two or more reservoirs with a temperature bias during all the cycle. We show that the…

We give an overview of a quantum adiabatic algorithm for Hilbert's tenth problem, including some discussions on its fundamental aspects and the emphasis on the probabilistic correctness of its findings. For the purpose of illustration, the…

Adiabatic quantum programming defines the time-dependent mapping of a quantum algorithm into an underlying hardware or logical fabric. An essential step is embedding problem-specific information into the quantum logical fabric. We present…

We elucidate the geometry of quantum adiabatic evolution. By minimizing the deviation from adiabaticity we find a Riemannian metric tensor underlying adiabatic evolution. Equipped with this tensor, we identify a unified geometric…