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Related papers: Geometry of the adiabatic theorem

200 papers

Adiabatic $U(2)$ geometric phases are studied for arbitrary quantum systems with a three-dimensional Hilbert space. Necessary and sufficient conditions for the occurrence of the non-Abelian geometrical phases are obtained without actually…

Quantum Physics · Physics 2008-11-26 Ali Mostafazadeh

We propose a method to obtain optimal protocols for adiabatic ground-state preparation near the adiabatic limit, extending earlier ideas from [D. A. Sivak and G. E. Crooks, Phys. Rev. Lett. 108, 190602 (2012)] to quantum non-dissipative…

Quantum Gases · Physics 2016-07-20 Michael Tomka , Tiago Souza , Steven Rosenberg , Anatoli Polkovnikov

We report the realization of a nuclear magnetic resonance computer with three quantum bits that simulates an adiabatic quantum optimization algorithm. Adiabatic quantum algorithms offer new insight into how quantum resources can be used to…

Quantum Physics · Physics 2007-05-23 Matthias Steffen , Wim van Dam , Tad Hogg , Greg Breyta , Isaac Chuang

The quantum adiabatic algorithm is a Hamiltonian based quantum algorithm designed to find the minimum of a classical cost function whose domain has size N. We show that poor choices for the Hamiltonian can guarantee that the algorithm will…

Quantum Physics · Physics 2008-06-30 Edward Farhi , Jeffrey Goldstone , Sam Gutmann , Daniel Nagaj

The goal of this paper is to introduce building blocks for adiabatic quantum algorithms. Adiabatic quantum computing uses the principle of quantum annealing, which implies that a carefully controlled energy solution is optimal and…

Quantum Physics · Physics 2014-08-27 Richard H. Warren

The covariant derivative capable of differentiating and parallel transporting tangent vectors and other geometric objects induced by a parameter-dependent quantum state is introduced. It is proved to be covariant under gauge and coordinate…

Quantum Physics · Physics 2023-11-03 Ryan Requist

We present the main aspects of the adiabatic theory and show that it can be used to study the motion of test particles in general relativity. The theory is based upon the use of vector elements of the orbits and adiabatic invariants. To…

A single-loop scenario is proposed to realize nonadiabatic geometric quantum computation. Conventionally, a so-called multi-loop approach is used to remove the dynamical phase accumulated in the operation process for geometric quantum…

Quantum Physics · Physics 2009-11-11 Xin-Ding Zhang , Shi-Liang Zhu , L. Hu , Z. D. Wang

In this thesis, it is presented a set of results in adiabatic dynamics (closed and open system) and transitionless quantum driving that promote some advances in our understanding on quantum control and Hamiltonian inverse engineering. In…

Quantum Physics · Physics 2021-07-27 Alan C. Santos

Adiabatic state engineering is a powerful technique in quantum information and quantum control. However, its performance is limited by the adiabatic theorem of quantum mechanics. In this scenario, shortcuts to adiabaticity, such as provided…

Quantum Physics · Physics 2015-11-03 Alan C. Santos , Marcelo S. Sarandy

We apply the method of shortcuts to adiabaticity to nonequilibrium systems. For unitary dynamics, the system Hamiltonian is separated into two parts. One of them defines the adiabatic states for the state to follow and the nonadiabatic…

Statistical Mechanics · Physics 2017-11-27 Kazutaka Takahashi

On-the-fly quantum nonadiabatic dynamics for large systems greatly benefits from the adiabatic representation readily available from the electronic structure programs. However, frequently occurring in this representation conical…

We explain why quantum adiabatic evolution and simulated annealing perform similarly in certain examples of searching for the minimum of a cost function of n bits. In these examples each bit is treated symmetrically so the cost function…

Quantum Physics · Physics 2007-05-23 Edward Farhi , Jeffrey Goldstone , Sam Gutmann

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…

Quantum Physics · Physics 2012-02-27 Yong Tao

It is known that for multi-level time-dependent quantum systems one can construct superadiabatic representations in which the coupling between separated levels is exponentially small in the adiabatic limit. For a family of two-state systems…

Mathematical Physics · Physics 2009-11-10 Volker Betz , Stefan Teufel

Adiabatic techniques have much potential to realise practical and robust optical waveguide devices. Traditionally photonic elements are limited to coupling schemes that rely on proximity to nearest neighbour elements. We combine adiabatic…

Quantum Physics · Physics 2015-08-31 Anthony P. Hope , Thach G. Nguyen , Arnan Mitchell , Andrew D. Greentree

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…

Quantum Physics · Physics 2009-09-21 A. T. Rezakhani , W. -J. Kuo , A. Hamma , D. A. Lidar , P. Zanardi

We generalize the adiabatic approximation to the case of open quantum systems, in the joint limit of slow change and weak open system disturbances. We show that the approximation is ``physically reasonable'' as under wide conditions it…

Quantum Physics · Physics 2016-08-16 Patrik Thunström , Johan Åberg , Erik Sjöqvist

We introduce a geometric framework for efficient few-parameter pulse optimization in multi-level quantum systems, enabling high-fidelity state transfer beyond the adiabatic limit. Our method interpolates smoothly between adiabatic and…

Adiabatic quantum computing enables the preparation of many-body ground states. This is key for applications in chemistry, materials science, and beyond. Realisation poses major experimental challenges: Direct analog implementation requires…