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Differential topology of adiabatically controlled quantum processes

Edmond A. Jonckheere, Ali T. Rezakhani, Farooq Ahmad
2012 Quantum Information Processing  
It is shown that in a controlled adiabatic homotopy between two Hamiltonians, H 0 and H 1 , the gap or "anti-crossing" phenomenon can be viewed as the development of cusps and swallow tails in the region  ...  topology.  ...  This supports our point that the adiabatic gap is indeed a differential topological issue, since differential topology mainly deals with the study of the critical points and the critical values of smooth  ... 
doi:10.1007/s11128-012-0445-0 fatcat:l2sh25fh4janbimdyfnezjsewe

Quantum simulation of the Kibble-Zurek mechanism using a semiconductor electron charge qubit

Li Wang, Cheng Zhou, Tao Tu, Hong-Wen Jiang, Guo-Ping Guo, Guang-Can Guo
2014 Physical Review A. Atomic, Molecular, and Optical Physics  
The high-level controllability of semiconductor two-level system make it a platform to test the key elements of topological defect formation process and shed a new insight on the aspect of non-equilibrium  ...  Here we demonstrate a proof-of-principle quantum simulation of Kibble-Zurek mechanism using a single electron charge qubit in double quantum dot, set to behave as Landau-Zener dynamics.  ...  Down: a controlled double passage Landau-Zener transition process is drawn. Figure 3 | 3 Observation of the controllable Landau-Zener dynamics.  ... 
doi:10.1103/physreva.89.022337 fatcat:sk6jqbzkn5ecbpeb2lyu7kb3vm

Optimal diabatic dynamics of Majorana-based quantum gates

Armin Rahmani, Babak Seradjeh, Marcel Franz
2017 Physical review B  
To enhance the performance of quantum information processing with Majorana zero modes, we apply the theory of optimal control to the diabatic dynamics of Majorana-based qubits.  ...  In topological quantum computing, unitary operations on qubits are performed by adiabatic braiding of non-Abelian quasiparticles, such as Majorana zero modes, and are protected from local environmental  ...  By relaxing the constraint of adiabaticity during the entire process, we give up strict topological protection.  ... 
doi:10.1103/physrevb.96.075158 fatcat:2f4565whubdvhoy3cpnjl6ymee

Effects of geometry on spin-orbit Kramers states in semiconducting nanorings [article]

G. Francica, P. Gentile, M. Cuoco
2019 arXiv   pre-print
Shape symmetries of the nanostructure act to constrain the adiabatic quantum evolution.  ...  We demonstrate that in nanoscale quantum rings the combination of arbitrary inhomogeneous curvature and adiabatic variation of the spin-orbit amplitude, e.g. through electric-field gating, can be generally  ...  Although experimental realizations of moving quantum dots have been successfully achieved [29] , the efficiency of such quantum engineering is sensitively dependent on the concomitant dynamical control  ... 
arXiv:1903.02455v1 fatcat:x5x4y4p3zvdlpmejulgtgfd2hy

Preparation of edge states by shaking boundaries

Z.C. Shi, S.C. Hou, L.C. Wang, X.X. Yi
2016 Annals of Physics  
Preparing topological states of quantum matter, such as edge states, is one of the most important directions in condensed matter physics.  ...  A numerical optimalization for the control is performed and the dependence of control process on the system size is discussed.  ...  INTRODUCTION Topological insulators(TIs) [1, 2] are new states of quantum matter with profound physical features that have their origin in topology.  ... 
doi:10.1016/j.aop.2016.07.017 fatcat:sateledtejctnchha3etoqkuuq

Dynamical Signatures of Ground‐State Degeneracy to Discriminate against Andreev Levels in a Majorana Fusion Experiment

A. Grabsch, Y. Cheipesh, C. W. J. Beenakker
2019 Advanced Quantum Technologies  
Detection of the fusion rule of Majora na zero-modes is a near-term milestone on the road to topological quantum computation.  ...  An obstacle is that the non-deterministic fusion outcome of topological zero-modes can be mimicked by the merging of non-topological Andreev levels.  ...  Conflict of Interest The authors declare no conflict of interest. Keywords Andreev levels, Majorana fermions, non-Abelian anyons, topological quantum computing  ... 
doi:10.1002/qute.201900110 fatcat:n4tqm2k645cdvlrgluftuobn4e

Geometric phase and helicity inversion of photons propagating inside a noncoplanarly curved optical fiber

Jian-Qi Shen, Li-Hong Ma
2003 Physics Letters A  
, our formulation therefore has several advantages over other treatments based on the classical Maxwell's theory and the Berry's adiabatic quantum theory.  ...  The Letter presents an exact expression for the non-adiabatic non-cyclic geometric phase of photons propagating inside a noncoplanarly curved optical fiber by using the Lewis-Riesenfeld invariant theory  ...  Acknowledgements This project is supported in part by the National Natural Science Foundation of China under the project No. 90101024.  ... 
doi:10.1016/s0375-9601(03)00118-x fatcat:j7erytwkirebhggtbm6em3ki5i

Dynamical signatures of ground-state degeneracy to discriminate against Andreev levels in a Majorana fusion experiment [article]

A. Grabsch, Y. Cheipesh, C.W.J. Beenakker
2019 arXiv   pre-print
Detection of the fusion rule of Majorana zero-modes is a near-term milestone on the road to topological quantum computation.  ...  An obstacle is that the non-deterministic fusion outcome of topological zero-modes can be mimicked by the merging of non-topological Andreev levels.  ...  The topological ground-state degeneracy of Majorana zero-modes causes a breakdown of adiabaticity that can be measured as a pathway-dependent fermion parity.  ... 
arXiv:1909.08335v1 fatcat:wpezudj7trbfhdxbjscl6vry6a

Geometrical Pumping with a Bose-Einstein Condensate

H.-I Lu, M. Schemmer, L. M. Aycock, D. Genkina, S. Sugawa, I. B. Spielman
2016 Physical Review Letters  
Topological charge pumps in filled bands yield quantized pumping set by the global -- topological -- properties of the bands.  ...  We realized a quantum geometric "charge" pump for a Bose-Einstein condensate (BEC) in the lowest Bloch band of a novel bipartite magnetic lattice.  ...  This curvature is the source of an anomalous velocity [24] , utilized to drive an adiabatic quantum pumping process.  ... 
doi:10.1103/physrevlett.116.200402 pmid:27258857 pmcid:PMC5100700 fatcat:dtfh6qnrangafago5zo5fozh6i

Adiabatic Swimming in an Ideal Quantum Gas

J. E. Avron, B. Gutkin, D. H. Oaknin
2006 Physical Review Letters  
We propose a quantum theory of swimming for swimmers that are small relative to the coherence length of the medium. The quantum swimming equation is derived from known results on quantum pumps.  ...  For a one-dimensional Fermi gas at zero temperature we find that swimming is topological: The distance covered in one swimming stroke is quantized in half integer multiples of the Fermi wave length.  ...  Allow the swimmer to change adiabatically the control parameters a j and ' i .  ... 
doi:10.1103/physrevlett.96.130602 pmid:16711976 fatcat:xw7jv3jrw5azniajte3p7xr4au

Protocol Discovery for the Quantum Control of Majoranas by Differentiable Programming and Natural Evolution Strategies [article]

Luuk Coopmans, Di Luo, Graham Kells, Bryan K. Clark, Juan Carrasquilla
2021 arXiv   pre-print
topological quantum computation.  ...  Quantum control, which refers to the active manipulation of physical systems described by the laws of quantum mechanics, constitutes an essential ingredient for the development of quantum technology.  ...  In addition, quantum optimal control algorithms based on DP can easily harness the acceleration afforded by graphics processing units (GPUs), which may speedup quantum control calculations by more than  ... 
arXiv:2008.09128v2 fatcat:vsyt3qkhnndfhigawzauhuosj4

Quasienergy Anholonomy and its Application to Adiabatic Quantum State Manipulation

Atushi Tanaka, Manabu Miyamoto
2007 Physical Review Letters  
The parametric dependence of a quantum map under the influence of a rank-1 perturbation is investigated.  ...  An application to quantum state manipulations is outlined.  ...  It is worth pointing out that the applications of adiabatic processes to the control of quantum states have already become textbook results [10] .  ... 
doi:10.1103/physrevlett.98.160407 pmid:17501402 fatcat:xbwidn2u5ngxtlbge6acan6uge

Quantum phases with differing computational power

Jian Cui, Mile Gu, Leong Chuan Kwek, Marcelo França Santos, Heng Fan, Vlatko Vedral
2012 Nature Communications  
respect to the processing of quantum information.  ...  In particular, we show that in certain quantum phases of the XY model, adiabatic perturbations of the external magnetic field can be simulated by local spin operations, whereas the resulting effect within  ...  The study of differential local convertibility of the ground state gives direct operational significance to phase transitions in the context of quantum information processing.  ... 
doi:10.1038/ncomms1809 pmid:22549841 fatcat:boabcvlxx5bdjoavtl42oh2wwu

Topological Quantum Computing Using Nanowire Devices [article]

C. Tutschku, R. W. Reinthaler, C. Lei, A. H. MacDonald, E. M. Hankiewicz
2020 arXiv   pre-print
The boundary of topological superconductors might lead to the appearance of Majorana edge modes, whose non-trivial exchange statistics can be used for topological quantum computing.  ...  We derive concrete experimental predictions for (quasi-)adiabatic braiding times and determine geometric conditions for successful Majorana exchange processes.  ...  through the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter -ct.qmat (EXC 2147, project-id 39085490).  ... 
arXiv:1910.11075v2 fatcat:zxc67qxj3nfqraojsp7sfdnjsq

Demonstrating Majorana nonabelian exchange using fast adiabatic charge-transfer [article]

Svend Krøjer, Rubén Seoane Souto, Karsten Flensberg
2021 arXiv   pre-print
Demonstration of Majorana nonabelian exchange properties is a major challenge in the field of topological superconductivity.  ...  We use an adiabatic perturbation theory to find fast adiabatic paths to perform operations and to account for non-adiabatic errors.  ...  [28] and formulate a framework for studying fast adiabatic processes, resulting in predictions for the optimal charge control. A.  ... 
arXiv:2107.11833v2 fatcat:fkcw6tcblzbvdegktzs7cxbeum
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