INTEGRABILITY, ENTROPY AND QUANTUM COMPUTATION

1999 ◽  
Vol 10 (07) ◽  
pp. 1205-1228 ◽  
Author(s):  
E. V. KRISHNAMURTHY
Keyword(s):  
Quantum Computation ◽  
Quantum Chaos ◽  
Quantum Control ◽  
Dynamical Evolution ◽  
Open Problems ◽  
Quantum Integrability ◽  
Feynman Path Integrals ◽  
Exact Integrability ◽  
Time Arrow ◽  
Computational Systems

The important requirements are stated for the success of quantum computation. These requirements involve coherent preserving Hamiltonians as well as exact integrability of the corresponding Feynman path integrals. Also we explain the role of metric entropy in dynamical evolutionary system and outline some of the open problems in the design of quantum computational systems. Finally, we observe that unless we understand quantum nondemolition measurements, quantum integrability, quantum chaos and the direction of time arrow, the quantum control and computational paradigms will remain elusive and the design of systems based on quantum dynamical evolution may not be feasible.

scholarly journals Quantum chaos for point scatterers on flat tori

2014 ◽  
Vol 372 (2007) ◽  
pp. 20120509 ◽  
Author(s):  
Henrik Ueberschär
Keyword(s):  
Wave Function ◽  
Strong Coupling ◽  
Quantum Chaos ◽  
Recent Progress ◽  
Three Dimensional ◽  
Point Scatterer ◽  
Open Problems ◽  
Survey Article ◽  
Delta Potential ◽  
Flat Tori

This survey article deals with a delta potential—also known as a point scatterer—on flat two- and three-dimensional tori. We introduce the main conjectures regarding the spectral and wave function statistics of this model in the so-called weak and strong coupling regimes. We report on recent progress as well as a number of open problems in this field.

Phase control for entanglement preparation in two-qubit systems

2005 ◽  
Vol 5 (4&5) ◽  
pp. 364-379
Author(s):  
V.S. Malinovsky ◽  
I.R. Sola
Keyword(s):  
Quantum Information ◽  
Quantum Computation ◽  
Quantum Control ◽  
Phase Control ◽  
Adiabatic Passage ◽  
Pulse Parameters ◽  
Qubit System ◽  
Phase Manipulation ◽  
Laser Control ◽  
Pi Pulses

The theory of Quantum Control is starting to lay bridges with the field of Quantum Information and Quantum Computation. Using key ideas of laser control of the dynamics by means of phase manipulation and adiabatic passage, we review laser schemes that allow entanglement preparation in a two-qubit system. The schemes are based on sequences that use four time-delayed pulses, with or without concerted decay, in or off resonance with the intermediate levels of the qubit space. We show how to control the fidelity and phase of the entanglement, as well as the sensitivity of the preparation to the different pulse parameters. In general the schemes provide an improvement in robustness and in the finesse of the control to phase, with respect to previously proposed schemes based on sequences of $\pi$ pulses.

Quantum integrability and quantum chaos in the micromaser

2000 ◽  
Vol 122 (2) ◽  
pp. 151-169
Author(s):  
R. K. Bullough ◽  
N. M. Bogolyubov ◽  
R. R. Puri
Keyword(s):  
Quantum Chaos ◽  
Quantum Integrability

scholarly journals Robust quantum computation of the kicked Harper model and quantum chaos

2007 ◽  
Vol 56 (7) ◽  
pp. 3709
Author(s):  
Ye Bin ◽  
Gu Rui-Jun ◽  
Xu Wen-Bo
Keyword(s):  
Quantum Computation ◽  
Quantum Chaos

scholarly journals CONTROL OF QUANTUM SYSTEMS

2003 ◽  
Vol 17 (28) ◽  
pp. 5397-5411 ◽  
Author(s):  
JOHN W. CLARK ◽  
DENNIS G. LUCARELLI ◽  
TZYH-JONG TARN
Keyword(s):  
Quantum Computation ◽  
Quantum Control ◽  
Sufficient Conditions ◽  
The State ◽  
Dimensional Manifold ◽  
Infinite Dimensional ◽  
Many Body Theory ◽  
Laser Control ◽  
Control Of Quantum Systems ◽  
The Impact

A quantum system subject to external fields is said to be controllable if these fields can be adjusted to guide the state vector to a desired destination in the state space of the system. Fundamental results on controllability are reviewed against the background of recent ideas and advances in two seemingly disparate endeavours: (i) laser control of chemical reactions and (ii) quantum computation. Using Lie-algebraic methods, sufficient conditions have been derived for global controllability on a finite-dimensional manifold of an infinite-dimensional Hilbert space, in the case that the Hamiltonian and control operators, possibly unbounded, possess a common dense domain of analytic vectors. Some simple examples are presented. A synergism between quantum control and quantum computation is creating a host of exciting new opportunities for both activities. The impact of these developments on computational many-body theory could be profound.

scholarly journals Avoiding quantum chaos in quantum computation

2001 ◽  
Vol 65 (1) ◽  
Author(s):  
G. P. Berman ◽  
F. Borgonovi ◽  
F. M. Izrailev ◽  
V. I. Tsifrinovich
Keyword(s):  
Quantum Computation ◽  
Quantum Chaos

scholarly journals Non-Classical Correlations in n-Cycle Setting

Entropy ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 134 ◽  
Author(s):  
Kishor Bharti ◽  
Maharshi Ray ◽  
Leong-Chuan Kwek
Keyword(s):  
Quantum Computation ◽  
Quantum Communication ◽  
Future Research ◽  
Simple Extension ◽  
Open Problems ◽  
N Cycle ◽  
Classical Simulation ◽  
Classical Correlations ◽  
Space Case ◽  
Non Locality

Quantum communication and quantum computation form the two crucial facets of quantum information theory. While entanglement and its manifestation as Bell non-locality have been proved to be vital for communication tasks, contextuality (a generalisation of Bell non-locality) has shown to be the crucial resource behind various models of quantum computation. The practical and fundamental aspects of these non-classical resources are still poorly understood despite decades of research. We explore non-classical correlations exhibited by some of these quantum as well as super-quantum resources in the n-cycle setting. In particular, we focus on correlations manifested by Kochen–Specker–Klyachko box (KS box), scenarios involving n-cycle non-contextuality inequalities and Popescu–Rohlrich boxes (PR box). We provide the criteria for optimal classical simulation of a KS box of arbitrary n dimension. The non-contextuality inequalities are analysed for n-cycle setting, and the condition for the quantum violation for odd as well as even n-cycle is discussed. We offer a simple extension of even cycle non-contextuality inequalities to the phase space case. Furthermore, we simulate a generalised PR box using KS box and provide some interesting insights. Towards the end, we discuss a few possible interesting open problems for future research. Our work connects generalised PR boxes, arbitrary dimensional KS boxes, and n-cycle non-contextuality inequalities and thus provides the pathway for the study of these contextual and nonlocal resources at their junction.

scholarly journals A Critique on Interdisciplinary Quantum Systems

2020 ◽  
Author(s):  
Abicumaran Uthamacumaran
Keyword(s):  
Quantum Mechanics ◽  
Quantum Computation ◽  
Quantum Chaos ◽  
Modern Science ◽  
Quantum Systems ◽  
Quantum Biology ◽  
Quantum Science

Three cross-disciplinary branches of quantum science, namely that of: Quantum Chaos, Quantum Biology and Quantum Computation, are concisely addressed herein. The implications of these fields in the progression of science are emphasized. This critique is to be treated as a metacognition on currently contentious branches of science interwoven with the foundations of modern science: Quantum Mechanics, made accessible in layman terms to all systems thinkers.

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