Cluster state quantum computation for many-level systems

2007 ◽  
Vol 7 (3) ◽  
pp. 184-208
Author(s):  
W. Hall
Keyword(s):  
Quantum Computation ◽  
Degrees Of Freedom ◽  
Cluster State ◽  
Quantum Systems ◽  
Explicit Description ◽  
State Model ◽  
Mutually Unbiased Bases ◽  
Large Set ◽  
Adaptive Computation ◽  
Complete Framework

The cluster state model for quantum computation [Phys. Rev. Lett. \textbf{86}, 5188] outlines a scheme that allows one to use measurement on a large set of entangled quantum systems in what is known as a cluster state to undertake quantum computations. The model itself and many works dedicated to it involve using entangled qubits. In this paper we consider the issue of using entangled qudits instead. We present a complete framework for cluster state quantum computation using qudits, which not only contains the features of the original qubit model but also contains the new idea of adaptive computation: via a change in the classical computation that helps to correct the errors that are inherent in the model, the implemented quantum computation can be changed. This feature arises through the extra degrees of freedom that appear when using qudits. Finally, for prime dimensions, we give a very explicit description of the model, making use of mutually unbiased bases.

scholarly journals Cluster State Computation with Quantum-Dot Charge Qubits

2010 ◽  
Vol 2010 ◽  
pp. 1-21
Author(s):  
Matthew Lubelski Katz ◽  
Jingbo Wang
Keyword(s):  
Quantum Computation ◽  
Resonant Tunneling ◽  
Cluster State ◽  
Quantum Systems ◽  
Quantum Computers ◽  
Charge Qubit ◽  
Cluster States ◽  
Theoretical Simulation ◽  
Ballistic Electron ◽  
Theoretical Foundations

Quantum computers are expected to far surpass the capabilities of today's most powerful supercomputers, particularly in areas such as the theoretical simulation of quantum systems, cryptography, and information processing. The cluster state is a special, highly entangled quantum state that forms the universal resource on which measurement-based quantum computation can be performed. This paper provides a brief review of the theoretical foundations of cluster state quantum computation and how it evolved from the traditional model of digital computers. It then proposes a scheme for the generation of such entanglement in a solid-state medium through the suppression of resonant tunneling of a ballistic electron by a single-electron charge qubit. To investigate the viability of the scheme for the creation of cluster states, numerical calculations are performed in which the entanglement interaction is modeled in detail.

Cluster State Quantum Computation

2014 ◽  
Author(s):  
Paul Alsing ◽  
Michael Fanto ◽  
Gordon Lott
Keyword(s):  
Quantum Computation ◽  
Cluster State

scholarly journals Multiparticle quantum plasmonics

Nanophotonics ◽  
2020 ◽  
Vol 9 (6) ◽  
pp. 1243-1269 ◽  
Author(s):  
Chenglong You ◽  
Apurv Chaitanya Nellikka ◽  
Israel De Leon ◽  
Omar S. Magaña-Loaiza
Keyword(s):  
Quantum Dynamics ◽  
Degrees Of Freedom ◽  
Single Photon ◽  
Quantum Systems ◽  
Many Body ◽  
Statistical Fluctuations ◽  
Quantum Plasmonics ◽  
Control Of Quantum Systems ◽  
Multiparticle Systems ◽  
Quantum Photonics

AbstractA single photon can be coupled to collective charge oscillations at the interfaces between metals and dielectrics forming a single surface plasmon. The electromagnetic near-fields induced by single surface plasmons offer new degrees of freedom to perform an exquisite control of complex quantum dynamics. Remarkably, the control of quantum systems represents one of the most significant challenges in the field of quantum photonics. Recently, there has been an enormous interest in using plasmonic systems to control multiphoton dynamics in complex photonic circuits. In this review, we discuss recent advances that unveil novel routes to control multiparticle quantum systems composed of multiple photons and plasmons. We describe important properties that characterize optical multiparticle systems such as their statistical quantum fluctuations and correlations. In this regard, we discuss the role that photon-plasmon interactions play in the manipulation of these fundamental properties for multiparticle systems. We also review recent works that show novel platforms to manipulate many-body light-matter interactions. In this spirit, the foundations that will allow nonexperts to understand new perspectives in multiparticle quantum plasmonics are described. First, we discuss the quantum statistical fluctuations of the electromagnetic field as well as the fundamentals of plasmonics and its quantum properties. This discussion is followed by a brief treatment of the dynamics that characterize complex multiparticle interactions. We apply these ideas to describe quantum interactions in photonic-plasmonic multiparticle quantum systems. We summarize the state-of-the-art in quantum devices that rely on plasmonic interactions. The review is concluded with our perspective on the future applications and challenges in this burgeoning field.

RELATIVISTIC NUCLEAR ENERGY DENSITY FUNCTIONALS

2010 ◽  
Vol 19 (04) ◽  
pp. 548-557 ◽  
Author(s):  
D. VRETENAR ◽  
T. NIKŠIĆ ◽  
P. RING
Keyword(s):  
Energy Density ◽  
Degrees Of Freedom ◽  
Nuclear Energy ◽  
Effective Interaction ◽  
Binding Energies ◽  
Large Set ◽  
Density Functionals ◽  
Heavy Nuclei ◽  
Interaction Terms ◽  
Range Dynamics

A class of relativistic nuclear energy density functionals is explored, in which only nucleon degrees of freedom are explicitly used in the construction of effective interaction terms. Short-distance correlations, as well as intermediate and long-range dynamics, are encoded in the nucleon-density dependence of the strength functionals of an effective interaction Lagrangian. The resulting phenomenological effective interaction, adjusted to experimental binding energies of a large set of axially deformed nuclei, together with a new separable pairing interaction adjusted to reproduce the pairing gap in nuclear matter calculated with the Gogny force, is applied in triaxial relativistic Hartree-Bogoliubov calculations of sequences of heavy nuclei: Th , U , Pu , Cm , Cf , Fm , and No .

scholarly journals MEASUREMENT-BASED QUANTUM COMPUTATION WITH CLUSTER STATES

2009 ◽  
Vol 07 (06) ◽  
pp. 1053-1203 ◽  
Author(s):  
ROBERT RAUßENDORF
Keyword(s):  
Computational Model ◽  
Quantum Computation ◽  
Quantum Logic ◽  
Network Model ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
Cluster State ◽  
Building Blocks ◽  
Network Simulator ◽  
Classical Level

In this thesis, we describe the one-way quantum computer [Formula: see text], a scheme of universal quantum computation that consists entirely of one-qubit measurements on a highly entangled multiparticle state, i.e. the cluster state. We prove the universality of the [Formula: see text], describe the underlying computational model and demonstrate that the [Formula: see text] can be operated fault-tolerantly. In Sec. 2, we show that the [Formula: see text] can be regarded as a simulator of quantum logic networks. In this way, we prove the universality and establish the link to the network model — the common model of quantum computation. We also indicate that the description of the [Formula: see text] as a network simulator is not adequate in every respect. In Sec. 3, we derive the computational model underlying the [Formula: see text], which is very different from the quantum logic network model. The [Formula: see text] has no quantum input, no quantum output and no quantum register, and the unitary gates from some universal set are not the elementary building blocks of [Formula: see text] quantum algorithms. Further, all information that is processed with the [Formula: see text] is the outcomes of one-qubit measurements and thus processing of information exists only at the classical level. The [Formula: see text] is nevertheless quantum-mechanical, as it uses a highly entangled cluster state as the central physical resource. In Sec. 4, we show that there exist nonzero error thresholds for fault-tolerant quantum computation with the [Formula: see text]. Further, we outline the concept of checksums in the context of the [Formula: see text], which may become an element in future practical and adequate methods for fault-tolerant [Formula: see text] computation.

scholarly journals Quasi-Lie Brackets and the Breaking of Time-Translation Symmetry for Quantum Systems Embedded in Classical Baths

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 518 ◽  
Author(s):  
Alessandro Sergi ◽  
Gabriel Hanna ◽  
Roberto Grimaudo ◽  
Antonino Messina
Keyword(s):  
Constant Temperature ◽  
Degrees Of Freedom ◽  
Open Quantum Systems ◽  
Hamiltonian Dynamics ◽  
Quantum Systems ◽  
Classical Dynamics ◽  
Open Quantum ◽  
Time Translation ◽  
Translation Symmetry ◽  
Lie Brackets

Many open quantum systems encountered in both natural and synthetic situations are embedded in classical-like baths. Often, the bath degrees of freedom may be represented in terms of canonically conjugate coordinates, but in some cases they may require a non-canonical or non-Hamiltonian representation. Herein, we review an approach to the dynamics and statistical mechanics of quantum subsystems embedded in either non-canonical or non-Hamiltonian classical-like baths which is based on operator-valued quasi-probability functions. These functions typically evolve through the action of quasi-Lie brackets and their associated Quantum-Classical Liouville Equations, or through quasi-Lie brackets augmented by dissipative terms. Quasi-Lie brackets possess the unique feature that, while conserving the energy (which the Noether theorem links to time-translation symmetry), they violate the time-translation symmetry of their algebra. This fact can be heuristically understood in terms of the dynamics of the open quantum subsystem. We then describe an example in which a quantum subsystem is embedded in a bath of classical spins, which are described by non-canonical coordinates. In this case, it has been shown that an off-diagonal open-bath geometric phase enters into the propagation of the quantum-classical dynamics. Next, we discuss how non-Hamiltonian dynamics may be employed to generate the constant-temperature evolution of phase space degrees of freedom coupled to the quantum subsystem. Constant-temperature dynamics may be generated by either a classical Langevin stochastic process or a Nosé–Hoover deterministic thermostat. These two approaches are not equivalent but have different advantages and drawbacks. In all cases, the calculation of the operator-valued quasi-probability function allows one to compute time-dependent statistical averages of observables. This may be accomplished in practice using a hybrid Molecular Dynamics/Monte Carlo algorithms, which we outline herein.

scholarly journals Paths of unitary access to exceptional points

2021 ◽  
Vol 2038 (1) ◽  
pp. 012026
Author(s):  
Miloslav Znojil
Keyword(s):  
Hilbert Space ◽  
Phase Transitions ◽  
Quantum Phase Transitions ◽  
Quantum Systems ◽  
Point Of View ◽  
Explicit Description ◽  
Direct Access ◽  
Exceptional Point ◽  
Exceptional Points ◽  
Innovative Idea

Abstract With an innovative idea of acceptability and usefulness of the non-Hermitian representations of Hamiltonians for the description of unitary quantum systems (dating back to the Dyson’s papers), the community of quantum physicists was offered a new and powerful tool for the building of models of quantum phase transitions. In this paper the mechanism of such transitions is discussed from the point of view of mathematics. The emergence of the direct access to the instant of transition (i.e., to the Kato’s exceptional point) is attributed to the underlying split of several roles played by the traditional single Hilbert space of states ℒ into a triplet (viz., in our notation, spaces K and ℋ besides the conventional ℒ ). Although this explains the abrupt, quantum-catastrophic nature of the change of phase (i.e., the loss of observability) caused by an infinitesimal change of parameters, the explicit description of the unitarity-preserving corridors of access to the phenomenologically relevant exceptional points remained unclear. In the paper some of the recent results in this direction are summarized and critically reviewed.

scholarly journals Noise thresholds for optical cluster-state quantum computation

2006 ◽  
Vol 73 (5) ◽  
Author(s):  
Christopher M. Dawson ◽  
Henry L. Haselgrove ◽  
Michael A. Nielsen
Keyword(s):  
Quantum Computation ◽  
Cluster State
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