共查询到20条相似文献,搜索用时 15 毫秒
1.
Pil H. Song ILki Kim 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2003,23(2):299-303
We study the effects of dissipation or leakage on the time evolution of Grover's algorithm for a quantum computer. We introduce
an effective two-level model with dissipation and randomness (imperfections), which is based upon the idea that ideal Grover's
algorithm operates in a 2-dimensional Hilbert space. The simulation results of this model and Grover's algorithm with imperfections
are compared, and it is found that they are in good agreement for appropriately tuned parameters. It turns out that the main
features of Grover's algorithm with imperfections can be understood in terms of two basic mechanisms, namely, a diffusion
of probability density into the full Hilbert space and a stochastic rotation within the original 2-dimensional Hilbert space.
Received 12 August 2002 / Received in final form 14 October 2002 Published online 4 February 2003 相似文献
2.
Franklin E. Schroeck Jr. 《International Journal of Theoretical Physics》2008,47(1):175-184
On any quantum mechanical Hilbert space, the phase space localization operators form a set of operators that are both physically
motivated and form the groundwork for a C* algebra. This set is shown to be informationally complete in the original Hilbert
space. We also revisit the relation between having a complete set of eigenvectors, commutability and compatibility.
Dedicated to G.G. Emch. 相似文献
3.
Sven Aerts 《International Journal of Theoretical Physics》2008,47(1):2-14
Quantum logic introduced a paradigm shift in the axiomatization of quantum theory by looking directly at the structural relations
between the closed subspaces of the Hilbert space of a system. The one dimensional closed subspaces correspond to testable
properties of the system, forging an operational link between theory and experiment. Thus a property is called actual, if
the corresponding test yields “yes” with certainty. We argue a truly operational definition should include a quantitative
criterion that tells us when we ought to be satisfied that the test yields “yes” with certainty. This question becomes particularly pressing when we inquire how the usual definition can be extended to cover potential,
rather than actual properties. We present a statistically operational candidate for such an extension and show that its representation
automatically captures some essential Hilbert space structure. If it is the nature of observation that is responsible for
the Hilbert space structure, then we should be able to give examples of theories with scope outside the domain of quantum
theory, that employ its basic structure, and that describe the optimal extraction of information. We argue signal analysis
is such an example.
This work was supported by the Flemish Fund for Scientific Research (FWO) project G.0362.03N. 相似文献
4.
In this paper is considered a problem of defining natural star-products on symplectic manifolds, admissible for quantization of classical Hamiltonian systems. First, a construction of a star-product on a cotangent bundle to an Euclidean configuration space is given with the use of a sequence of pair-wise commuting vector fields. The connection with a covariant representation of such a star-product is also presented. Then, an extension of the construction to symplectic manifolds over flat and non-flat pseudo-Riemannian configuration spaces is discussed. Finally, a coordinate free construction of related quantum mechanical operators from Hilbert space over respective configuration space is presented. 相似文献
5.
The usual notion of separability has to be reconsidered when applied to states describing identical particles. A definition of separability not related to any a priori Hilbert space tensor product structure is needed: this can be given in terms of commuting subalgebras of observables. Accordingly, the results concerning the use of the quantum Fisher information in quantum metrology are generalized and physically reinterpreted. 相似文献
6.
Daniel Lehmann 《International Journal of Theoretical Physics》2009,48(1):261-281
Similarity-Projection structures abstract the numerical properties of real scalar product of rays and projections in Hilbert
spaces to provide a more general framework for Quantum Physics. They are characterized by properties that possess direct physical
meaning. They provide a formal framework that subsumes both classical Boolean logic concerned with sets and subsets and quantum
logic concerned with Hilbert space, closed subspaces and projections. They shed light on the role of the phase factors that
are central to Quantum Physics. The generalization of the notion of a self-adjoint operator to SP-structures provides a novel
notion that is free of linear algebra.
This work was partially supported by the Jean and Helene Alfassa fund for research in Artificial Intelligence. 相似文献
7.
In the paper is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over configuration space is derived. An explicit form of position and momentum operators as well as their appropriate ordering in arbitrary curvilinear coordinates is demonstrated. Finally, the extension of presented formalism onto non-flat case and related ambiguities of the process of quantization are discussed. 相似文献
8.
We present a new point of view on the quantization of the massive gravitational field, namely we use exclusively the quantum framework of the second quantization. The Hilbert space of the many-gravitons system is a Fock space F+ (Hgraviton) where the one-particle Hilbert space Hgraviton carries the direct sum of two unitary irreducible representations of the Poincaré group corresponding to two particles of mass m > 0 and spins 2 and 0, respectively. This Hilbert space is canonically isomorphic to a space of the type Ker(Q)/Im(Q) where Q is a gauge charge defined in an extension of the Hilbert space Hgraviton generated by the gravitational field h and some ghosts fields u, (which are vector Fermi fields) and v (which is a vector Bose field).Then we study the self interaction of massive gravity in the causal framework. We obtain a solution which goes smoothly to the zero-mass solution of linear quantum gravity up to a term depending on the bosonic ghost field. This solution depends on two real constants as it should be; these constants are related to the gravitational constant and the cosmological constant. In the second order of the perturbation theory we do not need a Higgs field, in sharp contrast to Yang-Mills theory. 相似文献
9.
A theoretical framework is demonstrated to evaluate the degree of entanglement of bit states in quantum computing. Separability
of general superposition of Hilbert space unit vectors is discussed, and criteria in amplitude as well as in phase are derived.
By these criteria the possibility of different quantum gates such as controlled not (CN), controlled controlled not (CCN),
controlled rotation (CR), and controlled phase shift (CPS), to create the entanglement is examined. Furthermore, the selection
of measurement mode external to the quantum system is incorporated in the formula using Kronecker delta (δ
kx
), introducing the concept of dynamic entanglement. With this the process of wavefunction collapse upon measurement is understood as the result of the activation of the dynamic
entanglement. A firefly in a box model is used to show a pure state of ontological uncertainty, which is in a dynamically
entangled state in Hilbert space. 相似文献
10.
The Barut-Girardello coherent states for the parabolic cylinder functions are constructed. It is shown that the resolution
of unity condition is satisfied for the coherent states. In the Hilbert space spanned by the parabolic cylinder eigenstates,
the appropriate measure is also obtained. 相似文献
11.
We implement an algorithm which is aimed to reduce the dimensions of the Hilbert space of quantum many-body systems by means of a renormalization procedure. We test the role and importance of different representations on the reduction process by working out and analyzing the spectral properties of strongly interacting frustrated quantum spin systems. 相似文献
12.
《Physics letters. A》2020,384(21):126422
Binary classification is a fundamental problem in machine learning. Recent development of quantum similarity-based binary classifiers and kernel method that exploit quantum interference and feature quantum Hilbert space opened up tremendous opportunities for quantum-enhanced machine learning. To lay the fundamental ground for its further advancement, this work extends the general theory of quantum kernel-based classifiers. Existing quantum kernel-based classifiers are compared and the connection among them is analyzed. Focusing on the squared overlap between quantum states as a similarity measure, the essential and minimal ingredients for the quantum binary classification are examined. The classifier is also extended concerning various aspects, such as data type, measurement, and ensemble learning. The validity of the Hilbert-Schmidt inner product, which becomes the squared overlap for pure states, as a positive definite and symmetric kernel is explicitly shown, thereby connecting the quantum binary classifier and kernel methods. 相似文献
13.
Jamie Vicary 《International Journal of Theoretical Physics》2008,47(12):3408-3447
This paper describes how the structure of the state space of the quantum harmonic oscillator can be described by an adjunction
of categories, that encodes the raising and lowering operators into a commutative comonoid. The formulation is an entirely
general one in which Hilbert spaces play no special role.
Generalised coherent states arise through the hom-set isomorphisms defining the adjunction, and we prove that they are eigenstates
of the lowering operators. Generalised exponentials also emerge naturally in this setting, and we demonstrate that coherent
states are produced by the exponential of a raising morphism acting on the zero-particle state. Finally, we examine all of
these constructions in a suitable category of Hilbert spaces, and find that they reproduce the conventional mathematical structures. 相似文献
14.
A model Hamiltonian is proposed for the localization–delocalization transition in quantum dots. By considering most relevant degrees of freedom, we obtain a finite dimensional Hilbert space. Through exact diagonalization, we find the ground state energies of the system as the number of electrons is varied. This explains the peculiar pattern of the electron addition energies, which are measured as a function of the top and side gate voltages. 相似文献
15.
We propose a new method to understand quantum entanglement using the thermo field dynamics (TFD) described by a double Hilbert space. The entanglement states show a quantum-mechanically complicated behavior. Our new method using TFD makes it easy to understand the entanglement states, because the states in the tilde space in TFD play a role of tracer of the initial states. For our new treatment, we define an extended density matrix on the double Hilbert space. From this study, we make a general formulation of this extended density matrix and examine some simple cases using this formulation. Consequently, we have found that we can distinguish intrinsic quantum entanglement from the thermal fluctuations included in the definition of the ordinary quantum entanglement at finite temperatures. Through the above examination, our method using TFD can be applied not only to equilibrium states but also to non-equilibrium states. This is shown using some simple finite systems in the present paper. 相似文献
16.
We provide a method for constructing a set of four-photon states suitable for quantum communication applications. Among these
states is a set of concatenated quantum code states that span a decoherence-free subspace that is robust under collective-local
as well as global dephasing noise. This method requires only the use of spontaneous parametric down-conversion, quantum state
post-selection, and linear optics. In particular, we show how this method can be used to produce all sixteen elements of the
second-order Bell gem
, which includes these codes states and is an orthonormal basis for the Hilbert space of four qubits composed entirely of
states that are fully entangled under the four-tangle measure. 相似文献
17.
《Physics letters. A》2014,378(30-31):2054-2057
The non-bijective version of Wigner's theorem states that a map which is defined on the set of self-adjoint, rank-one projections (or pure states) of a complex Hilbert space and which preserves the transition probability between any two elements, is induced by a linear or antilinear isometry. We present a completely new, elementary and very short proof of this famous theorem which is very important in quantum mechanics. We do not assume bijectivity of the mapping or separability of the underlying space like in many other proofs. 相似文献
18.
This is a basically expository article, with some new observations, tracing connections of the quantum potential to Fisher information, to Kähler geometry of the projective Hilbert space of a quantum system, and to the Weyl-Ricci scalar curvature of a Riemannian flat spacetime with quantum matter.Á Denise 相似文献
19.
双参数变形玻色湮没算符高次幂的本征态及其量子统计性质 总被引:1,自引:1,他引:0
本文构造了双参数变形玻色湮没算符高次幂a'k(k≥3)的k个正交归一木征态的数学结构,发现它们能构成一个完备的Hilbert空间,并且讨论了它们的量子统计性质. 相似文献
20.
We study in this article the effects of external magnetic field on the electron Zitterbewegung in semiconductor quantum dots and wires with parabolic confinements and Rashba spin–orbit interaction. In doing so, we have calculated the dynamics of the expectation value of the position operator by means of the time evolution operator in an appropriate Hilbert space. The results show that the electron Zitterbewegung, its amplitude which is related to the electron confinement, and the period of the electron Zitterbewegung depend on the external magnetic field. We propose that the magnetic field can be used as an external agent to control the electron Zitterbewegung, a fundamental key for experimental detection of this phenomena. 相似文献