Protection Mechanics with a Quantum Operator for Anomaly Attacks

2010 ◽  
pp. 207-257
Keyword(s):  
Quantum Operator

scholarly journals Bootstrapping Bloch bands

2021 ◽  
Author(s):  
Serguei Tchoumakov ◽  
Serge Florens
Keyword(s):  
Search Space ◽  
Quantum Field Theories ◽  
New Techniques ◽  
Bootstrap Methods ◽  
Quantum Operator ◽  
Canonical Variables ◽  
Distribution Probability ◽  
Anharmonic Potential ◽  
Bloch Band ◽  
Band Spectra

Abstract Bootstrap methods, initially developed for solving statistical and quantum field theories, have recently been shown to capture the discrete spectrum of quantum mechanical problems, such as the single particle Schrödinger equation with an anharmonic potential. The core of bootstrap methods builds on exact recursion relations of arbitrary moments of some quantum operator and the use of an adequate set of positivity criteria. We extend this methodology to models with continuous Bloch band spectra, by considering a single quantum particle in a periodic cosine potential. We find that the band structure can be obtained accurately provided the bootstrap uses moments involving both position and momentum variables. We also introduce several new techniques that can apply generally to other bootstrap studies. First, we devise a trick to reduce by one unit the dimensionality of the search space for the variables parametrizing the bootstrap. Second, we employ statistical techniques to reconstruct the distribution probability allowing to compute observables that are analytic functions of the canonical variables. This method is used to extract the Bloch momentum, a quantity that is not readily available from the bootstrap recursion itself.

Abnormal Quantum State Search Based on Parallel Phase Comparison

2021 ◽  
Author(s):  
Guanlei Xu ◽  
Xiaogang Xu ◽  
Xiaotong Wang
Keyword(s):  
Quantum State ◽  
Search Algorithm ◽  
Quantum States ◽  
Quantum Search ◽  
Superposition State ◽  
Quantum Operator ◽  
Abnormal State ◽  
Number Formula ◽  
Speed Up ◽  
Grover Search

We discuss the problem of filtering out abnormal states from a larger number of quantum states. For this type of problem with [Formula: see text] items to be searched, both the traditional search by enumeration and classical Grover search algorithm have the complexity about [Formula: see text]. In this letter a novel quantum search scheme with exponential speed up is proposed for abnormal states. First, a new comprehensive quantum operator is well-designed to extract the superposition state containing all abnormal states with unknown number [Formula: see text] with complexity [Formula: see text] in probability 1 via well-designed parallel phase comparison. Then, every abnormal state is achieved respectively from [Formula: see text] abnormal states via [Formula: see text] times’ measurement. Finally, a numerical example is given to show the efficiency of the proposed scheme.

Quaternion quantum neurocomputing

2020 ◽  
pp. 2040001
Author(s):  
Eduardo Bayro-Corrochano ◽  
Samuel Solis-Gamboa
Keyword(s):  
Neural Network ◽  
Geometric Algebra ◽  
Neuron Model ◽  
Quaternion Algebra ◽  
Quantum States ◽  
Robust Performance ◽  
Quantum Neural Network ◽  
Quantum Operator ◽  
New Type

Since the introduction of quaternion by Hamilton in 1843, quaternions have been used in a lot of applications. One of the most interesting qualities is that we can use quaternions to carry out rotations and operate on other quaternions; this characteristic of the quaternions inspired us to investigate how the quantum states and quantum operator work in the field of quaternions and how we can use it to construct a quantum neural network. This new type of quantum neural network (QNN) is developed in the quaternion algebra framework that is isomorphic to the rotor algebra [Formula: see text] of the geometric algebra and is based on the so-called qubit neuron model. The quaternion quantum neural network (QQNN) is tested and shows robust performance.

scholarly journals A new quantum operator for distance

2019 ◽  
Vol 34 (06n07) ◽  
pp. 1950033
Author(s):  
Daniel Katz
Keyword(s):  
Quantum Mechanics ◽  
Equivalence Principle ◽  
Classical Mechanics ◽  
Proof Of Concept ◽  
Logical Relationship ◽  
Weak Equivalence Principle ◽  
Quantum Operator ◽  
Operator Means ◽  
Definition Of ◽  
Future Work

We introduce a new semirelativistic quantum operator for the length of the worldline a particle traces out as it moves. In this article the operator is constructed in a heuristic way and some of its elementary properties are explored. The operator ends up depending in a very complicated way on the potential of the system it is to act on so as a proof of concept we use it to analyze the expected distance traveled by a free Gaussian wave packet with some initial momentum. It is shown in this case that the distance such a particle travels becomes light-like as its mass vanishes and agrees with the classical result for macroscopic masses. This preliminary result has minor implications for the Weak Equivalence Principle (WEP) in quantum mechanics. In particular it shows that the logical relationship between two formulations of the WEP in classical mechanics extends to quantum mechanics. That our result is qualitatively consistent with the work of others emboldens us to start the task of evaluating the new operator in nonzero potentials. However, we readily acknowledge that the looseness in the definition of our operator means that all of our so-called results are highly speculative. Plans for future work with the new operator are discussed in the last section.

A theorem for quantum operator correspondence to the solution of the Helmholtz equation

2014 ◽  
Vol 23 (11) ◽  
pp. 110301
Author(s):  
Hong-Yi Fan ◽  
Jun-Hua Chen ◽  
Peng-Fei Zhang ◽  
Rui He
Keyword(s):  
Helmholtz Equation ◽  
Quantum Operator

A Numerical Scheme for the Quantum Fokker-Planck-Landau Equation Efficient in the Fluid Regime

2012 ◽  
Vol 12 (5) ◽  
pp. 1541-1561 ◽  
Author(s):  
Jingwei Hu ◽  
Shi Jin ◽  
Bokai Yan
Keyword(s):  
Numerical Scheme ◽  
Landau Equation ◽  
Collision Operator ◽  
Collision Term ◽  
Fluid Regime ◽  
Quantum Operator ◽  
Simple Quantum ◽  
Dirac Distribution ◽  
Bose Einstein ◽  
Fokker Planck

Abstract We construct an efficient numerical scheme for the quantum Fokker-Planck- Landau (FPL) equation that works uniformly from kinetic to fluid regimes. Such a scheme inevitably needs an implicit discretization of the nonlinear collision operator, which is difficult to invert. Inspired by work [9] we seek a linear operator to penalize the quantum FPL collision term QqFPL in order to remove the stiffness induced by the small Knudsen number. However, there is no suitable simple quantum operator serving the purpose and for this kind of operators one has to solve the complicated quantum Maxwellians (Bose-Einstein or Fermi-Dirac distribution). In this paper, we propose to penalize QqFPL by the "classical" linear Fokker-Planck operator. It is based on the observation that the classical Maxwellian, with the temperature replaced by the internal energy, has the same first five moments as the quantum Maxwellian. Numerical results for Bose and Fermi gases are presented to illustrate the efficiency of the scheme in both fluid and kinetic regimes.

scholarly journals TOWARDS THE CONSTRUCTION OF WIGHTMAN FUNCTIONS OF INTEGRABLE QUANTUM FIELD THEORIES

2004 ◽  
Vol 19 (supp02) ◽  
pp. 34-49 ◽  
Author(s):  
H. BABUJIAN ◽  
M. KAROWSKI
Keyword(s):  
Ising Model ◽  
Form Factors ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Operator Equations ◽  
Quantum Operator ◽  
Integrable Quantum ◽  
Wightman Functions ◽  
Distance Limit

The purpose of the "bootstrap program" for integrable quantum field theories in 1+1 dimensions is to construct a model in terms of its Wightman functions explicitly. In this article, the program is mainly illustrated in terms of the sine-Gordon and the sinh-Gordon model and (as an exercise) the scaling Ising model. We review some previous results on sine-Gordon breather form factors and quantum operator equations. The problem to sum over intermediate states is attacked in the short distance limit of the two point Wightman function for the sinh-Gordon and the scaling Ising model.

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