A survey on HHL algorithm: From theory to application in quantum machine learning

The Harrow-Hassidim-Lloyd (HHL) algorithm is a method to solve the quantum linear system of equations that may be found at the core of various scientific applications and quantum machine learning models including the linear regression, support vector machines and recommender systems etc. After reviewing the necessary background on elementary quantum algorithms, we provide detailed account of how HHL is exploited in different quantum machine learning (QML) models, and how it provides the desired quantum speedup in all these models. At the end, we briefly discuss some of the remaining challenges ahead for HHL-based QML models and related methods.     

Investigation of Commuting Hamiltonian in Quantum Markov Network

Graphical Models have various applications in science and engineering which include physics, bioinformatics, telecommunication and etc. Usage of graphical models needs complex computations in order to evaluation of marginal functions, so there are some powerful methods including mean field approximation, belief propagation algorithm and etc. Quantum graphical models have been recently developed in context of quantum information and computation, and quantum statistical physics, which is possible by generalization of classical probability theory to quantum theory. The main goal of this paper is preparing a primary generalization of Markov network, as a type of graphical models, to quantum case and applying in quantum statistical physics. We have investigated the Markov network and the role of commuting Hamiltonian terms in conditional independence with simple examples of quantum statistical physics.     

Comparative study between different quantum infrared photodetectors

This paper presents a theoretical analysis for the dark current characteristics of different quantum infrared photodetectors. These quantum photodetectors are quantum dot infrared photodetectors (QDIP), quantum wire infrared photodetectors (QRIP), and quantum well infrared photodetectors (QWIP). Mathematical models describing these devices are introduced. The developed models accounts for the self-consistent potential distribution. These models are taking the effect of donor charges on the spatial distribution of the electric potential in the active region. The developed model is used to investigate the behavior of dark current with different values of performance parameters such as applied voltage, number of quantum wire (QR) layers, QD layers, lateral characteristic size, doping quantum wire density and temperature. It explains strong sensitivity of dark current to the density of QDs/QRs and the doping level of the active region. In order to confirm our models and their validity on the practical applications, a comparison between the results obtained by proposed models and that experimentally published are conducted and full agreement is observed. Several performance parameters are tuned to enhance the performance of these quantum photodetectors through the presented modeling. The resultant performance characteristics and comparison among them are presented in this work. From the obtained results we notice that the total dark current in the QRIPs can be significantly lower than that in the QWIPs. Moreover, main features of the QRIPs such as the large gap between the induced photocurrent and dark current open the way for overcoming the problems of quantum dot infrared photodetectors.     

Why error-prone quantum measurements have outcomes

To solve the quantum measurement problem it is necessary to construct quantum mechanical models of measurement interactions to show why properly conducted measurements always yield definite outcomes. The main barrier to a solution has been the interpretive principle that a quantum system has a definite value for an observable only if it may be described by a quantum eigenstate of the corresponding operator. I have recently proposed a solution to the measurement problem based on alternative interpretive principles. The present paper defends this proposal against recent criticisms which seek to show that it fails to solve the problem unless quantum measurements meet highly idealized conditions which no actual measurement could hope to meet. Several models of error-prone measurements are shown to lead to definite outcomes, and a general defense of the appropriateness of these models is sketched.     

On the inverse FPR problem: Quantum is classical

The notion of quantum supports introduced by Foulis, Piron, and Randall can be used to construct combinatorial versions of contextualist hidden-variable models for finite quantum logics. The original logic can be uniquely recovered from appropriate such models as a solution of a combinatorial inverse problem. One can thus set up a classical ontology for a finite quantum logics that completely specifies it. Computer studies are used to explore the ideas.     

Quantum symmetry of Hubbard model unraveled

Superconducting quantum symmetries in extended one-band one-dimensional Hubbard models are shown to originate from the classical (pseudo-) spin symmetry of a new class of models; the standard Hubbard model is a special case. The quantum symmetric models provide extra parameters but are restricted to one dimension. All models discussed are related by generalized Lang-Firsov transformations, some have symmetries away from half filling.     

Feynman propagator for spin foam quantum gravity

We link the notion causality with the orientation of the spin foam 2-complex. We show that all current spin foam models are orientation independent. Using the technology of evolution kernels for quantum fields on Lie groups, we construct a generalized version of spin foam models, introducing an extra proper time variable. We prove that different ranges of integration for this variable lead to different classes of spin foam models: the usual ones, interpreted as the quantum gravity analogue of the Hadamard function of quantum field theory (QFT) or as inner products between quantum gravity states; and a new class of causal models, the quantum gravity analogue of the Feynman propagator in QFT, nontrivial function of the orientation data, and implying a notion of "timeless ordering".     

Importance of quantum tunneling in vacancy-hydrogen complexes in diamond

Our ab initio calculations of the hyperfine parameters for negatively charged vacancy-hydrogen and nitrogen-vacancy-hydrogen complexes in diamond compare static defect models and models which account for the quantum tunneling behavior of hydrogen. The static models give rise to hyperfine splittings that are inconsistent with the experimental electron paramagnetic resonance data. In contrast, the hyperfine parameters for the quantum dynamical models are in agreement with the experimental observations. We show that the quantum motion of the proton is crucial to the prediction of symmetry and hyperfine constants for two simple defect centers in diamond. Static a priori methods fail for these systems.     

Ground state structure in supersymmetric quantum mechanics

We present a rigorous analysis of the vacuum structure of two models of supersymmetric quantum mechanics. They are the quantum mechanics versions of the two-dimensional N = 1 and N = 2 Wess-Zumino quantum field models. We find that the N = 2 quantum mechanics has degenerate vacua. The space of vacuum states is bosonic, and its dimension is determined by the topological properties of the superpotential.     

Heat transport in quantum spin chains

We discuss the problem of heat conduction in quantum spin chain models. To investigate this problem it is necessary to consider the finite open system connected to heat baths. We describe two different procedures to couple the system with the reservoirs: a model of stochastic heat baths and the quantum trajectories solution of the quantum master equation. The stochastic heat bath procedure operates on the pure wave function of the isolated system, so that it is locally and periodically collapsed to a quantum state consistent with a boundary nonequilibrium state. In contrast, the quantum trajectories procedure evaluates ensemble averages in terms of the reduced density matrix operator of the system. We apply these procedures to different models of quantum spin chains and numerically show their applicability to study the heat flow.     

两量子比特非线性相互作用模型中的量子关联

运用量子态变换的方法论证了两个qubit纯态中量子关联与纠缠的等价性.并利用三种带有横场的非线性相互作用模型研究了两个qubit体系中的量子关联.发现合适的横场对于最大量子关联态的获得、平均量子关联的提高都有着积极的作用.两个qubit体系获得最大量子关联时,不同模型,不同的横场,对应的量子态却各不相同.     

General Non-Markovian Quantum Dynamics

A general approach to the construction of non-Markovian quantum theory is proposed. Non-Markovian equations for quantum observables and states are suggested by using general fractional calculus. In the proposed approach, the non-locality in time is represented by operator kernels of the Sonin type. A wide class of the exactly solvable models of non-Markovian quantum dynamics is suggested. These models describe open (non-Hamiltonian) quantum systems with general form of nonlocality in time. To describe these systems, the Lindblad equations for quantum observable and states are generalized by taking into account a general form of nonlocality. The non-Markovian quantum dynamics is described by using integro-differential equations with general fractional derivatives and integrals with respect to time. The exact solutions of these equations are derived by using the operational calculus that is proposed by Yu. Luchko for general fractional differential equations. Properties of bi-positivity, complete positivity, dissipativity, and generalized dissipativity in general non-Markovian quantum dynamics are discussed. Examples of a quantum oscillator and two-level quantum system with a general form of nonlocality in time are suggested.     

Simple quantum systems as a source of coherent information

A set of very important simple quantum systems is analyzed from the standpoint of the amount of coherent information that is accessible when information channels corresponding to the systems are used. It is shown that for simple quantum models the coherent information can be calculated and used for estimating the potential possibilities of the corresponding quantum channel as a source of physical information in experiments associated with the effects of the coherence of quantum states. The following physical models are studied: a two-level atom in a laser radiation field, an aggregate of two two-level subsystems in a multilevel atom (hydrogen), a system of two two-level atoms in the process of joint quantum-deterministic evolution and under the action of transformations of quantum measurement and quantum duplication, as well as one and two two-level atoms in the process of emission.     

Holographic topological semimetals

The holographic duality allows to construct and study models of strongly coupled quantum matter via dual gravitational theories.In general such models are characterized by the absence of quasiparticles, hydrodynamic behavior and Planckian dissipation times. One particular interesting class of quantum materials are ungapped topological semimetals which have many interesting properties from Hall transport to topologically protected edge states. We review the application of the holographic duality to this type of quantum matter including the construction of holographic Weyl semimetals, nodal line semimetals, quantum phase transition to trivial states(ungapped and gapped), the holographic dual of Fermi arcs and how new unexpected transport properties,such as Hall viscosities arise. The holographic models promise to lead to new insights into the properties of this type of quantum matter.     

An Inverse Problem in Quantum Statistical Physics

We address the following inverse problem in quantum statistical physics: does the quantum free energy (von Neumann entropy + kinetic energy) admit a unique minimizer among the density operators having a given local density n(x)? We give a positive answer to that question, in dimension one. This enables to define rigourously the notion of local quantum equilibrium, or quantum Maxwellian, which is at the basis of recently derived quantum hydrodynamic models and quantum drift-diffusion models. We also characterize this unique minimizer, which takes the form of a global thermodynamic equilibrium (canonical ensemble) with a quantum chemical potential.     

Dimerization,trimerization and quantum pumping

We study one-dimensional topological models with dimerization and trimerization and show that these models can be generated using interaction or optical superlattice. The topological properties of these models are demonstrated by the appearance of edge states and the mechanism of dimerization and trimerization is analyzed. Then we show that a quantum pumping process can be constructed based on each one-dimensional topological model. The quantum pumping process is explicitly demonstrated by the instantaneous energy spectrum and local current. The result shows that the pumping is assisted by the gapless states connecting the bands and one charge is pumped during a cycle, which also defines a nonzero Chern number. Our study systematically shows the connection of one-dimensional topological models and quantum pumping, and is useful for the experimental studies on topological phases in optical lattices and photonic quasicrystals.     

Zeno dynamics for open quantum systems

In this paper, we formulate limit Zeno dynamics of general open systems as the adiabatic elimination of fast components. We are able to exploit previous work on adiabatic elimination of quantum stochastic models to give explicitly the conditions under which open Zeno dynamics will exist. The open systems formulation is further developed as a framework for Zeno master equations, and Zeno filtering (that is, quantum trajectories based on a limit Zeno dynamical model). We discuss several models from the point of view of quantum control. For the case of linear quantum stochastic systems, we present a condition for stability of the asymptotic Zeno dynamics.     

Hidden variables in quantum mechanics: Generic models, set-theoretic forcing, and the appearance of probability

The hidden-variables premise is shown to be equivalent to the existence of generic filters for systems of commuting observables of a quantum system. The significance of this equivalence is interpreted in light of the theory of generic filters and boolean-valued models in set theory. The apparent stochastic nature of quantum observation is derived for these hidden-variables models.     

On the structure of the quantum-mechanical probability models

In this paper the role of the mathematical probability models in the classical and quantum physics is shortly analyzed. In particular the formal structure of the quantum probability spaces (QPS) is contrasted with the usual Kolmogorovian models of probability by putting in evidence the connections between this structure and the fundamental principles of the quantum mechanics. The fact that there is no unique Kolmogorovian model reproducing a QPS is recognized as one of the main reasons of the paradoxical behaviors pointed out in the quantum theory from its early days.Paper written in honor of L. de Broglie.