Journal articles: 'Quantum mappings'

1

Nijhoff, F. W., H. W. Capel, and V. G. Papageorgiou. "Integrable quantum mappings." Physical Review A 46, no. 4 (August 1, 1992): 2155–58. http://dx.doi.org/10.1103/physreva.46.2155.

Full text

APA, Harvard, Vancouver, ISO, and other styles

2

HEYDARI, HOSHANG. "ALGEBRAIC STRUCTURES OF MULTIPARTITE QUANTUM SYSTEMS." International Journal of Quantum Information 09, no. 01 (February 2011): 555–61. http://dx.doi.org/10.1142/s0219749911005515.

Full text

Abstract:

We investigate the relation between multilinear mappings and multipartite states. We show that the isomorphism between multilinear mapping and tensor product completely characterizes decomposable multipartite states in a mathematically well-defined manner.

APA, Harvard, Vancouver, ISO, and other styles

3

Filippov, S. N. "Tensor Products of Quantum Mappings." Journal of Mathematical Sciences 252, no. 1 (November 20, 2020): 116–24. http://dx.doi.org/10.1007/s10958-020-05146-9.

Full text

APA, Harvard, Vancouver, ISO, and other styles

4

Sergeev, A. G. "Quantum calculus and quasiconformal mappings." Mathematical Notes 100, no. 1-2 (July 2016): 123–31. http://dx.doi.org/10.1134/s0001434616070117.

Full text

APA, Harvard, Vancouver, ISO, and other styles

5

Quispel, G. R. W., and F. W. Nijhoff. "Integrable two-dimensional quantum mappings." Physics Letters A 161, no. 5 (January 1992): 419–22. http://dx.doi.org/10.1016/0375-9601(92)90681-b.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

Filippov, S. N. "Quantum Mappings and Characterization of Entangled Quantum States." Journal of Mathematical Sciences 241, no. 2 (August 2019): 210–36. http://dx.doi.org/10.1007/s10958-019-04418-3.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

Pankov, K. N. "ESTIMATES FOR NUMBERS OF BOOLEAN MAPPINGS USED IN QUANTUM KEY DISTRIBUTION PROTOCOLS." H&ES Research 14, no. 4 (2022): 4–18. http://dx.doi.org/10.36724/2409-5419-2022-14-4-4-18.

Full text

Abstract:

Introduction: In the near future, quantum cryptography will play an important role in maintaining a sufficient level of information security of modern telecommunication networks in the conditions of a quantum challenge, which refers to the emergence of quantum computers that will be able to effectively solve the mathematical problems on which, for example, modern key distribution systems are based. Now quantum cryptography is actively used by commercial and government agencies around the world and, in particular, in the Russian Federation. At the same time, a large amount of research is being carried out in the field of development and implementation of quantum key distribution systems, as the main part of quantum cryptography. In this regard, the task of developing new and refining existing protocols for quantum key distribution, as well as studying various mathematical and physical objects that are associated with these protocols, is an urgent task. In particular, one of the stages of the classical BB84 protocol implement ed in a noisy quantum channel is associated with the problem of studying correlation immune and stable mappings, part of which is the problem of estimating their number, which has not been completely solved. Purpose: to find mathematical expressions for exact and asymptotic estimates of the cardinalities of classes of (n,m,k) stable and correlation immune of order k boolean mappings. Results: The best currently asymptotic upper and lower bounds for the number of such classes of mappings with the number of outputs greater than or equal to five are obtained. Recurrent relations were also proved, which allow one to find the exact distribution of the cardinalities of classes of similar mappings for the case of small numbers n and m. Practical relevance: the results obtained allow us to estimate the probability that with a random choice of mapping to enhance secrecy at the stage of secondary processing of the BB84 protocol, the situation will be neutralized when the adversary has access to k photons sent over a communication chan nel of his choice.

APA, Harvard, Vancouver, ISO, and other styles

8

Schlunzen, F. "Induced quantum gravity and quasiconformal mappings." Classical and Quantum Gravity 8, no. 4 (April 1, 1991): 651–58. http://dx.doi.org/10.1088/0264-9381/8/4/010.

Full text

APA, Harvard, Vancouver, ISO, and other styles

9

SZCZȨSNY, JERZY, MAREK BIESIADA, and MAREK SZYDŁOWSKI. "TOPOLOGICAL QUANTUM NUMBERS AND CURVATURE — EXAMPLES AND APPLICATIONS." International Journal of Geometric Methods in Modern Physics 06, no. 03 (May 2009): 533–53. http://dx.doi.org/10.1142/s0219887809003667.

Full text

Abstract:

Using the idea of the degree of a smooth mapping between two manifolds of the same dimension we present here the topological (homotopical) classification of the mappings between spheres of the same dimension, vector fields, monopole and instanton solutions. Starting with a review of the elements of Riemannian geometry we also present an original elementary proof of the Gauss–Bonnet theorem and also one of the Poincaré–Hopf theorem.

APA, Harvard, Vancouver, ISO, and other styles

10

Hutchinson, J., J. P. Keating, and F. Mezzadri. "On Relations between One-Dimensional Quantum and Two-Dimensional Classical Spin Systems." Advances in Mathematical Physics 2015 (2015): 1–18. http://dx.doi.org/10.1155/2015/652026.

Full text

Abstract:

We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems characterised by long-range interactions and with critical properties equivalent to those of the class of one-dimensional quantum systems treated by the authors in a previous publication. In particular, we use three approaches: the Trotter-Suzuki mapping, the method of coherent states, and a calculation based on commuting the quantum Hamiltonian with the transfer matrix of a classical system. This enables us to establish universality of certain critical phenomena by extension from the results in the companion paper for the classical systems identified.

APA, Harvard, Vancouver, ISO, and other styles

11

Bellon, M. P., J.-M. Maillard, and C.-M. Viallet. "DYNAMICAL SYSTEMS FROM QUANTUM INTEGRABILITY." International Journal of Modern Physics B 07, no. 20n21 (September 30, 1993): 3567–96. http://dx.doi.org/10.1142/s0217979293003413.

Full text

Abstract:

We describe a class of non-linear transformations acting on many variables. These transformations have their origin in the theory of quantum integrability: they appear in the description of the symmetries of the Yang-Baxter equations and their higher dimensional generalizations. They are generated by involutions and act as birational mappings on various projective spaces. We present numerous figures, showing successive iterations of these mappings. The existence of algebraic invariants explains the aspect of these figures. We also study deformations of our transformations.

APA, Harvard, Vancouver, ISO, and other styles

12

You, Xue Xiao, Muhammad Aamir Ali, Hüseyin Budak, Miguel Vivas-Cortez, and Shahid Qaisar. "Some Parameterized Quantum Simpson’s and Quantum Newton’s Integral Inequalities via Quantum Differentiable Convex Mappings." Mathematical Problems in Engineering 2021 (December 26, 2021): 1–17. http://dx.doi.org/10.1155/2021/5526726.

Full text

Abstract:

In this work, two generalized quantum integral identities are proved by using some parameters. By utilizing these equalities, we present several parameterized quantum inequalities for convex mappings. These quantum inequalities generalize many of the important inequalities that exist in the literature, such as quantum trapezoid inequalities, quantum Simpson’s inequalities, and quantum Newton’s inequalities. We also give some new midpoint-type inequalities as special cases. The results in this work naturally generalize the results for the Riemann integral.

APA, Harvard, Vancouver, ISO, and other styles

13

Ali, Muhammad Aamir, Hüseyin Budak, Abdullah Akkurt, and Yu-Ming Chu. "Quantum Ostrowski-type inequalities for twice quantum differentiable functions in quantum calculus." Open Mathematics 19, no. 1 (January 1, 2021): 440–49. http://dx.doi.org/10.1515/math-2021-0020.

Full text

Abstract:

Abstract In this paper, we first prove an identity for twice quantum differentiable functions. Then, by utilizing the convexity of ∣ D q 2 b f ∣ | {}^{b}D_{q}^{2}\hspace{0.08em}f| and ∣ D q 2 a f ∣ | {}_{a}D_{q}^{2}\hspace{0.08em}f| , we establish some quantum Ostrowski inequalities for twice quantum differentiable mappings involving q a {q}_{a} and q b {q}^{b} -quantum integrals. The results presented here are the generalization of already published ones.

APA, Harvard, Vancouver, ISO, and other styles

14

Nijhoff, F. W., and H. W. Capel. "Integrability and fusion algebra for quantum mappings." Journal of Physics A: Mathematical and General 26, no. 22 (November 21, 1993): 6385–407. http://dx.doi.org/10.1088/0305-4470/26/22/035.

Full text

APA, Harvard, Vancouver, ISO, and other styles

15

AMICO, LUIGI. "ALGEBRAIC EQUIVALENCE BETWEEN CERTAIN MODELS FOR SUPERFLUID–INSULATOR TRANSITION." Modern Physics Letters B 14, no. 21 (September 10, 2000): 759–66. http://dx.doi.org/10.1142/s0217984900000963.

Full text

Abstract:

Algebraic contraction is proposed to realize mappings between Hamiltonian models. This transformation contracts the algebra of the degrees of freedom underlying the Hamiltonian. The rigorous mapping between the anisotropic XXZ Heisenberg model, the quantum phase model and the Bose Hubbard model is established as the contractions of the algebra u(2) underlying the dynamics of the XXZ Heisenberg model.

APA, Harvard, Vancouver, ISO, and other styles

16

O’Gorman, Bryan, Eleanor Gilbert Rieffel, Minh Do, Davide Venturelli, and Jeremy Frank. "Comparing planning problem compilation approaches for quantum annealing." Knowledge Engineering Review 31, no. 5 (November 2016): 465–74. http://dx.doi.org/10.1017/s0269888916000278.

Full text

Abstract:

AbstractOne approach to solving planning problems is to compile them to other problems for which powerful off-the-shelf solvers are available; common targets include SAT, CSP, and MILP. Recently, a novel optimization technique has become available: quantum annealing (QA). QA takes as input problem instances of quadratic unconstrained binary optimization (QUBO) problem. Early quantum annealers are now available, though their constraints restrict the types of QUBOs they can take as input. Here, we introduce the planning community to the key steps in compiling planning problems to QA hardware: a hardware-independent step, mapping, and a hardware-dependent step, embedding. After describing two approaches to mapping general planning problems to QUBO, we describe preliminary results from running an early quantum annealer on a parametrized family of hard planning problems. The results show that different mappings can substantially affect performance, even when many features of the resulting instances are similar. We conclude with insights gained from this early study that suggest directions for future work.

APA, Harvard, Vancouver, ISO, and other styles

17

Somma, Rolando, Gerardo Ortiz, Emanuel Knill, and James Gubernatis. "Quantum Simulations of Physics Problems." International Journal of Quantum Information 01, no. 02 (June 2003): 189–206. http://dx.doi.org/10.1142/s0219749903000140.

Full text

Abstract:

If a large Quantum Computer (QC) existed today, what type of physical problems could we efficiently simulate on it that we could not efficiently simulate on a classical Turing machine? In this paper we argue that a QC could solve some relevant physical "questions" more efficiently. The existence of one-to-one mappings between different algebras of observables or between different Hilbert spaces allow us to represent and imitate any physical system by any other one (e.g. a bosonic system by a spin-1/2 system). We explain how these mappings can be performed, and we show quantum networks useful for the efficient evaluation of some physical properties, such as correlation functions and energy spectra.

APA, Harvard, Vancouver, ISO, and other styles

18

Mukhamedov, Farrukh. "On Pure Quasi-Quantum Quadratic Operators of 𝕄2(ℂ) II." Open Systems & Information Dynamics 22, no. 04 (December 2015): 1550024. http://dx.doi.org/10.1142/s1230161215500249.

Full text

Abstract:

In this paper we study quasi quantum quadratic operators (QQO) acting on the algebra of [Formula: see text] matrices [Formula: see text]. We consider two kinds of quasi QQO the corresponding quadratic operator maps from the unit circle into the sphere and from the sphere into the unit circle, respectively. In our early paper we have defined a q-purity of quasi QQO. This notion is equivalent to the invariance of the unit sphere in [Formula: see text]. But to check this condition, in general, is tricky. Therefore, it would be better to find weaker conditions to check the q-purity. One of the main results of this paper is to provide a criterion of q-purity of quasi QQO in terms of the unit circles. Moreover, we are able to classify all possible kinds of quadratic operators which can produce q-pure quasi QQO. We think that such result will allow one to check whether a given mapping is a pure channel or not. This finding suggests us to study such a class of nonpositive mappings. Correspondingly, the complement of this class will be of potential interest for physicist since this set contains all completely positive mappings.

APA, Harvard, Vancouver, ISO, and other styles

19

Faraggi, Alon E. "Spinor-Vector Duality and the Swampland." Universe 8, no. 8 (August 18, 2022): 426. http://dx.doi.org/10.3390/universe8080426.

Full text

Abstract:

The Swampland Program aims to address the question, “when does an effective field theory model of quantum gravity have an ultraviolet complete embedding in string theory?”, and can be regarded as a bottom-up approach for investigations of quantum gravity. An alternative top-down approach aims to explore the imprints and the constraints imposed by string-theory dualities and symmetries on the effective field theory representations of quantum gravity. The most celebrated example of this approach is mirror symmetry. Mirror symmetry was first observed in worldsheet contructions of string compactifications. It was completely unexpected from the effective field theory point of view, and its implications in that context were astounding. In terms of the moduli parameters of toroidally compactified Narain spaces, mirror symmetry can be regarded as arising from mappings of the moduli of the internal compactified space. Spinor-vector duality, which was discovered in worldsheet constructions of string vacua, is an extension of mirror symmetry that arises from mappings of the Wilson line moduli and provide a probe to constrain and explore the moduli spaces of (2, 0) string compactifications. Mirror symmetry and spinor-vector duality are mere two examples of a much wider symmetry structure, whose implications have yet to be unravelled. A mapping between supersymmetric and non-supersymmetric vacua is briefly discussed. T-duality is another important property of string theory and can be thought of as phase-space duality in compact space. I propose that manifest phase-space duality and the related equivalence postulate of quantum mechanics provide the background independent overarching principles underlying quantum gravity.

APA, Harvard, Vancouver, ISO, and other styles

20

Denisov, L. V. "Infinitely Divisible Markov Mappings in Quantum Probability Theory." Theory of Probability & Its Applications 33, no. 2 (January 1989): 392–95. http://dx.doi.org/10.1137/1133064.

Full text

APA, Harvard, Vancouver, ISO, and other styles

21

Bakery, Awad A., and OM Kalthum S. K. Mohamed. "Kannan Contraction Maps on the Space of Null Variable Exponent Second-Order Quantum Backward Difference Sequences of Fuzzy Functions and Its Pre-Quasi Ideal." Discrete Dynamics in Nature and Society 2022 (August 27, 2022): 1–22. http://dx.doi.org/10.1155/2022/5339667.

Full text

Abstract:

In this paper, we construct and investigate the space of null variable exponent second-order quantum backward difference sequences of fuzzy functions, which are crucial additions to the concept of modular spaces. The idealization of the mappings has been achieved through the use of extended s − fuzzy functions and this sequence space of fuzzy functions. This new space’s topological and geometric properties and the mappings’ ideal that corresponds to them are discussed. We construct the existence of a fixed point of Kannan contraction mapping acting on this space and its associated pre-quasi ideal. To demonstrate our findings, we give a number of numerical experiments. There are also some significant applications of the existence of solutions to nonlinear difference equations of fuzzy functions.

APA, Harvard, Vancouver, ISO, and other styles

22

Bin-Mohsin, Bandar, Muhammad Zakria Javed, Muhammad Uzair Awan, Hüseyin Budak, Hasan Kara, and Muhammad Aslam Noor. "Quantum Integral Inequalities in the Setting of Majorization Theoryand Applications." Symmetry 14, no. 9 (September 14, 2022): 1925. http://dx.doi.org/10.3390/sym14091925.

Full text

Abstract:

In recent years, the theory of convex mappings has gained much more attention due to its massive utility in different fields of mathematics. It has been characterized by different approaches. In 1929, G. H. Hardy, J. E. Littlewood, and G. Polya established another characterization of convex mappings involving an ordering relationship defined over Rn known as majorization theory. Using this theory many inequalities have been obtained in the literature. In this paper, we study Hermite–Hadamard type inequalities using the Jensen–Mercer inequality in the frame of q̣-calculus and majorized l-tuples. Firstly we derive q̣-Hermite–Hadamard–Jensen–Mercer (H.H.J.M) type inequalities with the help of Mercer’s inequality and its weighted form. To obtain some new generalized (H.H.J.M)-type inequalities, we prove a generalized quantum identity for q̣-differentiable mappings. Next, we obtain some estimation-type results; for this purpose, we consider q̣-identity, fundamental inequalities and the convexity property of mappings. Later on, We offer some applications to special means that demonstrate the importance of our main results. With the help of numerical examples, we also check the validity of our main outcomes. Along with this, we present some graphical analyses of our main results so that readers may easily grasp the results of this paper.

APA, Harvard, Vancouver, ISO, and other styles

23

Georgiou, Tryphon T., and Michele Pavon. "Positive contraction mappings for classical and quantum Schrödinger systems." Journal of Mathematical Physics 56, no. 3 (March 2015): 033301. http://dx.doi.org/10.1063/1.4915289.

Full text

APA, Harvard, Vancouver, ISO, and other styles

24

Dias, Nuno Costa, and João Nuno Prata. "Quantum mappings acting by coordinate transformations on Wigner distributions." Revista Matemática Iberoamericana 35, no. 2 (February 5, 2019): 317–37. http://dx.doi.org/10.4171/rmi/1056.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

Nijhoff, F. W., and H. W. Capel. "Integrable quantum mappings and non-ultralocal Yang-Baxter structures." Physics Letters A 163, no. 1-2 (March 1992): 49–56. http://dx.doi.org/10.1016/0375-9601(92)90159-j.

Full text

APA, Harvard, Vancouver, ISO, and other styles

26

Busch, Paul, and Pekka J. Lahti. "Completely positive mappings in quantum dynamics and measurement theory." Foundations of Physics 20, no. 12 (December 1990): 1429–39. http://dx.doi.org/10.1007/bf01883516.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Hadfield, Stuart, Zhihui Wang, Bryan O'Gorman, Eleanor Rieffel, Davide Venturelli, and Rupak Biswas. "From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz." Algorithms 12, no. 2 (February 12, 2019): 34. http://dx.doi.org/10.3390/a12020034.

Full text

Abstract:

The next few years will be exciting as prototype universal quantum processors emerge, enabling the implementation of a wider variety of algorithms. Of particular interest are quantum heuristics, which require experimentation on quantum hardware for their evaluation and which have the potential to significantly expand the breadth of applications for which quantum computers have an established advantage. A leading candidate is Farhi et al.’s quantum approximate optimization algorithm, which alternates between applying a cost function based Hamiltonian and a mixing Hamiltonian. Here, we extend this framework to allow alternation between more general families of operators. The essence of this extension, the quantum alternating operator ansatz, is the consideration of general parameterized families of unitaries rather than only those corresponding to the time evolution under a fixed local Hamiltonian for a time specified by the parameter. This ansatz supports the representation of a larger, and potentially more useful, set of states than the original formulation, with potential long-term impact on a broad array of application areas. For cases that call for mixing only within a desired subspace, refocusing on unitaries rather than Hamiltonians enables more efficiently implementable mixers than was possible in the original framework. Such mixers are particularly useful for optimization problems with hard constraints that must always be satisfied, defining a feasible subspace, and soft constraints whose violation we wish to minimize. More efficient implementation enables earlier experimental exploration of an alternating operator approach, in the spirit of the quantum approximate optimization algorithm, to a wide variety of approximate optimization, exact optimization, and sampling problems. In addition to introducing the quantum alternating operator ansatz, we lay out design criteria for mixing operators, detail mappings for eight problems, and provide a compendium with brief descriptions of mappings for a diverse array of problems.

APA, Harvard, Vancouver, ISO, and other styles

28

Wang, Dong-Sheng. "Convex decomposition of dimension-altering quantum channels." International Journal of Quantum Information 14, no. 08 (December 2016): 1650045. http://dx.doi.org/10.1142/s0219749916500453.

Full text

Abstract:

Quantum channels, which are completely positive and trace preserving mappings, can alter the dimension of a system, e.g. a quantum channel from a qubit to a qutrit. We study the convex set properties of dimension-altering quantum channels, and particularly the channel decomposition problem in terms of convex sum of extreme channels. We provide various quantum circuit representations of extreme and generalized extreme channels, which can be employed in an optimization to approximately decompose an arbitrary channel. Numerical simulations of low-dimensional channels are performed to demonstrate our channel decomposition scheme.

APA, Harvard, Vancouver, ISO, and other styles

29

Cataldi, Giovanni, Ashkan Abedi, Giuseppe Magnifico, Simone Notarnicola, Nicola Dalla Pozza, Vittorio Giovannetti, and Simone Montangero. "Hilbert curve vs Hilbert space: exploiting fractal 2D covering to increase tensor network efficiency." Quantum 5 (September 29, 2021): 556. http://dx.doi.org/10.22331/q-2021-09-29-556.

Full text

Abstract:

We present a novel mapping for studying 2D many-body quantum systems by solving an effective, one-dimensional long-range model in place of the original two-dimensional short-range one. In particular, we address the problem of choosing an efficient mapping from the 2D lattice to a 1D chain that optimally preserves the locality of interactions within the TN structure. By using Matrix Product States (MPS) and Tree Tensor Network (TTN) algorithms, we compute the ground state of the 2D quantum Ising model in transverse field with lattice size up to 64×64, comparing the results obtained from different mappings based on two space-filling curves, the snake curve and the Hilbert curve. We show that the locality-preserving properties of the Hilbert curve leads to a clear improvement of numerical precision, especially for large sizes, and turns out to provide the best performances for the simulation of 2D lattice systems via 1D TN structures.

APA, Harvard, Vancouver, ISO, and other styles

30

Khan, Khuram Ali, Allah Ditta, Ammara Nosheen, Khalid Mahmood Awan, and Rostin Matendo Mabela. "Ostrowski Type Inequalities for s -Convex Functions via q -Integrals." Journal of Function Spaces 2022 (January 20, 2022): 1–8. http://dx.doi.org/10.1155/2022/8063803.

Full text

Abstract:

The new outcomes of the present paper are q -analogues ( q stands for quantum calculus) of Hermite-Hadamard type inequality, Montgomery identity, and Ostrowski type inequalities for s -convex mappings. Some new bounds of Ostrowski type functionals are obtained by using Hölder, Minkowski, and power mean inequalities via quantum calculus. Special cases of new results include existing results from the literature.

APA, Harvard, Vancouver, ISO, and other styles

31

Cassinelli, Gianni, and Pekka J. Lahti. "Spectral properties of observables and convex mappings in quantum mechanics." Journal of Mathematical Physics 34, no. 12 (December 1993): 5468–75. http://dx.doi.org/10.1063/1.530316.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Maupin, Oliver G., Andrew D. Baczewski, Peter J. Love, and Andrew J. Landahl. "Variational Quantum Chemistry Programs in JaqalPaq." Entropy 23, no. 6 (May 24, 2021): 657. http://dx.doi.org/10.3390/e23060657.

Full text

Abstract:

We present example quantum chemistry programs written with JaqalPaq, a python meta-programming language used to code in Jaqal (Just Another Quantum Assembly Language). These JaqalPaq algorithms are intended to be run on the Quantum Scientific Computing Open User Testbed (QSCOUT) platform at Sandia National Laboratories. Our exemplars use the variational quantum eigensolver (VQE) quantum algorithm to compute the ground state energies of the H2, HeH+, and LiH molecules. Since the exemplars focus on how to program in JaqalPaq, the calculations of the second-quantized Hamiltonians are performed with the PySCF python package, and the mappings of the fermions to qubits are obtained from the OpenFermion python package. Using the emulator functionality of JaqalPaq, we emulate how these exemplars would be executed on an error-free QSCOUT platform and compare the emulated computation of the bond-dissociation curves for these molecules with their exact forms within the relevant basis.

APA, Harvard, Vancouver, ISO, and other styles

33

Hansen, F. "Characterizations of symmetric monotone metrics on the state space of quantum systems." Quantum Information and Computation 6, no. 7 (November 2006): 597–605. http://dx.doi.org/10.26421/qic6.7-3.

Full text

Abstract:

The quantum Fisher information is a Riemannian metric, defined on the state space of a quantum system, which is symmetric and decreasing under stochastic mappings. Contrary to the classical case such a metric is not unique. We complete the characterization, initiated by Morozova, Chentsov and Petz, of these metrics by providing a closed and tractable formula for the set of Morozova-Chentsov functions. In addition, we provide a continuously increasing bridge between the smallest and largest symmetric monotone metrics.

APA, Harvard, Vancouver, ISO, and other styles

34

Awan, Muhammad Uzair, Sadia Talib, Artion Kashuri, Ibrahim Slimane, Kamsing Nonlaopon, and Y. S. Hamed. "Some new (p, q)-Dragomir–Agarwal and Iyengar type integral inequalities and their applications." AIMS Mathematics 7, no. 4 (2022): 5728–51. http://dx.doi.org/10.3934/math.2022317.

Full text

Abstract:

<abstract><p>The main objective of this paper is to derive some new post quantum analogues of Dragomir–Agarwal and Iyengar type integral inequalities essentially by using the strongly $ \varphi $-preinvexity and strongly quasi $ \varphi $-preinvexity properties of the mappings, respectively. We also discuss several new special cases which show that the results obtained are quite unifying. In order to illustrate the efficiency of our main results, some applications regarding $ ({\mathrm{p}}, {\mathrm{q}}) $-differentiable mappings that are in absolute value bounded are given.</p></abstract>

APA, Harvard, Vancouver, ISO, and other styles

35

SANCHEZ, N. "GENERALIZED ANALYTIC MAPPINGS AND FLAT-SPACE MODELS OF HAWKING RADIATION." International Journal of Modern Physics A 03, no. 05 (May 1988): 1123–46. http://dx.doi.org/10.1142/s0217751x88000485.

Full text

Abstract:

We generalize the approach to Q.F.T. in accelerated frames based on analytic mappings in a way which stresses further the comparison between the flat and curved space-time situations. Combined linear acceleration with uniform and nonuniform translations or rotations, and nonanalytic but asymptotically analytic mappings are included. A density matrix formulation is given for quantum states at global and asymptotic thermal equilibrium, and the role of the PCT symmetry is discussed. Flat space models of rotating and charged black holes are investigated, together with their surface gravity, chemical potentials, Hawking radiation and superradiance properties.

APA, Harvard, Vancouver, ISO, and other styles

36

BARRY, J. H., J. D. COHEN, and M. W. MEISEL. "EXACT SOLUTIONS IN A SPATIALLY ANISOTROPIC QUANTUM SPIN LADDER MODEL HAVING TWO- AND FOUR-SPIN EXCHANGE INTERACTIONS." International Journal of Modern Physics B 23, no. 08 (March 30, 2009): 1981–2019. http://dx.doi.org/10.1142/s0217979209052236.

Full text

Abstract:

We consider a two-leg S=1/2 quantum spin ladder model with two-spin (intra-rung) and four-spin (inter-rung) Heisenberg exchange interactions and a uniform magnetic field. Exact mappings are derived connecting the partition function and correlations in the three-parameter quantum model to those known in a two-parameter Ising chain. The quantum phase diagram of the ladder magnet is determined. Static correlations provide pertinent correlation lengths and underlie spatial fluctuation behaviors at arbitrary temperatures, including quantum fluctuations at absolute zero. Dynamic correlations in zero field are used to obtain an exact solution for the inelastic neutron scattering function Sxx(q, ω) at all temperatures, explicitly yielding the elementary excitation spectrum.

APA, Harvard, Vancouver, ISO, and other styles

37

Pietrzkowski, Gabriel. "On the Tensor Convolution and the Quantum Separability Problem." Open Systems & Information Dynamics 17, no. 04 (December 2010): 331–46. http://dx.doi.org/10.1142/s1230161210000217.

Full text

Abstract:

We consider the problem of separability: decide whether a Hermitian operator on a finite dimensional Hilbert tensor product [Formula: see text] is separable or entangled. We show that the tensor convolution [Formula: see text] defined for mappings [Formula: see text] on an almost arbitrary locally compact abelian group G , gives rise to formulation of an equivalent problem to the separability one.

APA, Harvard, Vancouver, ISO, and other styles

38

Steudtner, Mark, and Stephanie Wehner. "Fermion-to-qubit mappings with varying resource requirements for quantum simulation." New Journal of Physics 20, no. 6 (June 7, 2018): 063010. http://dx.doi.org/10.1088/1367-2630/aac54f.

Full text

APA, Harvard, Vancouver, ISO, and other styles

39

Arponen, Jouko S. "Independent-cluster methods as mappings of quantum theory into classical mechanics." Theoretica Chimica Acta 80, no. 2-3 (1991): 149–79. http://dx.doi.org/10.1007/bf01119618.

Full text

APA, Harvard, Vancouver, ISO, and other styles

40

Müller-Bahns, Michael F., and Nikolai Neumaier. "Some remarks on -invariant Fedosov star products and quantum momentum mappings." Journal of Geometry and Physics 50, no. 1-4 (April 2004): 257–72. http://dx.doi.org/10.1016/j.geomphys.2003.10.003.

Full text

APA, Harvard, Vancouver, ISO, and other styles

41

Pantzas, Konstantinos, Grégoire Beaudoin, Gilles Patriarche, Ludovic Largeau, Olivia Mauguin, Giulia Pegolotti, Angela Vasanelli, et al. "Sub-nanometrically resolved chemical mappings of quantum-cascade laser active regions." Semiconductor Science and Technology 31, no. 5 (April 5, 2016): 055017. http://dx.doi.org/10.1088/0268-1242/31/5/055017.

Full text

APA, Harvard, Vancouver, ISO, and other styles

42

Woods, M. P., R. Groux, A. W. Chin, S. F. Huelga, and M. B. Plenio. "Mappings of open quantum systems onto chain representations and Markovian embeddings." Journal of Mathematical Physics 55, no. 3 (March 2014): 032101. http://dx.doi.org/10.1063/1.4866769.

Full text

APA, Harvard, Vancouver, ISO, and other styles

43

M�ller-Bahns, Michael F., and Nikolai Neumaier. "Invariant Star Products of Wick Type: Classification and Quantum Momentum Mappings." Letters in Mathematical Physics 70, no. 1 (October 2004): 1–15. http://dx.doi.org/10.1007/s11005-004-0614-x.

Full text

APA, Harvard, Vancouver, ISO, and other styles

44

Xue, Shichuan, Yizhi Wang, Yong Liu, Weixu Shi, and Junjie Wu. "Variational Quantum Process Tomography of Non-Unitaries." Entropy 25, no. 1 (January 1, 2023): 90. http://dx.doi.org/10.3390/e25010090.

Full text

Abstract:

Quantum process tomography is a fundamental and critical benchmarking and certification tool that is capable of fully characterizing an unknown quantum process. Standard quantum process tomography suffers from an exponentially scaling number of measurements and complicated data post-processing due to the curse of dimensionality. On the other hand, non-unitary operators are more realistic cases. In this work, we put forward a variational quantum process tomography method based on the supervised quantum machine learning framework. It approximates the unknown non-unitary quantum process utilizing a relatively shallow depth parametric quantum circuit and fewer input states. Numerically, we verified our method by reconstructing the non-unitary quantum mappings up to eight qubits in two cases: the weighted sum of the randomly generated quantum circuits and the imaginary time evolution of the Heisenberg XXZ spin chain Hamiltonian. Results show that those quantum processes could be reconstructed with high fidelities (>99%) and shallow depth parametric quantum circuits (d≤8), while the number of input states required is at least two orders of magnitude less than the demands of the standard quantum process tomography. Our work shows the potential of the variational quantum process tomography method in characterizing non-unitary operators.

APA, Harvard, Vancouver, ISO, and other styles

45

Sabín, Carlos. "Digital Quantum Simulation of Linear and Nonlinear Optical Elements." Quantum Reports 2, no. 1 (March 4, 2020): 208–20. http://dx.doi.org/10.3390/quantum2010013.

Full text

Abstract:

We provide a recipe for the digitalization of linear and nonlinear quantum optics in networks of superconducting qubits. By combining digital techniques with boson-qubit mappings, we address relevant problems that are typically considered in analog simulators, such as the dynamical Casimir effect or molecular force fields, including nonlinearities. In this way, the benefits of digitalization are extended in principle to a new realm of physical problems. We present preliminary examples launched in IBM Q 5 Tenerife.

APA, Harvard, Vancouver, ISO, and other styles

46

Letia, Tiberiu Stefan, Elenita Maria Durla-Pasca, Dahlia Al-Janabi, and Octavian Petru Cuibus. "Development of Evolutionary Systems Based on Quantum Petri Nets." Mathematics 10, no. 23 (November 22, 2022): 4404. http://dx.doi.org/10.3390/math10234404.

Full text

Abstract:

Evolutionary systems (ES) include software applications that solve problems using heuristic methods instead of the deterministic ones. The classical computing used for ES development involves random methods to improve different kinds of genomes. The mappings of these genomes lead to individuals that correspond to the searched solutions. The individual evaluations by simulations serve for the improvement of their genotypes. Quantum computations, unlike the classical computations, can describe and simulate a large set of individuals simultaneously. This feature is used to diminish the time for finding the solutions. Quantum Petri Nets (QPNs) can model dynamical systems with probabilistic features that make them appropriate for the development of ES. Some examples of ES applications using the QPNs are given to show the benefits of the current approach. The current research solves quantum evolutionary problems using quantum genetic algorithms conceived and improved based on QPN. They were tested on a dynamic system using a Quantum Discrete Controlled Walker (QDCW).

APA, Harvard, Vancouver, ISO, and other styles

47

Hübener, R., M. Van den Nest, W. Dür, and H. J. Briegel. "Classical spin systems and the quantum stabilizer formalism: General mappings and applications." Journal of Mathematical Physics 50, no. 8 (August 2009): 083303. http://dx.doi.org/10.1063/1.3190486.

Full text

APA, Harvard, Vancouver, ISO, and other styles

48

SCHÜRMANN, MICHAEL. "OPERATOR PROCESSES MAJORIZING THEIR QUADRATIC VARIATION." Infinite Dimensional Analysis, Quantum Probability and Related Topics 03, no. 01 (March 2000): 99–120. http://dx.doi.org/10.1142/s0219025700000066.

Full text

Abstract:

We give a full classification of convolution semigroups of completely positive mappings on Hopf algebras. Using the theory of noncommutative Lévy processes, we prove that these convolution semigroups are solutions of Hudson–Parthasarathy quantum stochastic differential equations. The generating process satisfies a positivity condition on the kernel of the counit which is stronger than complete positivity. It majorizes its bracket process which is the noncommutative process given by the quadratic variation. Our work generalizes and improves parts of the theory of M. Fannes and J. Quaegebeur on infinitely divisible completely positive mappings on groups. It is shown that Azéma martingales in the sense of M. Emery arise as components of convolution semigroups on the q-version of the noncommutative polynomial algebra.

APA, Harvard, Vancouver, ISO, and other styles

49

Nys, Jannes, and Giuseppe Carleo. "Variational solutions to fermion-to-qubit mappings in two spatial dimensions." Quantum 6 (October 13, 2022): 833. http://dx.doi.org/10.22331/q-2022-10-13-833.

Full text

Abstract:

Through the introduction of auxiliary fermions, or an enlarged spin space, one can map local fermion Hamiltonians onto local spin Hamiltonians, at the expense of introducing a set of additional constraints. We present a variational Monte-Carlo framework to study fermionic systems through higher-dimensional (>1D) Jordan-Wigner transformations. We provide exact solutions to the parity and Gauss-law constraints that are encountered in bosonization procedures. We study the t-V model in 2D and demonstrate how both the ground state and the low-energy excitation spectra can be retrieved in combination with neural network quantum state ansatze.

APA, Harvard, Vancouver, ISO, and other styles

50

Bishop, R. F., and A. Vourdas. "Displaced and squeezed parity operator: Its role in classical mappings of quantum theories." Physical Review A 50, no. 6 (December 1, 1994): 4488–501. http://dx.doi.org/10.1103/physreva.50.4488.

Full text

APA, Harvard, Vancouver, ISO, and other styles

Journal articles on the topic 'Quantum mappings'

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles