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Journal articles on the topic 'Quantum embedding'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

ASSELMEYER-MALUGA, TORSTEN, and JERZY KRÓL. "QUANTUM GEOMETRY AND WILD EMBEDDINGS AS QUANTUM STATES." International Journal of Geometric Methods in Modern Physics 10, no. 10 (October 8, 2013): 1350055. http://dx.doi.org/10.1142/s0219887813500552.

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In this paper, we discuss wild embeddings like Alexanders horned ball and relate them to fractal spaces. We build a C*-algebra corresponding to a wild embedding. We argue that a wild embedding is the result of a quantization process applied to a tame embedding. Therefore, quantum states are directly the wild embeddings. Then we give an example of a wild embedding in the four-dimensional spacetime. We discuss the consequences for cosmology.

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2

Sun, Qiming, and Garnet Kin-Lic Chan. "Quantum Embedding Theories." Accounts of Chemical Research 49, no. 12 (November 7, 2016): 2705–12. http://dx.doi.org/10.1021/acs.accounts.6b00356.

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3

Abbott, Alastair A., Cristian S. Calude, Michael J. Dinneen, and Richard Hua. "A hybrid quantum-classical paradigm to mitigate embedding costs in quantum annealing." International Journal of Quantum Information 17, no. 05 (August 2019): 1950042. http://dx.doi.org/10.1142/s0219749919500424.

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Despite rapid recent progress towards the development of quantum computers capable of providing computational advantages over classical computers, it seems likely that such computers will, initially at least, be required to run in a hybrid quantum-classical regime. This realization has led to interest in hybrid quantum-classical algorithms allowing, for example, quantum computers to solve large problems despite having very limited numbers of qubits. Here we propose a hybrid paradigm for quantum annealers with the goal of mitigating a different limitation of such devices: the need to embed problem instances within the (often highly restricted) connectivity graph of the annealer. This embedding process can be costly to perform and may destroy any computational speedup. In order to solve many practical problems, it is moreover necessary to perform many, often related, such embeddings. We will show how, for such problems, a raw speedup that is negated by the embedding time can nonetheless be exploited to give a real speedup. As a proof-of-concept example we present an in-depth case study of a simple problem based on the maximum-weight independent set problem. Although we do not observe a quantum speedup experimentally, the advantage of the hybrid approach is robustly verified, showing how a potential quantum speedup may be exploited and encouraging further efforts to apply the approach to problems of more practical interest.

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4

Knizia, Gerald, and Garnet Kin-Lic Chan. "Density Matrix Embedding: A Strong-Coupling Quantum Embedding Theory." Journal of Chemical Theory and Computation 9, no. 3 (February 21, 2013): 1428–32. http://dx.doi.org/10.1021/ct301044e.

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5

Emms, D., R. Wilson, and E. Hancock. "Graph embedding using quantum hitting time." Quantum Information and Computation 9, no. 3&4 (March 2009): 231–54. http://dx.doi.org/10.26421/qic9.3-4-4.

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In this paper, we explore analytically and experimentally a quasi-quantum analogue of the hitting time of the continuous-time quantum walk on a graph. For the classical random walk, the hitting time has been shown to be robust to errors in edge weight structure and to lead to spectral clustering algorithms with improved performance. Our analysis shows that the quasi-quantum analogue of the hitting time of the continuous-time quantum walk can be determined via integrals of the Laplacian spectrum, calculated using Gauss-Laguerre quadrature. We analyse the quantum hitting times with reference to their classical counterpart. Specifically, we explore the graph embeddings that preserve hitting time. Experimentally, we show that the quantum hitting times can be used to emphasise cluster-structure.

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6

FROHMAN, CHARLES, and JOANNA KANIA-BARTOSZYŃSKA. "A quantum obstruction to embedding." Mathematical Proceedings of the Cambridge Philosophical Society 131, no. 2 (September 2001): 279–93. http://dx.doi.org/10.1017/s0305004101005230.

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7

Li, Panchi, and Xiande Liu. "A novel quantum steganography scheme for color images." International Journal of Quantum Information 16, no. 02 (March 2018): 1850020. http://dx.doi.org/10.1142/s021974991850020x.

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In quantum image steganography, embedding capacity and security are two important issues. This paper presents a novel quantum steganography scheme using color images as cover images. First, the secret information is divided into 3-bit segments, and then each 3-bit segment is embedded into the LSB of one color pixel in the cover image according to its own value and using Gray code mapping rules. Extraction is the inverse of embedding. We designed the quantum circuits that implement the embedding and extracting process. The simulation results on a classical computer show that the proposed scheme outperforms several other existing schemes in terms of embedding capacity and security.

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8

Huang, Chen, Michele Pavone, and Emily A. Carter. "Quantum mechanical embedding theory based on a unique embedding potential." Journal of Chemical Physics 134, no. 15 (April 21, 2011): 154110. http://dx.doi.org/10.1063/1.3577516.

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9

MÜGER, MICHAEL, and LARS TUSET. "MONOIDS, EMBEDDING FUNCTORS AND QUANTUM GROUPS." International Journal of Mathematics 19, no. 01 (January 2008): 93–123. http://dx.doi.org/10.1142/s0129167x08004558.

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We show that the left regular representation πl of a discrete quantum group (A, Δ) has the absorbing property and forms a monoid [Formula: see text] in the representation category Rep (A, Δ). Next we show that an absorbing monoid in an abstract tensor *-category [Formula: see text] gives rise to an embedding functor (or fiber functor) [Formula: see text], and we identify conditions on the monoid, satisfied by [Formula: see text], implying that E is *-preserving. As is well-known, from an embedding functor [Formula: see text] the generalized Tannaka theorem produces a discrete quantum group (A, Δ) such that [Formula: see text]. Thus, for a C*-tensor category [Formula: see text] with conjugates and irreducible unit the following are equivalent: (1) [Formula: see text] is equivalent to the representation category of a discrete quantum group (A, Δ), (2) [Formula: see text] admits an absorbing monoid, (3) there exists a *-preserving embedding functor [Formula: see text].

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10

Liu, Hanqing, and Shailesh Chandrasekharan. "Qubit Regularization and Qubit Embedding Algebras." Symmetry 14, no. 2 (February 2, 2022): 305. http://dx.doi.org/10.3390/sym14020305.

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Qubit regularization is a procedure to regularize the infinite dimensional local Hilbert space of bosonic fields to a finite dimensional one, which is a crucial step when trying to simulate lattice quantum field theories on a quantum computer. When the qubit-regularized lattice quantum fields preserve important symmetries of the original theory, qubit regularization naturally enforces certain algebraic structures on these quantum fields. We introduce the concept of qubit embedding algebras (QEAs) to characterize this algebraic structure associated with a qubit regularization scheme. We show a systematic procedure to derive QEAs for the O(N) lattice spin models and the SU(N) lattice gauge theories. While some of the QEAs we find were discovered earlier in the context of the D-theory approach, our method shows that QEAs are far richer. A more complete understanding of the QEAs could be helpful in recovering the fixed points of the desired quantum field theories.

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11

Vancliff, Michaela, and Kristel Van Rompay. "Embedding a Quantum Nonsingular Quadric in a Quantum P3." Journal of Algebra 195, no. 1 (September 1997): 93–129. http://dx.doi.org/10.1006/jabr.1997.7077.

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12

Crampin, S., M. Nekovee, and J. E. Inglesfield. "Embedding method for confined quantum systems." Physical Review B 51, no. 11 (March 15, 1995): 7318–20. http://dx.doi.org/10.1103/physrevb.51.7318.

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13

ISIDRO, JOSÉ M. "QUANTUM MECHANICS IN INFINITE SYMPLECTIC VOLUME." Modern Physics Letters A 19, no. 05 (February 20, 2004): 349–55. http://dx.doi.org/10.1142/s0217732304013118.

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We quantise complex, infinite-dimensional projective space CP(ℋ). We apply the result to quantise a complex, finite-dimensional, classical phase space [Formula: see text] whose symplectic volume is infinite, by holomorphically embedding it into CP(ℋ). The embedding is univocally determined by requiring it to be an isometry between the Bergman metric on [Formula: see text] and the Fubini–Study metric on CP(ℋ). Then the Hilbert-space bundle over [Formula: see text] is the pullback, by the embedding, of the Hilbert-space bundle over CP(ℋ).

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14

Beetle, C., J. S. Engle, M. E. Hogan, and P. Mendonça. "Quantum isotropy and the reduction of dynamics in Bianchi I." Classical and Quantum Gravity 38, no. 24 (November 22, 2021): 245001. http://dx.doi.org/10.1088/1361-6382/ac337c.

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Abstract The authors previously introduced a diffeomorphism-invariant definition of a homogeneous and isotropic sector of loop quantum gravity (LQG), along with a program to embed loop quantum cosmology (LQC) into it. The present paper works out that program in detail for the simpler, but still physically non-trivial, case where the target of the embedding is the homogeneous, but not isotropic, Bianchi I model. The diffeomorphism-invariant conditions imposing homogeneity and isotropy in the full theory reduce to conditions imposing isotropy on an already homogeneous Bianchi I spacetime. The reduced conditions are invariant under the residual diffeomorphisms still allowed after gauge fixing the Bianchi I model. We show that there is a unique embedding of the quantum isotropic model into the homogeneous quantum Bianchi I model that (a) is covariant with respect to the actions of such residual diffeomorphisms, and (b) intertwines both the (signed) volume operator and at least one directional Hubble rate. That embedding also intertwines all other operators of interest in the respective loop quantum cosmological models, including their Hamiltonian constraints. It thus establishes a precise equivalence between dynamics in the isotropic sector of the Bianchi I model and the quantized isotropic model, and not just their kinematics. We also discuss the adjoint relationship between the embedding map defined here and a projection map previously defined by Ashtekar and Wilson-Ewing. Finally, we highlight certain features that simplify this reduced embedding problem, but which may not have direct analogues in the embedding of homogeneous and isotropic LQC into full LQG.

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15

Vyskocil, Tomas, and Hristo Djidjev. "Embedding Equality Constraints of Optimization Problems into a Quantum Annealer." Algorithms 12, no. 4 (April 17, 2019): 77. http://dx.doi.org/10.3390/a12040077.

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Quantum annealers such as D-Wave machines are designed to propose solutions for quadratic unconstrained binary optimization (QUBO) problems by mapping them onto the quantum processing unit, which tries to find a solution by measuring the parameters of a minimum-energy state of the quantum system. While many NP-hard problems can be easily formulated as binary quadratic optimization problems, such formulations almost always contain one or more constraints, which are not allowed in a QUBO. Embedding such constraints as quadratic penalties is the standard approach for addressing this issue, but it has drawbacks such as the introduction of large coefficients and using too many additional qubits. In this paper, we propose an alternative approach for implementing constraints based on a combinatorial design and solving mixed-integer linear programming (MILP) problems in order to find better embeddings of constraints of the type ∑ x i = k for binary variables x i. Our approach is scalable to any number of variables and uses a linear number of ancillary variables for a fixed k.

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16

Vorwerk, Christian, Nan Sheng, Marco Govoni, Benchen Huang, and Giulia Galli. "Quantum embedding theories to simulate condensed systems on quantum computers." Nature Computational Science 2, no. 7 (July 2022): 424–32. http://dx.doi.org/10.1038/s43588-022-00279-0.

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17

Shelton, Brad, and Michaela Vancliff. "Embedding a quantum rank three quadric in a quantum P3." Communications in Algebra 27, no. 6 (January 1999): 2877–904. http://dx.doi.org/10.1080/00927879908826599.

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18

Kim, Jonathan, and Stefan Bekiranov. "Generalization Performance of Quantum Metric Learning Classifiers." Biomolecules 12, no. 11 (October 27, 2022): 1576. http://dx.doi.org/10.3390/biom12111576.

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Quantum computing holds great promise for a number of fields including biology and medicine. A major application in which quantum computers could yield advantage is machine learning, especially kernel-based approaches. A recent method termed quantum metric learning, in which a quantum embedding which maximally separates data into classes is learned, was able to perfectly separate ant and bee image training data. The separation is achieved with an intrinsically quantum objective function and the overall approach was shown to work naturally as a hybrid classical-quantum computation enabling embedding of high dimensional feature data into a small number of qubits. However, the ability of the trained classifier to predict test sample data was never assessed. We assessed the performance of quantum metric learning on test ants and bees image data as well as breast cancer clinical data. We applied the original approach as well as variants in which we performed principal component analysis (PCA) on the feature data to reduce its dimensionality for quantum embedding, thereby limiting the number of model parameters. If the degree of dimensionality reduction was limited and the number of model parameters was constrained to be far less than the number of training samples, we found that quantum metric learning was able to accurately classify test data.

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19

Zhou, RiGui, YouDe Cheng, Hou Ian, and XingAo Liu. "Quantum watermarking algorithm based on chaotic affine scrambling." International Journal of Quantum Information 17, no. 04 (June 2019): 1950038. http://dx.doi.org/10.1142/s0219749919500382.

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In order to improve the security of watermark image, a scheme of quantum watermarking algorithm which is based on chaotic affine scrambling is proposed and it includes scrambling, embedding and extracting procedures. In the embedding process, the position and the color of the watermark image are scrambled by chaotic affine and the size of the scrambled watermark image is extended from [Formula: see text] to [Formula: see text]. Meanwhile, the color value of the pixel is changed from 24-bits to 3-[Formula: see text](1-bit per channel) bits. The extended watermark image is embedded into the carrier image through a two-bit embedding strategy, and the extraction process is the inverse one of the embedding process. The simulation results show that the proposed scheme is superior to the comparison scheme in terms of visual quality, peak signal-to-noise ratio (PSNR).

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20

Garola, Claudio. "Embedding Quantum Mechanics into an Objective Framework." Foundations of Physics Letters 16, no. 6 (December 2003): 605–12. http://dx.doi.org/10.1023/b:fopl.0000012786.53840.37.

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21

Dzhafarov, Ehtibar N., and Janne V. Kujala. "Embedding Quantum into Classical: Contextualization vs Conditionalization." PLoS ONE 9, no. 3 (March 28, 2014): e92818. http://dx.doi.org/10.1371/journal.pone.0092818.

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22

Engle, Jonathan. "Embedding loop quantum cosmology without piecewise linearity." Classical and Quantum Gravity 30, no. 8 (March 19, 2013): 085001. http://dx.doi.org/10.1088/0264-9381/30/8/085001.

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23

Lagraa, M. "The quantum spheres and their embedding into quantum Minkowski space-time." Journal of Applied Mathematics 2, no. 7 (2002): 315–35. http://dx.doi.org/10.1155/s1110757x0211103x.

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We recast the Podleś spheres in the noncommutative physics context by showing that they can be regarded as slices along the time coordinate of the different regions of the quantum Minkowski space-time. The investigation of the transformations of the quantum sphere states under the left coaction of theSOq(3)group leads to a decomposition of the transformed Hilbert space states in terms of orthogonal subspaces exhibiting the periodicity of the quantum sphere states.

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24

Min-Allah, Nasro, Naya Nagy, Malak Aljabri, Mariam Alkharraa, Mashael Alqahtani, Dana Alghamdi, Razan Sabri, and Rana Alshaikh. "Quantum Image Steganography Schemes for Data Hiding: A Survey." Applied Sciences 12, no. 20 (October 13, 2022): 10294. http://dx.doi.org/10.3390/app122010294.

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Quantum steganography plays a critical role in embedding confidential data into carrier messages using quantum computing schemes. The quantum variant of steganography outperforms its classical counterpart from security, embedding efficiency and capacity, imperceptibility, and time-complexity perspectives. Considerable work has been carried out in the literature focusing on quantum steganography. However, a holistic view of available schemes is missing. This paper provides an overview of latest advances in the field of quantum-steganography and image-steganography schemes. Moreover, the paper includes discussion of improvements made in the aforementioned fields, a brief explanation of the methodologies used for each presented algorithm, and a comparative study of existing schemes.

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25

Yu, Kuang, and Emily A. Carter. "Extending density functional embedding theory for covalently bonded systems." Proceedings of the National Academy of Sciences 114, no. 51 (December 4, 2017): E10861—E10870. http://dx.doi.org/10.1073/pnas.1712611114.

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Quantum embedding theory aims to provide an efficient solution to obtain accurate electronic energies for systems too large for full-scale, high-level quantum calculations. It adopts a hierarchical approach that divides the total system into a small embedded region and a larger environment, using different levels of theory to describe each part. Previously, we developed a density-based quantum embedding theory called density functional embedding theory (DFET), which achieved considerable success in metals and semiconductors. In this work, we extend DFET into a density-matrix–based nonlocal form, enabling DFET to study the stronger quantum couplings between covalently bonded subsystems. We name this theory density-matrix functional embedding theory (DMFET), and we demonstrate its performance in several test examples that resemble various real applications in both chemistry and biochemistry. DMFET gives excellent results in all cases tested thus far, including predicting isomerization energies, proton transfer energies, and highest occupied molecular orbital–lowest unoccupied molecular orbital gaps for local chromophores. Here, we show that DMFET systematically improves the quality of the results compared with the widely used state-of-the-art methods, such as the simple capped cluster model or the widely used ONIOM method.

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26

Joseph, I., Y. Shi, M. D. Porter, A. R. Castelli, V. I. Geyko, F. R. Graziani, S. B. Libby, and J. L. DuBois. "Quantum computing for fusion energy science applications." Physics of Plasmas 30, no. 1 (January 2023): 010501. http://dx.doi.org/10.1063/5.0123765.

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This is a review of recent research exploring and extending present-day quantum computing capabilities for fusion energy science applications. We begin with a brief tutorial on both ideal and open quantum dynamics, universal quantum computation, and quantum algorithms. Then, we explore the topic of using quantum computers to simulate both linear and nonlinear dynamics in greater detail. Because quantum computers can only efficiently perform linear operations on the quantum state, it is challenging to perform nonlinear operations that are generically required to describe the nonlinear differential equations of interest. In this work, we extend previous results on embedding nonlinear systems within linear systems by explicitly deriving the connection between the Koopman evolution operator, the Perron–Frobenius evolution operator, and the Koopman–von Neumann evolution (KvN) operator. We also explicitly derive the connection between the Koopman and Carleman approaches to embedding. Extension of the KvN framework to the complex-analytic setting relevant to Carleman embedding, and the proof that different choices of complex analytic reproducing kernel Hilbert spaces depend on the choice of Hilbert space metric are covered in the appendixes. Finally, we conclude with a review of recent quantum hardware implementations of algorithms on present-day quantum hardware platforms that may one day be accelerated through Hamiltonian simulation. We discuss the simulation of toy models of wave–particle interactions through the simulation of quantum maps and of wave–wave interactions important in nonlinear plasma dynamics.

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27

Pintus, Alberto M., Andrea Gabrieli, Federico G. Pazzona, Giovanni Pireddu, and Pierfranco Demontis. "Molecular QCA embedding in microporous materials." Physical Chemistry Chemical Physics 21, no. 15 (2019): 7879–84. http://dx.doi.org/10.1039/c9cp00832b.

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We propose an environment for information encoding and transmission via a nanoconfined molecular Quantum Dot Cellular Automata (QCA) wire, composed of a single row of head-to-tail interacting 2-dots molecular switches.

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28

Takeuchi, Mitsuhiro. "Quantum orthogonal and symplectic groups and their embedding into quantum $GL$." Proceedings of the Japan Academy, Series A, Mathematical Sciences 65, no. 2 (1989): 55–58. http://dx.doi.org/10.3792/pjaa.65.55.

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29

ASSELMEYER-MALUGA, TORSTEN, and JERZY KRÓL. "DECOHERENCE IN QUANTUM COSMOLOGY AND THE COSMOLOGICAL CONSTANT." Modern Physics Letters A 28, no. 34 (October 17, 2013): 1350158. http://dx.doi.org/10.1142/s0217732313501587.

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We discuss a spacetime having the topology of S3×ℝ but with a different smoothness structure. The initial state of the cosmos in our model is identified with a wildly embedded 3-sphere (or a fractal space). In previous work we showed that a wild embedding is obtained by a quantization of a usual (or tame) embedding. Then a wild embedding can be identified with a (geometrical) quantum state. During a decoherence process this wild 3-sphere is changed to a homology 3-sphere. We are able to calculate the decoherence time for this process. After the formation of the homology 3-sphere, we obtain a spacetime with an accelerated expansion enforced by a cosmological constant. The calculation of this cosmological constant gives a qualitative agreement with the current measured value.

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30

Xiao, Hong, and Panchi Li. "Quantum steganography based on reflected gray code for color images." Intelligent Decision Technologies 14, no. 3 (September 29, 2020): 291–312. http://dx.doi.org/10.3233/idt-190034.

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Digital steganography is the art and science of hiding information in covert channels, so as to conceal the information and prevent the detection of hidden messages. On the classic computer, the principle and method of digital steganography has been widely and deeply studied, and has been initially extended to the field of quantum computing. Quantum image steganography is a relatively active branch of quantum image processing, and the main strategy currently used is to modify the LSB of the cover image pixels. For the existing LSB-based quantum image steganography schemes, the embedding capacity is no more than 3 bits per pixel. Therefore, it is meaningful to study how to improve the embedding capacity of quantum image steganography. This work presents a novel steganography using reflected Gray code for color quantum images, and the embedding capacity of this scheme is up to 6 bits per pixel. In proposed scheme, the secret qubit sequence is considered as a sequence of 6-bit segments. For 6 bits in each segment, the first 3 bits are embedded into the second LSB of RGB channels of the cover image, and the remaining 3 bits are embedded into the LSB of RGB channels of the cover image using reflected-Gray code to determine the embedded bit from secret information. Following the transforming rule, the LSBs of stego-image are not always same as the secret bits and the differences are up to almost 50%. Experimental results confirm that the proposed scheme shows good performance and outperforms the previous ones currently found in the literature in terms of embedding capacity.

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31

Beetle, Christopher, Jonathan S. Engle, Matthew E. Hogan, and Phillip Mendonça. "Diffeomorphism invariant cosmological symmetry in full quantum gravity." International Journal of Modern Physics D 25, no. 08 (July 2016): 1642012. http://dx.doi.org/10.1142/s0218271816420128.

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This paper summarizes a new proposal to define rigorously a sector of loop quantum gravity at the diffeomorphism invariant level corresponding to homogeneous and isotropic cosmologies, thereby enabling a detailed comparison of results in loop quantum gravity and loop quantum cosmology. The key technical steps we have completed are (a) to formulate conditions for homogeneity and isotropy in a diffeomorphism covariant way on the classical phase-space of general relativity, and (b) to translate these conditions consistently using well-understood techniques to loop quantum gravity. Some additional steps, such as constructing a specific embedding of the Hilbert space of loop quantum cosmology into a space of (distributional) states in the full theory, remain incomplete. However, we also describe, as a proof of concept, a complete analysis of an analogous embedding of homogeneous and isotropic loop quantum cosmology into the quantum Bianchi I model of Ashtekar and Wilson-Ewing. Details will appear in a pair of forthcoming papers.

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32

Cui, Zhi-Hao, Tianyu Zhu, and Garnet Kin-Lic Chan. "Efficient Implementation of Ab Initio Quantum Embedding in Periodic Systems: Density Matrix Embedding Theory." Journal of Chemical Theory and Computation 16, no. 1 (December 9, 2019): 119–29. http://dx.doi.org/10.1021/acs.jctc.9b00933.

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33

van Esbroeck, N. M., D. T. Lennon, H. Moon, V. Nguyen, F. Vigneau, L. C. Camenzind, L. Yu, et al. "Quantum device fine-tuning using unsupervised embedding learning." New Journal of Physics 22, no. 9 (September 22, 2020): 095003. http://dx.doi.org/10.1088/1367-2630/abb64c.

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34

Zgid, Dominika, and Emanuel Gull. "Finite temperature quantum embedding theories for correlated systems." New Journal of Physics 19, no. 2 (February 23, 2017): 023047. http://dx.doi.org/10.1088/1367-2630/aa5d34.

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35

Gates, James, Ahmed Jellal, EL Hassan Saidi, and Michael Schreiber. "Supersymmetric Embedding of the Quantum Hall Matrix Model." Journal of High Energy Physics 2004, no. 11 (November 27, 2004): 075. http://dx.doi.org/10.1088/1126-6708/2004/11/075.

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36

Garola, Claudio. "Embedding of posets into lattices in quantum logic." International Journal of Theoretical Physics 24, no. 5 (May 1985): 423–33. http://dx.doi.org/10.1007/bf00669903.

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37

Klymko, Christine, Blair D. Sullivan, and Travis S. Humble. "Adiabatic quantum programming: minor embedding with hard faults." Quantum Information Processing 13, no. 3 (November 20, 2013): 709–29. http://dx.doi.org/10.1007/s11128-013-0683-9.

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38

Huang, Minyi, Asutosh Kumar, and Junde Wu. "Embedding, simulation and consistency ofPT-symmetric quantum theory." Physics Letters A 382, no. 36 (September 2018): 2578–85. http://dx.doi.org/10.1016/j.physleta.2018.06.047.

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39

Fioresi, R., E. Latini, M. A. Lledó, and F. A. Nadal. "The Segre embedding of the quantum conformal superspace." Advances in Theoretical and Mathematical Physics 22, no. 8 (2018): 1939–2000. http://dx.doi.org/10.4310/atmp.2018.v22.n8.a4.

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40

Garola, Claudio, and Marco Persano. "Embedding Quantum Mechanics into a Broader Noncontextual Theory." Foundations of Science 19, no. 3 (October 26, 2013): 217–39. http://dx.doi.org/10.1007/s10699-013-9341-z.

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41

Ma, Yunpu, Volker Tresp, Liming Zhao, and Yuyi Wang. "Variational Quantum Circuit Model for Knowledge Graph Embedding." Advanced Quantum Technologies 2, no. 7-8 (February 12, 2019): 1800078. http://dx.doi.org/10.1002/qute.201800078.

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42

Sekaran, Sajanthan, Matthieu Saubanère, and Emmanuel Fromager. "Local Potential Functional Embedding Theory: A Self-Consistent Flavor of Density Functional Theory for Lattices without Density Functionals." Computation 10, no. 3 (March 18, 2022): 45. http://dx.doi.org/10.3390/computation10030045.

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Quantum embedding is a divide and conquer strategy that aims at solving the electronic Schrödinger equation of sizeable molecules or extended systems. We establish in the present work a clearer and in-principle-exact connection between density matrix embedding theory (DMET) and density-functional theory (DFT) within the simple but nontrivial one-dimensional Hubbard model. For that purpose, we use our recent reformulation of single-impurity DMET as a Householder transformed density-matrix functional embedding theory (Ht-DMFET). On the basis of well-identified density-functional approximations, a self-consistent local potential functional embedding theory (LPFET) is formulated and implemented. Combining both LPFET and DMET numerical results with our formally exact density-functional embedding theory reveals that a single statically embedded impurity can in principle describe the density-driven Mott–Hubbard transition, provided that a complementary density-functional correlation potential (which is neglected in both DMET and LPFET) exhibits a derivative discontinuity (DD) at half filling. The extension of LPFET to multiple impurities (which would enable to circumvent the modeling of DDs) and its generalization to quantum chemical Hamiltonians are left for future work.

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43

ANIELLO, P., G. MARMO, and G. F. VOLKERT. "CLASSICAL TENSORS FROM QUANTUM STATES." International Journal of Geometric Methods in Modern Physics 06, no. 03 (May 2009): 369–83. http://dx.doi.org/10.1142/s0219887809003576.

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The embedding of a manifold M into a Hilbert-space ℍ induces, via the pull-back, a tensor field on M out of the Hermitian tensor on ℍ. We propose a general procedure to compute these tensors in particular for Manifolds admitting a Lie-Group structure.

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Yalouz, Saad, Sajanthan Sekaran, Emmanuel Fromager, and Matthieu Saubanère. "Quantum embedding of multi-orbital fragments using the block-Householder transformation." Journal of Chemical Physics 157, no. 21 (December 7, 2022): 214112. http://dx.doi.org/10.1063/5.0125683.

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Recently, some of the authors introduced the use of the Householder transformation as a simple and intuitive method for embedding local molecular fragments [see Sekaran et al., Phys. Rev. B 104, 035121 (2021) and Sekaran et al., Computation 10, 45 (2022)]. In this work, we present an extension of this approach to the more general case of multi-orbital fragments using the block version of the Householder transformation applied to the one-body reduced density matrix, unlocking the applicability to general quantum chemistry/condensed matter physics Hamiltonians. A step-by-step construction of the block Householder transformation is presented. Both physical and numerical areas of interest of the approach are highlighted. The specific mean-field (noninteracting) case is thoroughly detailed as it is shown that the embedding of a given N spin–orbital fragment leads to the generation of two separated sub-systems: (1) a 2 N spin–orbitals “fragment+bath” cluster that exactly contains N electrons and (2) a remaining cluster’s “environment” described by so-called core electrons. We illustrate the use of this transformation in different cases of embedding scheme for practical applications. We particularly focus on the extension of the previously introduced Local Potential Functional Embedding Theory and Householder-transformed Density Matrix Functional Embedding Theory to the case of multi-orbital fragments. These calculations are realized on different types of systems, such as model Hamiltonians (Hubbard rings) and ab initio molecular systems (hydrogen rings).

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Liu, Guangcheng, Yuexian Hou, and Shikai Song. "A Quantum-inspired Complex-valued Representation for Encoding Sentiment Information (Student Abstract)." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 18 (May 18, 2021): 15831–32. http://dx.doi.org/10.1609/aaai.v35i18.17912.

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Recently, a Quantum Probability Drive Network (QPDN) is proposed to model different levels of semantic units by extending word embedding to complex-valued representation (CR). The extended complex-valued embeddings are still insensitive to polarity causing that they generalize badly in sentiment analysis (SA). To solve it, we propose a method of encoding sentiment information into sentiment words for SA. Attention mechanism and an auxiliary task are introduced to help learn the CR of sentiment words with the help of the sentiment lexicon. We use the amplitude part to represent the distributional information and the phase part to represent the sentiment information of the language. Experiments on three popular SA datasets show that our method is effective.

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PINZARI, CLAUDIA. "EMBEDDING ERGODIC ACTIONS OF COMPACT QUANTUM GROUPS ON C*-ALGEBRAS INTO QUOTIENT SPACES." International Journal of Mathematics 18, no. 02 (February 2007): 137–64. http://dx.doi.org/10.1142/s0129167x07003960.

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The notion of compact quantum subgroup is revisited and an alternative definition is given. Induced representations are considered and a Frobenius reciprocity theorem is obtained. A relationship between ergodic actions of compact quantum groups on C*-algebras and topological transitivity is investigated. A sufficient condition for embedding such actions in quantum quotient spaces is obtained.

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Gough, John E., Matthew R. James, and Hendra I. Nurdin. "Single photon quantum filtering using non-Markovian embeddings." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1979 (November 28, 2012): 5408–21. http://dx.doi.org/10.1098/rsta.2011.0524.

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We determine quantum master and filter equations for continuous measurement of systems coupled to input fields in certain non-classical continuous-mode states, specifically single photon states. The quantum filters are shown to be derivable from an embedding into a larger non-Markovian system, and are given by a system of coupled stochastic differential equations.

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Zhou, Ri-Gui, Peng Liu Yang, Xing Ao Liu, and Hou Ian. "Quantum color image watermarking based on fast bit-plane scramble and dual embedded." International Journal of Quantum Information 16, no. 07 (October 2018): 1850060. http://dx.doi.org/10.1142/s0219749918500600.

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Most of the studied quantum encryption algorithms are based on square images. In this paper, based on the improved novel quantum representation of color digital images model (INCQI), a quantum color image watermarking scheme is proposed. First, INCQI improved from NCQI is used to represent the carrier and watermark images with the size [Formula: see text] and [Formula: see text], respectively. Secondly, before embedding, the watermarking needs to be preprocessed. That is, the watermark image with the size of [Formula: see text] with 24-qubits color information is disordered by the fast bit-plane scramble algorithm, and then further expanded to an image with the size [Formula: see text] with 6-qubits pixel information by the nearest-neighbor interpolation method. Finally, the dual embedded algorithm is executed and a key image with 3-qubits information is generated for retrieving the original watermark image. The extraction process of the watermark image is the inverse process of its embedding, including inverse embedding, inverse expand and inverse scrambling operations. To show that our method has a better performance in visual quality and histogram graph, a simulation of different carrier and watermark images are conducted on the classical computer’s MATLAB.

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Gianani, Ilaria, Ivana Mastroserio, Lorenzo Buffoni, Natalia Bruno, Ludovica Donati, Valeria Cimini, Marco Barbieri, Francesco S. Cataliotti, and Filippo Caruso. "Front Cover: Experimental Quantum Embedding for Machine Learning (Adv. Quantum Technol. 8/2022)." Advanced Quantum Technologies 5, no. 8 (August 2022): 2270081. http://dx.doi.org/10.1002/qute.202270081.

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Salii, R. A., S. A. Mintairov, A. M. Nadtochiy, A. S. Payusov, P. N. Brunkov, M. Z. Shvarts, and N. A. Kalyuzhnyy. "Increasing the quantum efficiency of GaAs solar cells by embedding InAs quantum dots." Journal of Physics: Conference Series 769 (November 2016): 012036. http://dx.doi.org/10.1088/1742-6596/769/1/012036.

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