Quantum Reports

30 pages, 1732 KiB

Open AccessReview

Theory and Applications of Quantum Hashing

by Farid Ablayev, Kamil Khadiev, Alexander Vasiliev and Mansur Ziiatdinov

Quantum Rep. 2025, 7(2), 24; https://doi.org/10.3390/quantum7020024 - 15 May 2025

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We review recent results on quantum one-way functions, including quantum fingerprinting or quantum hashing (we use these two terms as synonyms even though they have very small difference). This includes the analysis of their properties, different modifications, circuit implementation on an IBM Q [...] Read more.

We review recent results on quantum one-way functions, including quantum fingerprinting or quantum hashing (we use these two terms as synonyms even though they have very small difference). This includes the analysis of their properties, different modifications, circuit implementation on an IBM Q platform, as well as on an experimental quantum setup. We discuss computational aspects of quantum hashing, its cryptographic properties and possible usage in communication protocols and algorithms. Full article

(This article belongs to the Special Issue 100 Years of Quantum Mechanics)

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16 pages, 346 KiB

Open AccessArticle

Evolving Probability Representations of Entangled Cat States in the Potentials of Harmonic and Inverted Oscillators

by Matyas Mechler, Margarita A. Man’ko, Vladimir I. Man’ko and Peter Adam

Quantum Rep. 2025, 7(2), 23; https://doi.org/10.3390/quantum7020023 - 2 May 2025

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Abstract

We determine the evolving probability representation of entangled cat states in the potential of either the harmonic oscillator or the inverted oscillator, assuming that the states are initially prepared in the potential of the harmonic oscillator. Such states have several applications in quantum [...] Read more.

We determine the evolving probability representation of entangled cat states in the potential of either the harmonic oscillator or the inverted oscillator, assuming that the states are initially prepared in the potential of the harmonic oscillator. Such states have several applications in quantum information processing. The inverted quantum harmonic oscillator, where the potential energy corresponds to imaginary frequencies of the oscillator, can be applied in relation to cosmological problems. We also determine the evolving probability representation of cat states of an oscillating spin-1/2 particle of the inverted oscillator, in which the time evolution of the spin state is described by an arbitrary unitary operator. The properties of the determined entangled probability distributions are discussed. Full article

(This article belongs to the Special Issue 100 Years of Quantum Mechanics)

20 pages, 503 KiB

Open AccessArticle

Probability Representation of Quantum States: Tomographic Representation in Standard Potentials and Peres–Horodecki Criterion for Probabilities

by Julio A. López-Saldívar, Margarita A. Man’ko and Vladimir I. Man’ko

Quantum Rep. 2025, 7(2), 22; https://doi.org/10.3390/quantum7020022 - 24 Apr 2025

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Abstract

In connection with the International Year of Quantum Science and Technology, a review of joint works of the Lebedev Institute and the Mexican research group at UNAM is presented, especially related to solving the old problem of the state description, not only by [...] Read more.

In connection with the International Year of Quantum Science and Technology, a review of joint works of the Lebedev Institute and the Mexican research group at UNAM is presented, especially related to solving the old problem of the state description, not only by wave functions but also by conventional probability distributions analogous to quasiprobability distributions, like the Wigner function. Also, explicit expressions of tomographic representations describing the quantum states of particles moving in known potential wells are obtained and briefly discussed. In particular, we present the examples of the tomographic distributions for the free evolution, finite and infinite potential wells, and the Morse potential. Additional to this, an extension of the Peres–Horodecki separability criteria for momentum probability distributions is presented in the case of bipartite, asymmetrical, real states. Full article

(This article belongs to the Special Issue 100 Years of Quantum Mechanics)

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16 pages, 707 KiB

Open AccessArticle

Simulating Methylamine Using a Symmetry-Adapted, Qubit Excitation-Based Variational Quantum Eigensolver

by Konstantin M. Makushin and Aleksey K. Fedorov

Quantum Rep. 2025, 7(2), 21; https://doi.org/10.3390/quantum7020021 - 21 Apr 2025

Cited by 1 | Viewed by 392

Abstract

Understanding the capabilities of quantum computer devices and computing the required resources to solve realistic tasks remain critical challenges associated with achieving useful quantum computational advantage. We present a study aimed at reducing the quantum resource overhead in quantum chemistry simulations using the [...] Read more.

Understanding the capabilities of quantum computer devices and computing the required resources to solve realistic tasks remain critical challenges associated with achieving useful quantum computational advantage. We present a study aimed at reducing the quantum resource overhead in quantum chemistry simulations using the variational quantum eigensolver (VQE). Our approach achieves up to a two-orders-of magnitude reduction in the required number of two-qubit operations for variational problem-inspired ansatzes. We propose and analyze optimization strategies that combine various methods, including molecular point-group symmetries, compact excitation circuits, different types of excitation sets, and qubit tapering. To validate the compatibility and accuracy of these strategies, we first test them on small molecules such as LiH and BeH₂, then apply the most efficient ones to restricted active-space simulations of methylamine. We complete our analysis by computing the resources required for full-valence, active-space simulations of methylamine (26 qubits) and formic acid (28 qubits) molecules. Our best-performing optimization strategy reduces the two-qubit gate count for methylamine from approximately 600,000 to about 12,000 and yields a similar order-of-magnitude improvement for formic acid. This resource analysis represents a valuable step towards the practical use of quantum computers and the development of better methods for optimizing computing resources. Full article

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21 pages, 4530 KiB

Open AccessArticle

Diffusion in a Comb-Structured Media: Non-Local Terms and Stochastic Resetting

by Ervin Kaminski Lenzi, Derik William Gryczak, Luciano Rodrigues da Silva, Haroldo Valentin Ribeiro and Rafael Soares Zola

Quantum Rep. 2025, 7(2), 20; https://doi.org/10.3390/quantum7020020 - 14 Apr 2025

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Abstract

We examine the dynamics of a system influenced by a backbone structure, incorporating linear non-local terms that account for both irreversible and reversible processes, such as absorption and adsorption–desorption. Additionally, we introduce stochastic resetting to analyze its effects on the system’s behavior from [...] Read more.

We examine the dynamics of a system influenced by a backbone structure, incorporating linear non-local terms that account for both irreversible and reversible processes, such as absorption and adsorption–desorption. Additionally, we introduce stochastic resetting to analyze its effects on the system’s behavior from both analytical and numerical perspectives. Our findings reveal a rich spectrum of dynamics, emphasizing connections to anomalous diffusion and providing new insights into transport phenomena in complex environments. Full article

(This article belongs to the Special Issue Recent Studies on Fokker–Planck Equation and Diffusion)

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19 pages, 3197 KiB

Open AccessArticle

Towards a Multiqudit Quantum Processor Based on a ¹⁷¹Yb⁺ Ion String: Realizing Basic Quantum Algorithms

by Ilia V. Zalivako, Anastasiia S. Nikolaeva, Alexander S. Borisenko, Andrei E. Korolkov, Pavel L. Sidorov, Kristina P. Galstyan, Nikita V. Semenin, Vasilii N. Smirnov, Mikhail A. Aksenov, Konstantin M. Makushin, Evgeniy O. Kiktenko, Aleksey K. Fedorov, Ilya A. Semerikov, Ksenia Yu. Khabarova and Nikolay N. Kolachevsky

Quantum Rep. 2025, 7(2), 19; https://doi.org/10.3390/quantum7020019 - 12 Apr 2025

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Abstract

We demonstrate a quantum processor based on a 3D linear Paul trap that uses

{}^{171}{Yb}^{+}

ions with eight individually controllable four-level qudits (ququarts), which is computationally equivalent to a sixteen-qubit quantum processor. The design of the developed ion trap provides high [...] Read more.

We demonstrate a quantum processor based on a 3D linear Paul trap that uses

{}^{171}{Yb}^{+}

ions with eight individually controllable four-level qudits (ququarts), which is computationally equivalent to a sixteen-qubit quantum processor. The design of the developed ion trap provides high secular frequencies and a low heating rate, which, together with individual addressing and readout optical systems, allows executing quantum algorithms. In each of the eight ions, we use four electronic levels coupled by E2 optical transition at 435 nm for qudit encoding. We present the results of single- and two-qubit operations benchmarking and realizing basic quantum algorithms, including the Bernstein–Vazirani and Grover’s search algorithms as well as H₂ and LiH molecular simulations. Our results pave the way to scalable qudit-based quantum processors using trapped ions. Full article

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25 pages, 975 KiB

Open AccessArticle

Quantum Classical Algorithm for the Study of Phase Transitions in the Hubbard Model via Dynamical Mean-Field Theory

by Anshumitra Baul, Herbert Fotso, Hanna Terletska, Ka-Ming Tam and Juana Moreno

Quantum Rep. 2025, 7(2), 18; https://doi.org/10.3390/quantum7020018 - 4 Apr 2025

Cited by 1 | Viewed by 471

Abstract

Modeling many-body quantum systems is widely regarded as one of the most promising applications for near-term noisy quantum computers. However, in the near term, system size limitation will remain a severe barrier for applications in materials science or strongly correlated systems. A promising [...] Read more.

Modeling many-body quantum systems is widely regarded as one of the most promising applications for near-term noisy quantum computers. However, in the near term, system size limitation will remain a severe barrier for applications in materials science or strongly correlated systems. A promising avenue of research is to combine many-body physics with machine learning for the classification of distinct phases. We present a workflow that synergizes quantum computing, many-body theory, and quantum machine learning (QML) for studying strongly correlated systems. In particular, it can capture a putative quantum phase transition of the stereotypical strongly correlated system, the Hubbard model. Following the recent proposal of the hybrid quantum-classical algorithm for the two-site dynamical mean-field theory (DMFT), we present a modification that allows the self-consistent solution of the single bath site DMFT. The modified algorithm can be generalized for multiple bath sites. This approach is used to generate a database of zero-temperature wavefunctions of the Hubbard model within the DMFT approximation. We then use a QML algorithm to distinguish between the metallic phase and the Mott insulator phase to capture the metal-to-Mott insulator phase transition. We train a recently proposed quantum convolutional neural network (QCNN) and then utilize the QCNN as a quantum classifier to capture the phase transition region. This work provides a recipe for application to other phase transitions in strongly correlated systems and represents an exciting application of small-scale quantum devices realizable with near-term technology. Full article

(This article belongs to the Topic Theoretical, Quantum and Computational Chemistry—2nd Edition)

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26 pages, 459 KiB

Open AccessArticle

Analysis of D-Wave Topologies with k-Hop-Based Graph Metrics

by Csaba Biró and Gábor Kusper

Quantum Rep. 2025, 7(2), 17; https://doi.org/10.3390/quantum7020017 - 2 Apr 2025

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Abstract

In this paper, we present a graph-based analysis of the topology of D-Wave quantum computers, focusing on the Pegasus, Chimera, and Zephyr architectures. We investigate these topologies under different parameter settings using k-hop-based graph metrics. Each of these architectures comprises distinct subgraphs [...] Read more.

In this paper, we present a graph-based analysis of the topology of D-Wave quantum computers, focusing on the Pegasus, Chimera, and Zephyr architectures. We investigate these topologies under different parameter settings using k-hop-based graph metrics. Each of these architectures comprises distinct subgraphs in which qubits are interconnected according to specific patterns dictated by their implementation. Our study pursues two primary objectives. First, we analyze the structural properties of the Chimera, Pegasus, and Zephyr topologies, examining their scalability and connectivity characteristics. Second, we evaluate the behavior of graph-based density and redundancy metrics within these architectures. The inherent symmetries of these quantum hardware designs provide a unique opportunity to systematically assess the effectiveness of these metrics across varying connectivity patterns. By leveraging these symmetries, our findings not only enhance the understanding of these topological structures but also offer deeper insights into the reliability and applicability of the proposed metrics in the broader context of quantum hardware design. Full article

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16 pages, 3297 KiB

Open AccessArticle

In-Field Quantum-Protected Control-Based Key Distribution with a Lossy Urban Fiber Link

by Vladlen Statiev, Abdufattokh Ashurov, Vladimir Semenov, Dmitrii Kozliuk, Vladislav Zemlyanov, Aleksei Kodukhov, Valeria Pastushenko, Valerii Vinokur and Markus Pflitsch

Quantum Rep. 2025, 7(2), 16; https://doi.org/10.3390/quantum7020016 - 28 Mar 2025

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Abstract

Quantum cryptography protocols offering unconditional protection open great rout to full information security in quantum era. Yet, implementing these protocols using the existing fiber networks remains challenging due to high signal losses reducing the efficiency of these protocols to zero. The recently proposed [...] Read more.

Quantum cryptography protocols offering unconditional protection open great rout to full information security in quantum era. Yet, implementing these protocols using the existing fiber networks remains challenging due to high signal losses reducing the efficiency of these protocols to zero. The recently proposed quantum-protected control-based key distribution (QCKD) addresses this issue by physically controlling interceptable losses and ensuring that leaked quantum states remain non-orthogonal. Here, we present the first in-field development and demonstration of the QCKD over an urban fiber link characterized by substantial losses. Using information-theoretic considerations, we configure the system ensuring security and investigate the interplay between line losses and secret key rates. As an example, we present calculation for the communication distance 4 km, QCKD rate 490 bits per second, and find that the corresponding system’s total loss is about 1.628 decibels. Our results, backed by the statistical analysis of the secret key, confirm QCKD’s robustness under real-world conditions, and establish it as a practical solution for quantum-safe communications over existing fiber infrastructures. Full article

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10 pages, 2400 KiB

Open AccessArticle

Superoperator Approach to the Lindbladian Dynamics of a Mirror-Field System

by Marco A. García-Márquez and Héctor M. Moya-Cessa

Quantum Rep. 2025, 7(2), 15; https://doi.org/10.3390/quantum7020015 - 24 Mar 2025

Viewed by 247

Abstract

We use superoperator techniques to solve the master equation for the interaction between a single-mode quantized field and a single mechanical mode of a moving mirror, which is coupled to a zero-temperature reservoir that damps its amplitude. The solution we provide allows for [...] Read more.

We use superoperator techniques to solve the master equation for the interaction between a single-mode quantized field and a single mechanical mode of a moving mirror, which is coupled to a zero-temperature reservoir that damps its amplitude. The solution we provide allows for its application in any initial state of the combined system. Furthermore, we obtain solutions to the stationary master equation for an initial number state for the field that is consistent with the result obtained for the average number of phonons. Full article

(This article belongs to the Special Issue 100 Years of Quantum Mechanics)

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Quantum Rep., Volume 7, Issue 2 (June 2025) – 10 articles

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