Quantum Reports

10 pages, 653 KB

Open AccessArticle

A Novel QCA Design of Energy-Efficient Three-Input AND/OR Circuit

by Amjad Almatrood

Quantum Rep. 2025, 7(3), 38; https://doi.org/10.3390/quantum7030038 (registering DOI) - 31 Aug 2025

One of the nanoscale technologies that shows its capability of implementing integrated digital circuits with low power, high speed, and high density is quantum-dot cellular automata (QCA). The fundamental device for designing and implementing circuits in QCA is majority logic. In this paper, [...] Read more.

One of the nanoscale technologies that shows its capability of implementing integrated digital circuits with low power, high speed, and high density is quantum-dot cellular automata (QCA). The fundamental device for designing and implementing circuits in QCA is majority logic. In this paper, a novel energy-efficient QCA design of three-input AND/OR logic functions is proposed. This design can perform both AND and OR logic operations using the same structure with an achievement of 58% and 64% approximate reductions in power consumption compared to majority-based structures, and 31% and 32% approximate reductions in power consumption compared to the best available circuits, respectively. In addition, other physical constraints such as area and latency are improved and have better or similar results compared to the best existing circuits. The proposed circuit can be considered as a fundamental and better alternative to the majority gate for energy-efficient circuit design in QCA. This will pave the way for developing efficient large-scale QCA-based sequential and combinational circuits. Full article

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25 pages, 435 KB

Open AccessArticle

HHL Algorithm for Tensor-Decomposable Matrices

by Cezary Pilaszewicz and Marian Margraf

Quantum Rep. 2025, 7(3), 37; https://doi.org/10.3390/quantum7030037 - 19 Aug 2025

Viewed by 163

Abstract

We use the HHL algorithm to retrieve a quantum state holding the algebraic normal form (ANF) of a Boolean function. Unlike the standard HHL applications, we do not describe the cipher as an exponentially big system of equations. Rather, we perform a set [...] Read more.

We use the HHL algorithm to retrieve a quantum state holding the algebraic normal form (ANF) of a Boolean function. Unlike the standard HHL applications, we do not describe the cipher as an exponentially big system of equations. Rather, we perform a set of small matrix inversions which correspond to the Boolean Möbius transform. This creates a superposition holding information about the ANF in the form

| A_{f} ⟩ = \frac{1}{C} \sum_{I = 0}^{2^{n} - 1} c_{I} | I ⟩

, where

c_{I}

is the coefficient of the ANF and C is a scaling factor. The procedure has a time complexity of

\tilde{O} (n)

for a Boolean function with n-bit input. We also propose two approaches by which some information about the ANF can be extracted from such a state. Next, we use a similar approach, the Dual Boolean Möbius transform, to compute the preimage under the algebraic transition matrix. We show that such a matrix is well-suited for the HHL algorithm when the attacker gets oracle access in the Q2 setting to the Boolean function. Full article

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24 pages, 649 KB

Open AccessPerspective

Quantum-Enhanced Algorithmic Fairness and the Advancement of AI Integrity and Responsibility

by Akhil Chintalapati, Khashbat Enkhbat, Ramanathan Annamalai, Geraldine Bessie Amali, Fatih Ozaydin and Mathew Mithra Noel

Quantum Rep. 2025, 7(3), 36; https://doi.org/10.3390/quantum7030036 - 11 Aug 2025

Viewed by 482

Abstract

In the evolving digital landscape, the pervasive influence of artificial intelligence (AI) on social media platforms reveals a compelling paradox: the capability to provide personalized experiences juxtaposed with inherent biases reminiscent of human imperfections. Such biases prompt rigorous contemplation on matters of fairness, [...] Read more.

In the evolving digital landscape, the pervasive influence of artificial intelligence (AI) on social media platforms reveals a compelling paradox: the capability to provide personalized experiences juxtaposed with inherent biases reminiscent of human imperfections. Such biases prompt rigorous contemplation on matters of fairness, equity, and societal ramifications, and penetrate the foundational essence of AI. Within this intricate context, the present work ventures into novel domains by examining the potential of quantum computing as a viable remedy for bias in artificial intelligence. The conceptual framework of the quantum sentinel is presented—an innovative approach that employs quantum principles for the detection and scrutiny of biases in AI algorithms. Furthermore, the study poses and investigates the question of whether the integration of advanced quantum computing to address AI bias is seen as an excessive measure or a requisite advancement commensurate with the intricacy of the issue. By intertwining quantum mechanics, AI bias, and the philosophical considerations they induce, this research fosters a discourse on the journey toward ethical AI, thus establishing a foundation for an ethically conscious and balanced digital environment. We also show that the quantum Zeno effect can protect SVM hyperplanes from bias through targeted simulations. Full article

(This article belongs to the Special Issue Beyond Classical Limits: Quantum Machine Learning for Multi-Field Research)

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15 pages, 7567 KB

Open AccessArticle

Classical Encryption Demonstration with BB84 Quantum Protocol-Inspired Coherent States Using Reduced Graphene Oxide

by Alexia Lopez-Bastida, Pablo Córdova-Morales, Donato Valdez-Pérez, Adrian Martinez-Rivas, José M. de la Rosa-Vázquez and Carlos Torres-Torres

Quantum Rep. 2025, 7(3), 35; https://doi.org/10.3390/quantum7030035 - 11 Aug 2025

Viewed by 391

Abstract

This study explores the integration of reduced graphene oxide (rGO) into an optoelectronic XOR logic gate to enhance BB84 protocol encryption in quantum communication systems. The research leverages the nonlinear optical properties of rGO, specifically its nonlinear refraction characteristics, in combination with a [...] Read more.

This study explores the integration of reduced graphene oxide (rGO) into an optoelectronic XOR logic gate to enhance BB84 protocol encryption in quantum communication systems. The research leverages the nonlinear optical properties of rGO, specifically its nonlinear refraction characteristics, in combination with a Michelson interferometer to implement an optoelectronic XOR gate. rGO samples were deposited using the Langmuir–Blodgett technique and characterized in morphology and structure. The optical setup utilized a frequency-modulated laser signal for the interferometer and a pulsed laser system that generates the quantum information carrier. This integration of quantum encryption with nonlinear optical materials offers enhanced security against classical attacks while providing adaptability for various applications from secure communications to quantum AI. Full article

(This article belongs to the Special Issue Opportunities and Challenges in Quantum AI)

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61 pages, 916 KB

Open AccessReview

Variance-Based Uncertainty Relations: A Concise Review of Inequalities Discovered Since 1927

by Viktor V. Dodonov

Quantum Rep. 2025, 7(3), 34; https://doi.org/10.3390/quantum7030034 - 5 Aug 2025

Viewed by 343

Abstract

A brief review of various existing mathematical formulations of the uncertainty relations in quantum mechanics, containing variances of two or more non-commuting operators, is given. In particular, inequalities for the products of higher-order moments of a coordinate and a momentum are considered, as [...] Read more.

A brief review of various existing mathematical formulations of the uncertainty relations in quantum mechanics, containing variances of two or more non-commuting operators, is given. In particular, inequalities for the products of higher-order moments of a coordinate and a momentum are considered, as well as inequalities making the uncertainty relations more accurate when additional information about a quantum system is available (for example, the correlation coefficient or the degree of mixing of a quantum state characterized by the trace of the squared statistical operator). The special cases of two, three, and four operators are discussed in detail. Full article

27 pages, 1332 KB

Open AccessArticle

Generalizing Coherent States with the Fox H Function

by Filippo Giraldi

Quantum Rep. 2025, 7(3), 33; https://doi.org/10.3390/quantum7030033 - 28 Jul 2025

Viewed by 480

Abstract

In the present scenario, coherent states of a quantum harmonic oscillator are generalized with positive Fox H auxiliary functions. The novel generalized coherent states provide canonical coherent states and Mittag-Leffler or Wright generalized coherent states, as particular cases, and resolve the identity operator, [...] Read more.

In the present scenario, coherent states of a quantum harmonic oscillator are generalized with positive Fox H auxiliary functions. The novel generalized coherent states provide canonical coherent states and Mittag-Leffler or Wright generalized coherent states, as particular cases, and resolve the identity operator, over the Fock space, with a weight function that is the product of a Fox H function and a Wright generalized hypergeometric function. The novel generalized coherent states, or the corresponding truncated generalized coherent states, are characterized by anomalous statistics for large values of the number of excitations: the corresponding decay laws exhibit, for determined values of the involved parameters, various behaviors that depart from exponential and inverse-power-law decays, or their product. The analysis of the Mandel Q factor shows that, for small values of the label, the statistics of the number of excitations becomes super-Poissonian, or sub-Poissonian, by simply choosing sufficiently large values of one of the involved parameters. The time evolution of a generalized coherent state interacting with a thermal reservoir and the purity are analyzed. Full article

(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports in 2024–2025)

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16 pages, 2746 KB

Open AccessArticle

Efficient Encoding of the Traveling Salesperson Problem on a Quantum Computer

by John P. T. Stenger, Sean T. Crowe, Joseph A. Diaz, Ramiro Rodriguez, Daniel Gunlycke and Joanna N. Ptasinski

Quantum Rep. 2025, 7(3), 32; https://doi.org/10.3390/quantum7030032 - 17 Jul 2025

Viewed by 511

Abstract

We propose an amplitude encoding of the traveling salesperson problem along with a method for calculating the cost function using a probability distribution obtained on a quantum computer. Our encoding requires a number of qubits that grows logarithmically with the number of cities. [...] Read more.

We propose an amplitude encoding of the traveling salesperson problem along with a method for calculating the cost function using a probability distribution obtained on a quantum computer. Our encoding requires a number of qubits that grows logarithmically with the number of cities. We propose to calculate the cost function using a nonlinear function of expectation values of quantum operators. This is in contrast to the typical method of evaluating the cost function by summing expectation values of quantum operators. We demonstrate our method using a variational quantum eigensolver algorithm to find the shortest route for a given graph. We find that there is a broad range in the hyperparameters of the optimization procedure for which the best route is found. Full article

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16 pages, 8172 KB

Open AccessArticle

A Comparative Analysis of a Nonlinear Phase Space Evolution of SU(2) and SU(1,1) Coherent States

by Rodrigo D. Aceves, Miguel Baltazar, Iván F. Valtierra and Andrei B. Klimov

Quantum Rep. 2025, 7(3), 31; https://doi.org/10.3390/quantum7030031 - 5 Jul 2025

Viewed by 394

Abstract

We carried out a comparative study of the phase space evolution of SU(2) and SU(1,1) coherent states generated by the same nonlinear two-mode Hamiltonian. We analyze the dynamics of the Wigner functions in the respective phase spaces and discuss the principal associated physical [...] Read more.

We carried out a comparative study of the phase space evolution of SU(2) and SU(1,1) coherent states generated by the same nonlinear two-mode Hamiltonian. We analyze the dynamics of the Wigner functions in the respective phase spaces and discuss the principal associated physical effects: the squeezing of the appropriate observables and the Schrödinger’s cat state generation characteristic of both the considered symmetry groups. Full article

(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports in 2024–2025)

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9 pages, 283 KB

Open AccessArticle

Neutrino Mixing Matrix with SU(2)₄ Anyon Braids

by Michel Planat

Quantum Rep. 2025, 7(3), 30; https://doi.org/10.3390/quantum7030030 - 23 Jun 2025

Viewed by 685

Abstract

We recently classified baryonic matter in the ground and first excited states thanks to the discrete group of braids inherent to

S U {(2)}_{2}

Ising anyons. Remarkably, the braids of

S U {(2)}_{4}

anyons allow the neutrino [...] Read more.

We recently classified baryonic matter in the ground and first excited states thanks to the discrete group of braids inherent to

S U {(2)}_{2}

Ising anyons. Remarkably, the braids of

S U {(2)}_{4}

anyons allow the neutrino mixing matrix to be generated with an accuracy close to measurements. This is an improvement over the model based on tribimaximal neutrino mixing, which predicts a vanishing solar neutrino angle

θ_{13}

, which has now been ruled out. The discrete group of braids for

S U {(2)}_{4}

anyons is isomorphic to the small group

(162, 14)

, generated by a diagonal matrix

σ_{1} = R

and a symmetric complex matrix

σ_{2} = F R F^{- 1}

, where the

(3 \times 3)

matrices F and R correspond to the fusion and exchange of anyons, respectively. We make use of the Takagi decomposition

σ_{2} = U^{T} D U

of

σ_{2}

, where U is the expected PMNS unitary matrix and D is real and diagonal. We obtain agreement with the experimental results in about the

3 σ

range for the complex entries of the PMNS matrix with the angles

θ_{13} \sim 10 °

,

θ_{12} \sim 30 °

,

θ_{23} \sim 38 °

, and

δ_{C P} \sim 240 °

. Potential physical consequences of our model are discussed. Full article

(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports in 2024–2025)

15 pages, 468 KB

Open AccessArticle

Contextual Hidden Fields Preclude the Derivation of Bell-Type Inequalities

by Álvaro G. López

Quantum Rep. 2025, 7(3), 29; https://doi.org/10.3390/quantum7030029 - 20 Jun 2025

Viewed by 520

Abstract

We show that loophole-free Bell-type no-go theorems cannot be derived in theories involving local hidden fields. At the time of measurement, a contextuality loophole appears because each particle’s electromagnetic field interacts with the field of its respective apparatus, preventing the expression of the [...] Read more.

We show that loophole-free Bell-type no-go theorems cannot be derived in theories involving local hidden fields. At the time of measurement, a contextuality loophole appears because each particle’s electromagnetic field interacts with the field of its respective apparatus, preventing the expression of the probability density as a function independent of the orientation of the measuring devices. Then, we use the dynamical evolution of the probability distribution to show that the spin-correlation integral cannot be expressed in terms of initial Cauchy data restricted to the particles. A measurement independence loophole ensues, which prevents the usage of the non-contextual correlation integrals required to demonstrate the CHSH-Bell inequality. We propose that correlated fields are the missing hidden variable triggering the coupled nonlinear oscillations of the particles, which bring about the synchronicities observed in the Einstein–Podolsky–Rosen–Bohm (EPRB) experiment. Full article

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Quantum Rep., Volume 7, Issue 3 (September 2025) – 10 articles

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