Quantum Reports

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63 pages, 3691 KiB

Open AccessArticle

Contribution to the Statistical Mechanics of Static Triplet Correlations and Structures in Fluids with Quantum Spinless Behavior

by Luis M. Sesé

Quantum Rep. 2024, 6(4), 564-626; https://doi.org/10.3390/quantum6040038 - 3 Nov 2024

Viewed by 656

Abstract

The current developments in the theory of quantum static triplet correlations and their associated structures (real r-space and Fourier k-space) in monatomic fluids are reviewed. The main framework utilized is Feynman’s path integral formalism (PI), and the issues addressed cover quantum [...] Read more.

The current developments in the theory of quantum static triplet correlations and their associated structures (real r-space and Fourier k-space) in monatomic fluids are reviewed. The main framework utilized is Feynman’s path integral formalism (PI), and the issues addressed cover quantum diffraction effects and zero-spin bosonic exchange. The structures are associated with the external weak fields that reveal their nature, and due attention is paid to the underlying pair-level structures. Without the pair, level one cannot fully grasp the triplet extensions in the hierarchical ladder of structures, as both the pair and the triplet structures are essential ingredients in the triplet response functions. Three general classes of PI structures do arise: centroid, total continuous linear response, and instantaneous. Use of functional differentiation techniques is widely made, and, as a bonus, this leads to the identification of an exact extension of the “classical isomorphism” when the centroid structures are considered. In this connection, the direct correlation functions, as borrowed from classical statistical mechanics, play a key role (either exact or approximate) in the corresponding quantum applications. Additionally, as an auxiliary framework, the traditional closure schemes for triplets are also discussed, owing to their potential usefulness for rationalizing PI triplet results. To illustrate some basic concepts, new numerical calculations (path integral Monte Carlo PIMC and closures) are reported. They are focused on the purely diffraction regime and deal with supercritical helium-3 and the quantum hard-sphere fluid. Full article

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

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17 pages, 630 KiB

Open AccessArticle

Quantum-Based Maximum Likelihood Detection in MIMO-NOMA Systems for 6G Networks

by Helen Urgelles, David Garcia-Roger and Jose F. Monserrat

Quantum Rep. 2024, 6(4), 533-549; https://doi.org/10.3390/quantum6040036 - 22 Oct 2024

Viewed by 1135

Abstract

As wireless networks advance toward the Sixth Generation (6G), which will support highly heterogeneous scenarios and massive data traffic, conventional computing methods may struggle to meet the immense processing demands in a resource-efficient manner. This paper explores the potential of quantum computing (QC) [...] Read more.

As wireless networks advance toward the Sixth Generation (6G), which will support highly heterogeneous scenarios and massive data traffic, conventional computing methods may struggle to meet the immense processing demands in a resource-efficient manner. This paper explores the potential of quantum computing (QC) to address these challenges, specifically by enhancing the efficiency of Maximum-Likelihood detection in Multiple-Input Multiple-Output (MIMO) Non-Orthogonal Multiple Access (NOMA) communication systems, an essential technology anticipated for 6G. The study proposes the use of the Quantum Approximate Optimization Algorithm (QAOA), a variational quantum algorithm known for providing quantum advantages in certain combinatorial optimization problems. While current quantum systems are not yet capable of managing millions of physical qubits or performing high-fidelity, long gate sequences, the results indicate that QAOA is a promising QC approach for radio signal processing tasks. This research provides valuable insights into the potential transformative impact of QC on future wireless networks. This sets the stage for discussions on practical implementation challenges, such as constrained problem sizes and sensitivity to noise, and opens pathways for future research aimed at fully harnessing the potential of QC for 6G and beyond. Full article

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

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16 pages, 381 KiB

Open AccessArticle

Ancilla-Mediated Higher Entanglement as T-Duality, a Categorial Conjecture

by Andrei T. Patrascu

Quantum Rep. 2024, 6(3), 493-508; https://doi.org/10.3390/quantum6030033 - 13 Sep 2024

Cited by 1 | Viewed by 1005

Abstract

In this article, I start with a general presentation of the ideas behind sigma models and higher gauge theories and introduce the possibility of a higher entanglement structure. Using a higher categorial interpretation of entanglement involving gauge theories and

σ

-models instead of [...] Read more.

In this article, I start with a general presentation of the ideas behind sigma models and higher gauge theories and introduce the possibility of a higher entanglement structure. Using a higher categorial interpretation of entanglement involving gauge theories and

σ

-models instead of qubits, one recovers T-duality as a form of ancilla aided entanglement generation. This opens the way towards new dualities in gauge theories and

σ

-models produced by means of analogies with quantum circuits of various types. Full article

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

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17 pages, 377 KiB

Open AccessArticle

Hidden Variables in Quantum Mechanics from the Perspective of Boltzmannian Statistical Mechanics

by Dustin Lazarovici

Quantum Rep. 2024, 6(3), 465-481; https://doi.org/10.3390/quantum6030031 - 6 Sep 2024

Viewed by 886

Abstract

This paper examines no-hidden-variables theorems in quantum mechanics from the point of view of statistical mechanics. It presents a general analysis of the measurement process in the Boltzmannian framework that leads to a characterization of (in)compatible measurements and reproduces several features of quantum [...] Read more.

This paper examines no-hidden-variables theorems in quantum mechanics from the point of view of statistical mechanics. It presents a general analysis of the measurement process in the Boltzmannian framework that leads to a characterization of (in)compatible measurements and reproduces several features of quantum probabilities often described as “non-classical”. The analysis is applied to versions of the Kochen–Specker and Bell theorems to shed more light on their implications. It is shown how, once the measurement device and the active role of the measurement process are taken into account, contextuality appears as a natural feature of random variables. This corroborates Bell’s criticism that no-go results of the Kochen–Specker type are based on gratuitous assumptions. In contrast, Bell-type theorems are much more profound, but should be understood as nonlocality theorems rather than no-hidden-variables theorems. Finally, the paper addresses misunderstandings and misleading terminology that have confused the debate about hidden variables in quantum mechanics. Full article

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

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35 pages, 986 KiB

Open AccessArticle

Digital Quantum Simulation of Scalar Yukawa Coupling

by Thierry N. Kaldenbach, Matthias Heller, Gernot Alber and Vladimir M. Stojanović

Quantum Rep. 2024, 6(3), 366-400; https://doi.org/10.3390/quantum6030024 - 18 Jul 2024

Viewed by 1039

Abstract

Motivated by the revitalized interest in the digital simulation of medium- and high-energy physics phenomena, we investigate the dynamics following a Yukawa interaction quench on IBM Q. Adopting the zero-dimensional version of the scalar Yukawa coupling model as our point of departure, we [...] Read more.

Motivated by the revitalized interest in the digital simulation of medium- and high-energy physics phenomena, we investigate the dynamics following a Yukawa interaction quench on IBM Q. Adopting the zero-dimensional version of the scalar Yukawa coupling model as our point of departure, we design low-depth quantum circuits, emulating its dynamics with up to three bosons. In the one-boson case, we demonstrate circuit compression, i.e., a constant-depth circuit containing only two controlled-NOT (CNOT) gates. In the more complex three-boson case, we design a circuit in which one Trotter step entails eight CNOTs. Using an analogy with the traveling salesman problem, we also provide a CNOT cost estimate for higher boson number truncations. Based on these circuits, we quantify the system dynamics by evaluating the expected boson number at an arbitrary time after the quench and the survival probability of the initial vacuum state (the Loschmidt echo). We also utilize these circuits to drive adiabatic transitions and compute the energies of the ground- and first-excited states of the considered model. Finally, through error mitigation, i.e., zero-noise extrapolation, we demonstrate the good agreement of our results with a numerically exact classical benchmark. Full article

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

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7 pages, 256 KiB

Open AccessArticle

Quantum Theory of Lee–Naughton–Lebed’s Angular Effect in Strong Electric Fields

by Andrei G. Lebed

Quantum Rep. 2024, 6(3), 359-365; https://doi.org/10.3390/quantum6030023 - 17 Jul 2024

Viewed by 946

Abstract

Some time ago, Kobayashi et al. experimentally studied the so-called Lee–Naughton–Lebed’s (LNL) angular effect in strong electric fields [Kobayashi, K.; Saito, M.; Omichi E.; Osada, T. Phys. Rev. Lett. 2006, 96, 126601]. They found that strong electric fields split the [...] Read more.

Some time ago, Kobayashi et al. experimentally studied the so-called Lee–Naughton–Lebed’s (LNL) angular effect in strong electric fields [Kobayashi, K.; Saito, M.; Omichi E.; Osada, T. Phys. Rev. Lett. 2006, 96, 126601]. They found that strong electric fields split the LNL conductivity maxima in an

α

-(ET)₂-based organic conductor and hypothetically introduced the corresponding equation for conductivity. In this paper, for the first time, we suggest the quantum mechanical theory of the LNL angular oscillations in moderately strong electric fields. In particular, we demonstrate that the approximate theoretical formula obtained by us well describes the above mentioned experiments. Full article

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

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31 pages, 2408 KiB

Open AccessFeature PaperArticle

A Dyson Brownian Motion Model for Weak Measurements in Chaotic Quantum Systems

by Federico Gerbino, Pierre Le Doussal, Guido Giachetti and Andrea De Luca

Quantum Rep. 2024, 6(2), 200-230; https://doi.org/10.3390/quantum6020016 - 16 May 2024

Cited by 2 | Viewed by 1361

Abstract

We consider a toy model for the study of monitored dynamics in many-body quantum systems. We study the stochastic Schrödinger equation resulting from continuous monitoring with a rate

Γ

of a random Hermitian operator, drawn from the Gaussian unitary ensemble (GUE) at every [...] Read more.

We consider a toy model for the study of monitored dynamics in many-body quantum systems. We study the stochastic Schrödinger equation resulting from continuous monitoring with a rate

Γ

of a random Hermitian operator, drawn from the Gaussian unitary ensemble (GUE) at every time t. Due to invariance by unitary transformations, the dynamics of the eigenvalues

{λ_{α}}_{α = 1}^{n}

of the density matrix decouples from that of the eigenvectors, and is exactly described by stochastic equations that we derive. We consider two regimes: in the presence of an extra dephasing term, which can be generated by imperfect quantum measurements, the density matrix has a stationary distribution, and we show that in the limit of large size

n \to \infty

it matches with the inverse-Marchenko–Pastur distribution. In the case of perfect measurements, instead, purification eventually occurs and we focus on finite-time dynamics. In this case, remarkably, we find an exact solution for the joint probability distribution of

λ

’s at each time t and for each size n. Two relevant regimes emerge: at short times

t Γ = O (1)

, the spectrum is in a Coulomb gas regime, with a well-defined continuous spectral distribution in the

n \to \infty

limit. In that case, all moments of the density matrix become self-averaging and it is possible to exactly characterize the entanglement spectrum. In the limit of large times

t Γ = O (n)

, one enters instead a regime in which the eigenvalues are exponentially separated

\log (λ_{α} / λ_{β}) = O (Γ t / n)

, but fluctuations

\sim O (\sqrt{Γ t / n})

play an essential role. We are still able to characterize the asymptotic behaviors of the entanglement entropy in this regime. Full article

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

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12 pages, 4665 KiB

Open AccessFeature PaperArticle

Spectral Analysis of Proton Eigenfunctions in Crystalline Environments

by Luca Gamberale and Giovanni Modanese

Quantum Rep. 2024, 6(2), 172-183; https://doi.org/10.3390/quantum6020014 - 6 May 2024

Cited by 1 | Viewed by 947

Abstract

The Schrödinger equation and Bloch theorem are applied to examine a system of protons confined within a periodic potential, accounting for deviations from ideal harmonic behavior due to real-world conditions like truncated and non-quadratic potentials, in both one-dimensional and three-dimensional scenarios. Numerical computation [...] Read more.

The Schrödinger equation and Bloch theorem are applied to examine a system of protons confined within a periodic potential, accounting for deviations from ideal harmonic behavior due to real-world conditions like truncated and non-quadratic potentials, in both one-dimensional and three-dimensional scenarios. Numerical computation of the energy spectrum of bound eigenfunctions in both cases reveals intriguing structures, including bound states with degeneracy matching the site number

N_{w}

, reminiscent of a finite harmonic oscillator spectrum. In contrast to electronic energy bands, the proton system displays a greater number of possible bound states due to the significant mass of protons. Extending previous research, this study rigorously determines the constraints on the energy gap and oscillation amplitude of the previously identified coherent states. The deviations in energy level spacing identified in the computed spectrum, leading to the minor splitting of electromagnetic modes, are analyzed and found not to hinder the onset of coherence. Finally, a more precise value of the energy gap is determined for the proton coherent states, ensuring their stability against thermal decoherence up to the melting temperature of the hosting metal. Full article

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

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