Superposition Of States Research Articles

Quantum superposition states features recognition method based on convolutional neural networks

Quantum superposition states features recognition method based on convolutional neural networks

Performance investigation of an OAM-SK optical communication system based on a PCNN-LDPC under atmospheric turbulence

This paper proposes a probabilistic convolutional neural network-low density parity check (PCNN-LDPC) demodulation scheme for orbital angular momentum shift keying free-space optical (OAM-SK-FSO) communication systems, with a focus on its bit error rate (BER) performance. Initially, the original information sequences were encoded by a low-density parity check (LDPC) and transformed into superposition state Laguerre Gaussian (LG) beams using a 16-Ary mapping scheme. The transmission of LG beams through atmospheric turbulence was then simulated using the power spectral inversion method, and the dataset was constructed and trained using a convolutional neural network (CNN). During demodulation, the CNN adaptive demodulator was integrated with the LDPC decoding algorithm. Classification probabilities from the CNN adaptive demodulator were used in the LDPC decoding process to enhance the channel estimation credibility. The computational results demonstrate that the BER of the PCNN-LDPC significantly outperforms both the CNN adaptive demodulator and CNN-LDPC demodulation strategy. Additionally, the performances of three LDPC decoding algorithms—min-sum (MS), normalized min-sum (NMS), and offset min-sum (OMS)—are compared, revealing that the probabilistic convolutional neural network-normalized min-sum (PCNN-NMS) achieves the best BER performance, highest convergence efficiency, and greatest decoding stability. These findings provide theoretical references and technical support for studying the BER performance of OAM-SK-FSO communication systems.

Quantum-inspired framework for big data analytics: evaluating the impact of movie trailers and its financial returns

In the context of the growing influence of businesses and marketers on social media platforms, understanding the impact of emotionally charged content on consumer behavior has become increasingly crucial. This study proposes a novel framework, leveraging quantum computing principles, to assess the emotional impact of movie trailers. The framework incorporates big data analytics and utilizes Quantum Walk andQuantum Time Series models to investigate the relationship between a movie trailer's emotional intensity and its financial performance. Unlike sequential problem-solving approach of traditional computing models, Quantum superposition allows exploring multiple options at once. An analysis of 141 movie trailers released after January 1, 2022, revealed a positive correlation between a trailer's emotive score and its financial success. These findings suggest that trailers evoking a stronger emotional response tend to achieve greater box office returns compared to those with a lower emotional impact. This research underscores the pivotal role of emotionally resonant content in shaping consumer behavior and cinematic outcomes. It would offer valuable insights for filmmakers and marketers to optimize audience engagement and financial returns.

DECOHERENCE-RESILIENT READONLY MEMORY ARCHITECTURE USING QUANTUM TECHNOLOGY

Quantum computation draws from theoretical physics, functional analysis, and algorithmic computer science, acting as an interdisciplinary field. The main aim of research in quantum computing is to demonstrate that certain tasks can be completed faster using quantum computers than traditional ones. For this, quantum memory is crucial to developing synchronization tools that coordinate various processes in quantum computers and quantum gates that preserve the identity of quantum states, such as superpositions, and methods to convert preset photons into on-demand photons. Quantum memories are essential for large-scale photonic quantum computing systems, enabling the coherent manipulation, buffering, and retiming of photonic signals. Unlike classical memory, quantum memory allows states to exist in quantum superposition, offering greater flexibility for quantum algorithms than conventional storage systems. While traditional Read-Only Memory (ROM) tends to be slower, quantum computing facilitates the development of novel computer types that operate with qubits as input states, leading to increased storage capacity. This paper proposes a quantum-based ROM (QROM) architecture that utilizes quantum-based binary logic operations and presents an analysis of the systems performance, focusing on heat generation and speed parameters.

Quantum computing for swarm robotics: a local-to-global approach.

Quantum computing is a branch of computer science derived from the fundamental laws of quantum mechanics, such as state superposition, multi-value logic and destructive measure. An open challenge in itself is to re-think in quantum terms classic problems and solving techniques. Another nature-inspired field is the development of swarm-based robotic applications, where the challenge is catching the fundamental laws governing swarm dynamics, such as pattern formation and target reaching. Here, we review some recent approaches on swarm dynamics, the organizational rules of which are formalized according to quantum computing. In this way, the shades of probability in decision-making for multiple-robot systems can be expressed according to the multi-value logic underlying quantum computing. In our review, specific quantum circuits are sketched to give an idea of how these problems have been faced in computational terms. The article is enriched by references to sonification, a strategy adding one more sensory dimension to data representation, a human-friendly tool to navigate the complexity of swarm-robotic movements in a given arena.This article is part of the theme issue 'The road forward with swarm systems'.

Isotropic and anisotropic edge enhancement using a lemon-star polarization dipole.

A spiral phase filter can perform a radial Hilbert transform (RHT) and is useful in isotropic edge enhancement. For selective edge enhancement, the inclusion of anisotropy warrants the filter to be replaced. In this Letter, we introduce for the first time, to our knowledge, a novel and versatile filter that can be tuned between isotropic/anisotropic edge detection and contrast enhancement protocols. To achieve this, we use a lemon-star polarization dipole: a special kind of spin-orbit beam that is a superposition of spin and orbital angular momentum states of light. We devised a 4f imaging setup in microscope configuration to encode the object Fourier spectrum into inhomogeneous polarization distribution. The novelty and advantages of the proposed method lie in selecting the spatial frequency content through polarization transformations in the image reconstruction path, just before the detector, without altering the Fourier plane parameters. Considering a scalar-to-vector diffraction approach and invoking the polarization degree of freedom of light, the edge enhancement capabilities of a lemon-star polarization dipole and a monopole (star or lemon) are shown through experiment results.

Probabilistic genotype-phenotype maps reveal mutational robustness of RNA folding, spin glasses, and quantum circuits

Recent studies of genotype-phenotype maps have reported universally enhanced phenotypic robustness to genotype mutations, a feature essential to evolution. Virtually all of these studies make a simplifying assumption that each genotype—represented as a sequence—maps deterministically to a single phenotype, such as a discrete structure. Here we introduce probabilistic genotype-phenotype (PrGP) maps, where each genotype maps to a vector of phenotype probabilities, as a more realistic and universal language for investigating robustness in a variety of physical, biological, and computational systems. We study three model systems to show that PrGP maps offer a generalized framework which can handle uncertainty emerging from various physical sources: (1) thermal fluctuation in RNA folding, (2) external field disorder in the spin-glass ground state search problem, and (3) superposition and entanglement in quantum circuits, which are realized experimentally on IBM quantum computers. In all three cases, we observe a biphasic robustness scaling which is enhanced relative to random expectation for more frequent phenotypes and approaches random expectation for less frequent phenotypes. We derive an analytical theory for the behavior of PrGP robustness, and we demonstrate that the theory is highly predictive of empirical robustness. Published by the American Physical Society 2025

Tighter Heisenberg limits for phase estimation in noisy environments based on the quantum Ziv-Zakai bound

In exploring the precision limits of quantum metrology, the quest for a tighter Heisenberg limit in real-world environments becomes a key challenge. For this reason, in this paper, we propose a tighter Heisenberg limit for phase estimation, called the photon loss (PL)-type bound and the photon diffusion (PD)-type bound in realistic scenarios under the framework of quantum Ziv-Zakai bound (QZZB). In order to demonstrate the superiority of the proposed Heisenberg limits for phase estimation, as a comparison, we also introduce the Margolus-Levitin (ML)-type and Mandelstam-Tamm (MT)-type bounds [Phys. Rev. A 90, 043818 (2014)10.1103/PhysRevA.90.043818] based on the QZZB framework when considering the same initial states, i.e., a coherent state, a superposition state of the vacuum and general Fock states, and an even coherent state. The simulation results show that for photon-loss scenario, the PL-type bounds for all given initial states are closer to the QZZB than the ML-type and MT-type bounds, thereby exhibiting a tighter Heisenberg limit. In contrast, for the phase-diffusion scenario, when the phase diffusion strength exceeds a certain threshold, the tightness of PD-type bounds for the coherent state and superposition state can present better than that of the ML-type and MT-type bounds. Furthermore, the tighter QZZB over the QCRB can be achieved using the superposition state in photon loss or the even coherent state in phase diffusion.

Decoherence-enabled unconditional strongly sub-Poissonian squeezing

It is generally accepted that the role of quantum decoherence is to spoil the quantum superpositions and to yield the emergence of the classical behaviors from quantum mechanics. Contrary to the common knowledge of decoherence, we propose a scheme to generate a steady-state bright source of strongly sub-Poissonian squeezed light using the environmentally induced decoherence. The disappearance of the process of decoherence disables the generation of the squeezed state of the combination modes, while the presence of the decoherence results in the strongly nonclassical light source at the sub-shot-noise level and even near-perfect sub-Poissonian squeezed state of light. This excludes the use of the paradigm that the good insulation of a quantum system from its surrounding environment is highly desirable to explore its quantum property and fuel the growth of quantum information science. The interactions with the atom make no contribution to the preparation of squeezed light. These counterintuitive results are originated from the intrinsic quantum reservoir in the dressed-atom combination mode picture, which may open the door to exploring high levels of squeezing induced by the decoherence in the stationary regime. Published by the American Physical Society 2025

Adaptive Circuit Learning of Born Machine: Towards Realization of Amplitude Embedding and Quantum Data Loading

Abstract Quantum data loading plays a central role in quantum algorithms and quantum information processing. Many quantum algorithms hinge on the ability to prepare arbitrary superposition states as a subroutine, with claims of exponential speedups often predicated on access to an efficient data-loading oracle. In practice, constructing a circuit to prepare a generic $n$-qubit quantum state typically demands computational efforts scaling as $\mathcal{O}(2^n)$, posing a significant challenge for quantum algorithms to outperform their classical counterparts. To address this critical issue, various hybrid quantum-classical approaches have been proposed. However, many of these solutions favor simplistic circuit architectures, which are susceptible to substantial optimization challenges.

In this study, we harness quantum circuits as Born machines to generate probability distributions. Drawing inspiration from methods used to investigate electronic structures in quantum chemistry and condensed matter physics, we propose a framework called Adaptive Circuit Learning of Born Machine, which dynamically expands the ansatz circuit. Our algorithm is designed to selectively integrate two-qubit entangled gates that best capture the intricate entanglement present within the target state. 
Empirical experiments underscore the efficacy of our approach in encoding real-world data through amplitude embedding, demonstrating not only compliance with but also enhancement over the performance benchmarks set by prior research.

How analogies helped novice students think about superposition states and collapse in quantum mechanics

In my active learning course on quantum mechanics, students build their knowledge by following the scientific process as outlined by the Investigative Science Learning Environment. In this course, open-ended questions on the effect of measurement (collapse) failed to elicit meaningful responses from students. Meaningful responses are crucial for the next steps of testing students’ ideas using hypothetico-deductive reasoning. I wanted to help the students in this process with a pictorial representation. To arrive at a pictorial representation that would have meaning for students, I first asked them to provide their analogies for a superposition state. A common suggestion was the mixture of colours, but other, more inventive analogies were also suggested. I developed a pictorial representation based on the colour analogy. I reformulated the questions on collapse using this representation and a more concretized formulation. The ability of students to meaningfully answer the questions increased to the point where it was possible to complete also the testing part of the process. In the article, I discuss the analogies that students suggested and what underlying ideas known from literature they could represent. I provide the derived representation, the reformulated questions and evidence of how this helped students articulate their answers and helped identify students’ productive ideas that they could not clearly articulate in words. This enabled students to arrive at conclusions about the effect of measurement following the scientific process. This study contributes to the literature by providing student-generated analogies, using a pictorial representation derived from student-generated analogies, and showing an example of an efficiently formulated question on a difficult topic that is able to elicit meaningful responses.

Faster and Better Quantum Software Testing through Specification Reduction and Projective Measurements

Quantum computing (QC) promises polynomial and exponential speedups in many domains, such as unstructured search and prime number factoring. However, quantum programs yield probabilistic outputs from exponentially growing distributions and are vulnerable to quantum-specific faults. Existing quantum software testing (QST) approaches treat quantum superpositions as classical distributions. This leads to two major limitations when applied to quantum programs: (1) an exponentially growing sample space distribution and (2) failing to detect quantum-specific faults such as phase flips. To overcome these limitations, we introduce a QST approach, which applies a reduction algorithm to a quantum program specification. The reduced specification alleviates the limitations (1) by enabling faster sampling through quantum parallelism and (2) by performing projective measurements in the mixed Hadamard basis. Our evaluation of 143 quantum programs across four categories demonstrates significant improvements in test runtimes and fault detection with our reduction approach. Average test runtimes improved from 169.9s to 11.8s, with notable enhancements in programs with large circuit depths (383.1s to 33.4s) and large program specifications (464.8s to 7.7s). Furthermore, our approach increases mutation scores from \(54.5\%\) to \(74.7\%\) , effectively detecting phase flip faults that non-reduced specifications miss. These results underline our approach’s importance to improve QST efficiency and effectiveness

Decoherence of quantum superpositions by Reissner-Nordström black holes

Recently, it was shown by Danielson (DSW) that, for the massive or charged body in a quantum spatial separated superposition state, the presence of a black hole can decohere the superposition inevitably toward capturing the radiation of soft photons or gravitons [D. L. Danielson , Black holes decohere quantum superpositions, ; D. L. Danielson , Killing horizons decohere quantum superpositions, ; D. L. Danielson , Local description of decoherence of quantum superpositions by black holes and other bodies, ]. In this work, we study the DSW decoherence effect for the static charged body in the Reissner-Nordström black holes. By calculating the decohering rate for this case, it is shown that the superposition is decohered by the low-frequency photons that propagate through the black hole horizon. For the extremal Reissner-Nordström black hole, the decoherence of quantum superposition is completely suppressed due to the black hole Meissner effect. It is also found that the decoherence effect caused by the Reissner-Nordström black hole is equivalent to that of an ordinary matter system with the same size and charge. Published by the American Physical Society 2025

Local description of decoherence of quantum superpositions by black holes and other bodies

It was previously shown that if an experimenter, Alice, puts a massive or charged body in a quantum spatial superposition, then the presence of a black hole (or more generally any Killing horizon) will eventually decohere the superposition. This decoherence was identified as resulting from the radiation of soft photons/gravitons through the horizon, thus suggesting that the global structure of the spacetime is essential for describing the decoherence. In this paper, we show that the decoherence can alternatively be described in terms of the local two-point function of the quantum field within Alice’s lab, without any direct reference to the horizon. From this point of view, the decoherence of Alice’s superposition in the presence of a black hole arises from the extremely low frequency Hawking quanta present in Alice’s lab. We explicitly calculate the decoherence occurring in Schwarzschild spacetime in the Unruh vacuum from the local viewpoint. We then use this viewpoint to elucidate (i) the differences in decoherence effects that would occur in Schwarzschild spacetime in the Boulware and Hartle-Hawking vacua; (ii) the difference in decoherence effects that would occur in Minkowski spacetime filled with a thermal bath as compared with Schwarzschild spacetime; (iii) the lack of decoherence in the spacetime of a static star even though the vacuum state outside the star is similar in many respects to the Boulware vacuum around a black hole; and (iv) the requirements on the degrees of freedom of a material body needed to produce a decoherence effect that mimics that of a black hole. Published by the American Physical Society 2025

Entanglement swapping using hyperentangled pairs of two‐level neutral atoms

AbstractHyperentangled swapping is a quantum communication technique that involves the exchange of hyperentangled states, which are quantum states entangled in multiple degrees of freedom, to enable secure and efficient quantum information transfer. In this paper, we demonstrate schematics for the hyperentanglement swapping between separate pairs of neutral atoms through the mathematical framework of atomic Bragg diffraction, which is efficient and resistant to decoherence, yielding deterministic results with superior overall fidelity. The utilised cavities are in a superposition state and interact with the incoming atoms off‐resonantly. Quantum information carried by the cavities is swapped through resonant interactions with two‐level auxiliary atoms. We also discuss entanglement swapping under a delayed‐choice scenario and provide a schematic generalisation covering multiple‐qubit scenarios. Finally, we introduce specific experimental parameters to demonstrate the experimental feasibility of the scheme.

Coherent Excitation of the CH Stretching Vibrations in C2H4 +: The Role of the Derivative Coupling Studied by theQuantum Ehrenfest Method.

We report nonadiabatic dynamics computations on C2H4 + initiated on a coherent superposition of the five lowest cationic states, employing the Quantum Ehrenfest method. In addition to the totally symmetric carbon-carbon double bond stretch and carbon-hydrogen stretches, we see that the three non-totally symmetric modes become stimulated; torsion and three different CH stretching patterns. Thus, a coherent superposition of states, of the type involved in an attochemistry experiment, leads to the stimulation of specific non-totally symmetric motions. The computations were also performed on the specific combination of the A and C states. In each case normal mode 9 (cis-asymmetric H2CCH2 stretch), out of the set of non-totally-symmetric normal modes, dominates. Thus, we can steer the nuclear motion along specific non-totally symmetric normal modes using a defined coherent superposition.

Tailoring beam profile and OAM spectrum in domain-engineered nonlinear photonic crystals

Nonlinear frequency conversion provides a powerful tool to generate and manipulate structured light at new wavelengths. In this work, to meet the demands of applications such as high-capacity optical communications and high-dimensional entanglement generation, we use ferroelectric domain engineering to generate frequency-doubled light beams carrying orbital angular momentum (OAM) superposition states and with adjustable radial intensity distribution. Angular and radial phase modulations were introduced into the modulation function of the second-order nonlinear coefficient distribution of lithium tantalate nonlinear photonic crystals, achieving simultaneous tailoring of the OAM spectrum and the radial intensity profile of the second harmonic (SH) waves. As a representative example, we demonstrate the generation of a SH wave that carries a comb-like OAM spectrum, with the radial intensity distribution concentrating on a ring with a specific radius. In addition, the nonlinear photonic devices developed in this work feature polarization insensitivity and broadband characteristics.

Quantum walk option pricing model based on binary tree

In this paper, we present a novel quantum model for financial markets constructed within the risk-neutral framework. We innovatively integrate the theory of quantum walks into the binomial tree model for option pricing, thereby achieving a more precise simulation of asset price dynamics. Furthermore, we explore the multi-step quantum binomial tree model and enhance the traditional approach by incorporating the concept of quantum superposition. This advancement enables our model to simultaneously consider multiple states of asset prices at various nodes, effectively reducing computational complexity as time steps increase while significantly improving option pricing accuracy. The superior performance of our quantum model is demonstrated through simulation experiments.

Spintronic effects and devices in nonlinear optics

In this perspective article, we discuss the analogy between spin transport in magnetization texture and the nonlinear process of sum frequency generation, where the signal and idler complex amplitudes represent the two-dimensional spinor, while the nonlinear coupling represents the material magnetization. This analogy unveils new nonlinear optical effects in both spatial and temporal domains, including the analog of the famous Stern–Gerlach effect, the topological Hall effect in magnetic skyrmion structures, and the transverse localization of spin currents in a disordered magnetic spin-glass phase. Moreover, it enables us to realize new all-optical devices that manipulate superposition states of the signal and idler. Examples include a pump-controlled spin valve, which can either reflect or transmit the signal-idler waves when they are in-phase, and a spin waveguide that guides only in-phase signal-idler waves.

Superselection Rules and Bosonic Quantum Computational Resources.

We present a method to systematically identify and classify quantum optical nonclassical states as classical or nonclassical based on the resources they create on a bosonic quantum computer. This is achieved by converting arbitrary bosonic states into multiple modes, each occupied by a single photon, thereby defining qubits of a bosonic quantum computer. Starting from a bosonic classical-like state in a representation that explicitly respects particle number superselection rules, we apply universal gates to create arbitrary superpositions of states with the same total particle number. The nonclassicality of the corresponding states can then be associated with the operations they induce in the quantum computer. We also provide a correspondence between the adopted representation and the more conventional one in quantum optics, where superpositions of Fock states describe quantum optical states, and we identify how multimode states can lead to quantum advantage. Our work contributes to establish a seamless transition from continuous to discrete properties of quantum optics while laying the grounds for a description of nonclassicality and quantum computational advantage that is applicable to spin systems as well.