Quantum Superposition States Research Articles

Quantum Representation based Preference Evolution Network for E-commerce recommendation

Quantum theory, originally developed to explain microscopic physical systems, has recently emerged as a novel conceptual and mathematical framework in information science. This paper applies quantum theory to address challenges in E-commerce recommendation, specifically those involving sequential behavior, aiming to mine effective patterns of preference evolution and more accurately predict user interests. Current recommender systems are limited by the sequence length and underutilize side information such as item attributes. To address these issues, we propose a Quantum Representation-based Preference Evolution Network (QRPEN) for E-commerce recommendations. Unlike traditional methods that focus solely on item-ID, our approach integrates a comprehensive set of side information, including both item-ID and attribute data, at each timestamp. We represent item attributes using quantum superposition states and employ density matrices to describe the probability distribution of same-type attributes. These matrices are then transformed into vectors through a quantum measurement-inspired process and fed into a Quasi-RNN model, enabling parallelization and the modeling of longer sequences. This approach effectively captures the dynamic evolution of user preferences. Experiments on public E-commerce datasets demonstrate that QRPEN achieves competitive performance.

QSIM: A Quantum-inspired hierarchical semantic interaction model for text classification

Semantic interaction modeling is a fundamental technology in natural language understanding that guides models to extract deep semantic information from text. Currently, the attention mechanism is one of the most effective techniques in semantic interaction modeling, which learns word-level attention representation by measuring the relevance between different words. However, the attention mechanism is limited to word-level semantic interaction, it cannot meet the needs of fine-grained interactive information for some text classification tasks. In recent years, quantum-inspired language modeling methods have successfully constructed quantized representations of language systems in Hilbert spaces, which use density matrices to achieve fine-grained semantic interaction modeling.This paper presents a Quantum-inspired hierarchical Semantic Interaction Model (QSIM), which follows the sememe-word-sentence language construction principle and utilizes quantum entanglement theory to capture hierarchical semantic interaction information in Hilbert space. Our work builds on the idea of the attention mechanism and extends it. Specifically, we explore the original semantic space from a quantum theory perspective and derive the core semantic space using the Schmidt decomposition technique, where: (1) Sememe is represented as the unit vector in the two-dimensional minimum semantic space; (2) Word is represented as reduced density matrices in the core semantic space, where Schmidt coefficients quantify sememe-level semantic interaction. Compared to density matrices, reduced density matrices capture fine-grained semantic interaction information with lower computational cost; (3) Sentence is represented as quantum superposition states of words, and the degree of word-level semantic interaction is measured using entanglement entropy.To evaluate the model’s performance, we conducted experiments on 15 text classification datasets. The experimental results demonstrate that our model is superior to classical neural network models and traditional quantum-inspired language models. Furthermore, the experiment also confirms two distinct advantages of QISM: (1) flexibility, as it can be integrated into various mainstream neural network text classification architectures; and (2) practicability, as it alleviates the problem of parameter growth inherent in density matrix calculation in quantum language model.

Thresholdless coherence in a superradiant laser

Lasing threshold in the conventional lasers is the minimum input power required to initiate laser oscillation. It has been widely accepted that the conventional laser threshold occurring around a unity intracavity photon number can be eliminated in the input-output curve by making the so-called β parameter approach unity. The recent experiments, however, have revealed that even in this case the photon statistics still undergo a transition from coherent to thermal statistics when the intracavity mean photon number is decreased below unity. Since the coherent output is only available above the diminished threshold, the long-sought promise of thresholdless lasers to produce always coherent light has become questionable. Here, we present an always-coherent thresholdless laser based on superradiance by two-level atoms in a quantum superposition state with the same phase traversing a high-Q cavity. Superradiant lasing was observed without the conventional lasing threshold around the unity photon number and the photon statistics remained near coherent even below it. The coherence was improved by reducing the coupling constant as well as the excited-state amplitude in the superposition state. Our results pave a way toward always-coherent thresholdless lasers with more practical media such as quantum dots, nitrogen-vacancy centers and doped ions in crystals.

Extracting work from two gravitational cat states

Gravitational cat states in the context of gravity are superpositions of quantum states that exhibit macroscopically distinct gravitational fields. These states represent a unique blend of quantum mechanics and general relativity, providing insights into the behavior of quantum systems under gravitational influences. This study investigates the impact of thermal environments on the extractable work from gravitational cat states, which are quantum superpositions of distinct gravitational configurations. It aims to offer a comprehensive analysis of how temperature and gravitational interactions between states with masses m influence work extraction. The findings indicate that both an increase in temperature and the interactions between states reduce the amount of work that can be extracted from gravitational cat states, highlighting the delicate balance between thermal and gravitational effects in quantum systems.

Robust Encryption Framework for IoT Devices Based on Bit-plane Extraction, Chaotic Sine Models, and Quantum Operations

In the domain of Internet of Things (IoT) applications, quantum computers offer the promise of addressing complex computational issues that traditional cryptographic methods find challenging. The unparalleled computational power of quantum computers makes existing cryptographic schemes, tailored to mitigate computational complexity, ineffective. This research introduces a robust encryption scheme designed specifically for digital data exchanged between IoT devices such as smartphones, smart sensors, and smart health monitoring devices. The proposed encryption framework is based on bit-plane extraction-based encryption, the chaotic sine model, the hyperchaotic map, the quantum baker map, and quantum operations such as quantum selective scrambling. The proposed methodology involves three key phases: the first and last phase related to permutation, which is performed at the bit level based on discrete bit-plane scrambling, bit-plane extraction, and hyperchaotic mapping. However, the second phase is based on diffusion, which depends on the chaotic sine model. During the initial stage, creating correlations among image pixels, along with a couple of chaotic sequences using a quantum baker map, is accomplished through a superposition of quantum-states. Before applying diffusion, the pixels of the grayscale image are encoded using a single qubit, and quantum operations are based on a quantum circuit featuring swap gates. To introduce pixel-level permutation, a hyperchaotic map generates random sequences within the range of 0 to 255. A circular shift further shuffles the pixel rows and pixel columns of the permuted image pixels. To enhance the digital image security further, bit-planes are extracted from the permuted bit-planes. Then, the bits within each bit plane are scrambled using a random sequence generated by the hyperchaotic map. Finally, the encoded bit planes are merged to produce a final encrypted image. Experimental results demonstrate the effectiveness of the proposed methodology, with security parameters such as correlation, entropy, and key space measuring at 0.0001, 7.999, and >2100, respectively. Furthermore, to assess performance in relation to computational complexity, a detailed analysis of computational time is conducted. The results reveal that the proposed encryption scheme can execute all encryption steps presented in the proposed method in less than one second. These findings demonstrate the secure transmission of digital data between IoT devices and show the suitability of the proposed encryption scheme for real-time applications.

Quick charging of a quantum battery with superposed trajectories

We propose charging protocols for quantum batteries based on quantum superpositions of trajectories. Specifically, we consider that a qubit (the battery) interacts with multiple cavities or a single cavity at various positions, where the cavities act as chargers. Further, we introduce a quantum control prepared in a quantum superposition state, allowing the battery to be simultaneously charged by multiple cavities (the multiple-charger protocol) or a single cavity with different entry positions (the single-charger protocol). To assess the battery's performance, we evaluate the maximum extractable work, referred to as ergotropy. The primary discovery lies in the quick charging effect, wherein we prove that the increase in ergotropy stems from the quantum coherence initially present in the quantum control. Moreover, the induced “Dicke-type interference effect” in the single-charger protocol can further lead to a “perfect charging phenomenon”, enabling a complete conversion of the stored energy into extractable work across the entire charging process, with just two entry positions in superposition. Furthermore, we propose circuit models for these charging protocols and conduct proof-of-principle demonstrations on IBMQ and IonQ quantum processors. The results validate our theoretical predictions, demonstrating a clear enhancement in ergotropy. Published by the American Physical Society 2024

Quantum control of a cat qubit with bit-flip times exceeding ten seconds.

Quantum bits (qubits) are prone to several types of error as the result of uncontrolled interactions with their environment. Common strategies to correct these errors are based on architectures of qubits involving daunting hardware overheads1. One possible solution is to build qubits that are inherently protected against certain types of error, so the overhead required to correct the remaining errors is greatly reduced2-7. However, this strategy relies on one condition: any quantum manipulations of the qubit must not break the protection that has been so carefully engineered5,8. A type of qubit known as a cat qubit is encoded in the manifold of metastable states of a quantum dynamical system, and thereby acquires continuous and autonomous protection against bit-flips. Here, in a superconducting-circuit experiment, we implemented a cat qubit with bit-flip times exceeding 10 s. This is an improvement of four orders of magnitude over previously published cat-qubit implementations. We prepared and imaged quantum superposition states, and measured phase-flip times greater than 490 ns. Most importantly, we controlled the phase of these quantum superpositions without breaking the bit-flip protection. This experiment demonstrates the compatibility of quantum control and inherent bit-flip protection at an unprecedented level, showing the viability of these dynamical qubits for future quantum technologies.

A Study of Quantum Game for Low-Carbon Transportation with Government Subsidies and Penalties

Traditional classical game theory struggles to effectively address the inefficiencies in subsidizing and penalizing the R&D and production of low-carbon transportation vehicles. To avoid the shortcomings of classic game theory, this research integrates quantum game theory with Nash games to explore the characteristics of automakers’ behavior for low-carbon transportation with government subsidies and penalties. We first constructed a low-carbon transportation game model between the government and automakers. Then, the optimal profit strategies for both parties in a quantum entangled state were analyzed. Finally, the impact of quantum superposition states and the initial entangled state on the profit strategies of both parties was simulated and analyzed using Monte Carlo simulations. We find that under the joint effects of government subsidies and penalties, quantum game states and the initial quantum entangled state have a crucial influence on the game’s outcomes. They can encourage the realization of Nash equilibrium and perfect coordination in the quantum game, significantly increasing the profits for both parties. This in turn effectively stimulates automakers to research and produce low-carbon transportation solutions, promoting the rapid development of low-carbon transportation technology. In theory, this research can enrich the Quantum game for improvements in the Nash equilibrium solution for the government to subsidize and penalize the low-carbon transportation problem. Meanwhile, in practice, it can provide guidance and reference in optimal strategy selection conditions for government policymakers and automakers for low-carbon transportation.

Quantum Interference Model for Semantic Biases of Glosses in Word Sense Disambiguation

Word Sense Disambiguation (WSD) aims to determine the meaning of the target word according to the given context. Currently, a single representation enhanced by glosses from different dictionaries or languages is used to characterize each word sense. By analyzing the similarity between glosses of the same word sense, we find semantic biases among them, revealing that the glosses have their own descriptive perspectives. Therefore, the traditional approach of integrating all glosses by a single representation results in failing to present the unique semantics revealed by the individual glosses. In this paper, a quantum superposition state is employed to formalize the representations of multiple glosses of the same word sense to reveal their distributions. Furthermore, the quantum interference model is leveraged to calculate the probability that the target word belongs to this superposition state. The advantage is that the interference term can be regarded as a confidence level to guide word sense recognition. Finally, experiments are performed under standard WSD evaluation framework and the latest cross-lingual datasets, and the results verify the effectiveness of our model.

A Robust Networking Model With Quantum Evolution for Internet of Things

The Internet of Things (IoT), which includes massive energy-limited sensor nodes, has become the foundation of smart city. Improving the ability of network topology to resist node cascading failures, namely robustness, is the key for IoT to provide stable data-aware services for upper-layer applications. However, the robustness optimization problem of complex topology is an NP-hard problem and cannot be optimally solved in polynomial time. The existing researches try to find the approximate solution by heuristic algorithms, but there are problems of slow convergence and easy to fall into local optimum. Quantum computing has more diverse search spaces due to the existence of quantum superposition states, which can jump out of the local optimum. Therefore, this paper firstly combines quantum computing with topology robustness evolution, and proposes a robust networking model based on quantum evolution. By using the quantum encoding, we design a novel quantum measurement method to collapse quantum states towards a more robust network topology. The experimental results show that our model can jump out of the local optimum with fewer population individuals and achieve higher robustness.

Quantum Dynamics of Cavity–Bose–Einstein Condensates in a Gravitational Field

We theoretically studied the quantum dynamics of a cavity–Bose–Einstein condensate (BEC) system in a gravitational field, which is composed of a Fabry–Pérot cavity and a BEC. We also show how to deterministically generate the transient macroscopic quantum superposition states (MQSSs) of the cavity by the use of optomechanical coupling between the cavity field and the BEC. The quantum dynamics of the cavity–BEC system specifically include phase space trajectory dynamics, system excitation number dynamics, quantum entanglement dynamics, and quantum coherence dynamics. We found that the system performs increasingly complex trajectories for larger values of the Newtonian gravity parameter. Moreover, the number of phonon excitations of the system can be increased by coupling the cavity–BEC system to Newtonian gravity, which is analogous to an external direct current drive. The scattering of atoms inside the BEC affects the periodicity of the quantum dynamics of the system. We demonstrate a curious complementarity relation between the quantum entanglement and quantum coherence of cavity–BEC systems and found that the complementarity property can be sustained to some extent, despite being in the presence of the cavity decay. This phenomenon also goes some way to show that quantum entanglement and quantum coherence can be referred to together as quantum resources.

Spontaneous collapse models lead to the emergence of classicality of the Universe

Assuming that Quantum Mechanics is universal and that it can be applied over all scales, then the Universe is allowed to be in a quantum superposition of states, where each of them can correspond to a different space-time geometry. How can one then describe the emergence of the classical, well-defined geometry that we observe? Considering that the decoherence-driven quantum-to-classical transition relies on external physical entities, this process cannot account for the emergence of the classical behaviour of the Universe. Here, we show how models of spontaneous collapse of the wavefunction can offer a viable mechanism for explaining such an emergence. We apply it to a simple General Relativity dynamical model for gravity and a perfect fluid. We show that, by starting from a general quantum superposition of different geometries, the collapse dynamics leads to a single geometry, thus providing a possible mechanism for the quantum-to-classical transition of the Universe. Similarly, when applying our dynamics to the physically-equivalent Parametrised Unimodular gravity model, we obtain a collapse on the basis of the cosmological constant, where eventually one precise value is selected, thus providing also a viable explanation for the cosmological constant problem. Our formalism can be easily applied to other quantum cosmological models where we can choose a well-defined clock variable.

An efficient quantum algorithm for preparation of uniform quantum superposition states

An efficient quantum algorithm for preparation of uniform quantum superposition states

Generating superpositions of quantum states via a beam splitter with position measurement

We use the quadrature measurement to generate the novel nonclassical states via the beam splitter with two input states, i.e., a Fock state and a vacuum state. It is interesting to find that the desired target states are the Hermite polynomial excited vacuum states. Our results have shown that the zero-position detection for the position detector, the little photon number in the input state, and the high transmittance of the beam splitter (BS) are beneficial to improve the detection efficiency of finding the output states. The proposed states quantum statistical properties and squeezing effects are also studied in detail via different criteria. Our numerical analysis demonstrates that the output quantum states are new nonclassical states. Compared with the method of photon catalysis, position detection is easier to realize in experiments. Therefore, the results in this paper shall provide theoretical support for the experimental generation of several new nonclassical states.

Coherence requirements for quantum communication from hybrid circuit dynamics

The coherent superposition of quantum states is an important resource for quantum information processing which distinguishes quantum dynamics and information from their classical counterparts. In this article we determine the coherence requirements to communicate quantum information in a broad setting encompassing monitored quantum dynamics and quantum error correction codes. We determine these requirements by considering hybrid circuits that are generated by a quantum information game played between two opponents, Alice and Eve, who compete by applying unitaries and measurements on a fixed number of qubits. Alice applies unitaries in an attempt to maintain quantum channel capacity, while Eve applies measurements in an attempt to destroy it. By limiting the coherence generating or destroying operations available to each opponent, we determine Alice’s coherence requirements. When Alice plays a random strategy aimed at mimicking generic monitored quantum dynamics, we discover a coherence-tuned phase transitions in entanglement and quantum channel capacity. We then derive a theorem giving the minimum coherence required by Alice in any successful strategy, and conclude by proving that coherence sets an upper bound on the code distance in any stabelizer quantum error correction code. Such bounds provide a rigorous quantification of the coherence resource requirements for quantum communication and error correction.

Double quantum images encryption scheme based on chaotic system

This paper explores a double quantum images representation (DNEQR) model that allows for simultaneous storage of two digital images in a quantum superposition state. Additionally, a new type of two-dimensional hyperchaotic system based on sine and logistic maps is investigated, offering a wider parameter space and better chaotic behavior compared to the sine and logistic maps. Based on the DNEQR model and the hyperchaotic system, a double quantum images encryption algorithm is proposed. Firstly, two classical plaintext images are transformed into quantum states using the DNEQR model. Then, the proposed hyperchaotic system is employed to iteratively generate pseudo-random sequences. These chaotic sequences are utilized to perform pixel value and position operations on the quantum image, resulting in changes to both pixel values and positions. Finally, the ciphertext image can be obtained by qubit-level diffusion using two XOR operations between the position-permutated image and the pseudo-random sequences. The corresponding quantum circuits are also given. Experimental results demonstrate that the proposed scheme ensures the security of the images during transmission, improves the encryption efficiency, and enhances anti-interference and anti-attack capabilities.

Feedback Control of Quantum Systems to Stabilize Superposition States

As a specific trait of quantum mechanics, quantum superposition is exploited in many applications such as quantum computation. This paper proposes a feedback scheme to stabilize the desired quantum superposition states. To this aim, a new factorization is derived for the stochastic master equation of a quantum system which is driven by the field in the superposition of coherent states. Then, a feedback scheme is proposed, which consists of a quantum system driven by the field in the superposition of coherent states and a classical feedback channel proportional to the observations of a Homodyne detector. Afterward, the quantum filter of the closed loop system is attained using the SLH framework. Finally, the factorization of the closed loop quantum filter is obtained and the control law is calculated such that the proposed factorization satisfies the stabilization condition. Finally, as an example, the control method is simulated for a two-level atom and the stabilization of the superposition states is achieved.

Bounds for imaginarity of quantum superpositions

Complex numbers play a key role in classical and quantum physics. Recently, the comprehensive formulation of the resource theory of imaginarity was proposed and various computable and meaningful measures of imaginarity were identified. In this work, we investigate the bounds for imaginarity of quantum superpositions in high dimension using the geometric imaginarity. We establish the relationship between the imaginarity of the superposition of quantum states and the imaginarity of the states being superposed.

Probing the evolution of quantum superposition states in a nuclear spin-5/2 system

Probing the evolution of quantum superposition states in a nuclear spin-5/2 system

A constant round quantum secure protocol for oblivious polynomial evaluation

Oblivious polynomial evaluation (OPE) is a secure two-party cryptographic protocol that enables a receiver to obliviously retrieve polynomial value on its private input for a private polynomial of a sender. This paper deals with the problem of OPE in the quantum domain. Herein, we propose the construction of the first quantum secure OPE, namely QuOPE. Our design is a constant round protocol that only requires quantum communication of one quantum superposition state that achieves all the stipulated security requirements of an OPE. In particular, privacy and security of the sender and receiver’s private data are ensured. In addition, we extend the idea of QuOPE to quantum rational polynomial evaluation (QuORPE). Furthermore, we explore the possibility of utilizing QuOPE as a building block in the automated medical diagnosis platform.