Quantum Superposition States Research Articles

Enhancement of feasibility of macroscopic quantum superposition state with the quantum Rabi-Stark model

We propose an efficient scheme to generate a macroscopical quantum superposition state with a cavity optomechanical system, which is composed of a quantum Rabi-Stark model coupling to a mechanical oscillator. In a low-energy subspace of the Rabi-Stark model, the dressed states and then the effective Hamiltonian of the system are given. Due to the coupling of the mechanical oscillator and the atom-cavity system, if the initial state of the atom-cavity system is one of the dressed states, the mechanical oscillator will evolve into a corresponding coherent state. Thus, if the initial state of the atom-cavity system is a superposition of two dressed states, a coherent state superposition of the mechanical oscillator can be generated. The quantum coherence and their distinguishable properties of the two coherent states are exhibited by Wigner distribution. We show that the Stark term can enhance significantly the feasibility and quantum coherence of the generated macroscopic quantum superposition state of the oscillator.

Some Major Studies in Experimental Verifications of Bell Inequality

Bell inequality plays a crucial role in the debate between quantum mechanical completeness and local realism. It vigorously promoted researches on these aspects, macroscopic quantum superposition states, especially entangled states, and it has brought the debate from theory to experiment, which generated a new discipline, quantum information theory. Thus, this work briefly summarizes some major situations in the verification process of Bell inequality. At the same time, this work analyses existent some problems in the verification process of Bell inequality, and states own perception for the debate.This work can help people better understand the foundation knowledge of quantum information theory, thus quantum information theory can be applied to more actual situations.

Quantum delegated computing ciphertext retrieval scheme

Quantum physics has some unique properties, such as quantum entanglement and quantum superposition. Encryption algorithms designed based on quantum physical properties usually have higher security than classical computing. Applying quantum cryptography to data retrieval can realize cloud database encryption of quantum information. We propose a cloud ciphertext retrieval scheme, which combines quantum encryption and quantum search algorithm to ensure the privacy of data while the server completes information retrieval. In this scheme, the data are stored in the form of qubits string and placed in the quantum superposition state. We establish the mapping relationship between classical information and quantum states. Our scheme solves the problem of a large amount of computing and lack of sufficient computing resources at the client, assigns computing tasks to servers with sufficient resources, and ensures the security of information.

Fast and Robust Image Encryption Scheme Based on Quantum Logistic Map and Hyperchaotic System

Topic of quantum chaos has begun to draw increasing attention in recent years. So, to ensure the security of digital image, an image encryption algorithm based on combining a hyperchaotic system and quantum 3D logistic map is proposed. This algorithm is applied in four stages. Initially, the key generator builds upon the foundation of mean for any row or column of the edges of the plain image. Its output value is used to yield initial conditions and parameters of the proposed image encryption scheme. Next, it diffuses the plain image by the random sequences generated by 3D hyperchaotic system, and the diffusion process is realized by implementing XOR operation. Then, the diffused image and chaotic sequences are produced by the 3D quantum chaotic logistic map, expressed as a quantum superposition state using density matrix which is a representation of the state of a quantum system, and finally the resulting quantum image is then confused and diffused simultaneously by a unitary matrix generated by logistic chaos using XNOR operation to obtain the final cipher image. Because of the dependence on the plain image, the algorithm can frustrate the chosen‐plaintext and known‐plaintext attacks. Simulation results and theoretical analysis verify that the presented scheme has high safety performance, a good encryption effect, and a large key space. The method can effectively resist exhaustive, statistical, and differential attacks. Moreover, the encryption time of the proposed method is satisfactory, and the method can be efficiently used in practice for the secure transmission of image information.

Research progress of material, physics, and device of topological superconductors for quantum computing

Since the physical limit of Moore's law is being approached, many alternative computing methods have been proposed, among which quantum computing is the most concerned and widely studied. Owing to the non closeability of quantum system, the uncontrollable external factors will lead to quantum dissipation and decoherence. In order to avoid the decoherence of quantum superposition state, the fabrication of robust quantum bits has become one of the key factors. Majorana zero mode (MZM) is a quasi-particle emerging in the topological and superconducting hybrid system. It has non-Abelian statistical properties. Therefore, the topological qubit constructed by MZM has natural robustness to quantum decoherence. Despite the arduous exploration by various experimental groups, the experimental verification of MZM is still lacking. This paper reviews the history and main technical routes of quantum computing, focusing on the theory of topological superconductors, observable experimental phenomena, and the latest experimental progress. Furthermore we discuss and analyze the present status of the topological superconductor research. Finally, we prospect the future experiments and applications of topological superconductors in quantum computing.

Efficient Quantum State Preparation for the Cauchy Distribution Based on Piecewise Arithmetic

The benefits of the quantum Monte Carlo algorithm heavily rely on the efficiency of the superposition state preparation. So far, most reported Monte Carlo algorithms use Grover's state preparation algorithm which is suitable for efficiently integrable distribution functions. Consequently, most reported works are based on log-concave distributions, such as normal distributions. However, non-log-concave distributions still have many uses, such as in financial modeling. Recently, a new method was proposed that does not need integration to calculate the rotation angle for state preparation. However, performing efficient state preparation is still difficult due to the high cost associated with high precision and low error in the calculation for the rotation angle. Many methods of quantum state preparation use polynomial Taylor approximations to reduce the computation cost. However, Taylor approximations do not work well with heavy-tailed distribution functions that are not bounded exponentially. In this work, we present a method of efficient state preparation for heavy-tailed distribution functions. Specifically, we present a quantum gate-level algorithm to prepare quantum superposition states based on the Cauchy distribution which is a non-log-concave heavy-tailed distribution. Our procedure relies on a piecewise polynomial function instead of a single Taylor approximation to reduce computational cost and increase accuracy. The Cauchy distribution is an even function, so the proposed piecewise polynomial contains only a quadratic term and a constant term to maintain the simplest approximation of an even function. Numerical analysis shows that the required number of subdomains increases linearly as the approximation error decreases exponentially. Furthermore, the computation complexity of the proposed algorithm is independent of the number of subdomains in the quantum implementation of the piecewise function due to quantum parallelism. An example of the proposed algorithm based on a simulation conducted in Qiskit is presented to demonstrate its capability to perform state preparation based on the Cauchy distribution.

Collapse dynamics and Hilbert-space stochastic processes

Spontaneous collapse models of state vector reduction represent a possible solution to the quantum measurement problem. In the present paper we focus our attention on the Ghirardi–Rimini–Weber (GRW) theory and the corresponding continuous localisation models in the form of a Brownian-driven motion in Hilbert space. We consider experimental setups in which a single photon hits a beam splitter and is subsequently detected by photon detector(s), generating a superposition of photon-detector quantum states. Through a numerical approach we study the dependence of collapse times on the physical features of the superposition generated, including also the effect of a finite reaction time of the measuring apparatus. We find that collapse dynamics is sensitive to the number of detectors and the physical properties of the photon-detector quantum states superposition.

An Overview on Quantum Image Watermarking for Security of COVID-19 Patient Record

The basics of Quantum Information Processing (QIP) is summarized below, in addition to a comprehensive survey of quantum image-based data hiding techniques. QIP is more efficient and provides higher security than classical information processing. A comparative analysis of the Flexible Representation of Quantum Images (FRQI) and Novel Enhanced Quantum Representation (NEQR) model is also presented. QIP is used in various potential applications, hence offering an interesting and demanding area for researchers [1]. Some of the important applications include medicine, military, environmental monitoring, image processing, communications, computations, and cryptography. This article focusses on the processing of information that can be represented using quantum mechanics [2]. Furthermore, coherence, entanglement, and superposition of quantum states makes quantum computing more suitable to its classical counterpart for information storage and processing [1], [3].

Efficient Cauchy distribution based quantum state preparation by using the comparison algorithm

The quantum Monte Carlo algorithm can provide significant speedup compared to its classical counterpart. So far, most reported works have utilized Grover’s state preparation algorithm. However, this algorithm relies on costly controlled Y rotations to apply the correct amplitudes onto the superposition states. Recently, a comparison-based state preparation method was proposed to reduce computational complexity by avoiding rotation operations. One critical aspect of this method is the generation of the comparison threshold associated with the amplitude of the quantum superposition states. The direct computation of the comparison threshold is often very costly. An alternative is to estimate the threshold with a Taylor approximation. However, Taylor approximations do not work well with heavy-tailed distribution functions such as the Cauchy distribution, which is widely used in applications such as financial modeling. Therefore, a new state preparation method needs to be developed. In this study, an efficient comparison-based state preparation method is proposed for the heavy-tailed Cauchy distribution. Instead of a single Taylor approximation for the entire function domain, this study uses quantum piecewise arithmetic to increase accuracy and reduce computational cost. The proposed piecewise function is in the simplest form to estimate the comparison threshold associated with the amplitudes. Numerical analysis shows that the number of required subdomains increases linearly as the maximum tolerated approximation error decreases exponentially. 197 subdomains are required to keep the error below 18192 of the maximum amplitude. Quantum parallelism ensures that the computational complexity of estimating the amplitudes is independent from the number of subdomains.

Quantum superposition demonstrated higher-order topological bound states in the continuum

Higher-order topological insulators, as newly found non-trivial materials and structures, possess topological phases beyond the conventional bulk-boundary correspondence. In previous studies, in-gap boundary states such as the corner states were regarded as conclusive evidence for the emergence of higher-order topological insulators. Here, we present an experimental observation of a photonic higher-order topological insulator with corner states embedded into the bulk spectrum, denoted as the higher-order topological bound states in the continuum. Especially, we propose and experimentally demonstrate a new way to identify topological corner states by exciting them separately from the bulk states with photonic quantum superposition states. Our results extend the topological bound states in the continuum into higher-order cases, providing an unprecedented mechanism to achieve robust and localized states in a bulk spectrum. More importantly, our experiments exhibit the advantage of using the time evolution of quantum superposition states to identify topological corner modes, which may shed light on future exploration between quantum dynamics and higher-order topological photonics.

Generating Long-Lived Macroscopically Distinct Superposition States in Atomic Ensembles.

We propose to create and stabilize long-lived macroscopic quantum superposition states in atomic ensembles. We show that using a fully quantum parametric amplifier can cause the simultaneous decay of two atoms and, in turn, create stabilized atomic Schrödinger cat states. Remarkably, even with modest parameters these intracavity atomic cat states can have an extremely long lifetime, up to 4 orders of magnitude longer than that of intracavity photonic cat states under the same parameter conditions, reaching tens of milliseconds. This lifetime of atomic cat states is ultimately limited to several seconds by extremely weak spin relaxation and thermal noise. Our work opens up a new way toward the long-standing goal of generating large-size and long-lived cat states, with immediate interests both in fundamental studies and noise-immune quantum technologies.

Macroscopic Superposition States in Isolated Quantum Systems

For any choice of initial state and weak assumptions about the Hamiltonian, large isolated quantum systems undergoing Schrodinger evolution spend most of their time in macroscopic superposition states. The result follows from von Neumann's 1929 Quantum Ergodic Theorem. As a specific example, we consider a box containing a solid ball and some gas molecules. Regardless of the initial state, the system will evolve into a quantum superposition of states with the ball in macroscopically different positions. Thus, despite their seeming fragility, macroscopic superposition states are ubiquitous consequences of quantum evolution. We discuss the connection to many worlds quantum mechanics.

Experimental study of decoherence of the two-mode squeezed vacuum state via second harmonic generation

Decoherence remains one of the most serious challenges to the implementation of quantum technology. It appears as a result of the transformation over time of a quantum superposition state into a classical mixture due to the quantum system interacting with the environment. Since quantum systems are never completely isolated from their environment, decoherence therefore cannot be avoided in realistic situations. Decoherence has been extensively studied, mostly theoretically, because it has many important implications in quantum technology, such as in the fields of quantum information processing, quantum communication and quantum computation. Here we report a novel experimental scheme on the study of decoherence of a two-mode squeezed vacuum state via its second harmonic generation signal. Our scheme can directly extract the decoherence of the phase-sensitive quantum correlation $\langle \hat{a}\hat{b}\rangle$ between two entangled modes $a$ and $b$. Such a correlation is the most important characteristic of a two-mode squeezed state. More importantly, this is an experimental study on the decoherence effect of a squeezed vacuum state, which has been rarely investigated.

Using deep learning for digitally controlled STIRAP

Stimulated Raman Adiabatic Passage (STIRAP) is a technique for preparing atoms and molecules in an arbitrary preselected coherent superposition of quantum states, ordinarily controlled by Gaussian laser pulses. We search novel pulse sequences by exploiting deep reinforcement learning algorithms in order to achieve fast and flexible solutions for integer and fractional STIRAP. By using the robustness of the PPO algorithm, we impose the agent to exploit only digital pulses corresponding to on/off states of the control radiation instead of continuous amplitudes. Such method allows to adapt to detuning of the energy levels and disturbances such as dephasing.

Quantum-Inspired Differential Evolution with Grey Wolf Optimizer for 0-1 Knapsack Problem

The knapsack problem is one of the most widely researched NP-complete combinatorial optimization problems and has numerous practical applications. This paper proposes a quantum-inspired differential evolution algorithm with grey wolf optimizer (QDGWO) to enhance the diversity and convergence performance and improve the performance in high-dimensional cases for 0-1 knapsack problems. The proposed algorithm adopts quantum computing principles such as quantum superposition states and quantum gates. It also uses adaptive mutation operations of differential evolution, crossover operations of differential evolution, and quantum observation to generate new solutions as trial individuals. Selection operations are used to determine the better solutions between the stored individuals and the trial individuals created by mutation and crossover operations. In the event that the trial individuals are worse than the current individuals, the adaptive grey wolf optimizer and quantum rotation gate are used to preserve the diversity of the population as well as speed up the search for the global optimal solution. The experimental results for 0-1 knapsack problems confirm the advantages of QDGWO with the effectiveness and global search capability for knapsack problems, especially for high-dimensional situations.

Hyperradiance by a stream of phase-correlated atomic dipole pairs traversing a high-Q cavity

Hyperradiance in which radiation rate exceeds that of superradiance has been theoretically investigated in various coherently-coupled emitter-field systems. In most cases, either proposed setups were experimentally challenging or the mean photon number in a cavity was limited. In this paper, with numerical simulations and analytic calculations, we demonstrate that significant hyperradiance with a large mean photon number can occur in a microlaser system, where pairs of two-level atoms prepared in quantum superposition states traverse a high-Q cavity in the presence of a pump field intersecting the cavity mode. Hyperradiance is induced when the intracavity-pump Rabi frequency is out of phase with respect to the atom-cavity coupling so that the reduction of atomic polarization by the atom-cavity coupling is compensated by the pump Rabi frequency in the steady state to maximize atomic photoemission.

The role of tunable nonlinear dark resonances on vacuum Rabi splitting and optical bistability in an atom-cavity system

The phenomenon of “dark resonances” is a well-known concept in quantum optics and laser spectroscopy. As a general rule, interactions involving in such a “dark state” lead to multiple quantum superposition states that interact coherently and are undesirable. In this paper, two types nonlinear interaction in an atomic cavity, namely the nested and cascaded interactions, are theoretically analyzed how the dark resonances form the dark state peak to modulate the vacuum Rabi splitting (VRS) and optical bistability (OB) behavior. In both the zero- and high order modes, there are four VRS peaks generated in the nested interaction and three in the cascade interaction. Dark resonance can modulate not only the peak number of VRS, but also the OB thresholds. It is found that dark state can determine the asymmetric OB distribution of nested type and symmetric OB distribution of cascade type. Besides that, the distinctive OB thresholds in two kinds of interaction also be studied. The observations not only conceptually extend the conventional “dark resonances” phenomenon, but also opens the door for a variety of new applications in tunable all-optical switch and quantum communication.

Quantum Cognitively Motivated Decision Fusion for Video Sentiment Analysis

Video sentiment analysis as a decision-making process is inherently complex, involving the fusion of decisions from multiple modalities and the so-caused cognitive biases. Inspired by recent advances in quantum cognition, we show that the sentiment judgment from one modality could be incompatible with the judgment from another, i.e., the order matters and they cannot be jointly measured to produce a final decision. Thus the cognitive process exhibits ``quantum-like'' biases that cannot be captured by classical probability theories. Accordingly, we propose a fundamentally new, quantum cognitively motivated fusion strategy for predicting sentiment judgments. In particular, we formulate utterances as quantum superposition states of positive and negative sentiment judgments, and uni-modal classifiers as mutually incompatible observables, on a complex-valued Hilbert space with positive-operator valued measures. Experiments on two benchmarking datasets illustrate that our model significantly outperforms various existing decision level and a range of state-of-the-art content-level fusion approaches. The results also show that the concept of incompatibility allows effective handling of all combination patterns, including those extreme cases that are wrongly predicted by all uni-modal classifiers.

Quantum random access memory via quantum walk

A novel concept of quantum random access memory (qRAM) employing a quantum walk is provided. Our qRAM relies on a bucket brigade scheme to access the memory cells. Introducing a bucket with chirality left and right as a quantum walker, and considering its quantum motion on a full binary tree, we can efficiently deliver the bucket to the designated memory cells, and fill the bucket with the desired information in the form of quantum superposition states. Our procedure has several advantages. First, we do not need to place any quantum devices at the nodes of the binary tree, and hence in our qRAM architecture, the cost to maintain the coherence can be significantly reduced. Second, our scheme is fully parallelized. Consequently, only O(n) steps are required to access and retrieve O(2 n ) data in the form of quantum superposition states. Finally, the simplicity of our procedure may allow the design of qRAM with simpler structures.

Estimating Coherence Measures with Untrusted Devices

AbstractThe superposition of quantum states, quantified by coherence, is a fundamental feature to distinguish quantum mechanics from classical theories. Estimations of coherence with perfectly characterised devices have been well‐studied. However, imperfections or malfunctions of realistic measurement devices might nullify the characterization. Device‐independent (DI) tests allow to witness and quantify the quantum feature of a system, such as entanglement, without trusting the implementation devices. Although DI test is a powerful tool in many quantum information tasks, it generally requires nonlocal settings. Little is known if single party coherence can be witnessed and estimated via untrusted devices. In this work, coherence witnesses and estimations with untrusted devices are systematically studied. First, a no‐go theorem for detecting existences of single party coherence via a DI or semi DI means is proven. A general prepare‐and‐measure semi DI scheme for witnessing and estimating the amount of coherence is then proposed. How to estimate the relative entropy and the l1 norm of single party coherence with analytical and numerical approaches is shown. As coherence is an essential resource for tasks such as quantum random number generation and quantum key distribution, it is expected that this result may shed light on designing new quantum cryptographic schemes.