Measurement Of Quantum States Research Articles

Image Similarity Quantum Algorithm and Its Application in Image Retrieval Systems

The measurement of image similarity represents a fundamental task within the domain of image processing, enabling the application of sophisticated computational techniques to ascertain the degree of similarity between two images. To enhance the performance of these similarity measurement algorithms, the academic community has investigated a range of quantum algorithms. Notably, the swap test-based quantum inner product algorithm (ST-QIP) has emerged as a pivotal method for computing image similarity. However, the inherent destructive nature of the swap test necessitates multiple quantum state evolutions and measurements, which leads to consumption of quantum resources and prolonged computational time, ultimately constraining its practical applicability. To address these limitations, this study introduces an advanced quantum inner product algorithm based on amplitude estimation (AE-QIP) designed to compute image similarity. This innovative approach circumvents the repetitive measurement processes associated with the swap test, thereby optimizing the utilization of quantum resources and substantially enhancing the algorithm’s performance. We conducted experiments using a quantum simulator to implement the AE-QIP algorithm and evaluate its effectiveness in the image retrieval tasks. It is found that the AE-QIP algorithm achieves comparable precision to the ST-QIP algorithm while exhibiting significant reductions in qubit consumption and average processing time. Additionally, our findings suggest that increasing the number of ancillary qubits can further enhance the accuracy of the AE-QIP algorithm. Overall, within the acceptable error thresholds, the AE-QIP algorithm exhibits enhanced efficiency relative to the ST-QIP algorithm. However, significant further research is needed to address the challenges involved in optimizing the performance of quantum retrieval systems as a whole.

Multi‐Party Semi‐Quantum Private Comparison Protocol of Size Relation with d‐Level GHZ States

AbstractA new multi‐party semi‐quantum private comparison protocol of size relation is designed based on d‐level GHZ states. Multiple classical participants could compare their privacies while keeping them secure under an ideal environment. Compared with some similar protocols, the classical participants in the designed protocol do not need to prepare and measure quantum states. Besides, the qubit efficiency of the protocol reaches 33.33%. It is demonstrated that the output result of the proposed protocol is correct. Finally, security analysis manifests that the proposed protocol behaves well in withstanding intercept‐resend attack, measure‐resend attack, entanglement attack, Trojan horse attack, and so on.

Variational quantum algorithm for designing quantum information maskers* *Supported by the National Natural Science Foundation of China (under Grant Nos. 12105090 and 12074107), the Program of Outstanding Young and Middle-aged Scientific and Technological Innovation Team of Colleges and Universities in Hubei Province of China (under Grant No. T2020001), and the Innovation Group Project of the Natural Science Foundation of Hubei

Since the concept of quantum information masking was proposed by Modi et al (2018 Phys. Rev. Lett. 120, 230 501), many interesting and significant results have been reported, both theoretically and experimentally. However, designing a quantum information masker is not an easy task, especially for larger systems. In this paper, we propose a variational quantum algorithm to resolve this problem. Specifically, our algorithm is a hybrid quantum–classical model, where the quantum device with adjustable parameters tries to mask quantum information and the classical device evaluates the performance of the quantum device and optimizes its parameters. After optimization, the quantum device behaves as an optimal masker. The loss value during optimization can be used to characterize the performance of the masker. In particular, if the loss value converges to zero, we obtain a perfect masker that completely masks the quantum information generated by the quantum information source, otherwise, the perfect masker does not exist and the subsystems always contain the original information. Nevertheless, these resulting maskers are still optimal. Quantum parallelism is utilized to reduce quantum state preparations and measurements. Our study paves the way for wide application of quantum information masking, and some of the techniques used in this study may have potential applications in quantum information processing.

Quantum support vector machines: theory and applications

Abstract. Quantum Support Vector Machines (QSVMs) combine the fundamental principles of quantum computing and classical Support Vector Machines (SVMs) to improve machine learning performance. In this paper, the author will further explore QSVM. Firstly, introduce the basics of classical SVM, including hyperplane, margin, support vector, and kernel methods. Then, introduce the basic theories of quantum computing, including quantum bits, entanglement, quantum states, superposition, and some related quantum algorithms. Focuses on the concept of QSVM, quantum kernel methods, and how SVM runs on a quantum computer. Key topics include quantum state preparation, measurement, and output interpretation. Theoretical advantages of QSVMs, such as faster computation speed, stronger performance to process high-dimensional data, and kernal computation. In addition, the author discussed the implementation of QSVM, quantum algorithms, quantum gradient descent, and optimization techniques for SVM training. The article also discusses practical issues such as error mitigation and quantum hardware requirements. The purpose of this paper is to show the advantages of QSVM by comparing SVM and QSVM.

Exploring the possibility of a complex-valued non-Gaussianity measure for quantum states of light

We consider a quantity that is the differential relative entropy between a generic Wigner function and a Gaussian one. We prove that said quantity is minimized with respect to its Gaussian argument, if both Wigner functions in the argument of the Wigner differential entropy have the same first and second moments, i.e., if the Gaussian argument is the Gaussian associate of the other, generic Wigner function. Therefore, we introduce the differential relative entropy between any Wigner function and its Gaussian associate and we examine its potential as a non-Gaussianity measure. The proposed, phase-space based non-Gaussianity measure is complex-valued, with its imaginary part possessing the physical meaning of the Wigner function’s negative volume. At the same time, the real part of this measure provides an extra layer of information, rendering the complex-valued quantity a measure of non-Gaussianity, instead of a quantity pertaining only to the negativity of the Wigner function. We prove that the measure (both the real and imaginary parts) is faithful, invariant under Gaussian unitary operations, and find a sufficient condition on its monotonic behavior under Gaussian channels. We provide numerical results supporting the aforesaid condition. In addition, we examine the measure’s usefulness to non-Gaussian quantum state engineering with partial measurements.

A chip-integrated homodyne detection system with enhanced bandwidth performance for quantum applications

The rapid development of quantum technology has driven the need for high-performance quantum signal processing modules. Balanced homodyne detector (BHD) is one of the most promising options for practical quantum state measurement, providing substantial advantages of cost-effectiveness, no cooling requirement, and system compactness. However, due to the stringent requirements in BHD design, it typically suffers from a relatively small operating bandwidth which limits the overall speed of a quantum system. In this study, we propose comprehensive modelling for the BHD in quantum applications and enhance the performance of BHDs based on our modelling. Specifically, we utilise a photonic chip approach and optimise the electronic design to create the integrated BHD, which significantly boosts the 3 dB bandwidth to 4.75 GHz and achieves a shot-noise-limited bandwidth of 23 GHz. We demonstrate the capability of this setup to generate quantum random numbers at a rate of 240 Gbit s−1, highlighting its potential for ultra-high-speed quantum communication and quantum cryptography applications.

Metasurface‐Empowered Quantum Photonics

In recent decades, quantum information technologies have attracted significant attention and experienced rapid development due to their ultrafast processing speeds and high level of information security. A significant trend in this field of study involves the ongoing pursuit of integrating and miniaturizing quantum devices. Metasurfaces, which are artificially designed planar nanostructure arrays with versatile wavefront shaping capabilities, present a promising platform for the development of integrated photonic quantum devices by effectively controlling quantum light in multiple degrees of freedom. In this review, recent advances in the field of quantum photonics facilitated by metasurfaces, encompassing quantum light sources, manipulation and measurement of quantum states, and the intriguing functionalities of quantum metasurfaces, are summarized. Additionally, potential future directions for the advancement of quantum metasurfaces are discussed.

Cross-platform comparison of arbitrary quantum processes

In this work, we present a protocol for comparing the performance of arbitrary quantum processes executed on spatially or temporally disparate quantum platforms using Local Operations and Classical Communication (LOCC). The protocol involves sampling local unitary operators, which are then communicated to each platform via classical communication to construct quantum state preparation and measurement circuits. Subsequently, the local unitary operators are implemented on each platform, resulting in the generation of probability distributions of measurement outcomes. The max process fidelity is estimated from the probability distributions, which ultimately quantifies the relative performance of the quantum processes. Furthermore, we demonstrate that this protocol can be adapted for quantum process tomography. We apply the protocol to compare the performance of five quantum devices from IBM and the “Qianshi" quantum computer from Baidu via the cloud. The experimental results unveil two notable aspects: Firstly, the protocol adeptly compares the performance of the quantum processes implemented on different quantum computers. Secondly, the protocol scales, although still exponentially, much more favorably with the number of qubits, when compared to the full quantum process tomography. We view our work as a catalyst for collaborative efforts in cross-platform comparison of quantum computers.

Direct measurement of nonlocal quantum states without approximation

Abstract Efficient acquiring information from a quantum state is important for research in fundamental quantum physics and quantum information applications. Instead of using standard quantum state tomography method with reconstruction algorithm, weak value was proposed to directly measure density matrix elements of quantum state. Recently, similar to the concept of weak value, modular values was introduced to extend the direct measurement scheme to nonlocal quantum wave function. However, this method still involves approximation, which leads to inherent low-precision. Here, we propose a new scheme which enables direct measurement for ideal value of the nonlocal density matrix element without taking approximations. Our scheme allows more accurate characterization of nonlocal quantum states, and therefore has greater advantages in practical measurement scenarios.

Anomaly detection in aeronautics data with quantum-compatible discrete deep generative model

Deep generative learning cannot only be used for generating new data with statistical characteristics derived from input data but also for anomaly detection, by separating nominal and anomalous instances based on their reconstruction quality. In this paper, we explore the performance of three unsupervised deep generative models—variational autoencoders (VAEs) with Gaussian, Bernoulli, and Boltzmann priors—in detecting anomalies in multivariate time series of commercial-flight operations. We created two VAE models with discrete latent variables (DVAEs), one with a factorized Bernoulli prior and one with a restricted Boltzmann machine (RBM) with novel positive-phase architecture as prior, because of the demand for discrete-variable models in machine-learning applications and because the integration of quantum devices based on two-level quantum systems requires such models. To the best of our knowledge, our work is the first that applies DVAE models to anomaly-detection tasks in the aerospace field. The DVAE with RBM prior, using a relatively simple—and classically or quantum-mechanically enhanceable—sampling technique for the evolution of the RBM’s negative phase, performed better in detecting anomalies than the Bernoulli DVAE and on par with the Gaussian model, which has a continuous latent space. The transfer of a model to an unseen dataset with the same anomaly but without re-tuning of hyperparameters or re-training noticeably impaired anomaly-detection performance, but performance could be improved by post-training on the new dataset. The RBM model was robust to change of anomaly type and phase of flight during which the anomaly occurred. Our studies demonstrate the competitiveness of a discrete deep generative model with its Gaussian counterpart on anomaly-detection problems. Moreover, the DVAE model with RBM prior can be easily integrated with quantum sampling by outsourcing its generative process to measurements of quantum states obtained from a quantum annealer or gate-model device.

Surface-induced vibrational energy redistribution in methane/surface scattering depends on catalytic activity.

Recent state-to-state experiments of methane scattering from Ni(111) and graphene-covered Ni(111) combined with quantum mechanical simulations suggest an intriguing correlation between the surface-induced vibrational energy redistribution (SIVR) during the molecule/surface scattering event and the catalytic activity for methane dissociation of the target surface (Werdecker, Phys. Rev. Res., 2020, 2, 043251). Herein, we report new quantum state and angle-resolved measurements for methane scattering from Ni(111) and Au(111) probing the extent of antisymmetric-to-symmetric conversion of methane stretching motion for two surfaces with different catalytic activities. Consistent with the expectations, the extent of SIVR occurring on the more catalytically active Ni(111) surface, as measured by the scattered population ratio, is found to be several times stronger than that on the more inert Au(111) surface. We also present additional insights on the rovibrational scattering dynamics contained in the angle- and state-resolved data. The results together highlight the power of state-resolved scattering measurements as a tool for investigating methane-surface interactions.

Multi-mode Gaussian state analysis with total-photon counting

The continuing improvement in the qualities of photon-number-resolving (PNR) detectors opens new possibilities for measuring quantum states of light. In this work we consider the question of what properties of an arbitrary multi-mode Gaussian state are determined by a single PNR detector that measures total-photon number. We find an answer to this question in the ideal case where the exact photon-number probabilities are known. We show that the quantities determined by the total-photon-number distribution are the spectrum of the covariance matrix, the absolute displacement in each eigenspace of the covariance matrix, and nothing else. In the case of pure Gaussian states, the spectrum determines the squeezing parameters.

Intelligent optimization based density matrix reconstruction method with semi-positive constraint

Quantum state tomography (QST) is a technique used to reconstruct the density matrix of unknown quantum states based on experimentally obtained measurements. QST is a fundamental tool in the field of quantum information and quantum technology. It is commonly employed to assess the quality and limitations of experimental platforms. However, the density matrix reconstructed using the standard QST method often fails to guarantee semi-positive definiteness, which is physically unacceptable, due to limitations imposed by the randomness of quantum state measurements, noise in practical applications, and the number of measurements. To address this issue, a method is proposed that combines maximum likelihood (ML) estimation with population intelligence optimization algorithms. First, the issue of guaranteeing the semi-positive definiteness of the density matrix reconstructed using standard QST methods is analyzed. Subsequently, the ML method is introduced, and four commonly used population intelligence optimization algorithms are applied to find the density matrix that maximizes the likelihood of reproducing the experimental measurements. Finally, the superiority of the proposed method is demonstrated using an IBM Quantum (IBMQ) processor in scenarios involving separable and entangled states of multiple qubits, and compared with the standard QST method.

Only Classical Parameterised States have Optimal Measurements under Least Squares Loss

Measurements of quantum states form a key component in quantum-information processing. It is therefore an important task to compare measurements and furthermore decide if a measurement strategy is optimal. Entropic quantities, such as the quantum Fisher information, capture asymptotic optimality but not optimality with finite resources. We introduce a framework that allows one to conclusively establish if a measurement is optimal in the non-asymptotic regime. Our method relies on the fundamental property of expected errors of estimators, known as risk, and it does not involve optimisation over entropic quantities. The framework applies to finite sample sizes and lack of prior knowledge, as well as to the asymptotic and Bayesian settings. We prove a no-go theorem that shows that only classical states admit optimal measurements under the most common choice of error measurement: least squares. We further consider the less restrictive notion of an approximately optimal measurement and give sufficient conditions for such measurements to exist. Finally, we generalise the notion of when an estimator is inadmissible (i.e. strictly worse than an alternative), and provide two sufficient conditions for a measurement to be inadmissible.

Characterization of Orbital Angular Momentum Quantum States Empowered by Metasurfaces

Twisted photons can in principle carry a discrete unbounded amount of orbital angular momentum (OAM), which are of great significance for quantum communication and fundamental tests of quantum theory. However, the methods for characterization of the OAM quantum states present a fundamental limit for miniaturization. Metasurfaces can exploit new degrees of freedom to manipulate optical fields beyond the capabilities of bulk optics, opening a broad range of novel and superior applications in quantum photonics. Here we present a scheme to reconstruct the density matrix of the OAM quantum states of single photons with all-dielectric metasurfaces composed of birefringent meta-atoms. We have also measured the Schmidt number of the OAM entanglement by the multiplexing of multiple degrees of freedom. Our work represents a step toward the practical application of quantum metadevices for the measurement of OAM quantum states in free-space quantum imaging and communications.

Experimental full-domain mapping of quantum correlation in Clauser-Horne-Shimony-Holt scenarios.

Quantum correlation between two parties serves as an important resource in the surging applications of quantum information. The Bell nonlocality and quantum steering have been proposed to describe non-classical correlations against local-hidden-variable and local-hidden-state theories, respectively. To characterize the two types of non-classical correlations, various nonlocality and steering inequalities have been established, and the amount of inequality violation serves as an important indicator for many entanglement-based tasks. Quantum state tomography has been employed for measuring quantum states, while the method requires intensive computation and does not directly verify either nonlocality or steering over the full domain independent of established theories. Here, we experimentally map the full-domain correlation with bipartite states for nonlocality and quantum steering in CHSH scenarios. The measurement of the maps automatically accounts for detection imperfections. Furthermore, we demonstrate the application of the correlation maps in the entanglement-based quantum key distribution protocol with arbitrary bipartite states. The correlation maps show direct measurements and simple interpretations that can answer fundamental questions about nonlocality and quantum steering as well as contribute to quantum information applications in a straightforward manner.

Noisy-Intermediate-Scale Quantum Electromagnetic Transients Program

Quantum-empowered electromagnetic transients program (QEMTP) is a promising paradigm for tackling EMTP’s computational burdens. Nevertheless, no existing studies truly achieve a practical and scalable QEMTP operable on today’s noisy-intermediate-scale quantum (NISQ) computers. The strong reliance on noise-free and fault-tolerant quantum devices–which appears to be decades away– hinder practical applications of current QEMTP methods. This paper devises a NISQ-QEMTP methodology which for the first time transitions the QEMTP operations from ideal, noise-free quantum simulators to real, noisy quantum computers. The main contributions lie in: (1) design of shallow-depth QEMTP quantum circuits for mitigating noises on NISQ quantum devices; (2) practical QEMTP linear solvers incorporating executable quantum state preparation and measurements for nodal voltage computations; (3) a noise-resilient QEMTP algorithm leveraging quantum resources logarithmically scaled with power system dimension; (4) a quantum shifted frequency analysis (QSFA) for accelerating QEMTP by exploiting dynamic phasor simulations with larger time steps; (5) a systematical analysis on QEMTP’s performance under various noisy quantum environments. Extensive experiments systematically verify the accuracy, efficacy, universality and noise-resilience of QEMTP on both noise-free simulators and IBM real quantum computers.

Harnessing nonlinear dynamics for quantum state synthesis of mechanical oscillators in tripartite optomechanics

Owing to their long lifetimes at cryogenic temperatures, mechanical oscillators have been recognized as an attractive resource for quantum information science and as a test bed to explore fundamental physics. Key to many of these applications is the ability to prepare, manipulate, and measure quantum states of mechanical motion. By capturing the exact nonlinear quantum dynamics, we show how tripartite optomechanical interactions, involving the mutual coupling between two distinct optical modes and an acoustic resonance, enable quantum states of mechanical oscillators to be synthesized and interrogated using classical state preparation.

Overlapped grouping measurement: A unified framework for measuring quantum states

Quantum algorithms designed for realistic quantum many-body systems, such as chemistry and materials, usually require a large number of measurements of the Hamiltonian. Exploiting different ideas, such as importance sampling, observable compatibility, or classical shadows of quantum states, different advanced measurement schemes have been proposed to greatly reduce the large measurement cost. Yet, the underline cost reduction mechanisms seem distinct from each other, and how to systematically find the optimal scheme remains a critical challenge. Here, we address this challenge by proposing a unified framework of quantum measurements, incorporating advanced measurement methods as special cases. Our framework allows us to introduce a general scheme – overlapped grouping measurement, which simultaneously exploits the advantages of most existing methods. An intuitive understanding of the scheme is to partition the measurements into overlapped groups with each one consisting of compatible measurements. We provide explicit grouping strategies and numerically verify its performance for different molecular Hamiltonians with up to 16 qubits. Our numerical result shows significant improvements over existing schemes. Our work paves the way for efficient quantum measurement and fast quantum processing with current and near-term quantum devices.

Semiclassical gravity phenomenology under the causal-conditional quantum measurement prescription

The semi-classical gravity sourced by the quantum expectation value of the matter's energy-momentum tensor will change the evolution of the quantum state of matter. This effect can be described by the Schroedinger-Newton (SN) equation, where the semi-classical gravity contributes a gravitational potential term depending on the matter quantum state. This state-dependent potential introduces the complexity of the quantum state evolution and measurement in SN theory, which is different for different quantum measurement prescriptions. Previous theoretical investigations on the SN-theory phenomenology in the optomechanical experimental platform were carried out under the so-called post/pre-selection prescription. This work will focus on the phenomenology of SN theory under the causal-conditional prescription, which fits the standard intuition on the continuous quantum measurement process. Under the causal-conditional prescription, the quantum state of the test mass mirrors is conditionally and continuously prepared by the projection of the outgoing light field in the optomechanical system. Therefore a gravitational potential depends on the quantum trajectory is created and further affects the system evolution. In this work, we will systematically study various experimentally measurable signatures of SN theory under the causal-conditional prescription in an optomechanical system, for both the self-gravity and the mutual gravity scenarios. Comparisons between the SN phenomenology under three different prescriptions will also be carefully made. Moreover, we find that quantum measurement can induce a classical correlation between two different optical fields via classical gravity, which is difficult to be distinguished from the quantum correlation of light fields mediated by quantum gravity.