Search Results (18)

The Quantum Amplitude Estimation (QAE) algorithm is a major quantum algorithm designed to achieve a quadratic speed-up. Until fault-tolerant quantum computing is achieved, being competitive over classical Monte Carlo (MC) remains elusive. Alternative methods have been developed so as to require fewer resources while maintaining an advantageous theoretical scaling. We compared the standard QAE algorithm with two Noisy Intermediate-Scale Quantum (NISQ)-friendly versions of QAE on a numerical integration task, with the Monte Carlo technique of Metropolis–Hastings as a classical benchmark. The algorithms were evaluated in terms of the estimation error as a function of the number of samples, computational time, and length of the quantum circuits required by the solutions, respectively. The effectiveness of the two QAE alternatives was tested on an 11-qubit trapped-ion quantum computer in order to verify which solution can first provide a speed-up in the integral estimation problems. We concluded that an alternative approach is preferable with respect to employing the phase estimation routine. Indeed, the Maximum Likelihood estimation guaranteed the best trade-off between the length of the quantum circuits and the precision in the integral estimation, as well as greater resistance to noise. Full article

Nearest-neighbour clustering is a simple yet powerful machine learning algorithm that finds natural application in the decoding of signals in classical optical-fibre communication systems. Quantum k-means clustering promises a speed-up over the classical k-means algorithm; however, it has been shown to not currently provide this speed-up for decoding optical-fibre signals due to the embedding of classical data, which introduces inaccuracies and slowdowns. Although still not achieving an exponential speed-up for NISQ implementations, this work proposes the generalised inverse stereographic projection as an improved embedding into the Bloch sphere for quantum distance estimation in k-nearest-neighbour clustering, which allows us to get closer to the classical performance. We also use the generalised inverse stereographic projection to develop an analogous classical clustering algorithm and benchmark its accuracy, runtime and convergence for decoding real-world experimental optical-fibre communication data. This proposed ‘quantum-inspired’ algorithm provides an improvement in both the accuracy and convergence rate with respect to the k-means algorithm. Hence, this work presents two main contributions. Firstly, we propose the general inverse stereographic projection into the Bloch sphere as a better embedding for quantum machine learning algorithms; here, we use the problem of clustering quadrature amplitude modulated optical-fibre signals as an example. Secondly, as a purely classical contribution inspired by the first contribution, we propose and benchmark the use of the general inverse stereographic projection and spherical centroid for clustering optical-fibre signals, showing that optimizing the radius yields a consistent improvement in accuracy and convergence rate. Full article

Non-photochemical quenching (NPQ) is an indicator of crop stress. Until now, only a limited number of studies have focused on how to estimate NPQ using remote sensing technology. The main challenge is the complicated regulatory mechanism of NPQ. NPQ can be divided into energy-dependent (qE) and non-energy-dependent (non-qE) quenching. The contribution of these two components varies with environmental factors, such as light intensity and stress level due to the different response mechanisms. This study aims to explore the feasibility of estimating NPQ using photosynthesis-related vegetation parameters available from remote sensing by considering the two components of NPQ. We concurrently measured passive vegetation reflectance spectra by spectrometer, as well as active fluorescence parameters by pulse-amplitude modulated (PAM) of rice (Oryza sativa) leaves. Subsequently, we explored the ability of the selected vegetation parameters (including the photochemical reflectance index (PRI), inverted red-edge chlorophyll index (IRECI), near-infrared reflectance of vegetation (NIR_v), and fluorescence quantum yield (ΦF)) to estimate NPQ. Based on different combinations of these remote sensing parameters, empirical models were established to estimate NPQ using the linear regression method. Experimental analysis shows that the contribution of qE and non-qE components varied under different illumination conditions. Under high illumination, the NPQ was attributed primarily to the qE component, while under low illumination, it was equally attributed to the qE and non-qE components. Among all tested parameters, ΦF was sensitive to the qE component variation, while IRECI and NIR_v were sensitive to the non-qE component variation. Under high illumination, integrating ΦF in the regression model captured NPQ variations well (R² > 0.74). Under low illumination, ΦF, IRECI, and NIR_v explained 24%, 62%, and 65% of the variation in NPQ, respectively, while coupling IRECI or NIR_v with ΦF considerably improved the accuracy of NPQ estimation (R² > 0.9). For all the samples under both low and high illumination, the combination of ΦF with at least one of the other parameters (including IRECI, NIR_v and PAR) offers a more versatile and reliable approach to estimating NPQ than using any single parameter alone. The findings of this study contribute to the further development of remote sensing methods for NPQ estimation at the canopy scale in the future. Full article

This work compares the performance of single- and two-qubit probes for estimating several phase rotations simultaneously under the action of different noisy channels. We compute the quantum limits for this simultaneous estimation using collective and individual measurements by evaluating the Holevo and Nagaoka–Hayashi Cramér-Rao bounds, respectively. Several quantum noise channels are considered, namely the decohering channel, the amplitude damping channel, and the phase damping channel. For each channel, we find the optimal single- and two-qubit probes. Where possible we demonstrate an explicit measurement strategy that saturates the appropriate bound and we investigate how closely the Holevo bound can be approached through collective measurements on multiple copies of the same probe. We find that under the action of the considered channels, two-qubit probes show enhanced parameter estimation capabilities over single-qubit probes for almost all non-identity channels, i.e., the achievable precision with a single-qubit probe degrades faster with increasing exposure to the noisy environment than that of the two-qubit probe. However, in sufficiently noisy channels, we show that it is possible for single-qubit probes to outperform maximally entangled two-qubit probes. This work shows that, in order to reach the ultimate precision limits allowed by quantum mechanics, entanglement is required in both the state preparation and state measurement stages. It is hoped the tutorial-esque nature of this paper will make it easily accessible. Full article

Continuous-variable quantum key distribution (CV–QKD) is a system that provides secret keys for symmetric key systems. In the application of CV–QKD, the practical security of the system is crucial. In this article, we investigate the practical security issues caused by non–ideal Gaussian modulation, which is caused by fitting defects of the amplitude modulator’s (AM) modulation curve. We provide the effect of fitting error on parameter estimation. We also give the relationship between the fitting order and the secret key rate. The simulation results indicate that the system is completely unable to communicate during first–order fitting. During second–order fitting, the system’s performance decreases by more than half. During third–order fitting, the system’s performance will be consistent with the ideal. Therefore, to ensure the performance of the CV–QKD system, the fitting order must be at least three or higher. Full article

We investigate the possibility to apply quantum machine learning techniques for data analysis, with particular regard to an interesting use-case in high-energy physics. We propose an anomaly detection algorithm based on a parametrized quantum circuit. This algorithm was trained on a classical computer and tested with simulations as well as on real quantum hardware. Tests on NISQ devices were performed with IBM quantum computers. For the execution on quantum hardware, specific hardware-driven adaptations were devised and implemented. The quantum anomaly detection algorithm was able to detect simple anomalies such as different characters in handwritten digits as well as more complex structures such as anomalous patterns in the particle detectors produced by the decay products of long-lived particles produced at a collider experiment. For the high-energy physics application, the performance was estimated in simulation only, as the quantum circuit was not simple enough to be executed on the available quantum hardware platform. This work demonstrates that it is possible to perform anomaly detection with quantum algorithms; however, as an amplitude encoding of classical data is required for the task, due to the noise level in the available quantum hardware platform, the current implementation cannot outperform classic anomaly detection algorithms based on deep neural networks. Full article

We present an extension of many-body downfolding methods to reduce the resources required in the quantum phase estimation (QPE) algorithm. In this paper, we focus on the Schrieffer–Wolff (SW) transformation of the electronic Hamiltonians for molecular systems that provides significant simplifications of quantum circuits for simulations of quantum dynamics. We demonstrate that by employing Fock-space variants of the SW transformation (or rank-reducing similarity transformations (RRST)) one can significantly increase the locality of the qubit-mapped similarity-transformed Hamiltonians. The practical utilization of the SW-RRST formalism is associated with a series of approximations discussed in the manuscript. In particular, amplitudes that define RRST can be evaluated using conventional computers and then encoded on quantum computers. The SW-RRST QPE quantum algorithms can also be viewed as an extension of the standard state-specific coupled-cluster downfolding methods to provide a robust alternative to the traditional QPE algorithms to identify the ground and excited states for systems with various numbers of electrons using the same Fock-space representations of the downfolded Hamiltonian. The RRST formalism serves as a design principle for developing new classes of approximate schemes that reduce the complexity of quantum circuits. Full article

Image matching is an important research topic in computer vision and image processing. However, existing quantum algorithms mainly focus on accurate matching between template pixels, and are not robust to changes in image location and scale. In addition, the similarity calculation of the matching process is a fundamentally important issue. Therefore, this paper proposes a hybrid quantum algorithm, which uses the robustness of SIFT (scale-invariant feature transform) to extract image features, and combines the advantages of quantum exponential storage and parallel computing to represent data and calculate feature similarity. Finally, the quantum amplitude estimation is used to extract the measurement results and realize the quadratic acceleration of calculation. The experimental results show that the matching effect of this algorithm is better than the existing classical architecture. Our hybrid algorithm broadens the application scope and field of quantum computing in image processing. Full article

We develop a novel quantum algorithm for approximating the price of a discrete floating-strike Asian option based on an underlying valuation tree. The paths of the tree are encoded in bit-representation into a qubit register, where quantum state preparation is used to load the corresponding distribution onto the states. We implement the expectation value of the option pricing formula as a composition of the price probabilities, the payout and an indicator function, mapping their respective values to amplitudes of additional qubits. Thus, the underlying no longer has to be discretized into the same bit values for different times, resulting in smaller quantum circuits. The algorithm may be used with quantum amplitude estimation, enabling a quadratic speed-up over classical Monte Carlo methods. Full article

We compare reconstructed quantum state images of a birefringent sample using direct quantum state tomography and inverse numerical optimization technique. Qubits are used to characterize birefringence in a flat transparent plastic sample by means of polarization sensitive measurement using density matrices of two-level quantum entangled photons. Pairs of entangled photons are generated in a type-II nonlinear crystal. About half of the generated photons interact with a birefringent sample, and coincidence counts are recorded. Coincidence rates of entangled photons are measured for a set of sixteen polarization states. Tomographic and inverse numerical techniques are used to reconstruct the density matrix, the degree of entanglement, and concurrence for each pixel of the investigated sample. An inverse numerical optimization technique is used to obtain a density matrix from measured coincidence counts with the maximum probability. Presented results highlight the experimental noise reduction, greater density matrix estimation, and overall image enhancement. The outcome of the entanglement distillation through projective measurements is a superposition of Bell states with different amplitudes. These changes are used to characterize the birefringence of a 3M tape. Well-defined concurrence and entanglement images of the birefringence are presented. Our results show that inverse numerical techniques improve overall image quality and detail resolution. The technique described in this work has many potential applications. Full article

Measurements leading to the collapse of states and the non-local quantum correlations are the key to all applications of quantum mechanics as well as in the studies of quantum foundation. The former is crucial for quantum parameter estimation, which is greatly affected by the physical environment and the measurement scheme itself. Its quantification is necessary to find efficient measurement schemes and circumvent the non-desirable environmental effects. This has led to the intense investigation of quantum metrology, extending the Cramér–Rao bound to the quantum domain through quantum Fisher information. Among all quantum states, the separable ones have the least quantumness; being devoid of the fragile non-local correlations, the component states remain unaffected in local operations performed by any of the parties. Therefore, using these states for the remote design of quantum states with high quantum Fisher information can have diverse applications in quantum information processing; accurate parameter estimation being a prominent example, as the quantum information extraction solely depends on it. Here, we demonstrate that these separable states with the least quantumness can be made extremely useful in parameter estimation tasks, and further show even in the case of the shared channel inflicted with the amplitude damping noise and phase flip noise, there is a gain in Quantum Fisher information (QFI). We subsequently pointed out that the symmetric W states, incapable of perfectly teleporting an unknown quantum state, are highly effective for remotely designing quantum states with high quantum Fisher information. Full article

This article proposes a new method for sensing THz waves that can allow electric field measurements traceable to the International System of Units and to the fundamental physical constants by using the comparison between precision measurements with cold trapped HD⁺ ions and accurate predictions of molecular ion theory. The approach exploits the lightshifts induced on the two-photon rovibrational transition at 55.9 THz by a THz wave around 1.3 THz, which is off-resonantly coupled to the HD⁺ fundamental rotational transition. First, the direction and the magnitude of the static magnetic field applied to the ion trap is calibrated using Zeeman spectroscopy of HD⁺. Then, a set of lightshifts are converted into the amplitudes and the phases of the THz electric field components in an orthogonal laboratory frame by exploiting the sensitivity of the lightshifts to the intensity, the polarization and the detuning of the THz wave to the HD⁺ energy levels. The THz electric field measurement uncertainties are estimated for quantum projection noise-limited molecular ion frequency measurements with the current accuracy of molecular ion theory. The method has the potential to improve the sensitivity and accuracy of electric field metrology and may be extended to THz magnetic fields and to optical fields. Full article

Photoelectrical and photoluminescent properties of multilayer graphene (MLG)–quantum dots (QD) hybrid structures have been studied. It has been shown that the average rate of transfer from QDs to the MLG can be estimated via photoinduced processes on the QDs’ surfaces. A monolayer of CdSe QDs can double the photoresponse amplitude of multilayer graphene, without influencing its characteristic photoresponse time. It has been found that efficient charge or energy transfer from QDs to MLG with a rate higher than 3 × 10⁸ s⁻¹ strongly inhibits photoinduced processes on the QD surfaces and provides photostability for QD-based structures. Full article

Small-amplitude quantum-gravity periodic perturbations of the metric tensor, occurring in sequences of phase-shifted oscillations, are investigated for vacuum conditions and in the context of the manifestly-covariant theory of quantum gravity. The theoretical background is provided by the Hamiltonian representation of the quantum hydrodynamic equations yielding, in turn, quantum modifications of the Einstein field equations. It is shown that in the case of the DeSitter space–time sequences of small-size periodic perturbations with prescribed frequency are actually permitted, each one with its characteristic initial phase. The same perturbations give rise to non-linear modifications of the Einstein field equations in terms of a suitable stochastic-averaged and divergence-free quantum stress-energy tensor. As a result, a quantum-driven screening effect arises which is shown to affect the magnitude of the cosmological constant. Observable features on the DeSitter space–time solution and on the graviton mass estimate are pointed out. Full article

An ecosystem model serves as an important tool to understand the carbon cycle in the forest ecosystem. However, the sensitivities of parameters and uncertainties of the model outputs are not clearly understood. Parameter sensitivity analysis (SA) and uncertainty analysis (UA) play a crucial role in the improvement of forest gross primary productivity GPP simulation. This study presents a global SA based on an extended Fourier amplitude sensitivity test (EFAST) method to quantify the sensitivities of 16 parameters in the Flux-based ecosystem model (FBEM). To systematically evaluate the parameters’ sensitivities, various parameter ranges, different model outputs, temporal variations of parameters sensitivity index (SI) were comprehensively explored via three experiments. Based on the numerical experiments of SA, the UA experiments were designed and performed for parameter estimation based on a Markov chain Monte Carlo (MCMC) method. The ratio of internal CO₂ to air CO₂ ( $f_C{}_i)$ , canopy quantum efficiency of photon conversion $({\alpha }_q)$ , maximum carboxylation rate at 25 $°\mathrm{C}$ ( $V_m^{25})$ were the most sensitive parameters for the GPP. It was also indicated that ${\mathsf{\alpha }}_{\mathrm{q}},E_{\mathrm{V}}{}_m^{}\mathrm{and}{Q}_{10}$ were influenced by temperature throughout the entire growth stage. The result of parameter estimation of only using four sensitive parameters (RMSE = 1.657) is very close to that using all the parameters (RMSE = 1.496). The results of SA suggest that sensitive parameters, such as $f_{ci},{\mathsf{\alpha }}_{\mathrm{q}},{\mathrm{E}}_{\mathrm{V}}{}_m^{},V_m^{25}$ strongly influence on the forest GPP simulation, and the temporal characteristics of the parameters’ SI on GPP and NEE were changed in different growth. The sensitive parameters were a major source of uncertainty and parameter estimation based on the parameter SA could lead to desirable results without introducing too great uncertainties. Full article