Phase Estimation Research Articles

Approaching the optimal phase estimation sensitivity of the lossy Mach-Zehnder interferometer with coincidence measurements

Approaching the optimal phase estimation sensitivity of the lossy Mach-Zehnder interferometer with coincidence measurements

Phase estimation via coherent and photon-catalyzed squeezed vacuum states.

The research focused on enhancing the measurement accuracy through the use of non-Gaussian states has garnered increasing attention. In this study, we propose a scheme to input the coherent state mixed with a photon-catalyzed squeezed vacuum state into the Mach-Zender interferometer to enhance phase measurement accuracy. The findings demonstrate that photon catalysis, particularly multi-photon catalysis, can effectively improve the phase sensitivity of parity detection and the quantum Fisher information. Moreover, the situation of photon losses in practical measurement was studied. The results indicate that external dissipation has a greater influence on phase sensitivity than the internal dissipation. Compared to input coherent state mixed with squeezed vacuum state, the utilization of coherent state mixed photon-catalyzed squeezed vacuum state, particularly the mixed multi-photon catalyzed squeezed vacuum state as input, can enhance the phase sensitivity and quantum Fisher information. Furthermore, the phase measurement accuracy can exceed the standard quantum limit, and even surpass the Heisenberg limit. This research is expected to significantly contribute to quantum precision measurement.

Low-complexity two-stage carrier phase recovery using principal component reconstruction analysis and optimal decision maximum likelihood for PS-MQAM systems.

A low-complexity two-stage carrier phase recovery (CPR) scheme based on principal component reconstruction analysis and optimal decision maximum likelihood (PCRA-OML) is proposed for probabilistic shaping (PS)-M quadrature amplitude modulation (QAM) coherent optical communication systems. In the first stage, symbols on the QPSK-shaped ring are selected, their amplitude noise is eliminated, and their amplitudes are increased, thus completing the reconstruction of the principal component. Lastly, the carrier phase is recovered using principal component phase estimation (PCPE). In the second stage, a maximum likelihood phase estimation algorithm based on optimal decision-making is employed to further enhance the stability and robustness of the scheme. The effectiveness of the proposed scheme is validated through 28 GBaud polarization division multiplexing PS-64QAM simulations and 28 GBaud PS-16QAM experiments. The experimental results indicate that in the PS-16QAM entropy of 3 bit/symbol system, when the threshold for normalized generalized mutual information is 0.9, the proposed scheme provides a 1.7 dB optical signal-to-noise ratio (OSNR) gain compared to blind phase search (BPS), and an additional 0.9 dB OSNR gain compared to the PCPE scheme. The proposed PCRA-OML scheme exhibits versatility across various shaping strengths and is less susceptible to probabilistic influences than the BPS and PCPE schemes. Additionally, under the premise of comparable performance in the PS-64QAM system, the proposed scheme reduces over 90% of the computational complexity associated with multiplication compared to BPS. In the PS-16QAM system, the proposed scheme's real multiplication complexity is only 17.8% of BPS, achieving an overall O(N) complexity.

Two quantum algorithms for solving the one-dimensional advection–diffusion equation

Two quantum algorithms are presented for the numerical solution of a linear one-dimensional advection–diffusion equation with periodic boundary conditions. Their accuracy and performance with increasing qubit number are compared point-by-point with each other. Specifically, we solve the linear partial differential equation with a Quantum Linear Systems Algorithm (QLSA) based on the Harrow–Hassidim–Lloyd method and a Variational Quantum Algorithm (VQA), for resolutions that can be encoded using up to 6 qubits, which corresponds to N=64 grid points on the unit interval. Both algorithms are hybrid in nature, i.e., they involve a combination of classical and quantum computing building blocks. The QLSA and VQA are solved as ideal statevector simulations using the in-house solver QFlowS and open-access Qiskit software, respectively. We discuss several aspects of both algorithms which are crucial for a successful performance in both cases. These are the accurate eigenvalue estimation with the quantum phase estimation for the QLSA and the choice of the algorithm of the minimization of the cost function for the VQA. The latter algorithm is also implemented in the noisy Qiskit framework including measurement noise. We reflect on the current limitations and suggest some possible routes of future research for the numerical simulation of classical fluid flows on a quantum computer.

Swap-test interferometry with biased qubit noise

The Mach-Zehnder interferometer is a powerful device for detecting small phase shifts between two light beams. Simple input states, such as coherent states or single photons, can reach the standard quantum limit of phase estimation, while more complex states can be used to reach Heisenberg scaling; the latter, however, require challenging preparation and measurement strategies. The quest for highly sensitive phase estimation therefore calls for interferometers with nonlinear devices which would make the preparation of these complex states more efficient. Here, we show that the Heisenberg scaling can be recovered with simple input states (including Fock and coherent states) when the linear mirrors in the interferometer are replaced with controlled-swap gates and measurements on auxiliary qubits. These swap tests project the input Fock and coherent states onto NOON and entangled coherent states, respectively, and allow optimal or near-optimal measurements, leading to improved sensitivity to small phase shifts in one of the interferometer arms. We analyze auxiliary qubit errors in detail, showing that biasing the qubit towards phase flips offers a great advantage, and perform thorough numerical simulations of a possible implementation in circuit quantum electrodynamics with an auxiliary Kerr-cat qubit. Our results thus present a viable approach to phase estimation approaching Heisenberg-limited sensitivity and demonstrate potential advantages of using biased-noise qubits in quantum metrology. Published by the American Physical Society 2024

Continuous Gait Phase Estimation by Muscle Deformations With Speed and Ramp Adaptability

Continuous Gait Phase Estimation by Muscle Deformations With Speed and Ramp Adaptability

Reductive quantum phase estimation

Estimating a quantum phase is a necessary task in a wide range of fields of quantum science. To accomplish this task, two well-known methods have been developed in distinct contexts, namely, Ramsey interferometry (RI) in atomic and molecular physics and quantum phase estimation (QPE) in quantum computing. We demonstrate that these canonical examples are instances of a larger class of phase estimation protocols, which we call reductive quantum phase estimation (RQPE) circuits. Here, we present an explicit algorithm that allows one to create an RQPE circuit. This circuit distinguishes an arbitrary set of phases with a smaller number of qubits and unitary applications, thereby solving a general class of quantum hypothesis testing to which RI and QPE belong. We further demonstrate a tradeoff between measurement precision and phase distinguishability, which allows one to tune the circuit to be optimal for a specific application. Published by the American Physical Society 2024

A systematic literature review on characteristics of the front-end phase of agile software development projects and their connections to project success

ContextSoftware development of new products and services often involves a front-end phase where user needs are analysed, costs and benefits are estimated, and initial plans are created. GoalThis study aims to learn more about how the introduction of agile software development has affected practices and outcomes related to cost and benefit estimation in this front-end phase and to understand better what would improve this phase. MethodWe identified, reviewed and aggregated the results from 42 relevant research articles by searching literature databases and snowballing relevant articles. ResultsThe front-end phase of agile was found to be, on average, similar and just as comprehensive as that of non-agile software development. This may be unfortunate, given the finding that more successful agile software development is connected with less detail in cost estimation and planning-related activities. A less comprehensive front-end phase may be especially beneficial for low-risk agile software development. ConclusionThe results of this review suggest that agile principles, so far, have had a limited influence on the front-end phase. We recommend more flexibility and context-dependency in how the front-end phase of agile software development is conducted, including less comprehensive estimation and planning activities for low-risk software development contexts.

Spreading Sea Clutter Suppression for High-Frequency Hybrid Sky-Surface Wave Radar Using Orthogonal Projection in Spatial–Temporal Domain

In recent years, the high-frequency hybrid sky-surface wave radar (HSSWR) has been increasingly used for target detection applications. Nevertheless, the specific bistatic system layout and the phase path disturbances induced by the ionospheric propagation channel may severely spread the sea clutter spectrum, thereby deteriorating the detection ability of the HSSWR for slow-moving targets. In this work, a novel subspace method based on the hybrid use of the amplitude and phase estimator (APES) and the orthogonal projection (OP) in the spatial–temporal domain, denoted as the APES-OP method, is proposed to suppress the spreading first-order sea clutter of the HSSWR. The distribution characteristics of targets and first-order sea clutter in the spatial–temporal domain were investigated, and a time-domain subspace signal model was adopted to describe targets perturbed by ionospheric phase path modulation. An APES filter was adopted to filter out the potential targets with a traversal approach to avoid attenuating desired signals while suppressing sea clutter. After that, sampling data from multi-channels and slow-time domains at the cell under test were employed to construct a spatial–temporal matrix, which was then utilized to obtain the sea clutter subspace by singular value decomposition. Simulation results indicate that the proposed algorithm can suppress sea clutter while retaining the target, even if the target is buried by sea clutter. The processing results of measured data further demonstrate the efficiency of the proposed algorithm. After sea clutter suppression, the target obscured by clutter can be revealed, and the signal-to-clutter ratio of the target is greatly improved.

Probing Quantum Efficiency: Exploring System Hardness in Electronic Ground State Energy Estimation.

We consider the question of how correlated the system hardness is between classical algorithms of electronic structure theory in ground state estimation and quantum algorithms. To define the system hardness for classical algorithms, we employ empirical criterion based on the deviation of electronic energies produced by coupled cluster and configuration interaction methods from the exact ones along multiple bonds dissociation in a set of molecular systems. For quantum algorithms, we have selected the Variational Quantum Eigensolver (VQE) and Quantum Phase Estimation (QPE) methods. As characteristics of the system hardness for quantum methods, we analyzed circuit depths for the state preparation, the number of quantum measurements needed for the energy expectation value, and various cost characteristics for the Hamiltonian encodings via Trotter approximation and linear combination of unitaries (LCU). Our results show that the quantum resource requirements are mostly unaffected by classical hardness, with the only exception being the state preparation part, which contributes to both VQE and QPE algorithm costs. However, there are clear indications that constructing the initial state with a significant overlap with the true ground state is easier than obtaining the state with an energy expectation value within chemical precision. These results support optimism regarding the identification of a molecular system where a quantum algorithm excels over its classical counterpart, as quantum methods can maintain efficiency in classically challenging systems.

Quantum-enhanced joint estimation of phase and phase diffusion

Accurate phase estimation in the presence of unknown phase diffusive noise is a crucial yet challenging task in noisy quantum metrology. This problem is particularly interesting due to the detrimental impact of the associated noise. Here, we investigate the joint estimation of phase and phase diffusion using generalized Holland–Burnett states, known for their experimental accessibility. These states provide performance close to the optimal state in single-parameter phase estimation, even in the presence of photon losses. We adopt a twofold approach by analyzing the joint information extraction through the double homodyne measurement and the joint information availability across all probe states. Through our analysis, we find that the highest sensitivities are obtained by using states created by directing all input photons into one port of a balanced beam splitter. Furthermore, we infer that good levels of sensitivity persist even in the presence of moderate photon losses, illustrating the remarkable resilience of our probe states under lossy conditions.

Improving Estimation of Specific Differential Phase and Assessing Differential Backscattering Phase

Abstract Polarimetric variables such as differential phase ΦDP and its range derivative, specific differential phase KDP, contain useful information for improving quantitative precipitation estimation (QPE) and microphysics retrieval. However, the usefulness of the current operationally utilized estimation method of KDP is limited by measurement error and artifacts resulting from the differential backscattering phase δ. The contribution of δ can significantly influence the ΦDP measurements and therefore negatively affect the KDP estimates. Neglecting the presence of δ within non-Rayleigh scattering regimes has also led to the adoption of incorrect terminology regarding signatures seen within current operational KDP estimates implying associated regions of unrealistic liquid water content. A new processing method is proposed and developed to estimate both KDP and δ using classification and linear programming (LP) to reduce bias in KDP estimates caused by the δ component. It is shown that by applying the LP technique specifically to the rain regions of Rayleigh scattering along a radial profile, accurate estimates of differential propagation phase, specific differential phase, and differential backscattering phase can be retrieved within regions of both Rayleigh and non-Rayleigh scattering. This new estimation method is applied to cases of reported hail and tornado debris, and the LP results are compared to the operationally utilized least squares fit (LSF) estimates. The results show the potential use of the differential backscattering phase signature in the detection of hail and tornado debris.

Updating direct methods II. Reduction of the structural complexity when triplet invariants are estimated via the Patterson map

Direct methods have practically solved the phase problem for small–medium-size molecules but have substantially failed in macromolecular crystallography. They have two main limitations: a strong dependence on structural complexity and the need to work with atomic-resolution data. Many attempts have been made to broaden their field of applicability, for example the use of some a priori information to make the estimate of the triplet invariant phases more effective. Unfortunately none of these new approaches allowed the successful application of direct methods to proteins and nucleic acids. Direct methods are still a niche tool in macromolecular crystallography. In a recent publication [Giacovazzo (2019). Acta Cryst. A75, 142–157] the method of joint probability distributions has been modified to take into account new sources of prior information, one of which is relevant to this article: the Patterson map. In practice, it has been shown that with prior knowledge of the interatomic vectors one is able to modify the classic Cochran reliability parameter for estimating the triplet invariant phases. The article was essentially theoretical in nature, and no attempt was described to test the practical usefulness of the new probabilistic formulas. This work is therefore the first application of the new method. It is shown that the use of the Patterson map as prior information substantially improves the Cochran estimate of triplet phases; the phase error distribution for the new estimates, even if it is related to macromolecular structures, becomes similar to that obtained for medium-size structures. In some ways, it is as if the use of the Patterson information reduces the structural complexity, thus allowing a more general use of direct methods in macromolecular crystallography. Atomic resolution no longer seems to be a necessary ingredient for the applicability of direct methods; tests show that the apparent reduction in structural complexity also occurs in macromolecular structures with experimental data having a resolution of 2.3 Å. A number of test structures have been used to show the potential of the new technique.

Local coherence by thermalized intra-system coupling

Quantum superposition of energy eigenstates can appear autonomously in a single quantum two-level system coupled to a low-temperature thermal bath, if such coupling has a proper composite nature. We propose here a principally different and more feasible approach employing engineered interactions between two-level systems being thermalized into a global Gibbs state by weakly coupled thermal bath at temperature T. Therefore, in such case quantum coherence appears by a different mechanism, whereas the system-bath coupling does not have to be engineered. We demonstrate such autonomous coherence generation reaching maximum values of coherence. Moreover, it can be alternatively built up by using weaker but collective interaction with several two-level systems. This approach surpasses the coherence generated by the engineered system-bath coupling for comparable interaction strengths and directly reduces phase estimation error in quantum sensing. This represents a necessary step towards the autonomous quantum sensing.

Theory of Compression Channels for Postselected Quantum Metrology.

The postselected quantum metrological scheme is especially advantageous when the final measurements are either very noisy or expensive in practical experiments. In this Letter, we put forward a general theory on the compression channels in postselected quantum metrology. We define the basic notions characterizing the compression quality and illuminate the underlying structure of lossless compression channels. Previous experiments on postselected optical phase estimation and weak-value amplification are shown to be particular cases of this general theory. Furthermore, for two categories of bipartite systems, we show that the compression loss can be made arbitrarily small even when the compression channel acts only on one subsystem. These findings can be employed to distribute quantum measurements so that the measurement noise and cost are dramatically reduced.

Dual grid energy management strategy for electric vehicles in hybrid microgrid utilizing matrix pencil method

Abstract This study introduces a cutting-edge Matrix Pencil-based Dual Grid Energy Management System (MP-DEMS) aimed at seamlessly integrating electric vehicles (EVs) into power grids while enhancing power quality (PQ) and reliability (PR). Operating within an AC-DC hybrid microgrid (HMG) framework, the MP-DEMS reduces the necessity for additional conversion devices, simplifying the integration of EVs and batteries. The core of the proposed DEMS comprises three key modules: the Wind Energy Management Module (WEMS), Smart Storage and EV Power Coordination (SS-EVPC), and Coordinated Power Conversion Control (CPCC). These modules work together to optimize energy usage, leverage renewable sources effectively, and manage EV charging/discharging schedules to minimize grid impact. An innovative aspect of the MP-DEMS is its use of Matrix Pencil-based techniques, offering several advantages over traditional Discrete Fourier Transform (DFT) methods. These advantages include swift dynamic response, resilience to voltage variations, and precise voltage phase estimation. Software simulations and Hardware-in-the-Loop (HIL-402) testing validate the efficacy of the MP-DEMS approach, showcasing enhanced power transfer capabilities, improved harmonic performance, and superior voltage/frequency regulation within EV-HMS applications. Overall, the MP-DEMS presents a promising solution for advancing the integration of EVs into microgrid systems, contributing to a more sustainable and reliable energy future.

Designing optimal protocols in Bayesian quantum parameter estimation with higher-order operations

Using quantum systems as sensors or probes has been shown to greatly improve the precision of parameter estimation by exploiting unique quantum features such as entanglement. A major task in quantum sensing is to design the optimal protocol, i.e., the most precise one. It has been solved for some specific instances of the problem, but in general even numerical methods are not known. Here, we focus on the single-shot Bayesian setting, where the goal is to find the optimal initial state of the probe (which can be entangled with an auxiliary system), the optimal measurement, and the optimal estimator function. We leverage the formalism of higher-order operations to develop a method based on semidefinite programming that finds a protocol that is close to the optimal one with arbitrary precision. Crucially, our method is not restricted to any specific quantum evolution, cost function, or prior distribution, and thus can be applied to any estimation problem. Moreover, it can be applied to both single-parameter or multiparameter estimation tasks. We demonstrate our method with three examples, consisting of unitary phase estimation, thermometry in a bosonic bath, and multiparameter estimation of an SU(2) transformation. Exploiting our methods, we extend several results from the literature. For example, in the thermometry case, we find the optimal protocol at any finite time and quantify the usefulness of entanglement. Published by the American Physical Society 2024

Quantum counting on the complete bipartite graph

Quantum counting is a key quantum algorithm that aims to determine the number of marked elements in a database. This algorithm is based on the quantum phase estimation algorithm and uses the evolution operator of Grover’s algorithm because its nontrivial eigenvalues are dependent on the number of marked elements. Since Grover’s algorithm can be viewed as a quantum walk on a complete graph, a natural way to extend quantum counting is to use the evolution operator of quantum-walk-based search on noncomplete graphs instead of Grover’s operator. In this paper, we explore this extension by analyzing the coined quantum walk on the complete bipartite graph with an arbitrary number of marked vertices. We show that some eigenvalues of the evolution operator depend on the number of marked vertices and using this fact we show that the quantum phase estimation can be used to obtain the number of marked vertices. The time complexity for estimating the number of marked vertices in the bipartite graph with our algorithm equates closely with that of the original quantum counting algorithm.

Early Fault-Tolerant Quantum Computing

In recent years, research in quantum computing has largely focused on two approaches: near-term intermediate-scale quantum (NISQ) computing and future fault-tolerant quantum computing (FTQC). A growing body of research into early fault-tolerant quantum computing (EFTQC) is exploring how to utilize quantum computers during the transition between these two eras. However, without agreed-upon characterizations of this transition, it is unclear how best to utilize EFTQC architectures. We argue for the perspective that this transition period will be characterized by a law of diminishing returns in quantum error correction (QEC), where the ability of the architecture to maintain quality operations at scale determines the point of diminishing returns. Two challenges emerge from this picture: how to model this phenomenon of diminishing return of QEC as the performance of devices is continually improving and how to design algorithms to make the most use of these devices. To address these challenges, we present models for the performance of EFTQC architectures, capturing the diminishing returns of QEC. We then use these models to elucidate the regimes in which algorithms suited to such architectures are advantageous. As a concrete example, we show that for the canonical task of phase estimation, in a regime of moderate scalability and using just over one million physical qubits, the “reach” of the quantum computer can be extended (compared to the standard approach) from 90-qubit instances to over 130-qubit instances using a simple early fault-tolerant quantum algorithm, which reduces the number of operations per circuit by a factor of 100 and increases the number of circuit repetitions by a factor of 10 000. This clarifies the role that such algorithms might play in the era of limited-scalability quantum computing. Published by the American Physical Society 2024

Machine learning and time-series decomposition for phase extraction and symbol classification in CV-QKD

The predictability of phase estimation and symbol classification using machine learning (ML) for experimental continuous-variable quantum key distribution (CV-QKD) is investigated. ML outperforms standard techniques, with up to 2.3% enhancement in the symbol accuracy, showcasing classical noise impact. The time-series decomposition method upper-bounds the predictable space due to shot noise. Ultimately, a 1 kbits/s secret key rate is achieved at 20 km for a 1.8 pW symbol power.