Assessment of quantum phase estimation protocols for early fault-tolerant quantum computers
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Nelson, Jacob S. (ORCID:0009000583778989)↗
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Evaluating energy differences on a quantum computer with robust phase estimation.
Abstract not provided.
Russo, Antonio↗
State preparation for robust phase estimation in molecular systems.
Abstract not provided.
Baczewski, Andrew David↗
QCVV-Inspired Quantum Simulation: Energy Gap Calculation With Robust Phase Estimation.
Abstract not provided.
Russo, Antonio↗
Specifying angular reference for robust three-phase state estimation
While the phase angle of any of the bus voltages can be chosen as the angular reference in the state estimation formulation of positive sequence networks, the same approach does not readily extend to three-phase network state estimation problem. It is commonly assumed that there is at least one bus where the bus voltages are perfectly balanced with phase angles displaced ±120° and these balanced three phase voltages are used as the three-phase reference in solving the three-phase state estimation problem. This assumption may be quite realistic in transmission networks, and for distribution networks with a strong transmission system connection. However, it might not be realistic to assume existence of a perfectly balanced reference bus in today’s distribution systems with ever increasing penetration of renewable sources or for isolated operation of microgrids. In this paper, a novel state estimation formulation will be presented which facilitates correct solution irrespective of the existence of buses with perfectly balanced voltages. The new formulation is general, and lends itself to bad data processing. It yields accurate results in any three-phase power system irrespective of its operating conditions (balanced or highly unbalanced), configuration (isolated microgrid, connected to transmission system, etc.) and whether or not it contains any synchronous generators. The performance of the method is validated using the IEEE 123 bus three-phase system.
24 POWER TRANSMISSION AND DISTRIBUTION↗
A deep neural network regressor for phase constitution estimation in the high entropy alloy system Al-Co-Cr-Fe-Mn-Nb-Ni
High Entropy Alloys (HEAs) are composed of more than one principal element and constitute a major paradigm in metals research. The HEA space is vast and an exhaustive exploration is improbable. Therefore, a thorough estimation of the phases present in the HEA is of paramount importance for alloy design. Machine Learning presents a feasible and non-expensive method for predicting possible new HEAs on-the-fly. A deep neural network (DNN) model for the elemental system of: Mn, Ni, Fe, Al, Cr, Nb, and Co is developed using a dataset generated by high-throughput computational thermodynamic calculations using Thermo-Calc. The features list used for the neural network is developed based on literature and freely available databases. A feature significance analysis matches the reported HEAs phase constitution trends on elemental properties and further expands it by providing so far-overlooked features. The final regressor has a coefficient of determination ( r 2 ) greater than 0.96 for identifying the most recurrent phases and the functionality is tested by running optimization tasks that simulate those required in alloy design. The DNN developed constitutes an example of an emulator that can be used in fast, real-time materials discovery/design tasks.
36 MATERIALS SCIENCE↗
Formulation of Three-Phase State Estimation Problem Using a Virtual Reference
State Estimation (SE) is the backbone of modern Energy Management System (EMS) due its capability of processing real time measurements and provide reliable information to system operators. Since its introduction to power systems in the 70’s, SE has been widely used in transmission networks. Distribution grids on the other hand lack sufficient number of real time measurements, and for that reason SE has not been widely implemented on these systems. The recent increase in the number of renewable energy sources connected to the grid at lower voltage levels, the advent of Distribution Automation (DA) and Smart Grids necessitate closer monitoring of distribution networks and thus forcing utilities to upgrade their operations and deploy Advanced Distribution Management Sytems (ADMS). Therefore, Distribution System State Estimation (DSE) is paramount to provide real time monitoring of active distribution grids. This papers investigates the formulation of the three-phase distribution state estimation where in the most general case, none of the system buses may have balanced three phase voltages. In such a case, the choice and definition of the slack bus need to be revisited. Most of the existing work arbitrarily assign the root bus of the distribution feeder as the balanced three-phase reference which may not be realistic for today’s active distribution systems. This paper addresses this shortcoming of the existing SE formulations by introducing a virtual reference bus. Here, the proposed approach is effectively validated by simulations carried out on distribution test systems.
24 POWER TRANSMISSION AND DISTRIBUTION↗
An Early Investigation of the HHL Quantum Linear Solver for Scientific Applications
In this paper, we explore using the Harrow–Hassidim–Lloyd (HHL) algorithm to address scientific and engineering problems through quantum computing, utilizing the NWQSim simulation package on a high-performance computing platform. Focusing on domains such as power-grid management and climate projection, we demonstrate the correlations of the accuracy of quantum phase estimation, along with various properties of coefficient matrices, on the final solution and quantum resource cost in iterative and non-iterative numerical methods such as the Newton–Raphson method and finite difference method, as well as their impacts on quantum error correction costs using the Microsoft Azure Quantum resource estimator. We summarize the exponential resource cost from quantum phase estimation before and after quantum error correction and illustrate a potential way to reduce the demands on physical qubits. This work lays down a preliminary step for future investigations, urging a closer examination of quantum algorithms’ scalability and efficiency in domain applications.
hybrid software for QC-HPC↗
Advanced Semi-Supervised Learning with Uncertainty Estimation for Phase Identification in Distribution Systems
The integration of advanced metering infrastructure (AMI) into power distribution networks generates valuable data for tasks such as phase identification; however, the limited and unreliable availability of labeled data in the form of customer phase connectivity presents challenges. To address this issue, we propose a semi-supervised learning (SSL) framework that effectively leverages labeled and unlabeled data. Our approach incorporates self-training, label spreading, and Bayesian neural networks (BNNs) to enhance phase identification with AMI data. Our method uses an ensemble of multilayer perceptron classifiers in a self-training setup, iteratively adding high-confidence pseudo-labels to improve robustness. We also apply label spread to propagate labels based on data similarity, which enhances generalization across diverse distributions. In addition, we employ a BNNs with uncertainty estimation, boosting confidence in predictions and reducing phase identification errors. In our case study, we achieved approximately 98% +/- 0.08 accuracy with uncertainty using minimal and unreliable labeled data from a real U.S. utility, Duquesne Light Company. Our SSL approach, combined with uncertainty estimation, provides an efficient solution for phase identification in AMI data, ultimately improving the reliability of smart grid applications.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Advanced Semi-Supervised Learning With Uncertainty Estimation for Phase Identification in Distribution Systems
The integration of advanced metering infrastructure (AMI) into power distribution networks generates valuable data for tasks such as phase identification; however, the limited and unreliable availability of labeled data in the form of customer phase connectivity presents challenges. To address this issue, we propose a semi-supervised learning (SSL) framework that effectively leverages labeled and unlabeled data. Our approach incorporates self-training, label spreading, and Bayesian neural networks (BNNs) to enhance phase identification with AMI data. Our method uses an ensemble of multilayer perceptron classifiers in a self-training setup, iteratively adding high-confidence pseudo-labels to improve robustness. We also apply label spread to propagate labels based on data similarity, which enhances generalization across diverse distributions. In addition, we employ a BNNs with uncertainty estimation, boosting confidence in predictions and reducing phase identification errors. In our case study, we achieved approximately 98% +/- 0.08 accuracy with uncertainty using minimal and unreliable labeled data from a real U.S. utility, Duquesne Light Company. Our SSL approach, combined with uncertainty estimation, provides an efficient solution for phase identification in AMI data, ultimately improving the reliability of smart grid applications.
24 POWER TRANSMISSION AND DISTRIBUTION↗
An improved framework for the dynamic likelihood filtering approach to data assimilation
Here, we propose improvements to the Dynamic Likelihood Filter (DLF), a Bayesian data assimilation filtering approach, specifically tailored to wave problems. The DLF approach was developed to address the common challenge in the application of data assimilation to hyperbolic problems in the geosciences and in engineering, where observation systems are sparse in space and time. When these observations have low uncertainties, as compared to model uncertainties, the DLF exploits the inherent nature of information and uncertainties to propagate along characteristics to produce estimates that are phase aware as well as amplitude aware, as would be the case in the traditional data assimilation approach. Along characteristics, the stochastic partial differential equations underlying the linear or nonlinear stochastic dynamics are differential equations. This study focuses on developing the explicit challenges of relating dynamics and uncertainties in the Eulerian and Lagrangian frames via dynamic Gaussian processes. It also implements the approach using the ensemble Kalman filter (EnKF) and compares the DLF approach to the conventional one with respect to wave amplitude and phase estimates in linear and nonlinear wave problems. Numerical comparisons show that the DLF/EnKF outperforms the EnKF estimates, when applied to linear and nonlinear wave problems. This advantage is particularly noticeable when sparse, low uncertainty observations are used.
97 MATHEMATICS AND COMPUTING↗
Solving generalized eigenvalue problems by ordinary differential equations on a quantum computer
Many eigenvalue problems arising in practice are often of the generalized form A x = λ B x . One particularly important case is symmetric, namely A , B are Hermitian and B is positive definite. The standard algorithm for solving this class of eigenvalue problems is to reduce them to Hermitian eigenvalue problems. For a quantum computer, quantum phase estimation is a useful technique to solve Hermitian eigenvalue problems. In this work, we propose a new quantum algorithm for symmetric generalized eigenvalue problems using ordinary differential equations. The algorithm has lower complexity than the standard one based on quantum phase estimation. Moreover, it works for a wider case than symmetric: B is invertible, B - 1 A is diagonalizable and all the eigenvalues are real.
Science & Technology - Other Topics↗
Quantum eigenvalue estimation via time series analysis
We present an efficient method for estimating the eigenvalues of a Hamiltonian H from the expectation values of the evolution operator for various times. For a given quantum state ρ, our method outputs a list of eigenvalue estimates and approximate probabilities. Each probability depends on the support of ρ in those eigenstates of H associated with eigenvalues within an arbitrarily small range. The complexity of our method is polynomial in the inverse of a given precision parameter ε, which is the gap between eigenvalue estimates. Unlike the well-known quantum phase estimation algorithm that uses the quantum Fourier transform, our method does not require large ancillary systems, large sequences of controlled operations, or preserving coherence between experiments, and is therefore more attractive for near-term applications. The output of our method can be used to estimate spectral properties of H and other expectation values efficiently, within additive error proportional to ε.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Solving Large‐Scale Linear Systems of Equations by a Quantum Hybrid Algorithm
Abstract Today's intermediate‐scale quantum computers, although imperfect, already perform computational tasks that are manifestly beyond the capabilities of modern classical supercomputers. However, so far, quantum‐enabled large‐scale solutions have been realized only for limited set of problems. Here a hybrid algorithm based on phase estimation and classical optimization of the circuit width and depth is employed for solving a specific class of large linear systems of equations ubiquitous to many areas of science and engineering. A classification of linear systems based on the entanglement properties of the associated phase‐estimation unitary operation is introduced, enabling a highly efficient search for solutions that is facilitated by a straightforward matrix‐to‐circuit map. A 2 17 ‐dimensional problem is implemented on several IBM quantum computer superconducting quantum processors, a record‐breaking result for a linear system solved by a quantum computer. Demonstrated realisation sets a clear benchmark in the quest for the future quantum speedup in the linear systems of equations solution.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Quantum Davidson algorithm for excited states
Abstract Excited state properties play a pivotal role in various chemical and physical phenomena, such as charge separation and light emission. However, the primary focus of most existing quantum algorithms has been the ground state, as seen in quantum phase estimation and the variational quantum eigensolver (VQE). Although VQE-type methods have been extended to explore excited states, these methods grapple with optimization challenges. In contrast, the quantum Krylov subspace (QKS) method has been introduced to address both ground and excited states, positioning itself as a cost-effective alternative to quantum phase estimation. However, conventional QKS methodologies depend on a pre-generated subspace through real or imaginary-time evolutions. This subspace is inherently expansive and can be plagued with issues like slow convergence or numerical instabilities, often leading to relatively deep circuits. Our research presents an economic QKS algorithm, which we term the quantum Davidson (QDavidson) algorithm. This innovation hinges on the iterative expansion of the Krylov subspace and the incorporation of a pre-conditioner within the Davidson framework. By using the residues of eigenstates to expand the Krylov subspace, we manage to formulate a compact subspace that aligns closely with the exact solutions. This iterative subspace expansion paves the way for a more rapid convergence in comparison to other QKS techniques, such as the quantum Lanczos. Using quantum simulators, we employ the novel QDavidson algorithm to delve into the excited state properties of various systems, spanning from the Heisenberg spin model to real molecules. Compared to the existing QKS methods, the QDavidson algorithm not only converges swiftly but also demands a significantly shallower circuit. This efficiency establishes the QDavidson method as a pragmatic tool for elucidating both ground and excited state properties on quantum computing platforms.
97 MATHEMATICS AND COMPUTING↗
Grand Unification of Quantum Algorithms
Quantum algorithms offer significant speed-ups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian simulation, which appear as subroutines for large families of composite quantum algorithms. A number of these quantum algorithms have recently been tied together by a novel technique known as the quantum singular value transformation (QSVT), which enables one to perform a polynomial transformation of the singular values of a linear operator embedded in a unitary matrix. In the seminal GSLW’19 paper on the QSVT [Gilyén et al., ACM STOC 2019], many algorithms are encompassed, including amplitude amplification, methods for the quantum linear systems problem, and quantum simulation. Here, we provide a pedagogical tutorial through these developments, first illustrating how quantum signal processing may be generalized to the quantum eigenvalue transform, from which the QSVT naturally emerges. Paralleling GSLW’19, we then employ the QSVT to construct intuitive quantum algorithms for search, phase estimation, and Hamiltonian simulation, and also showcase algorithms for the eigenvalue threshold problem and matrix inversion. This overview illustrates how the QSVT is a single framework comprising the three major quantum algorithms, suggesting a grand unification of quantum algorithms.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Real time evolution for ultracompact Hamiltonian eigenstates on quantum hardware
In this work we present a detailed analysis of variational quantum phase estimation (VQPE), a method based on real-time evolution for ground and excited state estimation on near-term hardware. We derive the theoretical ground on which the approach stands, and demonstrate that it provides one of the most compact variational expansions to date for solving strongly correlated Hamiltonians. At the center of VQPE lies a set of equations, with a simple geometrical interpretation, which provides conditions for the time evolution grid in order to decouple eigenstates out of the set of time evolved expansion states, and connects the method to the classical filter diagonalization algorithm. Further, we introduce what we call the unitary formulation of VQPE, in which the number of matrix elements that need to be measured scales linearly with the number of expansion states, and we provide an analysis of the effects of noise which substantially improves previous considerations. The unitary formulation allows for a direct comparison to iterative phase estimation. Our results mark VQPE as both a natural and highly efficient quantum algorithm for ground and excited state calculations of general many-body systems. We demonstrate a hardware implementation of VQPE for the transverse field Ising model. Further, we illustrate its power on a paradigmatic example of strong correlation (Cr2 in the SVP basis set), and show that it is possible to reach chemical accuracy with as few as ~50 timesteps.
Klymko, Katherine↗