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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Discriminating Quantum States with Quantum Machine Learning

Quantum machine learning (QML) algorithms have obtained great relevance in the machine learning (ML) field due to the promise of quantum speedups when performing basic linear algebra subroutines (BLAS), a fundamental element in most ML algorithms. By making use of BLAS operations, we propose, implement and analyze a quantum k-means (qk-means) algorithm with a low time complexity of O(NKlog(D)I/C) to apply it to the fundamental problem of discriminating quantum states at readout. Discriminating quantum states allows the identification of quantum states |0⟩ and |1⟩ from low-level in-phase and quadrature signal (IQ) data, and can be done using custom ML models. In order to reduce dependency on a classical computer, we use the qk-means to perform state discrimination on the IBMQ Bogota device and managed to find assignment fidelities of up to 98.7% that were only marginally lower than that of the k-means algorithm. We also performed a cross-talk benchmark on the quantum device by applying both algorithms to perform state discrimination on a combination of quantum states and using Pearson Correlation coefficients and assignment fidelities of discrimination results to conclude on the presence of cross-talk on qubits. Evidence shows cross-talk in the (1, 2) and (2, 3) neighboring qubit couples for the analyzed device.

Quiroga, David↗
DOE OSTI2022

Long-time simulations for fixed input states on quantum hardware

Publicly accessible quantum computers open the exciting possibility of experimental dynamical quantum simulations. While rapidly improving, current devices have short coherence times, restricting the viable circuit depth. Despite these limitations, we demonstrate long-time, high fidelity simulations on current hardware. Specifically, we simulate an XY-model spin chain on Rigetti and IBM quantum computers, maintaining a fidelity over 0.9 for 150 times longer than is possible using the iterated Trotter method. Our simulations use an algorithm we call fixed state Variational Fast Forwarding (fsVFF). Recent work has shown an approximate diagonalization of a short time evolution unitary allows a fixed-depth simulation. fsVFF substantially reduces the required resources by only diagonalizing the energy subspace spanned by the initial state, rather than over the total Hilbert space. We further demonstrate the viability of fsVFF through large numerical simulations, and provide an analysis of the noise resilience and scaling of simulation errors.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Exploring the Adoption Challenges of Post-Quantum Cryptography in EV Charging Infrastructure

The rapid evolution of electric vehicle (EV) technology and the corresponding growth of the Electric Vehicle Charging Infrastructure (EVCI) brings to light significant cybersecurity concerns, notably in the context of emerging post-quantum computing capabilities. This report, prepared by Pacific Northwest National Laboratory (PNNL) under the U.S. Department of Energy contract, delves into the challenges associated with integrating Post-Quantum Cryptography (PQC) into EVCI to safeguard against potential quantum computing threats. Post-quantum computers will eventually be able to invalidate technologies secured through public key cryptography. As part of this effort, the primary gaps and challenges in the EVCI were investigated with a focus on comparing traditional algorithms against PQC algorithms. One of the notable findings was that the P-521 algorithm was frequently surpassed in performance by PQC algorithms. This document provides a thorough examination of the hurdles the industry can expect when transitioning to PQC within the EVCI, such as interoperability concerns, the computational and memory demands of PQC algorithms, and the organizational readiness for such a transition. It emphasizes the necessity of a forward-thinking approach to cybersecurity, advocating for early and strategic engagement among EVCI stakeholders to ensure a seamless and cost-effective migration to quantum-resistant cryptographic standards. Through this report, the authors aim to catalyze awareness and action among policymakers, industry leaders, and cybersecurity professionals towards fortifying the EVCI against emerging quantum threats, thereby securing the infrastructure essential for the future of electric mobility.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2023

Short-Depth QAOA circuits and Quantum Annealing on Higher-Order Ising Models (Rev.2)

The Quantum Alternating Operator Ansatz (QAOA) and Quantum Annealing (QA) are quantum algorithms that are both based on the adiabatic theorem and both have the goal of sampling the optimal solution(s) of combinatorial optimization problems. Quantum annealing has been physically instantiated on D-Wave devices using superconducting flux qubits, and QAOA can be programmed on digital gate-model quantum computers such as the programmable superconducting transmon qubits devices of the IBMQ series, for instance ibm washington. QAOA and QA address the same types of problems, but it is unclear how they will scale to large problem sizes and to larger and higher-fidelity quantum computers. In this article, we present a direct comparison between QAOA, one and two rounds, run on all 127 qubits of ibm washington and QA run on D-Wave Advantage system4.1 and Advantage system6.1. The problems which allow for this comparison are random Ising model problems whose connectivity matches the heavy hexagonal lattice topology of ibm washington and the Pegasus graph connectivity of the two D-Wave devices. We create two classes of problem instances for this comparison: one with higher order terms (ZZZ variable interactions), linear terms, and quadratic terms, and a separate problem type with only linear and quadratic terms. Our QAOA circuits are novel and extremely short depth, with a CNOT depth of 6 per round, which allows whole chip usage of ibm washington’s heavy hexagonal lattice and can be applied to future heavy-hex chips. We also test the effectiveness of the error suppression technique digital dynamical decoupling on the QAOA circuits. The QAOA circuits compiled to ibm washington are composed of several thousand circuit instructions, approximately 3, 000 depending on the details of the circuit, making these some the largest quantum circuits ever executed on a digital quantum processor. QAOA and QA are compared against the classical heuristic algorithm of simulated annealing and all problem instances are exactly solved using CPLEX in order to evaluate which samplers, if any, correctly found the ground state solution(s) of the problem instances. We find that (i) QA outperforms QAOA on all problem instances, (ii) QAOA samples the problems better than random sampling, and (iii) QAOA angle computation exhibits clear parameter concentration across the ensemble of Ising models.

127 Qubits↗
DOE OSTI2023

Quantum machine learning with differential privacy

Abstract Quantum machine learning (QML) can complement the growing trend of using learned models for a myriad of classification tasks, from image recognition to natural speech processing. There exists the potential for a quantum advantage due to the intractability of quantum operations on a classical computer. Many datasets used in machine learning are crowd sourced or contain some private information, but to the best of our knowledge, no current QML models are equipped with privacy-preserving features. This raises concerns as it is paramount that models do not expose sensitive information. Thus, privacy-preserving algorithms need to be implemented with QML. One solution is to make the machine learning algorithm differentially private, meaning the effect of a single data point on the training dataset is minimized. Differentially private machine learning models have been investigated, but differential privacy has not been thoroughly studied in the context of QML. In this study, we develop a hybrid quantum-classical model that is trained to preserve privacy using differentially private optimization algorithm. This marks the first proof-of-principle demonstration of privacy-preserving QML. The experiments demonstrate that differentially private QML can protect user-sensitive information without signficiantly diminishing model accuracy. Although the quantum model is simulated and tested on a classical computer, it demonstrates potential to be efficiently implemented on near-term quantum devices [noisy intermediate-scale quantum (NISQ)]. The approach’s success is illustrated via the classification of spatially classed two-dimensional datasets and a binary MNIST classification. This implementation of privacy-preserving QML will ensure confidentiality and accurate learning on NISQ technology.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Properties of the contraction map for holographic entanglement entropy inequalities

We present a deterministic way of finding contraction maps for candidate holographic entanglement entropy inequalities modulo choices due to actual degeneracy. We characterize its complexity and give an argument for the completeness of the contraction map proof method as a necessary and sufficient condition for the validity of an entropy inequality for holographic entanglement.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Efficient QAOA Optimization using Directed Restarts and Graph Lookup

Variational Quantum Algorithms (VQA) aim to enhance the capabilities of Noisy Intermediate-Scale Quantum (NISQ) devices. These algorithms utilize parameterized circuits and classical optimizers to iteratively execute circuits with varying parameters. However, VQA faces computational overheads due to repeated iterations and random restarts. Prior work suggests using basic sub-graphs to transfer parameters for the input graph, reducing optimizer overheads but limiting applicability to structured regular graphs. In real-world applications, random irregular graphs are common, and existing methods are not scalable or practical for such graphs. This paper presents a framework that aims to improve random irregular graphs in VQA. The framework uses graph similarity and important features like total edge counts, average edge counts, and variance. It follows an iterative process to choose basis sub-graphs from a small database and adjust parameters accordingly. Classical optimizers then utilize these parameters to determine when to restart and perform gradient descent. This approach increases the chances of reaching global maximum points.

Wang, Meng↗
DOE OSTI2017

Computing properties of hadrons, nuclei and nuclear matter from quantum chromodynamics

The goal of the research of the William and Mary group (PI from Computer Science and Co-PI from Physics) is to develop algorithms that address the limitations in computational scalability of current methods in lattice QCD. Of particular interest is the problem of computing traces of certain functions of a matrix, which arises in nuclear physics calculations of disconnected diagrams and requires the solution of a large number of linear systems of equations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

SPARC-X: Quantum simulations at extreme scale - reactive dynamics from first principles

We have developed the massively parallel electronic structure code SPARC-X: a computational framework for performing Kohn-Sham Density Functional Theory (DFT) calculations that can scale linearly with the number of atoms in the system, while being able to leverage petascale and emerging exascale parallel computers to study chemical phenomena at unprecedented length and time scales. SPARC-X exploits a recent breakthrough in electronic structure methodologies: systematically improvable, strictly local, orthonormal, discontinuous real-space bases that efficiently and systematically capture the local chemistry of the system. With further adaptation using new machine-learning techniques and the use of the massively parallel Spectral Quadrature (SQ) electronic structure method, the algorithmic complexity and prefactor associated with DFT calculations involving semilocal as well as hybrid functionals are dramatically reduced. Using petascale computational resources, SPARC-X enables quantum mechanical simulations at length and time scales previously accessible only by empirical approaches, e.g., 1,000,000 atoms for a few picoseconds using semilocal functionals or 1,000 atoms for a few picoseconds using hybrid functionals. Using exascale resources, the sizes and times targeted are two orders of magnitude larger. Such a capability has applications in a wide variety of chemical sciences, including reactive interfaces where large length- and/or long time-scales are needed and traditional force fields fail. This is particularly important in dynamic catalysis, where bond breaking and formation must be understood in detail. We developed, tested, and employed the SPARC-X framework to understand the photocatalytic properties of TiO 2 nanoparticles, revealing finite size effects that cannot be captured with standard model systems or functionals. This integrated development and application strategy ensures that SPARC-X remains a robust, efficient, and scalable software package for quantum simulations on current petascale and emerging exascale computing resources.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Basic Research Needs in Quantum Computing and Networking

Employing quantum mechanical resources in computing, information processing, and networking opens the door to potential exponential advantages over classical counterparts. However, quantifying and realizing such advantages poses extensive scientific and engineering challenges. Department of Energy (DOE) investments have driven steady progress in addressing such challenges. Recently developed quantum algorithms offer asymptotic exponential advantages in speed or accuracy for fundamental scientific problems. These problems include simulating physical systems, solving systems of linear equations, differential equations, and optimization problems. Empirical demonstrations on nascent quantum hardware suggest better performance on contrived computational tasks than classical analogs. However, the requirements for a quantum computer or network to demonstrate an end-to-end rigorously quantifiable performance improvement over classical analogs remains a grand challenge, especially for problems of practical value. In particular, what will be required for quantum technology to ultimately exhibit scalable, rigorous, and transformative performance advantages for practical applications? In July 2023, DOE’s Advanced Scientific Computing Research program in the Office of Science convened the Workshop on Basic Research Needs in Quantum Computing and Networking, where major opportunities and grand challenges were identified. The following five priority research directions (PRDs) were identified as a result of the workshop.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Noise-Resilient Quantum Machine Learning for Stability Assessment of Power Systems

Transient stability assessment (TSA) is a cornerstone for resilient operations of todays interconnected power grids. This paper is a confluence of quantum computing, data science and machine learning to potentially address the power system TSA issue. Here, we devise a quantum TSA (QTSA) method to enable scalable and efficient data-driven transient stability prediction for bulk power systems, which is the first attempt to tackle the TSA issue with quantum computing. Our contributions are three-fold: 1) A high expressibility, low-depth (HELD) quantum circuit is designed for accurate and noise-resilient TSA; 2) A quantum natural gradient descent algorithm is developed for efficient HELD circuit training; 3) A systematical analysis on QTSAs performance under various quantum factors is per-formed. QTSA underpins a foundation of quantum-enabled and data-driven power grid stability analytics. It renders the intractable TSA straightforward and effortless in the Hilbert space, and therefore provides stability information for power system operations. Extensive experiments on quantum simulators and real quantum computers verify the accuracy, noise-resilience, scalability and universality of QTSA.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2021

Variational Monte Carlo Calculations of A ≤ 4 Nuclei with an Artificial Neural-Network Correlator Ansatz

Here, the complexity of many-body quantum wave functions is a central aspect of several fields of physics and chemistry where nonperturbative interactions are prominent. Artificial neural networks (ANNs) have proven to be a flexible tool to approximate quantum many-body states in condensed matter and chemistry problems. In this work we introduce a neural-network quantum state ansatz to model the ground-state wave function of light nuclei, and approximately solve the nuclear many-body Schrodinger equation. Using efficient stochastic sampling and optimization schemes, our approach extends pioneering applications of ANNs in the field, which present exponentially scaling algorithmic complexity. We compute the binding energies and point-nucleon densities of A ≤ 4 nuclei as emerging from a leading-order pionless effective field theory Hamiltonian. We successfully benchmark the ANN wave function against more conventional parametrizations based on two- and three-body Jastrow functions, and virtually exact Green's function Monte Carlo results.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Quantum computing based hybrid solution strategies for large-scale discrete-continuous optimization problems

Quantum computing (QC) has gained popularity due to its unique capabilities that are quite different from that of classical computers in terms of speed and methods of operations. This paper proposes hybrid models and methods that effectively leverage the complementary strengths of deterministic algorithms and QC techniques to overcome combinatorial complexity for solving large-scale mixed-integer programming problems. Four applications, namely the molecular conformation problem, job-shop scheduling problem, manufacturing cell formation problem, and the vehicle routing problem, are specifically addressed. Large-scale instances of these application problems across multiple scales ranging from molecular design to logistics optimization are computationally challenging for deterministic optimization algorithms on classical computers. To address the computational challenges, hybrid QC-based algorithms are proposed and extensive computational experimental results are presented to demonstrate their applicability and efficiency. The proposed QC-based solution strategies enjoy high computational efficiency in terms of solution quality and computation time, by utilizing the unique features of both classical and quantum computers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Efficient quantum algorithm for dissipative nonlinear differential equations

Significance Nonlinear differential equations appear in many domains and are notoriously difficult to solve. Whereas previous quantum algorithms for general nonlinear differential equations have complexity exponential in the evolution time, we give the first quantum algorithm for dissipative nonlinear differential equations that is efficient provided the dissipation is sufficiently strong relative to nonlinear and forcing terms and the solution does not decay too rapidly. We also establish a lower bound showing that differential equations with sufficiently weak dissipation have worst-case complexity exponential in time, giving an almost tight classification of the quantum complexity of simulating nonlinear dynamics. Furthermore, numerical results for the Burgers equation suggest that our algorithm may potentially address complex nonlinear phenomena even in regimes with weaker dissipation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Report for the ASCR Workshop on Basic Research Needs in Quantum Computing and Networking - 2023

Employing quantum mechanical resources in computing and networking opens the door to new computation and communication models and potential disruptive advantages over classical counterparts. However, quantifying and realizing such advantages face extensive scientific and engineering challenges. Investments by the Department of Energy (DOE) have driven progress toward addressing such challenges. Quantum algorithms have been recently developed, in some cases offering asymptotic exponential advantages in speed or accuracy, for fundamental scientific problems such as simulating physical systems, solving systems of linear equations, or solving differential equations. Empirical demonstrations on nascent quantum hardware suggest better performance than classical analogs on specialized computational tasks favorable to the quantum computing systems. However, demonstration of an end-to-end, substantial and rigorously quantifiable quantum performance advantage over classical analogs remains a grand challenge, especially for problems of practical value. The definition of requirements for quantum technologies to exhibit scalable, rigorous, and transformative performance advantages for practical applications also remains an outstanding open question, namely, what will be required to ultimately demonstrate practical quantum advantage?

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Report for the ASCR Workshop on Basic Research Needs in Quantum Computing and Networking - 2023

Employing quantum mechanical resources in computing and networking opens the door to new computation and communication models and potential disruptive advantages over classical counterparts. However, quantifying and realizing such advantages face extensive scientific and engineering challenges. Investments by the Department of Energy (DOE) have driven progress toward addressing such challenges. Quantum algorithms have been recently developed, in some cases offering asymptotic exponential advantages in speed or accuracy, for fundamental scientific problems such as simulating physical systems, solving systems of linear equations, or solving differential equations. Empirical demonstrations on nascent quantum hardware suggest better performance than classical analogs on specialized computational tasks favorable to the quantum computing systems. However, demonstration of an end-to-end, substantial and rigorously quantifiable quantum performance advantage over classical analogs remains a grand challenge, especially for problems of practical value. The definition of requirements for quantum technologies to exhibit scalable, rigorous, and transformative performance advantages for practical applications also remains an outstanding open question, namely, what will be required to ultimately demonstrate practical quantum advantage?

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Accelerating resonant spectroscopy simulations using multishifted biconjugate gradient

Resonant spectroscopies, which involve intermediate states with finite lifetimes, provide important insights into collective excitations in quantum materials that are otherwise inaccessible. However, theoretical understanding in this area is often limited by the numerical challenges of solving Kramers-Heisenberg-type response functions for large-scale systems. To address this, we introduce a multishifted biconjugate gradient algorithm that exploits the shared structure of Krylov subspaces across spectra with varying incident energies, effectively reducing the computational complexity to that of linear spectroscopies. Both mathematical proofs and numerical benchmarks confirm that this algorithm substantially accelerates spectral simulations, achieving constant complexity independent of the number of incident energies, while ensuring accuracy and stability. This development provides a scalable, versatile framework for simulating advanced spectroscopies in quantum materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Model Order Reduction Algorithm for Estimating the Absorption Spectrum

The ab initio description of the spectral interior of the absorption spectrum poses both a theoretical and computational challenge for modern electronic structure theory. Due to the often spectrally dense character of this domain in the quantum propagator’s eigenspectrum for medium-to-large sized systems, traditional approaches based on the partial diagonalization of the propagator often encounter oscillatory and stagnating convergence. Electronic structure methods which solve the molecular response problem through the solution of spectrally shifted linear systems, such as the complex polarization propagator, offer an alternative approach which is agnostic to the underlying spectral density or domain location. This generality comes at a seemingly high computational cost associated with solving a large linear system for each spectral shift in some discretization of the spectral domain of interest. In this work, we present a novel, adaptive solution to this high computational overhead based on model order reduction techniques via interpolation. Model order reduction reduces the computational complexity of mathematical models and is ubiquitous in the simulation of dynamical systems and control theory. The efficiency and effectiveness of the proposed algorithm in the ab initio prediction of X-ray absorption spectra is demonstrated using a test set of challenging water clusters which are spectrally dense in the neighborhood of the oxygen K-edge. On the basis of a single, user defined tolerance we automatically determine the order of the reduced models and approximate the absorption spectrum up to the given tolerance. We also illustrate that, for the systems studied, the automatically determined model order increases logarithmically with the problem dimension, compared to a linear increase of the number of eigenvalues within the energy window. Furthermore, we observed that the computational cost of the proposed algorithm only scales quadratically with respect to the problem dimension.

IDREAM, K-Edge, theoretical, computational, electr↗