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DOE OSTI2021

Investigating the Chinese postman problem on a quantum annealer

The recent availability of quantum annealers has fueled a new area of information technology where such devices are applied to address practically motivated and computationally difficult problems with hardware that exploits quantum mechanical phenomena. D-Wave annealers are promising platforms to solve these problems in the form of quadratic unconstrained binary optimization. Here we provide a formulation of the Chinese postman problem that can be used as a tool for probing the local connectivity of graphs and networks. We treat the problem classically with a tabu algorithm and simulated annealing, and using a D-Wave device. The efficiency of quantum annealing with respect to the simulated annealing has been demonstrated using the optimal time to solution metric. We systematically analyze computational parameters associated with the specific hardware. Our results clarify how the interplay between the embedding due to limited connectivity of the Chimera graph, the definition of logical qubits, and the role of spin-reversal controls the probability of reaching the expected solution

36 MATERIALS SCIENCE↗
DOE OSTI2019

Recent advances in machine learning towards multiscale soft materials design

The multiscale design of soft materials requires an ensemble of computational techniques spanning quantum-chemistry to molecular dynamics to continuum modeling. The recent emergence of machine-learning (ML) and modern optimization algorithms has accelerated material property prediction, as well as stimulated the development of hybrid ML/molecular modeling methodologies capable of providing physical insights unobtainable from purely physics-based modeling and intuition. Such hybrid techniques also have important ramifications for the ML-enhanced interpretation of results from simulations and experiments alike. Leveraging ML techniques for the design of chemical or morphological structures based on a target property or functionality represents an exciting goal for the general area of soft materials, including polymers, liquid crystals, colloids, or biomolecules, to name a few representative classes of systems. Furthermore, we provide a perspective on recent work using ML techniques of relevance for the multiscale design of soft materials and outline potential future directions of interest to the soft materials community.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Quantum annealing for jet clustering with thrust

Quantum computing holds the promise of substantially speeding up computationally expensive tasks, such as solving optimization problems over a large number of elements. In high-energy collider physics, quantum-assisted algorithms might accelerate the clustering of particles into jets. In this study, we benchmark quantum annealing strategies for jet clustering based on optimizing a quantity called “thrust” in electron-positron collision events. Here, we find that quantum annealing yields similar performance to exact classical approaches and classical heuristics, after tuning the annealing parameters. Without tuning, comparable performance can be obtained through a hybrid quantum/classical approach.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Quantum-inspired method for solving the Vlasov-Poisson equations

Kinetic simulations of collisionless (or weakly collisional) plasmas using the Vlasov equation are often infeasible due to high-resolution requirements and the exponential scaling of computational cost with respect to dimension. Recently, it has been proposed that matrix product state (MPS) methods, a quantum-inspired but classical algorithm, can be used to solve partial differential equations with exponential speed-up, provided that the solution can be compressed and efficiently represented as a MPS within some tolerable error threshold. Here, in this work, we explore the practicality of MPS methods for solving the Vlasov-Poisson equations for systems with one coordinate in space and one coordinate in velocity, and find that important features of linear and nonlinear dynamics, such as damping or growth rates and saturation amplitudes, can be captured while compressing the solution significantly. Furthermore, by comparing the performance of different mappings of the distribution functions onto the MPS, we develop an intuition of the MPS representation and its behavior in the context of solving the Vlasov-Poisson equations, which will be useful for extending these methods to higher-dimensional problems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

A Quantum Approach for Implementing Fixed-Point Arithmetic in Solving Ordinary Differential Equations

Differential equations (DEs) serve as fundamental tools in mathematical modeling across scientific disciplines, yet classical numerical solvers face limitations with large-scale or computationally intensive problems. This study explores a quantum-inspired approach to solving DEs, combining quantum-inspired techniques with classical methods. It focuses on fixed-point arithmetic on quantum circuits, utilizing basic quantum gates to manipulate DE solutions. We expand upon the techniques introduced by Zanger et al. [Quantum, 5, 502 (2021)] by offering a precise computation for a fixed-point signed multiplication scheme, while also presenting a quantum circuit capable of executing the fixed-point division algorithm. We demonstrate the feasibility of our approach through the simulation of a linear Ordinary Differential Equation (ODE), where initial conditions and parameters are encoded into quantum circuits using fixed-point representation. By executing sequences of quantum gates mimicking numerical integration steps, we obtain approximate solutions to the ODE with specified fixed-point precision.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2025

A Quantum Approach for Implementing Fixed-Point Arithmetic in Solving Ordinary Differential Equations

Differential equations (DEs) serve as fundamental tools in mathematical modeling across scientific disciplines, yet classical numerical solvers face limitations with large-scale or computationally intensive problems. This study explores a quantum-inspired approach to solving DEs, combining quantum- inspired techniques with classical methods. It focuses on fixed- point arithmetic on quantum circuits, utilizing basic quantum gates to manipulate DE solutions. We expand upon the techniques introduced by Zanger et al. [Quantum, 5, 502 (2021)] by offering a precise computation for a fixed-point signed multiplication scheme, while also presenting a quantum circuit capable of executing the fixed-point division algorithm. We demonstrate the feasibility of our approach through the simulation of a linear Ordinary Differential Equation (ODE), where initial conditions and parameters are encoded into quantum circuits using fixed- point representation. By executing sequences of quantum gates mimicking numerical integration steps, we obtain approximate solutions to the ODE with specified fixed-point precision.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Finding Maximum Cliques on the D-Wave Quantum Annealer

This work assesses the performance of the D-Wave 2X (DW) quantum annealer for finding a maximum clique in a graph, one of the most fundamental and important NP-hard problems. Because the size of the largest graphs DW can directly solve is quite small (usually around 45 vertices), we also consider decomposition algorithms intended for larger graphs and analyze their performance. For smaller graphs that fit DW, we provide formulations of the maximum clique problem as a quadratic unconstrained binary optimization (QUBO) problem, which is one of the two input types (together with the Ising model) acceptable by the machine, and compare several quantum implementations to current classical algorithms such as simulated annealing, Gurobi, and third-party clique finding heuristics. We further estimate the contributions of the quantum phase of the quantum annealer and the classical post-processing phase typically used to enhance each solution returned by DW. We demonstrate that on random graphs that fit DW, no quantum speedup can be observed compared with the classical algorithms. On the other hand, for instances specifically designed to fit well the DW qubit interconnection network, we observe substantial speed-ups in computing time over classical approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Degeneracy engineering for classical and quantum annealing: A case study of sparse linear regression in collider physics

Classical and quantum annealing are computing paradigms that have been proposed to solve a wide range of optimization problems. In this paper, we aim to enhance the performance of annealing algorithms by introducing the technique of degeneracy engineering, through which the relative degeneracy of the ground state is increased by modifying a subset of terms in the objective Hamiltonian. We illustrate this novel approach by applying it to the example of ℓ 0 -norm regularization for sparse linear regression, which is, in general, an NP-hard optimization problem. Specifically, we show how to cast ℓ 0 -norm regularization as a quadratic unconstrained binary optimization (QUBO) problem, suitable for implementation on annealing platforms. As a case study, we apply this QUBO formulation to energy flow polynomials in high-energy collider physics, finding that degeneracy engineering substantially improves the annealing performance. Furthermore, our results motivate the application of degeneracy engineering to a variety of regularized optimization problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Quantum-Inspired Power System Reliability Assessment

To enable an in-depth study of power system operation and planning, the assessment of standard reliability indices is inevitable. The Monte Carlo Simulation (MCS) approach is a broadly used method in replacing the analytical methods in reliability indices assessment. The accuracy of MCS, however, highly depends on the sampling size, and hence, a complicated system with large number of components requires a large sampling size and daunting computational effort. To address this shortcoming, we, in this paper attempt to take advantage of potentials of the quantum computing (QC) for power system reliability assessment by realizing the following contributions: 1) an innovative quantum model designed for reliability assessment; 2) a quantum circuit that achieves the quadratic speed up compared to the classical MCS method; 3) an efficient quantum amplitude estimation (QAE) algorithm to accurately evaluate the reliability indices. The accuracy and efficacy of the quantum reliability method are extensively verified and demonstrated on both radial and mesh distribution systems.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2023

A Backend-agnostic, Quantum-classical Framework for Simulations of Chemistry in C ++

As quantum computing hardware systems continue to advance, the research and development of performant, scalable, and extensible software architectures, languages, models, and compilers is equally as important to bring this novel coprocessing capability to a diverse group of domain computational scientists. For the field of quantum chemistry, applications and frameworks exist for modeling and simulation tasks that scale on heterogeneous classical architectures, and we envision the need for similar frameworks on heterogeneous quantum-classical platforms. Furthermore, we present the XACC system-level quantum computing framework as a platform for prototyping, developing, and deploying quantum-classical software that specifically targets chemistry applications. We review the fundamental design features in XACC, with special attention to its extensibility and modularity for key quantum programming workflow interfaces and provide an overview of the interfaces most relevant to simulations of chemistry. A series of examples demonstrating some of the state-of-the-art chemistry algorithms currently implemented in XACC are presented, while also illustrating the various APIs that would enable the community to extend, modify, and devise new algorithms and applications in the realm of chemistry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Variational quantum simulation of the critical Ising model with symmetry averaging

Here we investigate the use of deep multiscale entanglement renormalization ansatz (DMERA) circuits as a variational ansatz. We use the exactly solvable one-dimensional critical transverse-field Ising model as a test bed. Numerically exact simulation of the quantum circuit ansatz can in this case be carried out to hundreds of qubits by exploiting efficient classical algorithms for simulating matchgate circuits. We find that, for this system, the DMERA strongly outperforms a standard quantum approximate optimization algorithm (QAOA)–style ansatz, and that a major source of systematic error in correlation functions approximated using the DMERA is the breaking of the translational and Kramers-Wannier symmetries of the transverse-field Ising model. We are able to reduce this error by up to four orders of magnitude by symmetry averaging, without incurring additional cost in qubits or circuit depth. Here, we propose that this technique for mitigating systematic error could be applied to noisy intermediate-scale quantum (NISQ) simulations of physical systems with other symmetries.

1-dimensional spin chains↗
DOE OSTI2025

Potential quantum advantage for simulation of fluid dynamics

Numerical simulation of turbulent fluid dynamics needs to either parametrize turbulence—which introduces large uncertainties—or explicitly resolve the smallest scales—which is prohibitively expensive. Here, we provide evidence through analytic bounds and numerical studies that a potential quantum speedup can be achieved to simulate fluid dynamics using quantum computing. Specifically, we provide a lattice Boltzmann formulation of fluid dynamics for which we give evidence that low-order Carleman linearization is much more accurate than previously believed for these systems. This is achieved via a combination of reformulating the Navier-Stokes nonlinearity (u·$\triangledown$u) to lattice-Boltzmann nonlinearity (u 2 ) and accurately linearizing the dynamical equations, which effectively trades nonlinearity for additional degrees of freedom that add negligible expense in the quantum solver. Based on this, we apply a quantum algorithm for simulating the Carleman-linearized lattice Boltzmann equation and provide evidence that its cost scales logarithmically with system size compared with polynomial scaling in the best known classical algorithms. In this paper, we suggest that a quantum advantage may exist for simulating fluid dynamics, paving the way for simulating nonlinear multiscale transport phenomena in a wide range of disciplines using quantum computing.

42 ENGINEERING↗
DOE OSTI2024

Early Exploration of a Flexible Framework for Efficient Quantum Linear Solvers in Power Systems

The rapid integration of renewable energy resources presents formidable challenges in managing power grids. While advanced computing and machine learning techniques offer some solutions for accelerating grid modeling and simulation, there remain complex problems that classical computers cannot effectively address. Quantum computing, a promising technology, has the potential to fundamentally transform how we manage power systems, especially in scenarios with a higher proportion of renewable energy sources. One critical aspect is solving linear systems of equations, crucial for power system applications like power flow analysis, for which the Harrow-Hassidim-Lloyd (HHL) algorithm is a well-known quantum solution. However, HHL quantum circuits often exhibit excessive depth, making them impractical for current Noisy-Intermediate-Scale-Quantum (NISQ) devices. In this paper, we introduce a versatile framework, powered by NWQSim, that bridges the gap between power system applications and quantum linear solvers available in Qiskit. This framework empowers researchers to efficiently explore power system applications using quantum linear solvers. Through innovative gate fusion strategies, reduced circuit depth, and GPU acceleration, our simulator significantly enhances resource efficiency. Power flow case studies have demonstrated up to a eight-fold speedup compared to Qiskit Aer, all while maintaining comparable levels of accuracy.

quantum computing, Harrow-Hassidim-Lloyd, high-per↗
DOE OSTI2018

Numerical parameter optimizations of the Ignition and Growth model for a HMX plastic bonded explosive

We present here a novel method for optimizing parameters of the Ignition and Growth (I&G) reactive flow model for high explosives. The I&G model predicts the shock initiation response of explosives subjected to dynamic loading. However, calibrating the model is a time-consuming process because it has several parameters, typically requires multiple data sets, and there are no direct correlations between parameters and data. In this study, we couple a scalable optimization algorithm to simulations of shock initiation experiments in the multi-physics code ALE3D. We develop four I&G model parameter sets for the HMX (1,3,5,7-tetranitro-1,3,5,7-tetrazocane)-based explosive LX-07 [90 wt. % HMX, 10 wt. % Viton A] based on minimizing the difference between calculations and measurements at the embedded pressure gauges in 1D gun shock experiments. Our study shows that a cost function based on both shock time of arrival and pressure pulse shape demonstrates the best agreement with experimental data.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Cabana: A Performance Portable Library for Particle-Based Simulations

Particle-based simulations are ubiquitous throughout many fields of computational science and engineering, spanning the atomistic level with molecular dynamics (MD), to mesoscale particle-in-cell (PIC) simulations for solid mechanics, device-scale modeling with PIC methods for plasma physics, and massive N-body cosmology simulations of galaxy structures, with many other methods in between (Hockney & Eastwood, 1989). While these methods use particles to represent significantly different entities with completely different physical models, many low-level details are shared including performant algorithms for short- and/or long-range particle interactions, multi-node particle communication patterns, and other data management tasks such as particle sorting and neighbor list construction. Cabana is a performance portable library for particle-based simulations, developed as part of the Co-Design Center for Particle Applications (CoPA) within the Exascale Computing Project (ECP) (Alexander et al., 2020). The CoPA project and its full development scope, including ECP partner applications, algorithm development, and similar software libraries for quantum MD, is described in (Mniszewski et al., 2021). Cabana uses the Kokkos library for on-node parallelism (Edwards et al., 2014; Trott et al., 2022), enabling simulation on multi-core CPU and GPU architectures, and MPI for GPU-aware, multi-node communication. Cabana provides particle simulation capabilities on almost all current Kokkos backends, including serial execution, OpenMP (including OpenMP-Target for GPUs), CUDA (NVIDIA GPUs), HIP (AMD GPUs), and SYCL (Intel GPUs), providing a clear path for the coming generation of accelerator-based exascale hardware. Cabana builds on Kokkos by providing new particle data structures and particle algorithms resulting in a similar execution policy-based, node-level programming model that is intended to be used in addition to the core Kokkos library within an application. Cabana is designed as an application and physics agnostic, but particle-specific toolkit which can either be used to generate a new application, or to be used as needed in existing applications at various levels of invasiveness including through interfaces that wrap user memory in existing data structures.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Classical optimization with imaginary-time block encoding on quantum computers: The MaxCut problem

Optimization problems in finance, physics, and computer science are typically very hard to tackle in classical computing; quantum computing could help speed up computations and provide efficient methods for tackling large problems. Typically, to treat a problem with a quantum computer, the optimal solution is cast as the ground state of a diagonal Hamiltonian. Here, we develop a method, called imaginary-time evolution block encoding (ITE-BE), based on a recent imaginary-time algorithm, which requires no variational parameter optimization, as all parameters can be derived analytically from the target Hamiltonian. We also demonstrate that our method can be successfully combined with other quantum algorithms such as the quantum approximate optimization algorithm (QAOA). For illustration, here we study the MaxCut problem. We find that the QAOA ansatz increases the postselection success of ITE-BE, and shallow QAOA circuits, when boosted with ITE-BE, achieve better performance than deeper QAOA circuits. For the special case of the transverse initial state, we adapt our block-encoding scheme to allow for a deterministic application of the first layer of the circuit.

Zhong, Dawei [University of Southern California, L↗