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DOE OSTI2022

A QUBO formulation for top-τ eigencentrality nodes

The efficient calculation of the centrality or “hierarchy” of nodes in a network has gained great relevance in recent years due to the generation of large amounts of data. The eigenvector centrality (aka eigencentrality) is quickly becoming a good metric for centrality due to both its simplicity and fidelity. In this work we lay the foundations for solving the eigencentrality problem of ranking the importance of the nodes of a network with scores from the eigenvector of the network, using quantum computational paradigms such as quantum annealing and gate-based quantum computing. The problem is reformulated as a quadratic unconstrained binary optimization (QUBO) that can be solved on both quantum architectures. The results focus on correctly identifying a given number of the most important nodes in numerous networks given by the sparse vector solution of our QUBO formulation of the problem of identifying the top- τ highest eigencentrality nodes in a network on both the D-Wave and IBM quantum computers.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Quantum Machine Learning Applications in High-Energy Physics

Some of the most significant achievements of the modern era of particle physics, such as the discovery of the Higgs boson, have been made possible by the tremendous effort in building and operating large-scale experiments like the Large Hadron Collider or the Tevatron. In these facilities, the ultimate theory to describe matter at the most fundamental level is constantly probed and verified. These experiments often produce large amounts of data that require storing, processing, and analysis techniques that continually push the limits of traditional information processing schemes. Thus, the High-Energy Physics (HEP) field has benefited from advancements in information processing and the development of algorithms and tools for large datasets. More recently, quantum computing applications have been investigated to understand how the community can benefit from the advantages of quantum information science. Nonetheless, to unleash the full potential of quantum computing, there is a need to understand the quantum behavior and, thus, scale up current algorithms beyond what can be simulated in classical processors. In this work, we explore potential applications of quantum machine learning to data analysis tasks in HEP and how to overcome the limitations of algorithms targeted for Noisy Intermediate-Scale Quantum (NISQ) devices.

Delgado, Andrea↗

DOE OSTI2020

Quantum Matter: Computation Meets Experiments

The past few years have seen tremendous advances in our understanding of strongly interacting quantum systems. By combining progress in theoretical concepts and methods with algorithmic advances, computational methods have shed new light on key open questions in the physics of quantum matter, both for materials with strong electronic correlations and for interacting quantum gases. At the same time, new materials and new techniques have greatly increased the range of experimental information available. This Aspen Winter Conference will bring leading theorists with expertise in a broad range of computational methods together with experimentalists to discuss the potential of new methods, the accomplishments of existing methods and opportunities for future experiment/ theory collaboration. The meeting will focus on a broad set of physics questions of current interest in the field, for which computational methods and experiments have brought or have the potential to bring new insights.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Simultaneous estimation of multiple eigenvalues with short-depth quantum circuit on early fault-tolerant quantum computers

We introduce a multi-modal, multi-level quantum complex exponential least squares (MM-QCELS) method to simultaneously estimate multiple eigenvalues of a quantum Hamiltonian on early fault-tolerant quantum computers. Our theoretical analysis demonstrates that the algorithm exhibits Heisenberg-limited scaling in terms of circuit depth and total cost. Notably, the proposed quantum circuit utilizes just one ancilla qubit, and with appropriate initial state conditions, it achieves significantly shorter circuit depths compared to circuits based on quantum phase estimation (QPE). Numerical results suggest that compared to QPE, the circuit depth can be reduced by around two orders of magnitude under several settings for estimating ground-state and excited-state energies of certain quantum systems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2026

Tough Errors are no Match (TEAM): Optimizing the Quantum Compiler for Noise Resilience

This report summarizes our contributions to the Department of Energy’s Tough Errors are no Match (TEAM) project (DE-SC0020377) under Thrust 2: Quantum Programming and Compilation. The central outcomes of this work included a novel efficient quantum compiling algorithm which works without requiring the quantum computer to exactly invert its operations, answering a longstanding open problem in quantum compiling. Additional results include the implementation of zero-noise extrapolation error mitigation in collaboration with the Unitary Fund, as well as novel quantum algorithms for entanglement detection and pseudorandomness.

Bouland, Adam [Stanford Univ., CA (United States)]↗

DOE OSTI2023

Data-driven quantum approximate optimization algorithm for power systems

Abstract Quantum technology provides a ground-breaking methodology to tackle challenging computational issues in power systems. It is especially promising for Distributed Energy Resources (DERs) dominant systems that have been widely developed to promote energy sustainability. In those systems, knowing the maximum sections of power and data delivery is essential for monitoring, operation, and control. However, high computational effort is required. By leveraging quantum resources, Quantum Approximate Optimization Algorithm (QAOA) provides a means to search for these sections efficiently. However, QAOA performance relies heavily on critical parameters, especially for weighted graphs. Here we present a data-driven QAOA, which transfers quasi-optimal parameters between weighted graphs based on the normalized graph density. We verify the strategy with 39,774 expectation value calculations. Without parameter optimization, our data-driven QAOA is comparable with the Goemans-Williamson algorithm. This work advances QAOA and pilots its practical application to power systems in noisy intermediate-scale quantum devices.

Jing, Hang (ORCID:0000000256343489)↗

DOE OSTI2026

Lyapunov controlled counterdiabatic quantum optimization

We introduce a quantum algorithm that integrates counterdiabatic (CD) protocols with quantum Lyapunov control (QLC) to address combinatorial optimization problems. This approach offers versatility, allowing implementation as either a digital-analog or purely digital algorithm based on selected control strategies. By examining spin-glass Hamiltonians, we illustrate how the algorithm can explore alternative paths to enhance solution outcomes compared to conventional CD techniques. This method reduces dependence on extensive higher-order CD terms and on classical optimization techniques, making it more suitable for existing quantum computing platforms. The combination of digital compression via CD protocols and the adaptable nature of QLC methods positions this approach as a promising candidate for near-term quantum devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Quantum-parallel vectorized data encodings and computations on trapped-ion and transmon QPUs

Compact data representations in quantum systems are crucial for the development of quantum algorithms for data analysis. In this study, we present two innovative data encoding techniques, known as QCrank and QBArt, which exhibit significant quantum parallelism via uniformly controlled rotation gates. The QCrank method encodes a series of real-valued data as rotations on data qubits, resulting in increased storage capacity. On the other hand, QBArt directly incorporates a binary representation of the data within the computational basis, requiring fewer quantum measurements and enabling well-established arithmetic operations on binary data. We showcase various applications of the proposed encoding methods for various data types. Notably, we demonstrate quantum algorithms for tasks such as DNA pattern matching, Hamming weight computation, complex value conjugation, and the retrieval of a binary image with 384 pixels, all executed on the Quantinuum trapped-ion QPU. Furthermore, we employ several cloud-accessible QPUs, including those from IBMQ and IonQ, to conduct supplementary benchmarking experiments.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Unfolding quantum computer readout noise

Abstract In the current era of noisy intermediate-scale quantum computers, noisy qubits can result in biased results for early quantum algorithm applications. This is a significant challenge for interpreting results from quantum computer simulations for quantum chemistry, nuclear physics, high energy physics (HEP), and other emerging scientific applications. An important class of qubit errors are readout errors. The most basic method to correct readout errors is matrix inversion, using a response matrix built from simple operations to probe the rate of transitions from known initial quantum states to readout outcomes. One challenge with inverting matrices with large off-diagonal components is that the results are sensitive to statistical fluctuations. This challenge is familiar to HEP, where prior-independent regularized matrix inversion techniques (“unfolding”) have been developed for years to correct for acceptance and detector effects, when performing differential cross section measurements. We study one such method, known as iterative Bayesian unfolding, as a potential tool for correcting readout errors from universal gate-based quantum computers. This method is shown to avoid pathologies from commonly used matrix inversion and least squares methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Quantum neuromorphic computing

Quantum neuromorphic computing physically implements neural networks in brain-inspired quantum hardware to speed up their computation. In this perspective article, we show that this emerging paradigm could make the best use of the existing and near future intermediate size quantum computers. Some approaches are based on parametrized quantum circuits and use neural network-inspired algorithms to train them. Other approaches, closer to classical neuromorphic computing, take advantage of the physical properties of quantum oscillator assemblies to mimic neurons and synapses to compute. In this work, we discuss the different implementations of quantum neuromorphic networks with digital and analog circuits, highlight their respective advantages, and review exciting recent experimental results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Limitations for Quantum Algorithms to Solve Turbulent and Chaotic Systems

We investigate the limitations of quantum computers for solving nonlinear dynamical systems. In particular, we tighten the worst-case bounds of the quantum Carleman linearisation (QCL) algorithm answering one of their open questions. We provide a further significant limitation for any quantum algorithm that aims to output a quantum state that approximates the normalized solution vector. Given a natural choice of coordinates for a dynamical system with one or more positive Lyapunov exponents and solutions that grow sub-exponentially, we prove that any such algorithm has complexity scaling at least exponentially in the integration time. As such, an efficient quantum algorithm for simulating chaotic systems or regimes is likely not possible.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Dyson maps and unitary evolution for Maxwell equations in tensor dielectric media

The propagation and scattering of electromagnetic waves in dielectric media is of theoretical and experimental interest in a wide variety of fields. An understanding of observational results generally requires a numerical solution of Maxwell equations—usually implemented on conventional computers using sophisticated numerical algorithms. In recent years, advances in quantum information science and in the development of quantum computers have piqued curiosity about taking advantage of these resources for an alternate numerical approach to Maxwell equations. This requires a reformulation of the classical Maxwell equations into a form suitable for quantum computers which, unlike conventional computers, are limited to unitary operations. In this paper, a unitary framework is developed for the propagation of electromagnetic waves in a spatially inhomogeneous, passive, nondispersive, and anisotropic dielectric medium. For such a medium, generally, the evolution operator in the combined Faraday-Ampere equations is not unitary. There are two steps needed to convert this equation into a unitary evolution equation. In the first step, a weighted Hilbert space is formulated in which the generator of dynamics is a pseudo-Hermitian operator. In the second step, a Dyson map is constructed which maps the weighted-physical-Hilbert space to the original Hilbert space. Furthermore, the resulting evolution equation for the electromagnetic wave fields is unitary. Utilizing the framework developed in these steps, a unitary evolution equation is derived for electromagnetic wave propagation in a uniaxial dielectric medium. The resulting form is suitable for quantum computing.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Quantum algorithms for disordered physics

We show how a quantum computer may efficiently simulate a disordered Hamiltonian, by incorporating a pseudo-random number generator directly into the time evolution circuit. This technique is applied to quantum simulation of few-body disordered systems in the large volume limit; in particular, Anderson localization. The method requires a number of (error corrected) qubits proportional to the logarithm of the volume of the system, and each time evolution step requires a number of gates polylogarithmic in the volume. We simulate the method to observe the metal-insulator transition on a three-dimensional lattice. Additionally, we demonstrate the algorithm on a one-dimensional lattice, using physical quantum processors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Assessing VQLS for Fluid Dynamics on a Hybrid Quantum-HPC Stack

Recent advances in quantum linear solvers offer a promising direction for accelerating extreme scientific computations such as fluid dynamics. However, the deep and complex circuits required by many quantum algorithms limit their practical use on current quantum hardware. The Variational Quantum Linear Solver (VQLS) presents a viable alternative for near-term quantum devices (NISQ), and initial efforts have explored its application to select fluid dynamics problems. In this work, we evaluate the use of VQLS for canonical fluid dynamics problems, aiming to identify pathways for generalizing its implementation across a broader class of systems. We analyze the impact of various circuit ansatz and classical optimizers on solution quality and convergence behavior. Furthermore, we assess the algorithm's feasibility within a hybrid quantum–high-performance computing (HPC) framework by porting it to QFw, a state-of-the-art quantum-HPC software stack. 11This manuscript has been authored by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan. This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the US DOE under Contract No. DE-AC05-00OR22725.

Gopalakrishnan Meena, Murali [ORNL] (ORCID:0000000↗

DOE OSTI2025

Efficient sparse state preparation via quantum walks

Continuous-time quantum walks (CTQWs) on dynamic graphs, referred to as dynamic CTQWs, are a recently introduced universal model of computation that offers a new paradigm in which to envision quantum algorithms. In this work, we develop an algorithm that converts single-edge and self-loop dynamic CTQWs to the gate model of computation. We use this mapping to introduce an efficient sparse quantum state preparation framework based on dynamic CTQWs. Our approach utilizes combinatorics techniques such as minimal hitting sets, minimum spanning trees, and shortest Hamiltonian paths to reduce the number of controlled gates required to prepare sparse states. We show that our framework encompasses the current state of the art ancilla-free sparse state preparation method by reformulating this method as a CTQW. This CTQW-based framework offers an alternative to the uniformly controlled rotation method used by Qiskit by requiring fewer CX gates when the target state has a polynomial number of non-zero amplitudes.

dynamic continuous time quantum walks↗

DOE OSTI2025

Quantum dynamics simulation of the advection-diffusion equation

The advection-diffusion equation is simulated via several quantum algorithms. Three formulations are considered: (1) Trotterization, (2) variational quantum time evolution (VarQTE), and (3) adaptive variational quantum dynamics simulation (AVQDS). These schemes were originally developed for the Hamiltonian simulation of many-body quantum systems. The finite-difference discretized operator of the transport equation is formulated as a Hamiltonian and solved without the need for ancillary qubits. Computations are conducted on a quantum simulator (IBM Qiskit Aer) and a superconducting quantum hardware (IBM Fez). The former emulates the latter without the noise. The actual hardware implementation experiences significant noise. The results of the quantum simulator are compared with data from direct numerical simulation (DNS) with infidelities of the order 10 −5 . In the quantum simulator, Trotterization is observed to have the lowest infidelity and is suitable for fault-tolerant computation. The AVQDS algorithm requires the lowest gate count and circuit depth. The VarQTE algorithm is the next best in terms of gate counts, but the number of its optimization variables is directly proportional to the number of qubits. Due to current hardware limitations, Trotterization cannot be implemented, as it has an overwhelmingly large number of operations. Meanwhile, AVQDS and VarQTE can be executed at the hardware level. These algorithms present a new paradigm for computational transport phenomena on quantum computers.

Alipanah, Hirad [Univ. of Pittsburgh, PA (United S↗

DOE OSTI2025

Practical Scalability of LuGo: Benchmarking the HHL Algorithm Using an Enhanced QPE Algorithm

The HHL algorithm is a prominent quantum algorithm that offers exponential speedup over its classical counterparts for solving a system of linear equations. However, synthesizing and executing HHL circuits demand significant computational resources from both classical and quantum systems. In this paper, we benchmark the HHL algorithm using the optimized Quantum Phase Estimation (QPE) generation algorithm, LuGo \cite{lu2025lugo}, to enhance its scalability and efficiency. We leverage the National Energy Research Scientific Computing Center's (NERSC) Perlmutter supercomputer to evaluate the scalability of generating HHL circuits and to measure the time to simulate the generated circuits. Additionally, we provide a comprehensive analysis of the algorithm's performance on various state-of-the-art superconducting and trapped-ion quantum devices, including studies on qubit connectivity, fidelity comparisons, and hardware compatibility and robustness. Our results offer preliminary insights into potential practical applications of the HHL algorithm enabled by LuGo and the performance of various types of quantum hardware.

Lu, Chao [ORNL] (ORCID:0000000179346933)↗

DOE OSTI2023

Adaptive variational quantum minimally entangled typical thermal states for finite temperature simulations

Scalable quantum algorithms for the simulation of quantum many-body systems in thermal equilibrium are important for predicting properties of quantum matter at finite temperatures. Here we describe and benchmark a quantum computing version of the minimally entangled typical thermal states (METTS) algorithm for which we adopt an adaptive variational approach to perform the required quantum imaginary time evolution. The algorithm, which we name AVQMETTS, dynamically generates compact and problem-specific quantum circuits, which are suitable for noisy intermediate-scale quantum (NISQ) hardware. We benchmark AVQMETTS on statevector simulators and perform thermal energy calculations of integrable and nonintegrable quantum spin models in one and two dimensions and demonstrate an approximately linear system-size scaling of the circuit complexity. We further map out the finite-temperature phase transition line of the two-dimensional transverse field Ising model. Finally, we study the impact of noise on AVQMETTS calculations using a phenomenological noise model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗