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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A Polynomial-Time Classical Algorithm for Noisy Quantum Circuits

We provide a polynomial-time classical algorithm for noisy quantum circuits. The algorithm computes the expectation value of any observable for any circuit, with a small average error over input states drawn from an ensemble (e.g., the computational basis). Our approach is based upon the intuition that noise exponentially damps nonlocal correlations relative to local correlations. This enables one to classically simulate a noisy quantum circuit by keeping track of only the dynamics of local quantum information. Our algorithm also enables sampling from the output distribution of a circuit in quasipolynomial time, so long as the distribution anticoncentrates. A number of implications are discussed, including a fundamental limit on the efficacy of noise mitigation strategies: For constant noise rates, any quantum circuit for which error mitigation succeeds in polynomial-time on most input states can also be classically simulated in polynomial-time on most input states. Our algorithms scale exponentially in the inverse noise rate, which is fundamental and makes them impractical for current quantum devices.

decoherence↗
DOE OSTI2022

Efficient Hierarchical State Vector Simulation of Quantum Circuits via Acyclic Graph Partitioning

Early but promising results in quantum computing have been enabled by the concurrent development of quantum algorithms, devices, and materials. Classical simulation of quantum programs has enabled the design and analysis of algorithms and implementation strategies targeting current and anticipated quantum device architectures. In this paper, we present a graph-based approach to achieve efficient quantum circuit simulation. Our approach involves partitioning the graph representation of a given quantum circuit into sub-graphs/circuits that exhibit better data locality. Simulation of each sub-circuit is organized hierarchically, with the iterative construction and simulation of smaller state vectors, improving overall performance. Also, this partitioning reduces the number of passes through data, improving the total computation time. We present three partitioning strategies and observe that acyclic graph partitioning typically results in the best time-to-solution. In contrast, other strategies reduce the partitioning time at the expense of potentially increased simulation times. Experimental evaluation demonstrates the effectiveness of our approach.

Fang, Bo↗
DOE OSTI2024

Evidence of scaling advantage for the quantum approximate optimization algorithm on a classically intractable problem

The quantum approximate optimization algorithm (QAOA) is a leading candidate algorithm for solving optimization problems on quantum computers. However, the potential of QAOA to tackle classically intractable problems remains unclear. Here, we perform an extensive numerical investigation of QAOA on the low autocorrelation binary sequences (LABS) problem, which is classically intractable even for moderately sized instances. We perform noiseless simulations with up to 40 qubits and observe that the runtime of QAOA with fixed parameters scales better than branch-and-bound solvers, which are the state-of-the-art exact solvers for LABS. The combination of QAOA with quantum minimum finding gives the best empirical scaling of any algorithm for the LABS problem. We demonstrate experimental progress in executing QAOA for the LABS problem using an algorithm-specific error detection scheme on Quantinuum trapped-ion processors. Our results provide evidence for the utility of QAOA as an algorithmic component that enables quantum speedups.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Variational Adiabatic Gauge Transformation on Real Quantum Hardware for Effective Low-Energy Hamiltonians and Accurate Diagonalization

Effective low-energy theories represent powerful theoretical tools to reduce the complexity in modeling interacting quantum many-particle systems. However, common theoretical methods rely on perturbation theory, which limits their applicability to weak interactions. Here we introduce the Variational Adiabatic Gauge Transformation (VAGT), a nonperturbative hybrid quantum algorithm that can use nowadays quantum computers to learn the variational parameters of the unitary circuit that brings the Hamiltonian to either its block-diagonal or full-diagonal form. If a Hamiltonian can be diagonalized via a shallow quantum circuit, then VAGT can learn the optimal parameters using a polynomial number of runs. The accuracy of VAGT is tested through numerical simulations, as well as simulations on Rigetti and IonQ quantum computers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Distributed Quantum Learning with co-Management in a Multi-tenant Quantum System

The rapid advancement of quantum computing has pushed classical designs into the quantum domain, breaking physical boundaries for computing-intensive and data-hungry applications with the hope that some systems may provide a quantum speedup. For example, variational quantum algorithms have been proposed for quantum neural networks to train deep learning models on qubits, achieving promising results. Existing quantum learning architectures and systems rely on single, monolithic quantum machines with abundant and stable resources, such as qubits. However, fabricating a large, monolithic quantum device is considerably more challenging than producing an array of smaller devices. In this paper, we investigate a distributed quantum system that combines multiple quantum machines into a unified system. We propose DQuLearn, which divides a quantum learning task into multiple subtasks. Each subtask can be executed distributively on individual quantum machines, with the results looping back to classical machines for subsequent training iterations. Additionally, our system supports multiple concurrent clients and dynamically manages their circuits according to the runtime status of quantum workers. Through extensive experiments, we demonstrate that DQuLearn achieves similar accuracies with significant runtime reduction, by up to 68.7% and an increase per-second circuit processing speed, by up to 3.99 times, in a 4-worker multi-tenant setting.

quantum computing↗
DOE OSTI2024

Enhancing scalability and accuracy of quantum poisson solver

The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far either suffer from lack of accuracy and/or are limited to very small sizes of the problem and thus have no practical usage. In this regard, our previous work showed a proof-of-concept demonstration in advancing quantum Poisson solver algorithm and validated preliminary results for a simple case of 3 x 3 problem. In this work, we delve into comprehensive research details, presenting the results on up to 15 x 15 problems that include step-by-step improvements in Poisson equation solutions, scaling performance, and experimental exploration. In particular, we demonstrate the implementation of eigenvalue amplification by a factor of up to 2 8 , achieving a significant improvement in the accuracy of our quantum Poisson solver and comparing that to the exact solution. Additionally, we present success probability results, highlighting the reliability of our quantum Poisson solver. Moreover, we explore the scaling performance of our algorithm against the circuit depth and width, demonstrating how our approach scales with larger problem sizes and thus further solidifies the practicality of easy adaptation of this algorithm in real-world applications. We also discuss a multilevel strategy for how this algorithm might be further improved to explore much larger problems with greater performance. Finally, through our experiments on the IBM quantum hardware, we conclude that though overall results on the existing NISQ hardware are dominated by the error in the CNOT gates, this work opens a path to realizing a multidimensional Poisson solver on near-term quantum hardware.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Quantum computing in power systems

Electric power systems provide the backbone of modern industrial societies. Enabling scalable grid analytics is the keystone to successfully operating large transmission and distribution systems. However, today's power systems are suffering from ever-increasing computational burdens in sustaining the expanding communities and deep integration of renewable energy resources, as well as managing huge volumes of data accordingly. These unprecedented challenges call for transformative analytics to support the resilient operations of power systems. Recently, the explosive growth of quantum computing techniques has ignited new hopes of revolutionizing power system computations. Quantum computing harnesses quantum mechanisms to solve traditionally intractable computational problems, which may lead to ultra-scalable and efficient power grid analytics. This paper reviews the newly emerging application of quantum computing techniques in power systems. We present a comprehensive overview of existing quantum-engineered power analytics from different operation perspectives, including static analysis, transient analysis, stochastic analysis, optimization, stability, and control. We thoroughly discuss the related quantum algorithms, their benefits and limitations, hardware implementations, and recommended practices. We also review the quantum networking techniques to ensure secure communication of power systems in the quantum era. Finally, we discuss challenges and future research directions. This paper will hopefully stimulate increasing attention to the development of quantum-engineered smart grids.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Metropolis-style random sampling of quantum gates for the estimation of low-energy observables

In this work, we propose a quantum algorithm to compute low-energy expectation values of a quantum Hamiltonian by sampling a partition function associated with the average energy of that Hamiltonian. For any given quantum circuit-Hamiltonian pair, there is an associated average energy. The sampling is done through an accept/reject Metropolis-style algorithm on the quantum gates of the circuit itself. Observables calculated under the canonical ensemble from these samples of circuits are extrapolated from higher energies to the ground state.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Alternative approach to quantum imaginary time evolution

There is increasing interest in quantum algorithms (QAs) that are based on the imaginary time evolution (ITE), a successful classical numerical approach to obtain ground states. However, most of the proposals so far require heavy postprocessing computational steps on a classical computer, such as solving linear equations. Here we provide an alternative approach to implement ITE. A key feature in our approach is the use of an orthogonal basis set: the propagated state is efficiently expressed in terms of orthogonal basis states at every step of the evolution. We argue that the number of basis states needed at those steps to achieve an accurate solution can be kept on the order of n , the number of qubits, by controlling the precision (number of significant digits) and the imaginary time increment. The number of quantum gates per imaginary time step is estimated to be polynomial in n . Additionally, while in many QAs the locality of the Hamiltonian is a key assumption, in our algorithm this restriction is not required. This characteristic of our algorithm renders it useful for studying highly nonlocal systems, such as the occupation-representation nuclear shell model. Here, we illustrate our algorithm through numerical implementation on an IBM quantum simulator.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Random coordinate descent: A simple alternative for optimizing parameterized quantum circuits

Variational quantum algorithms rely on the optimization of parameterized quantum circuits in noisy settings. The commonly used back-propagation procedure in classical machine learning is not directly applicable in this setting due to the collapse of quantum states after measurements. Thus, gradient estimations constitute a significant overhead in a gradient-based optimization of such quantum circuits. This paper introduces a random coordinate descent algorithm as a practical and easy-to-implement alternative to the full gradient descent algorithm. This algorithm only requires one partial derivative at each iteration. Motivated by the behavior of measurement noise in the practical optimization of parameterized quantum circuits, this paper presents an optimization problem setting that is amenable to analysis. Under this setting, the random coordinate descent algorithm exhibits the same level of stochastic stability as the full gradient approach, making it as resilient to noise. The complexity of the random coordinate descent method is generally no worse than that of the gradient descent and can be much better for various quantum optimization problems with anisotropic Lipschitz constants. Theoretical analysis and extensive numerical experiments validate our findings. Published by the American Physical Society 2024

Ding, Zhiyan (ORCID:000000018863403X)↗
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 OSTI2021

Adapting Quantum Approximation Optimization Algorithm (QAOA) for Unit Commitment

In the present Noisy Intermediate-Scale Quantum (NISQ), hybrid algorithms that leverage classical resources to reduce quantum costs are particularly appealing. We formulate and apply such a hybrid quantum-classical algorithm to a power system optimization problem called Unit Commitment, which aims to satisfy a target power load at minimal cost. Our algorithm extends the Quantum Approximation Optimization Algorithm (QAOA) with a classical minimizer in order to support mixed binary optimization. Using Qiskit, we simulate results for sample systems to validate the effectiveness of our approach. Here, we also compare to purely classical methods. Our results indicate that classical solvers are effective for our simulated Unit Commitment instances with fewer than 400 power generation units. However, for larger problem instances, the classical solvers either scale exponentially in runtime or must resort to coarse approximations. This opens the door to potential quantum advantage for systems with several hundred units, though quantum error correction may be necessary at this scale.

42 ENGINEERING↗
DOE OSTI2022

Quantum Krylov subspace algorithms for ground- and excited-state energy estimation

Quantum Krylov subspace diagonalization (QKSD) algorithms provide a low-cost alternative to the conventional quantum phase estimation algorithm for estimating the ground- and excited-state energies of a quantum many-body system. While QKSD algorithms typically rely on using the Hadamard test for estimating Krylov subspace matrix elements of the form $\langle \phi_i|e^{-\widehat{H}τ}|\phi_j\rangle$, the associated quantum circuits require an ancilla qubit with controlled multiqubit gates that can be quite costly for near-term quantum hardware. In this paper, we show that a wide class of Hamiltonians relevant to condensed-matter physics and quantum chemistry contain symmetries that can be exploited to avoid the use of the Hadamard test. We propose a multifidelity estimation protocol that can be used to compute such quantities, showing that our approach, when combined with efficient single-fidelity estimation protocols, provides a substantial reduction in circuit depth. In addition, here we develop a unified theory of quantum Krylov subspace algorithms and present three quantum-classical algorithms for the ground- and excited-state energy estimation problems, where each algorithm provides various advantages and disadvantages in terms of total number of calls to the quantum computer, gate depth, classical complexity, and stability of the generalized eigenvalue problem within the Krylov subspace.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Direct estimation of the density of states for fermionic systems

Simulating time evolution is one of the most natural applications of quantum computers and is thus one of the most promising prospects for achieving practical quantum advantage. Here, we develop quantum algorithms to extract thermodynamic properties by estimating the density of states (DOS), which is a central object in quantum statistical mechanics. We introduce several key innovations that significantly improve the practicality and extend the generality of previous techniques. First, our approach allows one to estimate the DOS only for a specific subspace of the full Hilbert space. This is crucial for fermionic systems, since both canonical and grand canonical ensemble thermal equilibrium properties depend on subspaces of fixed number. Second, in our approach, by time evolving very simple, random initial states, such as randomly chosen computational basis states, we can exactly recover the DOS on average. Third, due to circuit-depth limitations, we only reconstruct the DOS up to a convolution with a Gaussian window—thus all imperfections that shift the energy levels by less than the width of the convolution window will not significantly affect the estimated DOS. For these reasons, we find the approach is a promising candidate for early quantum advantage as even short-time, noisy dynamics can yield a semiquantitative reconstruction of the DOS (convolution with a broad Gaussian window), while early fault-tolerant devices will likely enable higher-resolution DOS reconstruction through longer time evolutions. We demonstrate the practicality of our approach in representative Fermi-Hubbard and spin models and indeed find that our approach is highly robust against algorithmic errors in the time evolution and against gate noise. We further demonstrate that our approach is compatible with noisy intermediate-scale quantum (NISQ) computing NISQ-friendly variational techniques, introducing and leveraging a technique for variational time evolution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Quantum simulations of nuclear resonances with variational methods

Background: The many-body nature of nuclear physics problems poses significant computational challenges. These challenges become even more pronounced when studying the resonance states of nuclear systems, which are governed by the non-Hermitian Hamiltonian. Quantum computing, particularly for quantum many-body systems, offers a promising alternative, especially within the constraints of current noisy intermediate-scale quantum (NISQ) devices. Purpose: This work aims to simulate nuclear resonances using quantum algorithms by developing a variational framework compatible with non-Hermitian Hamiltonians and implementing it fully on a quantum simulator. Methods: We employ the complex scaling technique to extract resonance positions classically and adapt it for quantum simulations using a two-step algorithm. First, we transform the non-Hermitian Hamiltonian into a Hermitian form by using the energy variance as a cost function within a variational framework. Second, we perform 𝜃-trajectory calculations to determine optimal resonance positions in the complex energy plane. To address resource constraints on NISQ devices, we utilize Gray code (GC) encoding to reduce qubit requirements. Results: We first validate our approach using a schematic potential model that mimics a nuclear potential, successfully reproducing known resonance energies with high fidelity. We then extend the method to a more realistic 𝛼−𝛼 nuclear potential and compute the 𝐷- and 𝐺-wave resonance energies with a basis size of 𝑁=16, using only four qubits. The quantum simulation results closely match the classical values, demonstrating the feasibility of our approach. Conclusions: This study demonstrates, for the first time, that the complete 𝜃-trajectory method can be implemented on a quantum computer without relying on any classical input beyond the Hamiltonian. The results establish a scalable and efficient quantum framework for simulating resonance phenomena in nuclear systems. This work represents a significant step toward quantum simulations of open quantum systems and lays the foundation for future investigations into resonance structures in nuclear, atomic, and molecular physics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Simulation of Linear Non-Hermitian Boundary-Value Problems with Quantum Singular-Value Transformation

Herein we propose a quantum algorithm for simulating dissipative waves in inhomogeneous linear media as a boundary-value problem. Using the so-called quantum singular value transformation (QSVT), we construct a quantum circuit that models the propagation of electromagnetic waves in a one-dimensional system with outgoing boundary conditions. The corresponding measurement procedure is also discussed. Limitations of the QSVT algorithm are identified in connection with the large condition numbers that the dispersion matrices exhibit at weak dissipation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Graph Neural Networks for Parameterized Quantum Circuits Expressibility Estimation (Rev.1)

Parameterized quantum circuits (PQCs) are fundamental to quantum machine learning (QML), quantum optimization, and variational quantum algorithms (VQAs). The expressibility of PQCs is a measure that determines their capability to harness the full potential of the quantum state space. It is thus a crucial guidepost to know when selecting a particular PQC ansatz. However, the existing technique for expressibility computation through statistical estimation requires a large number of samples, which poses significant challenges due to time and computational resource constraints. This paper introduces a novel approach for expressibility estimation of PQCs using Graph Neural Networks (GNNs). We demonstrate the predictive power of our GNN model with a dataset consisting of 25,000 samples from the noiseless IBM QASM Simulator and 12,000 samples from three distinct noisy quantum backends. The model accurately estimates expressibility, with root mean square errors (RMSE) of 0.05 and 0.06 for the noiseless and noisy backends, respectively. We compare our model’s predictions with reference circuits from Sim et al. and IBM Qiskit’s hardwareefficient ansatz sets to further evaluate our model’s performance. Our experimental evaluation in noiseless and noisy scenarios reveals a close alignment with ground truth expressibility values, highlighting the model’s efficacy. Moreover, our model exhibits promising extrapolation capabilities, predicting expressibility values with low RMSE for out-of-range qubit circuits trained solely on only up to 5-qubit circuit sets. This work thus provides a reliable means of efficiently evaluating the expressibility of diverse PQCs on noiseless simulators and hardware.

97 MATHEMATICS AND COMPUTING↗