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DOE OSTI2026

Quantum Computing in Next-Generation Transportation Optimization

We explore how quantum computing (QC) can advance transportation optimization, with a focus on two high-impact areas: traffic signal control and vehicle electrification with grid integration. As transportation systems grow in complexity, classical optimization methods increasingly struggle to deliver scalable and efficient solutions, particularly for real-time, data-rich environments. This work identifies key challenges within these two domains where QC may offer advantages, particularly in handling combinatorial decision spaces and dynamic constraints. We begin by outlining the limitations of classical approaches for traffic signal control optimization and electric vehicle charging coordination, highlighting where computational limitations arise. Previous quantum formulations are presented and new formulations are proposed to demonstrate how emerging quantum algorithms, including quantum annealing and the Quantum Approximation Optimization Algorithm, could be leveraged to reformulate and address these problems. We also evaluate the suitability of current quantum hardware and discuss recent trends that indicate when QC may become a viable tool for transportation applications. While acknowledging the present limitations of QC technologies, this poster emphasizes the importance of preparing quantum-compatible models today. By reviewing and establishing formulations that align with the strengths of quantum algorithms, researchers and practitioners can better position themselves to take advantage of QC advancements as they occur. This work aims to provide a practical, forward-looking perspective on the near-term potential of quantum computing in transportation optimization.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2022

VQE method: a short survey and recent developments

Abstract The variational quantum eigensolver (VQE) is a method that uses a hybrid quantum-classical computational approach to find eigenvalues of a Hamiltonian. VQE has been proposed as an alternative to fully quantum algorithms such as quantum phase estimation (QPE) because fully quantum algorithms require quantum hardware that will not be accessible in the near future. VQE has been successfully applied to solve the electronic Schrödinger equation for a variety of small molecules. However, the scalability of this method is limited by two factors: the complexity of the quantum circuits and the complexity of the classical optimization problem. Both of these factors are affected by the choice of the variational ansatz used to represent the trial wave function. Hence, the construction of an efficient ansatz is an active area of research. Put another way, modern quantum computers are not capable of executing deep quantum circuits produced by using currently available ansatzes for problems that map onto more than several qubits. In this review, we present recent developments in the field of designing efficient ansatzes that fall into two categories—chemistry–inspired and hardware–efficient—that produce quantum circuits that are easier to run on modern hardware. We discuss the shortfalls of ansatzes originally formulated for VQE simulations, how they are addressed in more sophisticated methods, and the potential ways for further improvements.

Fedorov, Dmitry A. (ORCID:0000000316598580)↗
DOE OSTI2021

Optimal Protocols in Quantum Annealing and Quantum Approximate Optimization Algorithm Problems

Quantum annealing (QA) and the quantum approximate optimization algorithm (QAOA) are two special cases of the following control problem: apply a combination of two Hamiltonians to minimize the energy of a quantum state. Which is more effective has remained unclear. Here we analytically apply the framework of optimal control theory to show that generically, given a fixed amount of time, the optimal procedure has the pulsed (or “bang-bang”) structure of QAOA at the beginning and end but can have a smooth annealing structure in between. This is in contrast to previous works which have suggested that bang-bang (i.e., QAOA) protocols are ideal. To support this theoretical work, we carry out simulations of various transverse field Ising models, demonstrating that bang-anneal-bang protocols are more common. Futher, the general features identified here provide guideposts for the nascent experimental implementations of quantum optimization algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Quantum optimization algorithms: Energetic implications

Since the dawn of quantum computing (QC), theoretical developments like Shor's algorithm proved the conceptual superiority of QC over traditional computing. However, such quantum supremacy claims are difficult to achieve in practice because of the technical challenges of realizing noiseless qubits. In the near future, QC applications will need to rely on noisy quantum devices that offload part of their work to classical devices. One way to achieve this is by using parameterized quantum circuits in optimization or even in machine learning tasks. The energy requirements of quantum algorithms have not yet been studied extensively. Here in this article, we explore several optimization algorithms using both theoretical insights and numerical experiments to understand their impact on energy consumption. Specifically, we highlight why and how algorithms like quantum natural gradient descent, simultaneous perturbation stochastic approximations or circuit learning methods, are at least 2x to 4x more energy efficient than their classical counterparts; why feedback-based quantum optimization is energy-inefficient; and how techniques like Rosalin can improve the energy efficiency of other algorithms by a factor of ≥2 0 x. Finally, we use the NchooseK high-level programming model to run optimization problems on both gate-based quantum computers and quantum annealers. Empirical data indicate that these optimization problems run faster, have better success rates, and consume less energy on quantum annealers than on their gate-based counterparts.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

PQML: Enabling the Predictive Reproducibility on NISQ Machines for Quantum ML Applications

Quantum computing represents a groundbreaking approach to high-performance computing. In recent years, quantum computers have progressed from single-qubit processors to systems boasting over 400 qubits. The presence of such a large number of qubits offers significant advantages, including enhanced computational speed—a capability beyond classical computing methods. However, the current stage of quantum computing is referred to as the noisy intermediate-scale quantum (NISQ) era. The existence of noise in this era presents challenges in testing quantum computing applications, leading to considerable variance in application results. Furthermore, the diverse noise characteristics observed across different machines exacerbate this issue, complicating the selection of the appropriate machine for application execution. In response to these challenges, we introduce our Predictive Quantum Machine Learning (PQML) tool. This tool is designed to predict outcomes when executing identical quantum machine learning applications—specifically, a critical suite of variational quantum algorithms—across various quantum computers during the NISQ era. This effort relies on data collected over a 12-month period. To the best of our knowledge, this study represents the first attempt to ensure reproducibility across quantum computers for complex circuits. Additionally, we have developed a model capable of forecasting the accuracy of quantum computers for variational quantum algorithms, with a particular emphasis on quantum machine learning as a case study.

Senapati, Priyabrata [Kent State University]↗
DOE OSTI2021

Benchmarking Quantum Chemistry Computations with Variational, Imaginary Time Evolution, and Krylov Space Solver Algorithms

Quantum chemistry is a key application area for noisy-intermediate scale quantum (NISQ) devices, and therefore serves as an important benchmark for current and future quantum computer performance. Previous benchmarks in this field have focused on variational methods for computing ground and excited states of various molecules, including a benchmarking suite focused on the performance of computing ground states for alkali-hydrides under an array of error mitigation methods. State-of-the-art methods to reach chemical accuracy in hybrid quantum-classical electronic structure calculations of alkali hydride molecules on NISQ devices from IBM are outlined here. Here it is demonstrated how to extend the reach of variational eigensolvers with symmetry preserving Ansätze. Next, it is outlined how to use quantum imaginary time evolution and Lanczos as a complementary method to variational techniques, highlighting the advantages of each approach. Finally, a new error mitigation method is demonstrated which uses systematic error cancellation via hidden inverse gate constructions, improving the performance of typical variational algorithms. These results show that electronic structure calculations have advanced rapidly, to routine chemical accuracy for simple molecules, from their inception on quantum computers a few short years ago, and they point to further rapid progress to larger molecules as the power of NISQ devices grows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Lower bounds on circuit depth of the quantum approximate optimization algorithm

The quantum approximate optimization algorithm (QAOA) is a method of approximately solving combinatorial optimization problems. While QAOA is developed to solve a broad class of combinatorial optimization problems, it is not clear which classes of problems are best suited for it. One factor in demonstrating quantum advantage is the relationship between a problem instance and the circuit depth required to implement the QAOA method. As errors in noisy intermediate-scale quantum (NISQ) devices increase exponentially with circuit depth, identifying lower bounds on circuit depth can provide insights into when quantum advantage could be feasible. In this work, we identify how the structure of problem instances can be used to identify lower bounds for circuit depth for each iteration of QAOA and examine the relationship between problem structure and the circuit depth for a variety of combinatorial optimization problems including MaxCut and MaxIndSet. Specifically, we show how to derive a graph, G, that describes a general combinatorial optimization problem and show that the depth of circuit is at least the chromatic index of G. By looking at the scaling of circuit depth, we argue that MaxCut, MaxIndSet, and some instances of vertex covering and Boolean satisfiability problems are suitable for QAOA approaches while knapsack and traveling salesperson problems are not.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Multi-angle quantum approximate optimization algorithm

The quantum approximate optimization algorithm (QAOA) generates an approximate solution to combinatorial optimization problems using a variational ansatz circuit defined by parameterized layers of quantum evolution. In theory, the approximation improves with increasing ansatz depth but gate noise and circuit complexity undermine performance in practice. Here, we investigate a multi-angle ansatz for QAOA that reduces circuit depth and improves the approximation ratio by increasing the number of classical parameters. Even though the number of parameters increases, our results indicate that good parameters can be found in polynomial time for a test dataset we consider. This new ansatz gives a 33% increase in the approximation ratio for an infinite family of MaxCut instances over QAOA. The optimal performance is lower bounded by the conventional ansatz, and we present empirical results for graphs on eight vertices that one layer of the multi-angle anstaz is comparable to three layers of the traditional ansatz on MaxCut problems. Similarly, multi-angle QAOA yields a higher approximation ratio than QAOA at the same depth on a collection of MaxCut instances on fifty and one-hundred vertex graphs. Many of the optimized parameters are found to be zero, so their associated gates can be removed from the circuit, further decreasing the circuit depth. These results indicate that multi-angle QAOA requires shallower circuits to solve problems than QAOA, making it more viable for near-term intermediate-scale quantum devices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Scaling adaptive quantum simulation algorithms via operator pool tiling

Adaptive variational quantum simulation algorithms use information from a quantum computer to dynamically create optimal trial wave functions for a given problem Hamiltonian. A key ingredient in these algorithms is a predefined operator pool from which trial wave functions are constructed. Finding suitable pools is critical for the efficiency of the algorithm as the problem size increases. Here, we present a technique called operator pool tiling that facilitates the construction of problem-tailored pools for arbitrarily large problem instances. By first performing an Adaptive Derivative-Assembled Problem-Tailored Ansatz Variational Quantum Eigensolver (ADAPT-VQE) calculation on a smaller instance of the problem using a large, but computationally inefficient, operator pool, we extract the most relevant operators and use them to design more efficient pools for larger instances. We demonstrate the method here on strongly correlated quantum spin models in one and two dimensions, finding that ADAPT automatically finds a highly effective ansatz for these systems. Given that many problems, such as those arising in condensed matter physics, have a naturally repeating lattice structure, we expect the pool tiling method to be a widely applicable technique apt for such systems. Published by the American Physical Society 2024

Van Dyke, John S. (ORCID:0000000167815480)↗
DOE OSTI2024

Quantum Davidson algorithm for excited states

Abstract Excited state properties play a pivotal role in various chemical and physical phenomena, such as charge separation and light emission. However, the primary focus of most existing quantum algorithms has been the ground state, as seen in quantum phase estimation and the variational quantum eigensolver (VQE). Although VQE-type methods have been extended to explore excited states, these methods grapple with optimization challenges. In contrast, the quantum Krylov subspace (QKS) method has been introduced to address both ground and excited states, positioning itself as a cost-effective alternative to quantum phase estimation. However, conventional QKS methodologies depend on a pre-generated subspace through real or imaginary-time evolutions. This subspace is inherently expansive and can be plagued with issues like slow convergence or numerical instabilities, often leading to relatively deep circuits. Our research presents an economic QKS algorithm, which we term the quantum Davidson (QDavidson) algorithm. This innovation hinges on the iterative expansion of the Krylov subspace and the incorporation of a pre-conditioner within the Davidson framework. By using the residues of eigenstates to expand the Krylov subspace, we manage to formulate a compact subspace that aligns closely with the exact solutions. This iterative subspace expansion paves the way for a more rapid convergence in comparison to other QKS techniques, such as the quantum Lanczos. Using quantum simulators, we employ the novel QDavidson algorithm to delve into the excited state properties of various systems, spanning from the Heisenberg spin model to real molecules. Compared to the existing QKS methods, the QDavidson algorithm not only converges swiftly but also demands a significantly shallower circuit. This efficiency establishes the QDavidson method as a pragmatic tool for elucidating both ground and excited state properties on quantum computing platforms.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A New Hybrid Quantum-Classical Algorithm for Solving the Unit Commitment Problem

Solving problems related to planning and operations of large-scale power systems is challenging on classical computers due to their inherent nature as mixed-integer and nonlinear problems. Quantum computing provides new avenues to approach these problems. We develop a hybrid quantum-classical algorithm for the Unit Commitment (UC) problem in power systems which aims at minimizing the total cost while optimally allocating generating units to meet the hourly demand of the power loads. The hybrid algorithm combines a variational quantum algorithm (VQA) with a classical Benders-type heuristic. The resulting algorithm computes approximate solutions to UC in three stages: i) a collection of UC vectors capable meeting the power demand with lowest possible operating costs is generated based on VQA; ii) a classical sequential least squares programming (SLSQP) routine is leveraged to find the optimal power level corresponding to a predetermined number of candidate vectors; iii) in the last stage, the approximate solution of UC along with generating units power level combination is given. To demonstrate the effectiveness of the presented method, three different systems with 3 generating units, 10 generating units, and 26 generating units were tested for different time periods. In addition, convergence of the hybrid quantum-classical algorithm for select time periods is proven out on IonQ's Forte system.

Aboumrad, Willie [IonQ, Inc]↗
DOE OSTI2022

Solving Large‐Scale Linear Systems of Equations by a Quantum Hybrid Algorithm

Abstract Today's intermediate‐scale quantum computers, although imperfect, already perform computational tasks that are manifestly beyond the capabilities of modern classical supercomputers. However, so far, quantum‐enabled large‐scale solutions have been realized only for limited set of problems. Here a hybrid algorithm based on phase estimation and classical optimization of the circuit width and depth is employed for solving a specific class of large linear systems of equations ubiquitous to many areas of science and engineering. A classification of linear systems based on the entanglement properties of the associated phase‐estimation unitary operation is introduced, enabling a highly efficient search for solutions that is facilitated by a straightforward matrix‐to‐circuit map. A 2 17 ‐dimensional problem is implemented on several IBM quantum computer superconducting quantum processors, a record‐breaking result for a linear system solved by a quantum computer. Demonstrated realisation sets a clear benchmark in the quest for the future quantum speedup in the linear systems of equations solution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Porting Classical Approaches for Quantum Simulations to Quantum Computers

Simulating quantum many-body systems is one of the most promising problems in which we might anticipate that quantum computers should show quantum advantage. Unfortunately, there is still a gap between this promise and actual practice. New quantum algorithms need to be developed and the current quantum algorithms have various difficulties - e.g efficient state preparation - which must be overcome and improved upon. In many cases, classical approaches need to be ported over to quantum devices. In this project we have developed a suite of new quantum algorithms which makes progress in this regard. We developed a new optimization scheme for variational quantum eigensolvers, UBOS, which mitigates problems with local minimas and barren plateaus while improving convergence to the ground state by an order of magnitude. We developed a new way to utilize qubitization to find ground states of nearly frustration-free Hamiltonians faster than all previous methods. We developed a series of state preparation techniques which helps initialize parameterized quantum circuits into reasonable starting points on which quantum algorithms are then applied. In addition to the development of novel algorithms, it is critical to have classical simulation techniques for approximately simulating quantum circuits which can be used to benchmark and understand quantum algorithms. Toward that end, we developed a novel POVM formalism to simulate quantum circuits as well as exemplify the massive parallelization of tensor network methodologies. Finally, we developed physical understanding of entanglement phase transitions such as many-body localization and random tensor networks.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

A Multireference Quantum Krylov Algorithm for Strongly Correlated Electrons

We introduce a multireference selected quantum Krylov (MRSQK) algorithm suitable for quantum simulation of many-body problems. MRSQK is a low-cost alternative to the quantum phase estimation algorithm that generates a target state as a linear combination of non-orthogonal Krylov basis states. This basis is constructed from a set of reference states via real-time evolution; thus, avoiding the numerical optimization of parameters. An efficient algorithm for the evaluation of the off-diagonal matrix elements of the overlap and Hamiltonian matrices is discussed and a selection procedure is introduced to identify a basis of orthogonal references that ameliorates the linear dependency problem. Preliminary benchmarks on linear H 6 , H 8 , and BeH 2 indicate that MRSQK can predict the energy of these systems accurately using very compact Krylov bases.

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

Hybrid quantum-classical algorithms for approximate graph coloring

We show how to apply the recursive quantum approximate optimization algorithm (RQAOA) to MAX- k -CUT, the problem of finding an approximate k -vertex coloring of a graph. We compare this proposal to the best known classical and hybrid classical-quantum algorithms. First, we show that the standard (non-recursive) QAOA fails to solve this optimization problem for most regular bipartite graphs at any constant level p : the approximation ratio achieved by QAOA is hardly better than assigning colors to vertices at random. Second, we construct an efficient classical simulation algorithm which simulates level- 1 QAOA and level- 1 RQAOA for arbitrary graphs. In particular, these hybrid algorithms give rise to efficient classical algorithms, and no benefit arising from the use of quantum mechanics is to be expected. Nevertheless, they provide a suitable testbed for assessing the potential benefit of hybrid algorithm: We use the simulation algorithm to perform large-scale simulation of level- 1 QAOA and RQAOA with up to 300 qutrits applied to ensembles of randomly generated 3 -colorable constant-degree graphs. We find that level- 1 RQAOA is surprisingly competitive: for the ensembles considered, its approximation ratios are often higher than those achieved by the best known generic classical algorithm based on rounding an SDP relaxation. This suggests the intriguing possibility that higher-level RQAOA may be a potentially useful algorithm for NISQ devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Application-level benchmarking of quantum computers using nonlocal game strategies

In a nonlocal game, two noncommunicating players cooperate to convince a referee that they possess a strategy that does not violate the rules of the game. Quantum strategies allow players to optimally win some games by performing joint measurements on a shared entangled state, but computing these strategies can be challenging. We present a variational quantum algorithm to compute quantum strategies for nonlocal games by encoding the rules of a nonlocal game into a Hamiltonian. We show how this algorithm can generate a short-depth optimal quantum strategy for a graph coloring game with a quantum advantage. This quantum strategy is then evaluated on fourteen different quantum hardware platforms to demonstrate its utility as a benchmark. Finally, we discuss potential sources of errors that can explain the observed decreased performance of the executed task and derive an expression for the number of samples required to accurately estimate the win rate in the presence of noise.

nonlocal games↗