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DOE OSTI2024

Quantum-classical tradeoffs and multi-controlled quantum gate decompositions in variational algorithms

The computational capabilities of near-term quantum computers are limited by the noisy execution of gate operations and a limited number of physical qubits. Hybrid variational algorithms are well-suited to near-term quantum devices because they allow for a wide range of tradeoffs between the amount of quantum and classical resources used to solve a problem. This paper investigates tradeoffs available at both the algorithmic and hardware levels by studying a specific case – applying the Quantum Approximate Optimization Algorithm (QAOA) to instances of the Maximum Independent Set (MIS) problem. We consider three variants of the QAOA which offer different tradeoffs at the algorithmic level in terms of their required number of classical parameters, quantum gates, and iterations of classical optimization needed. Since MIS is a constrained combinatorial optimization problem, the QAOA must respect the problem constraints. This can be accomplished by using many multi-controlled gate operations which must be decomposed into gates executable by the target hardware. We study the tradeoffs available at this hardware level, combining the gate fidelities and decomposition efficiencies of different native gate sets into a single metric called the gate decomposition cost .

Tomesh, Teague↗

DOE OSTI2024

Grover-QAOA for 3-SAT: quadratic speedup, fair-sampling, and parameter clustering

Abstract The SAT problem is a prototypical NP-complete problem of fundamental importance in computational complexity theory with many applications in science and engineering; as such, it has long served as an essential benchmark for classical and quantum algorithms. This study shows numerical evidence for a quadratic speedup of the Grover Quantum Approximate Optimization Algorithm (G-QAOA) over random sampling for finding all solutions to 3-SAT (All-SAT) and Max-SAT problems. G-QAOA is less resource-intensive and more adaptable for these problems than Grover’s algorithm, and it surpasses conventional QAOA in its ability to sample all solutions. We show these benefits by classical simulations of many-round G-QAOA on thousands of random 3-SAT instances. We also observe G-QAOA advantages on the IonQ Aria quantum computer for small instances, finding that current hardware suffices to determine and sample all solutions. Interestingly, a single-angle-pair constraint that uses the same pair of angles at each G-QAOA round greatly reduces the classical computational overhead of optimizing the G-QAOA angles while preserving its quadratic speedup. We also find parameter clustering of the angles. The single-angle-pair protocol and parameter clustering significantly reduce obstacles to classical optimization of the G-QAOA angles.

Zhang, Zewen (ORCID:000000032258613X)↗

DOE OSTI2024

Hamiltonian switching control of noisy bipartite qubit systems

Abstract We develop a Hamiltonian switching ansatz for bipartite control that is inspired by the quantum approximate optimization algorithm, to mitigate environmental noise on qubits. We demonstrate the control for a central spin coupled to bath spins via isotropic Heisenberg interactions, and then make physical applications to the protection of quantum gates performed on superconducting transmon qubits coupling to environmental two-level-systems (TLSs) through dipole-dipole interactions, as well as on such qubits coupled to both TLSs and a Lindblad bath. The control field is classical and acts only on the system qubits. We use reinforcement learning with policy gradient to optimize the Hamiltonian switching control protocols, using a fidelity objective for specific target quantum gates. We use this approach to demonstrate effective suppression of both coherent and dissipative noise, with numerical studies achieving target gate implementations with fidelities over 0.9999 (four nines) in the majority of our test cases and showing improvement beyond this to values of 0.999 999 999 (nine nines) upon a subsequent optimization by GRadient Ascent Pulse Engineering (GRAPE). We analyze how the control depth, total evolution time, number of environmental TLS, and choice of optimization method affect the fidelity achieved by the optimal protocols and reveal some critical behaviors of bipartite control of quantum gates.

Physics↗

DOE OSTI2025

Quantum Simulators and Applications on Quantum Framework

Simulating quantum circuits is essential for validating quantum algorithms. However, no single simulator consistently performs best - efficiency depends on circuit structure, entanglement, and depth. In this work, we integrate Qiskit-Aer (state-vector and matrix product state) and QTensor, a tree-tensor-network based simulator, into the Quantum Framework (QFw), a modular platform that supports multiple quantum backends via a unified interface. We also enable distributed quantum approximate optimization algorithm (DQAOA) application compatibility with QFw, allowing sub-problems to be solved in parallel at scale. We then benchmark DQAOA and TFIM (transverse field Ising model) circuits across supported simulators, showing how performance varies significantly with problem type. All simulations are deployed on the Frontier supercomputer using QFw's MPI-based orchestration for distributed, multinode execution. These results underscore the need for simulatoragnostic infrastructure to enable systematic evaluation and highperformance scaling of quantum workloads. QFw provides a practical and extensible path toward reproducible quantum algorithm development across diverse application domains.

Chundury, Srikar [ORNL] (ORCID:0009000183359259)↗

DOE OSTI2025

Efficient state preparation for the Schwinger model with a theta term

We present a comparison of different quantum state preparation algorithms and their overall efficiency for the Schwinger model with a theta term. While adiabatic state preparation is proved to be effective, in practice it leads to large gate counts to prepare the ground state. The quantum approximate optimization algorithm (QAOA) provides excellent results while keeping the counts small by design, at the cost of an expensive classical minimization process. We introduce a “blocked” modification of the Schwinger Hamiltonian to be used in the QAOA that further decreases the length of the algorithms as the size of the problem is increased. The rodeo algorithm (RA) provides a powerful tool to efficiently prepare any eigenstate of the Hamiltonian, as long as its overlap with the initial guess is large enough. We obtain the best results when combining the blocked QAOA ansatz and the RA, as this provides an excellent initial state with a relatively short algorithm without the need to perform any classical steps for large problem sizes. Published by the American Physical Society 2025

Bazavov, Alexei (ORCID:0000000321411901)↗

DOE OSTI2024

QFw: A Quantum Framework for Large-scale HPC Ecosystems

This work extends Quantum Framework (QFw) by integrating it with Northwest Quantum Simulator (NWQ-Sim) and by introducing a lightweight python library that allows multiple frontends (e.g., Qiskit) to interact with QFw. This extension enables QFw to flexibly decouple frontends from backends (e.g., NWQ-Sim). We demonstrate this capability by executing a Greenberger-Horne-Zeilinger (GHZ) circuit using Qiskit and Pennylane with NWQ-Sim and Tensor-Network Quantum Virtual-Machine (TN-QVM). QFw enables easy scaling to multiple nodes. We showcase this with scaling tests using GHZ with up to 32 qubits for different number of nodes on the Frontier supercomputer. And, to demonstrate the use of QFw for real world problems, we solve a metamaterial optimization problem, using a Quantum Approximate Optimization Algorithm (QAOA). We observe that QFw over NWQ-Sim marginally improves Qiskit-aer’s accuracy in reaching the lowest energy state. These additions to QFw prepare it to run hybrid applications in a hybrid resource environment since it treats actual quantum hardware and simulators alike.

Chundury, Srikar↗

DOE OSTI2024

Provable bounds for noise-free expectation values computed from noisy samples

Quantum computing has emerged as a powerful computational paradigm capable of solving problems beyond the reach of classical computers. However, today’s quantum computers are noisy, posing challenges to obtaining accurate results. Here, we explore the impact of noise on quantum computing, focusing on the challenges in sampling bit strings from noisy quantum computers and the implications for optimization and machine learning. We formally quantify the sampling overhead to extract good samples from noisy quantum computers and relate it to the layer fidelity, a metric to determine the performance of noisy quantum processors. Further, we show how this allows us to use the conditional value at risk of noisy samples to determine provable bounds on noise-free expectation values. We discuss how to leverage these bounds for different algorithms and demonstrate our findings through experiments on real quantum computers involving up to 127 qubits. The results show strong alignment with theoretical predictions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Simulating large one-dimensional neutral-atom quantum systems

While abstract models of quantum computation assume a closed system of two-level states, practical quantum devices inevitably couple to the environment in some way, creating sources of noise. Understanding the tolerance to noise of specific quantum algorithms run on specific devices is important for determining the feasibility of quantum computing in the current noisy intermediate-scale quantum era. Of particular interest is understanding the noise sensitivity of these devices as more qubits are added to the system. Classical simulations are a useful tool to understand the effects of this noise, but direct classical simulations of open quantum systems are burdened by an exponentially growing cost in the number of qubits and a large local Hilbert space dimension. For onedimensional, shallow circuits, using tensor networks can replace this exponential cost with a linear one and simulate far wider systems than what would normally be available. In this paper, we describe a tensor network simulation of a neutral atom quantum system under the presence of noise, while introducing a purity-preserving truncation technique that compromises between the simplicity of the matrix product state and the positivity of the matrix product density operator. We apply this simulation to a near-optimized iteration of the quantum approximate optimization algorithm on a transverse field Ising model in order to investigate the influence of large system sizes on the performance of the algorithm. We find that while circuits with a large number of qubits fail more often under noise that depletes the qubit population, their outputs on a successful measurement are just as robust under Rydberg atom dissipation or qubit dephasing as smaller systems. However, such circuits might not perform as well under coherent multiqubit errors such as Rydberg atom crosstalk. We also find that the optimized parameters are especially robust to noise, suggesting that a noisier quantum system can be used to find the optimal parameters before switching to a cleaner system for measurements of observables.

Allen, James↗

DOE OSTI2026

Promise of Graph Sparsification and Decomposition for Noise Reduction in QAOA: Analysis for Trapped-Ion Compilations

We develop new approximate compilation schemes that significantly reduce the expense of compiling the Quantum Approximate Optimization Algorithm (QAOA) for solving the Max-Cut problem. Our main focus is on compilation with trapped-ion simulators using Pauli-X operations and all-to-all Ising Hamiltonian HIsing evolution generated by Molmer-Sorensen or optical dipole force interactions, though some of our results also apply to standard gate-based compilations. Our results are based on principles of graph sparsification and decomposition; the former reduces the number of edges in a graph while maintaining its cut structure, while the latter breaks a weighted graph into a small number of unweighted graphs. Though these techniques have been used as heuristics in various hybrid quantum algorithms, there have been no guarantees on their performance, to the best of our knowledge. This work provides the first provable guarantees using sparsification and decomposition to improve quantum noise resilience and reduce quantum circuit complexity. For quantum hardware that uses edge-by-edge QAOA compilations, sparsification leads to a direct reduction in circuit complexity. For trapped-ion quantum simulators implementing all-to-all HIsing pulses, we show that for a (1−ϵ) factor loss in the Max-Cut approximation (ϵ>0), our compilations improve the (worst-case) number of HIsing pulses from O(n2) to O(nlog(n/ϵ)) and the (worst-case) number of Pauli-X bit flips from O(n2) to O(nlog(n/ϵ)ϵ2) for n-node graphs. This is an asymptotic improvement for any constant ϵ>0. We demonstrate that significant improvements to the approximation ratio are obtained using decomposition in simulated trapped-ion experiments with dephasing noise. We further present a generic argument showing that sparsification results in an exponentially improved circuit fidelity lower bound in digital computing schemes based on one- and two-qubit gates, which are relevant to a wide variety of hardwares such as superconducting qubits and certain neutral atom or trapped ion setups, and more sophisticated noise models. We anticipate these approximate compilation techniques will be useful tools in a variety of future quantum computing experiments.

Moondra, Jai [Georgia Institute of Technology]↗

DOE OSTI2024

Scaling whole-chip QAOA for higher-order ising spin glass models on heavy-hex graphs

Abstract We show that the quantum approximate optimization algorithm (QAOA) for higher-order, random coefficient, heavy-hex compatible spin glass Ising models has strong parameter concentration across problem sizes from 16 up to 127 qubits for p = 1 up to p = 5, which allows for computationally efficient parameter transfer of QAOA angles. Matrix product state (MPS) simulation is used to compute noise-free QAOA performance. Hardware-compatible short-depth QAOA circuits are executed on ensembles of 100 higher-order Ising models on noisy IBM quantum superconducting processors with 16, 27, and 127 qubits using QAOA angles learned from a single 16-qubit instance using the JuliQAOA tool. We show that the best quantum processors find lower energy solutions up to p = 2 or p = 3, and find mean energies that are about a factor of two off from the noise-free distribution. We show that p = 1 QAOA energy landscapes remain very similar as the problem size increases using NISQ hardware gridsearches with up to a 414 qubit processor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Self-consistent mean-field quantum approximate optimization

We introduce a self-consistent mean-field quantum optimization algorithm that approximates the ground state of classical Ising Hamiltonians. The algorithm decomposes the problem into independent subproblems and treats the interactions between them in a mean-field manner. These interactions are captured by a common environment, constructed self-consistently through a variational quantum circuit, and which modifies the subproblems to account for mutual influence while maintaining computational independence. Consequently, subproblems can be solved individually, avoiding the computational cost of the full problem. We explore the properties of the generated environment and assess the algorithm's performance through extensive numerical simulations on Sherrington-Kirkpatrick spin glasses. Furthermore, we apply it experimentally to a weighted maximum clique problem applied to molecular docking. This framework enables the solution of problems that would otherwise exceed the qubit and gate counts of current quantum hardware.

Dupont, Maxime [Rigetti Computing] (ORCID:00000001↗

DOE OSTI2026

Self-consistent mean-field quantum approximate optimization

Dupont, Maxime [Rigetti Computing] (ORCID:00000001↗

DOE OSTI2026

Self-consistent mean-field quantum approximate optimization

Dupont, Maxime [Rigetti Computing] (ORCID:00000001↗

DOE OSTI2026

Optimization performance, fidelity, and cost: SIAM VQE

This dataset contains files storing results from classically-simulated quantum subroutines within a dynamical mean-field theory workflow, and jupyter notebooks processing the data in these files to generate plots. The files store: (1) Results from variational quantum eigensolver (VQE) simulations searching for optimal parameters allowing parametrized quantum circuits to prepare approximations to ground states of different Anderson impurity models (AIMs) (2) Results from simulations of a quantum Lanczos algorithm (QLA) estimating the Lanczos coefficients defining the continued-fraction representation of an (AIM) Green’s function Description: Any file named vqe_gs_results* stores approximations to the ground state and energy of a given AIM estimated using three different methods: (1) Numerical diagonalization (2) Ideal VQE simulation (3) VQE simulation with sampling noise For each VQE simulations metadata about the optimization (optimization results plus number of quantum circuits that would have been executed on real hardware) is also stored. Any file named qla_dos_results* estimations for the Lanczos coefficients defining the Green’s function of an AIM. The stored estimations are achieved using different methods: (1) Numerical Lanczos algorithm from initial states obtained from numerical diagonalization (2) Simulated quantum Lanczos algorithm from initial states prepared from parametrized quantum circuits yielded by corresponding ideal and noisy VQE subroutines. The dataset is used and described in M. Karabin et al., "Quantum solver for single-impurity Anderson models with particle-hole symmetry", Phys. Rev. Research 8, 033066 (2026). DOI: https://doi.org/10.1103/7ys3-tl4l

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

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 OSTI2025

Performance evaluations of signed and unsigned noisy approximate quantum Fourier arithmetic

The Quantum Fourier Transform (QFT) grants competitive advantages, especially in resource usage and circuit approximation, for performing arithmetic operations on quantum computers, and offers a potential route toward a numerical quantum-computational paradigm. In this paper, we utilize efficient techniques to implement QFT-based integer addition and multiplications. These operations are fundamental to various quantum applications including Shor’s algorithm, weighted-sum optimization problems in data processing and machine learning, and quantum algorithms requiring inner products. We carry out performance evaluations of these implementations based on IBM’s superconducting-qubit architecture using different compatible noise models. We isolate the sensitivity of the component quantum circuits on both one-/two-qubit gate error rates, and the number of the arithmetic operands’ superposed integer states. We analyze performance and identify the most effective approximation depths for unsigned quantum addition and quantum multiplication within the given context. We then perform a similar analysis of signed addition and compare to the unsigned results. We observe significant dependency of the optimal approximation depth on the degree of machine noise and the number of superposed states in certain performance regimes. Finally, we elaborate on the algorithmic challenges—relevant to signed, unsigned, modular and non-modular versions—that could also be applied to current implementations of QFT-based subtraction, division, exponentiation, and their potential tensor extensions. Here, we analyze the performance trends in our results and speculate on possible future developments within this computational paradigm.

Computational models↗

DOE OSTI2024

Faster Tensor Network Decoding for Topological Quantum Codes

We present a fast and Bayes-optimal-approximating tensor network decoder for planar quantum LDPC codes based on the tensor renormalization group algorithm, originally proposed by Levin, and Nave. By precomputing the renormalization group flow for the null syndrome, we need only recompute tensor contractions in the causal cone of the measured syndrome at the time of decoding. This allows us to achieve an overall runtime complexity of ($pnχ^6$) where p is the depolarizing noise rate, and χ is the cutoff value used to control singular value decomposition approximations used in the algorithm. We apply our decoder to the surface code in the code capacity noise model and compare its performance to the original matrix product state (MPS) tensor network decoder introduced by Bravyi, Suchara, and Vargo. The MPS decoder has a p-independent runtime complexity of $\mathcal{O}(nχ^3)$ resulting in significantly slower decoding times compared to our algorithm in the low-p regime.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Fully quantum algorithm for mesoscale fluid simulations with application to partial differential equations

Fluid flow simulations marshal our most powerful computational resources. In many cases, even this is not enough. Quantum computers provide an opportunity to speed up traditional algorithms for flow simulations. We show that lattice-based mesoscale numerical methods can be executed as efficient quantum algorithms due to their statistical features. This approach revises a quantum algorithm for lattice gas automata to reduce classical computations and state preparation at every time step. For this, the algorithm approximates the qubit relative phases and subtracts them at the end of each time step. Phases are evaluated using the iterative phase estimation algorithm and subtracted using single-qubit rotation phase gates. Further, this method optimizes the quantum resource required and makes it more appropriate for near-term quantum hardware. We also demonstrate how the checkerboard deficiency that the D1Q2 scheme presents can be resolved using the D1Q3 scheme. The algorithm is validated by simulating two canonical partial differential equations: the diffusion and Burgers' equations on different quantum simulators. We find good agreement between quantum simulations and classical solutions for the presented algorithm.

97 MATHEMATICS AND COMPUTING↗