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NASA NTRS2018

XY vs X Mixer in Quantum Alternating Operator Ansatz for Optimization Problems with Constraints

Quantum Approximate Optimization Algorithm, further generalized as Quantum Alternating Operator Ansatz (QAOA), is a family of algorithms for combinatorial optimization problems. It is a leading candidate to run on emerging universal quantum computers to gain insight into quantum heuristics. In constrained optimization, penalties are often introduced so that the ground state of the cost Hamiltonian encodes the solution (a standard practice in quantum annealing). An alternative is to choose a mixing Hamiltonian such that the constraint corresponds to a constant of motion and the quantum evolution stays in the feasible subspace. Better performance of the algorithm is speculated due to a much smaller search space. We consider problems with a constant Hamming weight as the constraint. We also compare different methods of generating the generalized W-state, which serves as a natural initial state for the Hamming-weight constraint. Using graph-coloring as an example, we compare the performance of using XY model as a mixer that preserves the Hamming weight with the performance of adding a penalty term in the cost Hamiltonian.

quantum computing↗
NASA NTRS2019

On Benchmarking Quantum Heuristics

Present an outline of important aspects for benchmarking quantum algorithms, in particular quantum heuristics. Using quantum approximate optimization algorithm as an example, we demonstrate how the choice of cost Hamiltonian, of mixer, and of initial states can affect the performance. We also discuss how realistic aspects of near-term quantum hardware will influence the algorithm performance.

Wang, Zhihui↗
NASA NTRS2019

Exploring Network-Related Optimization Problems Using Quantum Heuristics

Network-related connectivity optimization problems are underlying a wide range of applications and are also of high computational complexity. We consider studying network optimization problems using two types of quantum heuristics.One is quantum annealing, and the other Quantum Alternating Operator Ansatz, an extension of the Quantum Approximate Optimization Algorithms for gate-model quantum computation, in which a cost-function based unitary and a non-commuting mixing unitary are applied alternately. We present problem mappings for problems of finding the spanning-tree or spanning-graph of a graph that optimizes certain costs, and a variant that further requires the spanning-tree be degree-bounded. With quantum annealing, all constraints are cast into penalty terms in the cost Hamiltonian, and the solution is encoded as the ground state of the Hamiltonian. We provide three mappings to the quadratic unconstrained binary optimization (QUBO) form, compare the resource requirements, and analyze the tradeoffs. For QAOA, we give special focus on the design of mixers based on the constraints presented in the problem, such that the system evolution remains in a subspace of the full Hilbert space where all constraints are satisfied. In the spanning-tree problem, one such hard constraint is that a mixer applied to a spanning-tree needs also be a spanning tree. This involves checking the connectivity of a subgraph, which is a global condition common for most network-related problems. We show how this feature can be efficiently represented in the mixer in a quantum coherent way, based on manipulation of a descendant-matrix and an adjacent matrix. We further develop a mixer for the spanning-graphs based on the spanning-tree mixer.

Wang, Zhihui↗
NASA NTRS2019

Study network-related optimization problems using quantum alternating optimization ansatz

Network-related connectivity optimization problems are underlying a wide range of applications and are also of high computational complexity. We consider studying network optimization problems using two types of quantum heuristics. One is quantum annealing, and the other Quantum Alternating Operator Ansatz, an extension of the Quantum Approximate Optimization Algorithms for gate-model quantum computation, in which a cost-function based unitary and a non-commuting mixing unitary are applied alternately. We present problem mappings for problems of finding the spanning-tree or spanning-graph of a graph that optimizes certain costs, and a variant that further requires the spanning-tree be degree-bounded. With quantum annealing, all constraints are cast into penalty terms in the cost Hamiltonian, and the solution is encoded as the ground state of the Hamiltonian. We provide three mappings to the quadratic unconstrained binary optimization (QUBO) form, compare the resource requirements, and analyze the tradeoffs. For QAOA, we give special focus on the design of mixers based on the constraints presented in the problem, such that the system evolution remains in a subspace of the full Hilbert space where all constraints are satisfied. In the spanning-tree problem, one such hard constraint is that a mixer applied to a spanning-tree needs also be a spanning tree. This involves checking the connectivity of a subgraph, which is a global condition common for most network-related problems. We show how this feature can be efficiently represented in the mixer in a quantum coherent way, based on manipulation of a descendant-matrix and an adjacent matrix. We further develop a mixer for the spanning-graphs based on the spanning-tree mixer.

Zhihui Wang↗
DOE OSTI2024

A Novel Noise-Aware Classical Optimizer for Variational Quantum Algorithms

A key component of variational quantum algorithms (VQAs) is the choice of classical optimizer employed to update the parameterization of an ansatz. It is well recognized that quantum algorithms will, for the foreseeable future, necessarily be run on noisy devices with limited fidelities. Thus, the evaluation of an objective function (e.g., the guiding function in the quantum approximate optimization algorithm (QAOA) or the expectation of the electronic Hamiltonian in variational quantum eigensolver (VQE)) required by a classical optimizer is subject not only to stochastic error from estimating an expected value but also to error resulting from intermittent hardware noise. Model-based derivative-free optimization methods have emerged as popular choices of a classical optimizer in the noisy VQA setting, based on empirical studies. However, these optimization methods were not explicitly designed with the consideration of noise. In this work we adapt recent developments from the “noise-aware numerical optimization” literature to these commonly used derivative-free model-based methods. We introduce the key defining characteristics of these novel noise-aware derivative-free model-based methods that separate them from standard model-based methods. In conclusion, we study an implementation of such noise-aware derivative-free model-based methods and compare its performance on demonstrative VQA simulations to classical solvers packaged in scikit-quant.

classical optimizers↗
DOE OSTI2024

Efficient quantum circuits based on the quantum natural gradient

Efficient preparation of arbitrary entangled quantum states is crucial for quantum computation. This is particularly important for noisy intermediate-scale quantum simulators relying on variational hybrid quantum-classical algorithms. To that end, we propose symmetry-conserving modified quantum approximate optimization algorithm (SCom-QAOA) circuits. The depths of these circuits depend not only on the desired fidelity to the target state but also on the amount of entanglement the state contains. The parameters of the SCom-QAOA circuits are optimized using the quantum natural gradient method based on the Fubini-Study metric. The SCom-QAOA circuit transforms an unentangled state into a ground state of a gapped one-dimensional Hamiltonian with a circuit depth that depends not on the system size but rather on the finite correlation length. In contrast, the circuit depth grows proportionally to the system size for preparing low-lying states of critical one-dimensional systems. Even in the latter case, SCom-QAOA circuits with depth less than the system size were sufficient to generate states with fidelity in excess of 99%, which is relevant for near-term applications. The proposed scheme enlarges the set of the initial states accessible for variational quantum algorithms and widens the scope of investigation of nonequilibrium phenomena in quantum simulators. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
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↗
NASA NTRSDate not supplied

Dynamical Decoupling of Crosstalk on Superconducting Qubit Devices

Current NISQ devices are prone to errors. In order to be used for practical applications or achieve fault-tolerant thresholds, strategies to suppress error rates will be needed to maximize the potential of noisy devices. Dynamical decoupling (DD) is one such strategy for suppressing — or at least alleviating — the effects of decoherence, in which sequences of pulses are applied to qubits to decouple their interaction with the environment. Through experimental runs performed on several Rigetti quantum computing units (QPUs), we first demonstrate that DD is capable of improving coherence times for isolated qubits, as well as suppressing errors caused by the ZZ coupling between pairs of qubits. Extending this framework to cycles containing2-qubit gates, we show that DD can be inserted to decouple qubits from crosstalk occurring during neighboring 2-qubit gates, and demonstrate the efficacy of this procedure on quantum approximate optimization algorithm (QAOA) circuits. We also explore the usage of tailored DD sequences for the suppression of characterized error channels. We are grateful for support from the NASA Ames Research Center and from the DARPA ONISQ program under interagency agreement IAA 8839,Annex 114. HYH is supported by the USRA Feynman QuantumAcademy funded by the NAMS R&D Student Program and a UCHellman Fellowship. JS, ZGI and ZW are supported by USRA NASAAcademic Mission Service (NNA16BD14C).

Dynamical decoupling↗
NASA NTRS2019

Quantum Gate-Model Approaches to Exact and Approximate Optimization

Many of the most challenging computational problems arising in practical applications are tackled by heuristic algorithms which have not been rigorously proven to outperform other approaches but rather have been empirically demonstrated to be effective. While quantum heuristics have been proposed since the early days of quantum computing, true empirical evaluation of the real-world performance of these algorithms is only becoming possible now as increasingly powerful quantum gate-model devices continue to come online.In this talk, I will give an overview of the NASA QuAIL team's ongoing investigation into quantum gate-model heuristic algorithms for exact and approximate optimization. In particular, we consider the performance of the Quantum Approximate Optimization Algorithm on NP-hard optimization problems, and describe algorithm parameter setting strategies for real-world quantum hardware. We then show a generalization of QAOA circuits, the Quantum Alternating Operator Ansatz, especially suitable for low-resource implementations of QAOA for problems with hard (feasibility) constraints. The talk will conclude with a discussion of research challenges, particularly for optimization and sampling applications of QAOA, and the potential of more general quantum heuristics to give advantages over classical computers.

Hadfield, Stuart↗
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↗