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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 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 OSTI2023

Seven open problems in applied combinatorics

We present and discuss seven different open problems in applied combinatorics. Additionally, the application areas relevant to this compilation include quantum computing, algorithmic differentiation, topological data analysis, iterative methods, hypergraph cut algorithms, and power systems.

97 MATHEMATICS AND COMPUTING↗

NASA NTRSDate not supplied

Introduction to Quantum Computing

Quantum computing offers the potential to revolutionize high-performance computing by providing a means to solve certain computational problems asymptotically faster than any classical computer. Quantum computing has advanced recently from merely a theoretical possibility to engineered reality, including commercial entities offering early prototype quantum processors, both special-purpose quantum annealers and general-purpose gate-model processors. The media have been showcasing each new development and implicitly conveying the message that quantum-computing ubiquity is nigh. Here, we will respond to this hype and provide an overview of the exciting but still early state of the field. In this tutorial, we introduce participants to the computational models that give quantum computing its immense computational power. We examine the thought processes that programmers need to map problems to quantum computers. And we discuss hardware and algorithmic challenges that must be overcome before quantum computing becomes a component of every software developer's repertoire.

Quantum computing↗

NASA NTRSDate not supplied

Introduction to Quantum Computing

Quantum computing↗

DOE OSTI2024

U(1) fields from qubits: An approach via D-theory algebra

A new quantum link microstructure was proposed for the lattice quantum chromodynamics (QCD) Hamiltonian, replacing the Wilson gauge links with a bilinear of fermionic qubits, later generalized to D-theory. This formalism provides a general framework for building lattice field theory algorithms for quantum computing. We focus mostly on the simplest case of a quantum rotor for a single compact U(1) field. We also make some progress for non-Abelian setups, making it clear that the ideas developed in the U(1) case extend to other groups. These in turn are building blocks for 1 + 0 -dimensional ( 1 + 0 -D) matrix models, 1 + 1 -D sigma models and non-Abelian gauge theories in 2 + 1 and 3 + 1 dimensions. By introducing multiple flavors for the U(1) field, where the flavor symmetry is gauged, we can efficiently approach the infinite-dimensional Hilbert space of the quantum O(2) rotor with increasing flavors. The emphasis of the method is on preserving the symplectic algebra exchanging fermionic qubits by sigma matrices (or hard bosons) and developing a formal strategy capable of generalization to a SU ( 3 ) field for lattice QCD and other non-Abelian 1 + 1 -D sigma models or 3 + 1 -D gauge theories. For U(1), we discuss briefly the qubit algorithms for the study of the discrete 1 + 1 -D sine-Gordon equation. Published by the American Physical Society 2024

Astronomy & Astrophysics↗

DOE OSTI2025

Opportunities in full-stack design of low-overhead fault-tolerant quantum computation

Quantum error correction provides a route to realizing large-scale quantum computation but incurs substantial resource overheads. Here, in this work, we highlight recent advances that reduce these overheads by co-designing different levels of the computational stack, including algorithms, quantum-error-correction strategies and hardware architecture. We then discuss opportunities for further optimization such as leveraging flexible qubit connectivity and quantum low-density parity check codes. These strategies can bring useful quantum computation closer to reality as experiments advance in the coming years.

quantum information↗

DOE OSTI2020

QCOR; A Language Extension Specification for the Heterogeneous Quantum-Classical Model of Computation

Quantum computing (QC) is an emerging computational paradigm that leverages the laws of quantum mechanics to perform elementary logic operations. Existing programming models for QC were designed with fault-tolerant hardware in mind, envisioning stand-alone applications. However, the susceptibility of near-term quantum computers to noise limits their stand-alone utility. To better leverage limited computational strengths of noisy quantum devices, hybrid algorithms have been suggested whereby quantum computers are used in tandem with their classical counterparts in a heterogeneous fashion. This modus operandi calls out for a programming model and a high-level programming language that natively and seamlessly supports heterogeneous quantum-classical hardware architectures in a single-source-code paradigm. Motivated by the lack of such a model, we introduce a language extension specification, called QCOR, which enables single-source quantum-classical programming. Programs written using the QCOR library–based language extensions can be compiled to produce functional hybrid binary executables. After defining QCOR’s programming model, memory model, and execution model, we discuss how QCOR enables variational, iterative, and feed-forward QC. Additionally, QCOR approaches quantum-classical computation in a hardware-agnostic heterogeneous fashion and strives to build on best practices of high-performance computing. The high level of abstraction in the language extension is intended to accelerate the adoption of QC by researchers familiar with classical high-performance computing.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2011

NASA Tech Briefs, March 2011

Topics covered include: Optimal Tuner Selection for Kalman-Filter-Based Aircraft Engine Performance Estimation; Airborne Radar Interferometric Repeat-Pass Processing; Plug-and-Play Environmental Monitoring Spacecraft Subsystem; Power-Combined GaN Amplifier with 2.28-W Output Power at 87 GHz; Wallops Ship Surveillance System; Source Lines Counter (SLiC) Version 4.0; Guidance, Navigation, and Control Program; Single-Frame Terrain Mapping Software for Robotic Vehicles; Auto Draw from Excel Input Files; Observation Scheduling System; CFDP for Interplanetary Overlay Network; X-Windows Widget for Image Display; Binary-Signal Recovery; Volumetric 3D Display System with Static Screen; MMIC Replacement for Gunn Diode Oscillators; Feature Acquisition with Imbalanced Training Data; Mount Protects Thin-Walled Glass or Ceramic Tubes from Large Thermal and Vibration Loads; Carbon Nanotube-Based Structural Health Monitoring Sensors; Wireless Inductive Power Device Suppresses Blade Vibrations; Safe, Advanced, Adaptable Isolation System Eliminates the Need for Critical Lifts; Anti-Rotation Device Releasable by Insertion of a Tool; A Magnetically Coupled Cryogenic Pump; Single Piezo-Actuator Rotary-Hammering Drill; Fire-Retardant Polymeric Additives; Catalytic Generation of Lift Gases for Balloons; Ionic Liquids to Replace Hydrazine; Variable Emittance Electrochromics Using Ionic Electrolytes and Low Solar Absorptance Coatings; Spacecraft Radiator Freeze Protection Using a Regenerative Heat Exchanger; Multi-Mission Power Analysis Tool; Correction for Self-Heating When Using Thermometers as Heaters in Precision Control Applications; Gravitational Wave Detection with Single-Laser Atom Interferometers; Titanium Alloy Strong Back for IXO Mirror Segments; Improved Ambient Pressure Pyroelectric Ion Source; Multi-Modal Image Registration and Matching for Localization of a Balloon on Titan; Entanglement in Quantum-Classical Hybrid; Algorithm for Autonomous Landing; Quantum-Classical Hybrid for Information Processing; Small-Scale Dissipation in Binary-Species Transitional Mixing Layers; Superpixel-Augmented Endmember Detection for Hyperspectral Images; Coding for Parallel Links to Maximize the Expected Value of Decodable Messages; and Microwave Tissue Soldering for Immediate Wound Closure.

Source record↗

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

Integrating subsystem embedding subalgebras and coupled cluster Green’s function: a theoretical foundation for quantum embedding in excitation manifold

Here, in this study, we introduce a novel approach to coupled-cluster Green's function (CCGF) embedding by seamlessly integrating conventional CCGF theory with the state-of-the-art sub-system embedding sub-algebras coupled cluster (SES-CC) formalism. This integration focuses primarily on delineating the characteristics of the sub-system and the corresponding segments of the Green's function, defined explicitly by active orbitals. Crucially, our work involves the adaptation of the SES-CC paradigm, addressing the left eigenvalue problem through a distinct form of Hamiltonian similarity transformation. This advancement not only facilitates a comprehensive representation of the interaction between the embedded sub-system and its surrounding environment but also paves the way for the quantum mechanical description of multiple embedded domains, particularly by employing the emergent quantum flow algorithms. Our theoretical underpinnings further set the stage for a generalization to multiple embedded sub-systems. This expansion holds significant promise for the exploration and application of non-equilibrium quantum systems, enhancing the understanding of system–environment interactions. In doing so, the research underscores the potential of SES-CC embedding within the realm of quantum computations and multi-scale simulations, promising a good balance between accuracy and computational efficiency.

97 MATHEMATICS AND COMPUTING↗

NASA NTRSDate not supplied

A NASA Perspective on Quantum Computing, with Ties to Operator Algebras

The talk will survey work done by the NASA Quantum Artificial Intelligence Laboratory (QuAIL), particularly algorithms and protocols in which operator algebras may play a role. The talk will focus on recent work advancing quantum error correction and error mitigation, and will touch on other topics related to quantum algorithms and funda- mental quantum physics.

Quantum Computing↗

DOE OSTI2021

Quantum Machine-Learning for Eigenstate Filtration in Two-Dimensional Materials

Quantum machine-learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure calculations of molecular systems and spin models in magnetic systems. However, the discussion in all these recipes focuses specifically on targeting the ground state. Herein we demonstrate a quantum algorithm that can filter any energy eigenstate of the system based on either symmetry properties or a predefined choice of the user. The workhorse of our technique is a shallow neural network encoding the desired state of the system with the amplitude computed by sampling the Gibbs–Boltzmann distribution using a quantum circuit and the phase information obtained classically from the nonlinear activation of a separate set of neurons. We show that the resource requirements of our algorithm are strictly quadratic. To demonstrate its efficacy, we use state filtration in monolayer transition metal dichalcogenides which are hitherto unexplored in any flavor of quantum simulations. We implement our algorithm not only on quantum simulators but also on actual IBM-Q quantum devices and show good agreement with the results procured from conventional electronic structure calculations. We thus expect our protocol to provide a new alternative in exploring the band structures of exquisite materials to usual electronic structure methods or machine-learning techniques that are implementable solely on a classical computer.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Time-dependent variational principle for mixed matrix product states in the thermodynamic limit

Here, we describe a time evolution algorithm for quantum spin chains whose Hamiltonians are composed of an infinite uniform left and right bulk part, and an arbitrary finite region in between. The left and right bulk parts are allowed to be different from each other. The algorithm is based on the time-dependent variational principle (TDVP) of matrix product states. It is inversion-free and very simple to adapt from an existing TDVP code for finite systems. The importance of working in the projective Hilbert space is highlighted. We study the quantum Ising model as a benchmark and an illustrative example. The spread of information after a local quench is studied in both the ballistic and the diffusive case. We also offer a derivation of TDVP directly from symplectic geometry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus

Abstract Variational quantum eigensolvers (VQEs) represent a powerful class of hybrid quantum-classical algorithms for computing molecular energies. Various numerical issues exist for these methods, however, including barren plateaus and large numbers of local minima. In this work, we consider the Adaptive, Problem-Tailored Variational Quantum Eiegensolver (ADAPT-VQE) ansätze, and examine how they are impacted by these local minima. We find that while ADAPT-VQE does not remove local minima, the gradient-informed, one-operator-at-a-time circuit construction accomplishes two things: First, it provides an initialization strategy that can yield solutions with over an order of magnitude smaller error compared to random initialization, and which is applicable in situations where chemical intuition cannot help with initialization, i.e., when Hartree-Fock is a poor approximation to the ground state. Second, even if an ADAPT-VQE iteration converges to a local trap at one step, it can still “burrow” toward the exact solution by adding more operators, which preferentially deepens the occupied trap. This same mechanism helps highlight a surprising feature of ADAPT-VQE: It should not suffer optimization problems due to barren plateaus and random initialization. Even if such barren plateaus appear in the parameter landscape, our analysis suggests that ADAPT-VQE avoids such regions by design.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Fermionic quantum processing with programmable neutral atom arrays

Simulating the properties of many-body fermionic systems is an outstanding computational challenge relevant to material science, quantum chemistry, and particle physics.-5.4pc]Please note that the spelling of the following author names in the manuscript differs from the spelling provided in the article metadata: D. González-Cuadra, D. Bluvstein, M. Kalinowski, R. Kaubruegger, N. Maskara, P. Naldesi, T. V. Zache, A. M. Kaufman, M. D. Lukin, H. Pichler, B. Vermersch, Jun Ye, and P. Zoller. The spelling provided in the manuscript has been retained; please confirm. Although qubit-based quantum computers can potentially tackle this problem more efficiently than classical devices, encoding nonlocal fermionic statistics introduces an overhead in the required resources, limiting their applicability on near-term architectures. In this work, we present a fermionic quantum processor, where fermionic models are locally encoded in a fermionic register and simulated in a hardware-efficient manner using fermionic gates. We consider in particular fermionic atoms in programmable tweezer arrays and develop different protocols to implement nonlocal gates, guaranteeing Fermi statistics at the hardware level. We use this gate set, together with Rydberg-mediated interaction gates, to find efficient circuit decompositions for digital and variational quantum simulation algorithms, illustrated here for molecular energy estimation. Finally, we consider a combined fermion-qubit architecture, where both the motional and internal degrees of freedom of the atoms are harnessed to efficiently implement quantum phase estimation as well as to simulate lattice gauge theory dynamics.

74 ATOMIC AND MOLECULAR PHYSICS↗