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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Real-Time Krylov Theory for Quantum Computing Algorithms

Quantum computers provide new avenues to access ground and excited state properties of systems otherwise difficult to simulate on classical hardware. New approaches using subspaces generated by real-time evolution have shown efficiency in extracting eigenstate information, but the full capabilities of such approaches are still not understood. In recent work, we developed the variational quantum phase estimation (VQPE) method, a compact and efficient real-time algorithm to extract eigenvalues on quantum hardware. Here we build on that work by theoretically and numerically exploring a generalized Krylov scheme where the Krylov subspace is constructed through a parametrized real-time evolution, which applies to the VQPE algorithm as well as others. We establish an error bound that justifies the fast convergence of our spectral approximation. We also derive how the overlap with high energy eigenstates becomes suppressed from real-time subspace diagonalization and we visualize the process that shows the signature phase cancellations at specific eigenenergies. We investigate various algorithm implementations and consider performance when stochasticity is added to the target Hamiltonian in the form of spectral statistics. To demonstrate the practicality of such real-time evolution, we discuss its application to fundamental problems in quantum computation such as electronic structure predictions for strongly correlated systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Solving reaction dynamics with quantum computing algorithms

The description of quantum many-body dynamics is extremely challenging on classical computers, as it can involve many degrees of freedom. However, the time evolution of quantum states is a natural application for quantum computers that are designed to efficiently perform unitary transformations. Here, in this paper, we study quantum algorithms for response functions, relevant for describing different reactions governed by linear response. We focus on nuclear-physics applications and consider a qubit-efficient mapping on the lattice, which can efficiently represent the large volumes required for realistic scattering simulations. For the case of a contact interaction, we develop an algorithm for time evolution based on the Trotter approximation that scales logarithmically with the lattice size and is combined with quantum phase estimation. We eventually focus on the nuclear two-body system and a typical response function relevant for electron scattering as an example. We also investigate ground-state preparation and examine the total circuit depth required for a realistic calculation and the hardware noise level required to interpret the signal.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Assessing Ground State Energy of Molecules and Energy Profile of the NH3 Capturing CO2 System Using the Quantum Computing Algorithms

Molecule size correlates with the number of electrons on electronic energies and strength of anharmonicity on vibrational properties, however, it is challenging to address using classical computing. In this study, variational quantum eigensolver (VQE) algorithm was implemented on a quantum simulator to quantify electronic and vibrational energies and reaction pathways of CO2 + NH3 = NH2COOH. The VQE-based Hartree-Fock-Embedding algorithm was adopted to benchmark electronic energies for a series of molecules (doi.org/10.1063/5.0188249) and quantify the reaction energy profile of the CO2 capture reaction (doi.org/10.1116/5.0137750). The generated reaction profile is in good agreement with the classical high-level Coupled-Cluster-Singles-and-Doubles (CCSD) results. The quantum computing algorithm also helps enhance the calculation of vibrational ground-state energies by considering the many-body coupling using the Vibrational Self-Consistent Field method, providing results for CO2 and NH3 molecules with accuracy comparable to the direct diagonalization method. Our approach indicates quantum computing can be applied to solve practical problems.

Lee, Yueh-Lin↗
DOE OSTI2023

Description of reaction and vibrational energetics of CO 2 –NH 3 interaction using quantum computing algorithms

CO 2 capture is critical to solving global warming. Amine-based solvents are extensively used to chemically absorb CO 2 . Thus, it is crucial to study the chemical absorption of CO 2 by amine-based solvents to better understand and optimize CO 2 capture processes. Here, we use quantum computing algorithms to quantify molecular vibrational energies and reaction pathways between CO 2 and a simplified amine-based solvent model—NH 3 . Molecular vibrational properties are important to understanding kinetics of reactions. However, the molecule size correlates with the strength of anharmonicity effect on vibrational properties, which can be challenging to address using classical computing. Quantum computing can help enhance molecular vibrational calculations by including anharmonicity. We implement a variational quantum eigensolver (VQE) algorithm in a quantum simulator to calculate ground state vibrational energies of reactants and products of the CO 2 and NH 3 reaction. The VQE calculations yield ground vibrational energies of CO 2 and NH 3 with similar accuracy to classical computing. In the presence of hardware noise, Compact Heuristic for Chemistry (CHC) ansatz with shallower circuit depth performs better than Unitary Vibrational Coupled Cluster. The “Zero Noise Extrapolation” error-mitigation approach in combination with CHC ansatz improves the vibrational calculation accuracy. Excited vibrational states are accessed with quantum equation of motion method for CO 2 and NH 3 . Using quantum Hartree–Fock (HF) embedding algorithm to calculate electronic energies, the corresponding reaction profile compares favorably with Coupled Cluster Singles and Doubles while being more accurate than HF. Our research showcases quantum computing applications in the study of CO 2 capture reactions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Quantum Computing Algorithms and Applications for Coherent and Strongly Correlated Chemical Systems

This project advanced quantum algorithms, quantum information theory, strongly correlated electronic structure methods, molecular quantum materials, and exciton transport imaging in coherent condensed phase systems. Across the award period, the team developed new methods for open-quantum-system simulation, Hamiltonian learning, state tomography, reduced-density-matrix and contracted-quantum eigensolver approaches, and quantum diagnostics for device capability and openness.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Rodeo Algorithm for Quantum Computing

We present a stochastic quantum computing algorithm that can prepare any eigenvector of a quantum Hamiltonian within a selected energy interval $\ [E-\epsilon, E+\epsilon]$. In order to reduce the spectral weight of all other eigenvectors by a suppression factor δ, the required computational effort scales as $\ O[|\log \delta|/(p \epsilon)]$, where p s the squared overlap of the initial state with the target eigenvector. The method, which we call the rodeo algorithm, uses auxiliary qubits to control the time evolution of the Hamiltonian minus some tunable parameter E . In this manner, we converge to the target eigenvector with exponential accuracy in the number of measurements. In addition to preparing eigenvectors, the method can also compute the full spectrum of the Hamiltonian. We illustrate the performance with several examples. For energy eigenvalue determination with error $\epsilon$, the computational scaling is $\ O[(\log \epsilon)^2/(p \epsilon)]$. For eigenstate preparation, the computational scaling is $\ O(\log \Delta/p)$, where $\Delta$ is the magnitude of the orthogonal component of the residual vector. The speed for eigenstate preparation is exponentially faster than that for phase estimation or adiabatic evolution.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Demonstration of the rodeo algorithm on a quantum computer

The rodeo algorithm is an efficient algorithm for eigenstate preparation and eigenvalue estimation for any observable on a quantum computer. This makes it a promising tool for studying the spectrum and structure of atomic nuclei as well as other fields of quantum many-body physics. The only requirement is that the initial state has sufficient overlap probability with the desired eigenstate. While it is exponentially faster than well-known algorithms such as phase estimation and adiabatic evolution for eigenstate preparation, it has yet to be implemented on an actual quantum device. In this work, we apply the rodeo algorithm to determine the energy levels of a random one-qubit Hamiltonian, resulting in a relative error of 0.08% using mid-circuit measurements on the IBM Q device Casablanca. This surpasses the accuracy of directly-prepared eigenvector expectation values using the same quantum device. We take advantage of the high-accuracy energy determination and use the Hellmann-Feynman theorem to compute eigenvector expectation values for a different random one-qubit observable. For the Hellmann-Feynman calculations, we find a relative error of 0.7%. Here, we conclude by discussing possible future applications of the rodeo algorithm for multi-qubit Hamiltonians.

algorithm↗
DOE OSTI2022

Quantum Algorithm Implementations for Beginners

As quantum computers become available to the general public, the need has arisen to train a cohort of quantum programmers, many of whom have been developing classical computer programs for most of their careers. While currently available quantum computers have less than 100 qubits, quantum computing hardware is widely expected to grow in terms of qubit count, quality, and connectivity. This review aims at explaining the principles of quantum programming, which are quite different from classical programming, with straightforward algebra that makes understanding of the underlying fascinating quantum mechanical principles optional. We give an introduction to quantum computing algorithms and their implementation on real quantum hardware. We survey 20 different quantum algorithms, attempting to describe each in a succinct and self-contained fashion. We show how these algorithms can be implemented on IBM’s quantum computer, and in each case, we discuss the results of the implementation with respect to differences between the simulator and the actual hardware runs. This article introduces computer scientists, physicists, and engineers to quantum algorithms and provides a blueprint for their implementations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Quantum tensor network algorithms for evaluation of spectral functions on quantum computers

We investigate quantum algorithms derived from tensor networks to simulate the static and dynamic properties of quantum many-body systems. Using a sequentially prepared quantum circuit representation of a matrix product state (MPS) that we call a quantum tensor network (QTN), we demonstrate algorithms to prepare ground and excited states on a quantum computer and apply them to molecular nanomagnets (MNMs) as a paradigmatic example. In this setting, we develop two approaches for extracting the spectral correlation functions measured in neutron-scattering experiments: (a) a generalization of the SWAP test for computing wave function overlaps and, (b) a generalization of the notion of matrix product operators to the QTN setting which generates a linear combination of unitaries. The latter method is discussed in detail for translationally invariant spin-half systems, where it is shown to reduce the qubit resource requirements compared with the SWAP method and may be generalized to other systems. We demonstrate the versatility of our approaches by simulating spin-1/2 and spin-3/2 MNMs, with the latter being an experimentally relevant model of a Cr$^{3+}_{8}$ ring. Here, our approach has qubit requirements that are independent of the number of constituents of the many-body system and scale only logarithmically with the bond dimension of the MPS representation, making them appealing for implementation on near-term quantum hardware with mid-circuit measurement and reset.

Neutron scattering↗
DOE OSTI2023

Exploring the scaling limitations of the variational quantum eigensolver with the bond dissociation of hydride diatomic molecules

Abstract Materials simulations involving strongly correlated electrons pose fundamental challenges to state‐of‐the‐art electronic structure methods but are hypothesized to be the ideal use case for quantum computing algorithms. To date, no quantum computer has simulated a molecule of a size and complexity relevant to real‐world applications, despite the fact that the variational quantum eigensolver (VQE) algorithm can predict chemically accurate total energies. Nevertheless, because of the many applications of moderately sized, strongly correlated systems, such as molecular catalysts, the successful use of the VQE stands as an important waypoint in the advancement toward useful chemical modeling on near‐term quantum processors. In this paper, we take a significant step in this direction. We lay out the steps, write, and run parallel code for an (emulated) quantum computer to compute the bond dissociation curves of the TiH, LiH, NaH, and KH diatomic hydride molecules using the VQE. TiH was chosen as a relatively simple chemical system that incorporates d orbitals and strong electron correlation. Because current VQE implementations on existing quantum hardware are limited by qubit error rates, the number of qubits available, and the allowable gate depth, recent studies using it have focused on chemical systems involving s and p block elements. Through VQE + UCCSD calculations of TiH, we evaluate the near‐term feasibility of modeling a molecule with d‐orbitals on real quantum hardware. We demonstrate that the inclusion of d‐orbitals and the use of the UCCSD ansatz, which are both necessary to capture the correct TiH physics, dramatically increase the cost of this problem. We estimate the approximate error rates necessary to model TiH on current quantum computing hardware using VQE + UCCSD and show them to likely be prohibitive until significant improvements in hardware and error correction algorithms are available.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Scalable Circuits for Preparing Ground States on Digital Quantum Computers: The Schwinger Model Vacuum on 100 Qubits

The vacuum of the lattice Schwinger model is prepared on up to 100 qubits of IBM’s Eagle-processor quantum computers. A new algorithm to prepare the ground state of a gapped translationally invariant system on a quantum computer is presented, which we call “scalable circuits ADAPT-VQE” (SC-ADAPT-VQE). This algorithm uses the exponential decay of correlations between distant regions of the ground state, together with ADAPT-VQE, to construct quantum circuits for state preparation that can be scaled to arbitrarily large systems. These scalable circuits can be determined with use of classical computers, avoiding the challenging task of optimizing parameterized circuits on a quantum computer. SC-ADAPT-VQE is applied to the Schwinger model, and is shown to be systematically improvable, with an accuracy that converges exponentially with circuit depth. Both the structure of the circuits and the deviations of prepared wave functions are found to become independent of the number of spatial sites, L . This allows a controlled extrapolation of the circuits, determined with use of small or modest-sized systems, to arbitrarily large L . The circuits for the Schwinger model are determined on lattices up to L = 14 (28 qubits) with the Qiskit classical simulator, and are subsequently scaled up to prepare the L = 50 (100 qubits) vacuum on IBM’s 127-superconducting-qubit quantum computers ibm_brisbane and ibm_cusco. After introduction of an improved error-mitigation technique, which we call “operator decoherence renormalization”, the chiral condensate and charge-charge correlators obtained from the quantum computers are found to be in good agreement with classical matrix product state simulations. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

A formally certified end-to-end implementation of Shor’s factorization algorithm

Quantum computing technology may soon deliver revolutionary improvements in algorithmic performance, but it is useful only if computed answers are correct. While hardware-level decoherence errors have garnered significant attention, a less recognized obstacle to correctness is that of human programming errors—“bugs.” Techniques familiar to most programmers from the classical domain for avoiding, discovering, and diagnosing bugs do not easily transfer, at scale, to the quantum domain because of its unique characteristics. To address this problem, we have been working to adapt formal methods to quantum programming. With such methods, a programmer writes a mathematical specification alongside the program and semiautomatically proves the program correct with respect to it. The proof’s validity is automatically confirmed—certified—by a “proof assistant.” Formal methods have successfully yielded high-assurance classical software artifacts, and the underlying technology has produced certified proofs of major mathematical theorems. As a demonstration of the feasibility of applying formal methods to quantum programming, we present a formally certified end-to-end implementation of Shor’s prime factorization algorithm, developed as part of a framework for applying the certified approach to general applications. By leveraging our framework, one can significantly reduce the effects of human errors and obtain a high-assurance implementation of large-scale quantum applications in a principled way.

Science & Technology - Other Topics↗
DOE OSTI2025

Quantum algorithm for polaritonic chemistry based on an exact ansatz

Abstract Cavity-modified chemistry uses strong light-matter interactions to modify the electronic properties of molecules in order to enable new physical phenomena such as novel reaction pathways. As cavity chemistry often involves critical regions where configurations become nearly degenerate, the ability to treat multireference problems is crucial to understanding polaritonic systems. In this Letter, we show through the use of a unitary ansatz derived from the anti-Hermitian contracted Schrödinger equation that cavity-modified systems with strong correlation, such as the deformation of rectangular H 4 coupled to a cavity mode, can be solved efficiently and accurately on a quantum device. In contrast, while our quantum algorithm can be made formally exact, classical-computing methods as well as other quantum-computing algorithms often yield answers that are both quantitatively and qualitatively incorrect. Additionally, we demonstrate the current feasibility of the algorithm on near intermediate-scale quantum hardware by computing the dissociation curve of H 2 strongly coupled to a bosonic bath.

Warren, Samuel (ORCID:0000000157134454)↗
DOE OSTI2026

A 1-km photonic link connecting superconducting circuits in two dilution refrigerators

Superconducting quantum processors are a leading platform for implementing practical quantum computation algorithms. Although superconducting quantum processors with hundreds of qubits have been demonstrated, their further scale-up is constrained by the physical size and cooling power of dilution refrigerators. This constraint can be overcome by constructing a quantum network to interconnect qubits hosted in different refrigerators, which requires microwave-to-optical transducers to enable low-loss signal transmission over long distances. Although various designs and demonstrations have achieved high-efficiency and low-added-noise transducers, a coherent photonic link between separate refrigerators has not yet been realized. Here, in this work, we experimentally demonstrate coherent signal transfer between two superconducting circuits housed in separate dilution refrigerators, enabled by a pair of frequency-matched aluminium nitride electro-optic transducers connected via a 1-km telecom optical fibre. The optical frequency matching between two transducers is realized by an asymmetric photonic molecule design, and an overall 80 dB improvement in transduction efficiency over commercial electro-optic modulators is achieved, paving the way towards a fully quantum-enabled link. This work provides critical design guidelines for scalable superconducting quantum networks interconnected by photonic links.

nonlinear optics↗
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]↗