Search NASA⌕ Search

SEARCH · Search NASA

Results for “Quantum algorithm”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Localization in Energy Materials (Final Project Report)

The last year of this award we have continued our research on using quantum machine learning to identify phase transitions. By combining quantum machine learning with quantum computing, we extended a hybrid classical-quantum algorithm to capture the metal-insulator quantum phase transition of the Hubbard model. We have also continued our studies of non-equilibrium dynamics of interacting disordered systems. In particular, we studied the non-equilibrium transient dynamics of a system described by the Anderson-Hubbard model following an interaction and disorder quench, and the effect of disorder on the out-of-time-order correlator on the Hubbard model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Fundamental Algorithmic Research for Quantum Computing (FAR‐QC) (Final report)

This document is the final technical report for the "Fundamental Algorithmic Research for Quantum Computing" (FAR-QC) project at Dartmouth College (PI: J. Whitfield, co-PI: L. Viola). It details the project's primary scientific accomplishments from 2019 to 2025, focusing on advances in quantum simulation algorithms, resource-efficient fermionic encodings, bosonic topology, and optimization methods for near-term quantum devices. The report also summarizes project impacts, including software development (Quiqbox.jl), workforce training, and a complete list of resulting publications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Recursive algorithm for constructing antisymmetric fermionic states in first quantization mapping

We devise a deterministic quantum algorithm to produce antisymmetric states of single-particle orbitals in the first quantization mapping. Unlike sorting-based antisymmetrization algorithms, which require ordered input states and high Clifford-gate overhead, our approach initializes the state of each particle independently. For a system of $η$ particles and $N$ single-particle states, our algorithm prepares antisymmetrized states of non-trivial localized (e.g., Hartree-Fock) orbitals using $O(η^2\sqrt{N})$ $T$-gates, outperforming alternative algorithms when $η ≲ \sqrt{N}$. To achieve such scaling, we require $O(\sqrt{N})$ dirty ancilla qubits for intermediate calculations. Knowledge of the single-particle states to be antisymmetrized can be leveraged to further improve the efficiency of the circuit, and a measurement-based variant reduces gate cost by roughly a factor of two. We show example circuits for two- and three-particle systems and discuss the generalization to an arbitrary number of particles. For a specific three-particle example, we decompose the circuit into Clifford $+T$ gates and study the impact of noise on the prepared state.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRSDate not supplied

High-Dimensional Similarity Search with Quantum-Assisted Variational Autoencoder

Recent progress in quantum algorithms and hardware indicates the potential importance of quantum computing in the near future. However, finding suitable application areas remains an active area of research. Quantum machine learning is touted as a potential approach to demonstrate quantum advantage within both the gate-model and the adiabatic schemes. For instance, the QVAE has been proposed as a quantum enhancement to the discrete VAE. We extend on previous work and study the real-world applicability of a QVAE by presenting a proof-of-concept for similarity search in large-scale high-dimensional datasets. While exact and fast similarity search algorithms are available for low dimensional datasets, scaling to high-dimensional data is non-trivial. We show how to construct a space-efficient search index based on the latent space representation of a QVAE. Our experiments show a correlation between the Hamming distance in the embedded space and the Euclidean distance in the original space on the MODIS dataset. Further, we find real-world speedups compared to linear search and demonstrate memory-efficient scaling to half a billion data points.

Data mining, similarity search, quantum machine le↗
NASA NTRS2005

Scheme for Entering Binary Data Into a Quantum Computer

A quantum algorithm provides for the encoding of an exponentially large number of classical data bits by use of a smaller (polynomially large) number of quantum bits (qubits). The development of this algorithm was prompted by the need, heretofore not satisfied, for a means of entering real-world binary data into a quantum computer. The data format provided by this algorithm is suitable for subsequent ultrafast quantum processing of the entered data. Potential applications lie in disciplines (e.g., genomics) in which one needs to search for matches between parts of very long sequences of data. For example, the algorithm could be used to encode the N-bit-long human genome in only log2N qubits. The resulting log2N-qubit state could then be used for subsequent quantum data processing - for example, to perform rapid comparisons of sequences.

Williams, Colin↗
DOE OSTI2025

Emergent hydrodynamic mode on SU(2) plaquette chains and quantum simulation

We search for emergent hydrodynamic modes in real-time Hamiltonian dynamics of 2+1-dimensional SU(2) lattice gauge theory on a quasi-one-dimensional plaquette chain, by numerically computing symmetric correlation functions of energy densities on lattice sizes of about 20 with the local Hilbert space truncated at 𝑗 max = $\frac{1}{2}$. Because of the Umklapp processes, we only find a mode for energy diffusion. The symmetric correlator exhibits transport peak near zero frequency with a width approximately proportional to momentum squared at small momentum, when the system is fully quantum ergodic, as indicated by the eigenenergy level statistics. This transport peak leads to a power-law 𝑡 −$\frac{1}{2}$ decay of the symmetric correlator at late time, also known as the long-time tail, as well as diffusionlike spreading in position space. We also introduce a quantum algorithm for computing the symmetric correlator on a quantum computer and find it gives results consistent with exact diagonalization when tested on the IBM emulator. Finally we discuss the future prospect of searching for the sound modes.

Hamiltonian systems↗
DOE OSTI2025

Potential quantum advantage for simulation of fluid dynamics

Numerical simulation of turbulent fluid dynamics needs to either parametrize turbulence—which introduces large uncertainties—or explicitly resolve the smallest scales—which is prohibitively expensive. Here, we provide evidence through analytic bounds and numerical studies that a potential quantum speedup can be achieved to simulate fluid dynamics using quantum computing. Specifically, we provide a lattice Boltzmann formulation of fluid dynamics for which we give evidence that low-order Carleman linearization is much more accurate than previously believed for these systems. This is achieved via a combination of reformulating the Navier-Stokes nonlinearity (u·$\triangledown$u) to lattice-Boltzmann nonlinearity (u 2 ) and accurately linearizing the dynamical equations, which effectively trades nonlinearity for additional degrees of freedom that add negligible expense in the quantum solver. Based on this, we apply a quantum algorithm for simulating the Carleman-linearized lattice Boltzmann equation and provide evidence that its cost scales logarithmically with system size compared with polynomial scaling in the best known classical algorithms. In this paper, we suggest that a quantum advantage may exist for simulating fluid dynamics, paving the way for simulating nonlinear multiscale transport phenomena in a wide range of disciplines using quantum computing.

42 ENGINEERING↗
DOE OSTI2024

Visual Analytics of Performance of Quantum Computing Systems and Circuit Optimization

Driven by potential exponential speedups in business, security, and scientific scenarios, interest in quantum computing is surging. This interest feeds the development of quantum computing hardware, but several challenges arise in optimizing application performance for hardware metrics (e.g., qubit coherence and gate fidelity). In this work, we describe a visual analytics approach for analyzing the performance properties of quantum devices and quantum circuit optimization. Our approach allows users to explore spatial and temporal patterns in quantum device performance data and it computes similarities and variances in key performance metrics. Detailed analysis of the error properties characterizing individual qubits is also supported. We also describe a method for visualizing the optimization of quantum circuits. The resulting visualization tool allows researchers to design more efficient quantum algorithms and applications by increasing the interpretability of quantum computations.

Chae, Junghoon↗
DOE OSTI2022

Quantum Circuits for the Preparation of Spin Eigenfunctions on Quantum Computers

The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wave functions that are relevant in the behavior of the system under study. Hamiltonian symmetries are important instruments used to classify relevant many-particle wave functions and to improve the efficiency of numerical simulations. In this work, quantum circuits for the exact and approximate preparation of total spin eigenfunctions on quantum computers are presented. Two different strategies are discussed and compared: exact recursive construction of total spin eigenfunctions based on the addition theorem of angular momentum, and heuristic approximation of total spin eigenfunctions based on the variational optimization of a suitable cost function. The construction of these quantum circuits is illustrated in detail, and the preparation of total spin eigenfunctions is demonstrated on IBM quantum devices, focusing on three- and five-spin systems on graphs with triangle connectivity.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2003

On the Critical Behaviour, Crossover Point and Complexity of the Exact Cover Problem

Research into quantum algorithms for NP-complete problems has rekindled interest in the detailed study a broad class of combinatorial problems. A recent paper applied the quantum adiabatic evolution algorithm to the Exact Cover problem for 3-sets (EC3), and provided an empirical evidence that the algorithm was polynomial. In this paper we provide a detailed study of the characteristics of the exact cover problem. We present the annealing approximation applied to EC3, which gives an over-estimate of the phase transition point. We also identify empirically the phase transition point. We also study the complexity of two classical algorithms on this problem: Davis-Putnam and Simulated Annealing. For these algorithms, EC3 is significantly easier than 3-SAT.

Morris, Robin D.↗
DOE OSTI2025

Ansatz-Free Hamiltonian Learning with Heisenberg-Limited Scaling

Learning the unknown interactions that govern a quantum system is crucial for quantum information processing, device benchmarking, and quantum sensing. The problem, known as Hamiltonian learning, is well understood under the assumption that interactions are local, but this assumption may not hold for arbitrary Hamiltonians. Previous methods all require high-order inverse polynomial dependency with precision, unable to surpass the standard quantum limit and reach the gold-standard Heisenberg-limited scaling. Whether Heisenberg-limited Hamiltonian learning is possible without prior assumptions about the interaction structures, a challenge we term ansatz-free Hamiltonian learning , remains an open question. In this work, we present a quantum algorithm to learn arbitrary sparse Hamiltonians without any structure constraints using only black-box queries of the system’s real-time evolution and minimal digital controls to attain Heisenberg-limited scaling in estimation error. Our method is also resilient to state-preparation-and-measurement errors, enhancing its practical feasibility. We numerically demonstrate our ansatz-free protocol for learning physical Hamiltonians and validating analog quantum simulations, benchmarking our performance against the state-of-the-art Heisenberg-limited learning approach. Moreover, we establish a fundamental trade-off between total evolution time and quantum control on learning arbitrary interactions, revealing the intrinsic interplay between controllability and total evolution-time complexity for any learning algorithm. These results pave the way for further exploration into Heisenberg-limited Hamiltonian learning in complex quantum systems under minimal assumptions, potentially enabling new benchmarking and verification protocols.

machine learning↗
DOE OSTI2025

Randomized Adiabatic Quantum Linear Solver Algorithm with Optimal Complexity Scaling and Detailed Running Costs

Solving linear systems of equations is a fundamental problem with a wide variety of applications across many fields of science, and there is increasing effort to develop quantum linear solver algorithms. Subaşı et al. [Phys. Rev. Lett. 122, 060504 (2019)] proposed a randomized algorithm inspired by adiabatic quantum computing, based on a sequence of random Hamiltonian simulation steps, with suboptimal scaling in the condition number 𝜅 of the linear system and the target error 𝜖. Here we go beyond these results in several ways. Firstly, using filtering [Lin and Tong, Quantum 4, 361 (2020)] and Poissonization techniques [Cunningham and Roland, ArXiv:2406.03972 (2024)], the algorithm complexity is improved to the optimal scaling 𝑂⁡(𝜅⁢log (1/𝜖))—an exponential improvement in 𝜖, and a shaving of a log 𝜅 scaling factor in 𝜅. Secondly, the algorithm is further modified to achieve constant factor improvements, which are vital as we progress towards hardware implementations on fault-tolerant devices. We introduce a cheaper randomized walk operator method replacing Hamiltonian simulation—which also removes the need for potentially challenging classical precomputations; randomized routines are sampled over optimized random variables; circuit constructions are improved. We obtain a closed formula rigorously upper bounding the expected number of times one needs to apply a block-encoding of the linear system matrix to output a quantum state encoding the solution to the linear system. The upper bound is 837⁢𝜅 at 𝜖 = 10 −10 for Hermitian matrices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

LLNL FESP Theory Highlights: October 2024

I. Novikau, I. Y. Dodin, E. A. Startsev, I. Joseph, Quantum algorithms for simulating dissipative linear and nonlinear dynamics of plasmas. Invited talk at the 66th Annual Meeting of the APS Division of Plasma Physics, Atlanta, Georgia. Novikau I., Dodin I.Y., Startsev E.A., Encoding of linear kinetic plasma problems in quantum circuits via data compression, Journal of Plasma Physics. 2024;90(4):805900401, doi:10.1017/S0022377824000795. We propose an algorithm for encoding linear kinetic plasma problems in quantum circuits. The focus is on modelling electrostatic linear waves in a one-dimensional Maxwellian electron plasma. The waves are described by the linearized Vlasov–Ampère system with a spatially localized external current that drives plasma oscillations. This system is formulated as a boundary-value problem and cast in the form of a linear vector equation to be solved by using the quantum signal processing algorithm. The latter requires encoding of a matrix in a quantum circuit as a sub-block of a unitary matrix. We propose how to encode in a circuit in a compressed form and discuss how the resulting circuit scales with the problem size and the desired precision.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Block encoding bosons by signal processing

Block Encoding (BE) is a crucial subroutine in many modern quantum algorithms, including those with near-optimal scaling for simulating quantum many-body systems, which often rely on Quantum Signal Processing (QSP). Currently, the primary methods for constructing BEs are the Linear Combination of Unitaries (LCU) and the sparse oracle approach. In this work, we demonstrate that QSP-based techniques, such as Quantum Singular Value Transformation (QSVT) and Quantum Eigenvalue Transformation for Unitary Matrices (QETU), can themselves be efficiently utilized for BE implementation. Specifically, we present several examples of using QSVT and QETU algorithms, along with their combinations, to block encode Hamiltonians for lattice bosons, an essential ingredient in simulations of high-energy physics. We also introduce a straightforward approach to BE based on the exact implementation of Linear Operators Via Exponentiation and LCU (LOVE-LCU). We find that, while using QSVT for BE results in the best asymptotic gate count scaling with the number of qubits per site, LOVE-LCU outperforms all other methods for operators acting on up to qubits, highlighting the importance of concrete circuit constructions over mere comparisons of asymptotic scalings. Using LOVE-LCU to implement the BE, we simulate the time evolution of single-site and two-site systems in the lattice theory using the Generalized QSP algorithm and compare the gate counts to those required for Trotter simulation.

Kane, Christopher F↗
DOE OSTI2025

Determining the Ensemble N -Representability of Reduced Density Matrices

The N-representability problem for reduced density matrices remains a fundamental challenge in electronic structure theory. Following our previous work that employs a unitary-evolution algorithm based on an adaptive derivative-assembled pseudo-Trotter variational quantum algorithm to probe pure-state N-representability of reduced density matrices [J. Chem. Theory Comput. 2024, 20, 9968], in this work we propose a practical framework for determining the ensemble N-representability of a p-body matrix. This is accomplished using a purification strategy that embeds an ensemble state into a pure state defined on an extended Hilbert space, such that the reduced density matrices of the purified state reproduce those of the original ensemble. By iteratively applying variational unitaries to an initial purified state, the proposed algorithm minimizes the Hilbert-Schmidt distance between its p-body reduced density matrix and a specified target p-body matrix, which serves as a measure of the N-representability of the target. This methodology facilitates both error correction of defective ensemble reduced density matrices and quantum-state reconstruction on a quantum computer, offering a route for density-matrix refinement. We validate the algorithm with numerical simulations on systems of two, three, and four electrons in both simple models as well as molecular systems at finite temperature, demonstrating its robustness.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRSDate not supplied

High dimensional similarity search with quantum assisted variational autoencoder

Recent progress in quantum algorithms and hardware is indicator of the potential importance of quantum computing in the next future. However, finding suitable application areas remains an active area of research. Quantum machine learning [1] is touted as a potential approach to demonstrate quantum advantage within both the gate-model [2,3] and the adiabatic [4,5] schemes. For instance, the Quantum-assisted Variational Autoencoder (QVAE) [6] has been proposed as a quantum enhancement to the discrete VAE [7]. We extend on previous work and study the real-world applicability of a QVAE, specifically, for similarity search in large-scale high dimensional datasets. While similarity search algorithms are available for low dimensional datasets, scaling to billion-scale datasets with thousands of dimensions is non-trivial. We show how the latent-space representation of a QVAE can be used to construct a space-efficient search index. We back up our claims by experimental results which show a correlation between the Hamming distance in the embedded space and the Euclidean distance in the original space on the Moderate Resolution Imaging Spectroradiometer (MODIS) dataset. Further, we show real-world speedups compared to linear search and demonstrate memory efficient scaling to large-scale datasets.

Nicholas D Gao↗
NASA NTRSDate not supplied

Self-consistent Quantum Iteratively Sparsified Hamiltonian Algorithm (SQuISH)

Due to coherence time limitations, reducing the resources required to run quantum algorithms and simulate physical systems on a quantum computer is crucial. With regards to Hamiltonian simulation, a significant effort has focused on building efficient algorithms using various factorizations and truncations, typically derived from the Hamiltonian alone. We introduce a new paradigm for improving Hamiltonian simulation and reducing the cost of ground state problems based on ideas recently developed for classical chemistry simulations. The key idea is that one can find efficient ways to reduce resources needed by quantum algorithms by making use of two key pieces of information: the Hamiltonian operator and an approximate ground state wavefunction. We refer to our algorithm as the self-consistent quantum iteratively sparsified Hamiltonian (SQuISH). By performing our scheme iteratively, one can drive SQuISH to create an accurate wavefunction using a truncated, resource-efficient Hamiltonian. By utilizing this more compact Hamiltonian, our algorithm provides an approach to reduce the gate complexity of ground state calculations on quantum hardware. As proof of principle, we implement SQuISH using configuration interaction for small molecules and coupled cluster for larger systems. Through our combination of approaches, we demonstrate how it performs on a range of systems, the largest of which would require more than 200 qubits to run on quantum hardware.

Diana Chamaki↗
NASA NTRS1998

Nested Quantum Search and NP-Complete Problem

A quantum algorithm is known that solves an unstructured search problem in a number of iterations of order square-root of d, where d is the dimension of the search space, whereas any classical algorithm scales as O(d).

NP-complete problems quantum search algorithm tree↗