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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Clifford Circuit-Based Heuristic Optimization of Fermion-To-Qubit Mappings

Simulation of interacting Fermionic Hamiltonians is one of the most promising applications of quantum computers. However, the feasibility of analyzing Fermionic systems with a quantum computer hinges on the efficiency of Fermion-to-qubit mappings that encode nonlocal Fermionic degrees of freedom in local qubit degrees of freedom. While recent studies have highlighted the importance of designing Fermion-to-qubit mappings that are tailored to specific problem Hamiltonians, the methods proposed so far either are restricted to a narrow class of mappings or they use computationally expensive and unscalable brute-force search algorithms. Here, in this work, we address this challenge by designing a heuristic numerical optimization framework for Fermion-to-qubit mappings. To this end, we first translate the Fermion-to-qubit mapping problem to a Clifford circuit optimization problem and then use simulated annealing to optimize the average Pauli weight of the problem Hamiltonian. For all Fermionic Hamiltonians we have considered, the numerically optimized mappings outperform their conventional counterparts, including ternary-tree-based mappings that are known to be optimal for single creation and annihilation operators. We find that our optimized mappings yield between 15% and 40% improvements on the average Pauli weight when the simulation Hamiltonian has an intermediate level of complexity. Most remarkably, the optimized mappings improve the average Pauli weight for 6 × 6 nearest-neighbor hopping and Hubbard models by more than 40% and 20%, respectively. Surprisingly, we also find specific interaction Hamiltonians for which the optimized mapping outperforms any ternary-tree-based mapping. Our results establish heuristic numerical optimization as an effective method for obtaining mappings tailored for specific Fermionic Hamiltonian.

Hamiltonians↗
DOE OSTI2025

Lanczos Algorithm, the Transfer Matrix, and the Signal-to-Noise Problem

This Letter introduces a method for determining the energy spectrum of lattice quantum chromodynamics by applying the Lanczos algorithm to the transfer matrix and using a bootstrap generalization of the Cullum-Willoughby method to filter out spurious eigenvalues. Proof-of-principle analyses of the simple harmonic oscillator and the lattice quantum chromodynamics proton mass demonstrate that this method provides faster ground-state convergence than the “effective mass,” which is related to the power-iteration algorithm. Lanczos provides more accurate energy estimates than multistate fits to correlation functions with small imaginary times while achieving comparable statistical precision. Two-sided error bounds are computed for Lanczos results and guarantee that excited-state effects cannot shift Lanczos results far outside their statistical uncertainties.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Quantum Solvers for Plane-Wave Hamiltonians: Abridging Virtual Spaces Through the Optimization of Pairwise Correlations

For many-body methods such as MCSCF and CASSCF, in which the number of one-electron orbitals is optimized and independent of the basis set used, there are no problems with using plane-wave basis sets. However, for methods currently used in quantum computing such as select configuration interaction (CI) and coupled cluster (CC) methods, it is necessary to have a virtual space that is able to capture a significant amount of electron-electron correlation in the system. The virtual orbitals in a pseudopotential plane-wave Hartree–Fock calculation, because of Coulomb repulsion, are often scattering states that interact very weakly with the filled orbitals. As a result, very little correlation energy is captured from them. The use of virtual spaces derived from the one-electron operators has also been tried, and while some correlations are captured, the amount is quite low. To overcome these limitations, we have been developing new classes of algorithms to define virtual spaces by optimizing orbitals from small pairwise CI Hamiltonians, which we term as correlation optimized virtual orbitals with the abbreviation COVOs. With these procedures, we have been able to derive virtual spaces, containing only a few orbitals, which are able to capture a significant amount of correlation. The focus in this manuscript is on using these derived basis sets to target full CI (FCI) quality results for H2 on near-term quantum computers. However, the initial results for this approach were promising. We were able to obtain good agreement with FCI/cc-pVTZ results for this system with just 4 virtual orbitals, using both FCI and quantum simulations. The quality of the results using COVOs suggests that it may be possible to use them in other many-body approaches, including coupled cluster and Møller–Plesset perturbation theories, and open up the door to many-body calculations for pseudopotential plane-wave basis set methods.

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

Indexed improvements for real-time trotter evolution of a (1 + 1) field theory using NISQ quantum computers

Today's quantum computers offer the possibility of performing real-time calculations for quantum field theory scattering processes motivated by high energy physics. In order to follow the successful roadmap which has been established for the calculation of static properties at Euclidean time, it is crucial to develop new algorithmic methods to deal with the limitations of current noisy intermediate-scale quantum (NISQ) devices and to establish quantitative measures of the progress made with different devices. In this paper, we report recent progress in these directions. We show that nonlinear aspects of the trotter errors allow us to take much larger step then suggested by low-order analysis. This is crucial to reach physically relevant time scales with today's NISQ technology. We propose to use an index averaging absolute values of the difference between the accurately calculated trotter evolution of site occupations and their actual measurements on NISQ machines (G index) as a measure to compare results that have been obtained from different hardware platforms. Using the transverse Ising model in one spatial dimension with four sites we apply this metric across several hardware platforms. We study the results including readout mitigation and Richardson extrapolations and show that the mitigated measurements are very effective based on the analysis of the trotter step size modifications. Furthermore, we discuss how this advance in the trotter step size procedures can improve quantum computing physics scattering results and how this technical advance can be applied to other machines and noise mitigation methods.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

PySpawn: Software for Nonadiabatic Quantum Molecular Dynamics

The ab initio multiple spawning (AIMS) method enables nonadiabatic quantum molecular dynamics simulations in an arbitrary number of dimensions, with potential energy surfaces provided by electronic structure calculations performed on-the-fly. However, the intricacy of the AIMS algorithm complicates software development, deployment on modern shared computer resources, and post-simulation data analysis. PySpawn is a nonadiabatic molecular dynamics software package that addresses these issues. Here, the program is designed to be easily interfaced with electronic structure software, and an interface to the TeraChem software package is described here. PySpawn introduces a task-based reorganization of the AIMS algorithm, allowing fine-grained restart capability and setting the stage for efficient parallelization in a future release. PySpawn includes a user-friendly and interactive Python analysis module that will enable novice users to painlessly adopt AIMS. As a demonstration of PySpawn’s simulation capability and analysis module, we report complete active space self-consistent field–based AIMS simulations of the 1,2- dithienyl-1,2-dicyanoethene molecule, a promising molecular photoswitch.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Energy–Geometry Dependency of Molecular Structures: A Multistep Machine Learning Approach

There is growing interest in estimating quantum observables while circumventing expensive computational overhead for facile in silico materials screening. Machine learning (ML) methods are implemented to perform such calculations in shorter times. In this paper, we introduce a multistep method based on machine learning algorithms to estimate total energy on the basis of spatial coordinates and charges for various chemical structures, including organic molecules, inorganic molecules, and ions. This method quickly calculates total energy with 0.76 au in root-mean-square error (RMSE) and 1.5% in mean absolute percent error (MAPE) when tested on a database of optimized and unoptimized structures. Using similar molecular representations, experimental thermochemical properties were estimated, with MAPE as low as 6% and RMSE of 8 cal/mol·K for heat capacity in a 10-fold cross-validation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Quantum pixel representations and compression for N-dimensional images

Abstract We introduce a novel and uniform framework for quantum pixel representations that overarches many of the most popular representations proposed in the recent literature, such as (I)FRQI, (I)NEQR, MCRQI, and (I)NCQI. The proposed QPIXL framework results in more efficient circuit implementations and significantly reduces the gate complexity for all considered quantum pixel representations. Our method scales linearly in the number of pixels and does not use ancilla qubits. Furthermore, the circuits only consist of $$R_y$$ R y gates and $$\text {CNOT}$$ CNOT gates making them practical in the NISQ era. Additionally, we propose a circuit and image compression algorithm that is shown to be highly effective, being able to reduce the necessary gates to prepare an FRQI state for example scientific images by up to 90% without sacrificing image quality. Our algorithms are made publicly available as part of , a Quantum Image Pixel Library.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Self-learning Monte Carlo method and cumulative update in fermion systems

In this study, we develop the self-learning Monte Carlo (SLMC) method, a general-purpose numerical method recently introduced to simulate many-body systems, for studying interacting fermion systems. Our method uses a highly efficient update algorithm, which we design and dub “cumulative update”, to generate new candidate configurations in the Markov chain based on a self-learned bosonic effective model. From a general analysis and a numerical study of the double exchange model as an example, we find that the SLMC with cumulative update drastically reduces the computational cost of the simulation, while remaining statistically exact. Remarkably, its computational complexity is far less than the conventional algorithm with local updates.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Neural Networks and Graph Algorithms with Next-Generation Processors

The use of graphical processors for distributed computation revolutionized the field of high performance scientific computing. As the Moore's Law era of computing draws to a close, the development of non-Von Neumann systems: neuromorphic processing units, and quantum annealers; again are redefining new territory for computational methods. While these technologies are still in their nascent stages, we discuss their potential to advance computing in two domains: machine learning, and solving constraint satisfaction problems. Each of these processors utilize fundamentally different theoretical models of computation. This raises questions about how to best use them in the design and implementation of applications. While many processors are being developed with a specific domain target, the ubiquity of spin-glass models and neural networks provides an avenue for multi-functional applications. This provides hints at the future infrastructure needed to integrate many next-generation processing units into conventional high-performance computing systems.

Hamilton, Kathleen↗
NASA NTRSDate not supplied

Quantum-Compatible Variational Segmentation for Image-to-Image Wildfire Detection Using Satellite Data

Wildfire occurrences have been increasing for the past decade, leaving devastating traces across the world. In the recent efforts, remote sensing and airborne missions have been utilized to better understand and manage wildfires. This has resulted in an exponential increase in volume of remote sensing data, which has pushed the need for intelligent automation of data extraction for wildfire studies. Machine learning offers accurate automation in detecting such natural anomalies and enable decision-makers to take actions in a timely manner. Recent advances in machine learning algorithms, namely probabilistic generative methods, allow researchers and decisionmakers to step beyond detection and study “what-if” scenarios for wildfire occurrences. Additionally, they offer better imitations to the stochastic behavior of nature, and wildfire events. However, optimizing the performance of these probabilistic generative models is a computationally expensive process, specially using digital computers. On the other hand, quantum computers have recently shown a promise to reduce computationally costly training of such models and provide performance improvements. There is a body of research investigating the potential for improved machine learning methods in which key operations are performed on a quantum computer. In this study, we propose a probabilistic image-toimage segmentation approach combining a very well-known segmentation method, U-NET, with a Conditional Variational Auto-Encoder (CVAE) to not only detect wildfires but also describe the stochasticity of the phenomenon and be capable of running “what-if” scenarios. Our proposed model is compatible with training on quantum computers, which results in a quantum-assisted image-to-image segmentation approach and can be used to benchmark the potential benefit of quantum computing over the classical one.

quantum↗
DOE OSTI2024

HHL algorithm with mapping function and enhanced sampling for model predictive control in microgrids

Here, this paper presents a refined quantum Harrow Hassidim Lloyd (HHL) algorithm for microgrid control. The first novelty of the developed method is that a mapping shift function enables the original HHL algorithm to handle general linear equations with non-singular and indefinite matrix. Second, a method of Matrix Extension for Amplifying Sampling Probabilities of Intended Solution (ME-ASPI) is proposed to design the reformulated linear algebraic equations, allowing for improved sampling efficiency of the quantum tomography in the refined HHL algorithm. Then, we applied the method to solve the model predictive control (MPC) problem in nonlinear dynamical microgrids. Specifically, with the ME-ASPI method, the refined HHL algorithm can effectively obtain the intended partial optimal control inputs for MPC. The optimization of quadratic programming problem in each time step of MPC is transformed into a linear system problem, which is addressed by the proposed quantum solver through using only partial information, with the time complexity improved from $\mathscr{O}(\mathscr{N}^{2.37286})$ classically to $\mathscr{O}(\mathscr{N}^{2} log \mathscr{N}$ x $p$ log $p)$ in quantum. Numerical examples have validated the effectiveness of the refined HHL algorithm with the proposed mapping function and the ME-ASPI method. By leveraging quantum properties, the proposed method provides a hybrid quantum–classical framework for microgrid control. This generic method can also potentially tackle many other challenges in analyzing and controlling general complex engineered systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth

Matrix chain multiplication -- computing $\mathcal{W} = M^{(0)}\cdots M^{(K-1)}$ where $M^{(k)} \in \mathbb{R}^{P_k \times P_{k+1}}$-- arises in scientific computing, machine learning, and graph analysis. Despite the importance of this problem, for chains of distinct matrices, the classical number of operations grows linearly with the chain length $K$ and polynomially in the matrix dimensions. We present \emph{Two-Tower Matrix Multiplication}, a quantum subroutine that encodes the product $\mathcal{W}$ of the $K$ matrices into a quantum state in circuit depth $\mathcal{O}(\max_{k} \mathrm{polylog} (P_k P_{k+1}))$, which is independent of~$K$ within the QRAM-based state-preparation model, whereas the qubit count is $\mathcal{O}\bigl(\sum_{k} \log P_k \bigr)$; the total gate count remains linear in $K$, so the gain is in the circuit depth. The construction interleaves state-preparation operators across two layers; within each layer, all operators act on disjoint registers and execute in parallel. This subroutine can be specialized for the chain-vector case, which computes the product of $K-1$ matrices applied to a vector. We prove the correctness of the subroutine for all $K$ and provide two implementations using the Qiskit and QCLAB frameworks. The subroutine is applicable to any downstream quantum algorithm that operates on a matrix encoded in the statevector, including norm estimation, graph-matrix powers, linear system solving, and quantum machine learning kernels.

Antonioli, Giacomo [Pisa U.] (ORCID:00090000668703↗
DOE OSTI2021

Optimal Protocols in Quantum Annealing and Quantum Approximate Optimization Algorithm Problems

Quantum annealing (QA) and the quantum approximate optimization algorithm (QAOA) are two special cases of the following control problem: apply a combination of two Hamiltonians to minimize the energy of a quantum state. Which is more effective has remained unclear. Here we analytically apply the framework of optimal control theory to show that generically, given a fixed amount of time, the optimal procedure has the pulsed (or “bang-bang”) structure of QAOA at the beginning and end but can have a smooth annealing structure in between. This is in contrast to previous works which have suggested that bang-bang (i.e., QAOA) protocols are ideal. To support this theoretical work, we carry out simulations of various transverse field Ising models, demonstrating that bang-anneal-bang protocols are more common. Futher, the general features identified here provide guideposts for the nascent experimental implementations of quantum optimization algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Improved ALE mesh velocities for complex flows

A key choice in the development of arbitrary Lagrangian-Eulerian solution algorithms is how to move the computational mesh. The most common approaches are smoothing and relaxation techniques, or to compute a mesh velocity field that produces smooth mesh displacements. We present a method in which the mesh velocity is specified by the irrotational component of the fluid velocity as computed from a Helmholtz decomposition, and excess compression of mesh cells is treated through a noniterative, local spring-force model. This approach allows distinct and separate control over rotational and translational modes. In conclusion, the utility of the new mesh motion algorithm is demonstrated on a number of 3D test problems, including problems that involve both shocks and significant amounts of vorticity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Orchestrated trios: compiling for efficient communication in Quantum programs with 3-Qubit gates

Current quantum computers are especially error prone and require high levels of optimization to reduce operation counts and maximize the probability the compiled program will succeed. These computers only support operations decomposed into one- and two-qubit gates and only two-qubit gates between physically connected pairs of qubits. Typical compilers first decompose operations, then route data to connected qubits. We propose a new compiler structure, Orchestrated Trios, that first decomposes to the three-qubit Toffoli, routes the inputs of the higher-level Toffoli operations to groups of nearby qubits, then finishes decomposition to hardware-supported gates. This significantly reduces communication overhead by giving the routing pass access to the higher-level structure of the circuit instead of discarding it. A second benefit is the ability to now select an architecture-tuned Toffoli decomposition such as the 8-CNOT Toffoli for the specific hardware qubits now known after the routing pass. Furthermore, we perform real experiments on IBM Johannesburg showing an average 35% decrease in two-qubit gate count and 23% increase in success rate of a single Toffoli over Qiskit. We additionally compile many near-term benchmark algorithms showing an average 344% increase in (or 4.44x) simulated success rate on the Johannesburg architecture and compare with other architecture types.

compiler↗
DOE OSTI2021

MLPF: efficient machine-learned particle-flow reconstruction using graph neural networks

In general-purpose particle detectors, the particle-flow algorithm may be used to reconstruct a comprehensive particle-level view of the event by combining information from the calorimeters and the trackers, significantly improving the detector resolution for jets and the missing transverse momentum. In view of the planned high-luminosity upgrade of the CERN Large Hadron Collider (LHC), it is necessary to revisit existing reconstruction algorithms and ensure that both the physics and computational performance are sufficient in an environment with many simultaneous proton–proton interactions (pileup). Machine learning may offer a prospect for computationally efficient event reconstruction that is well-suited to heterogeneous computing platforms, while significantly improving the reconstruction quality over rule-based algorithms for granular detectors. We introduce MLPF, a novel, end-to-end trainable, machine-learned particle-flow algorithm based on parallelizable, computationally efficient, and scalable graph neural network optimized using a multi-task objective on simulated events. We report the physics and computational performance of the MLPF algorithm on a Monte Carlo dataset of top quark–antiquark pairs produced in proton–proton collisions in conditions similar to those expected for the high-luminosity LHC. The MLPF algorithm improves the physics response with respect to a rule-based benchmark algorithm and demonstrates computationally scalable particle-flow reconstruction in a high-pileup environment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Quantum Monte Carlo Calculations of Chemical Binding and Reactions

The auxiliary field quantum Monte Carlo method developed by the PIs has been shown to provide the most accurate description of strongly correlated electronic systems, from molecules to solids. Unlike other explicitly many‐body approaches, the quantum Monte Carlo method scales as a low order polynomial of systems size, similar to mean‐field methods such as density functional theory. However, the auxiliary field quantum Monte Carlo algorithm is significantly more expensive than traditional density functional calculations. This creates a bottleneck for applications to extended systems, such as large molecules and solids. One principal objective of this proposal was to develop new auxiliary field quantum Monte Carlo computational strategies to achieve improved scaling with system size, using downfolding and localization schemes, without sacrificing the predictive power of the calculations. A second goal is to extend the reach of auxiliary field quantum Monte Carlo to calculate excited states. This final report summarizes what has been achieved during the course the project toward these goals.

97 MATHEMATICS AND COMPUTING↗