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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Towards large-scale quantum optimization solvers with few qubits

Quantum computers hold the promise of more efficient combinatorial optimization solvers, which could be game-changing for a broad range of applications. However, a bottleneck for materializing such advantages is that, in order to challenge classical algorithms in practice, mainstream approaches require a number of qubits prohibitively large for near-term hardware. Here we introduce a variational solver for MaxCut problems over $m={{\mathcal{O}}}({n}^{k})$ binary variables using only n qubits, with tunable k > 1. The number of parameters and circuit depth display mild linear and sublinear scalings in m , respectively. Moreover, we analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature. Altogether, this leads to high quantum-solver performances. For instance, for m = 7000, numerical simulations produce solutions competitive in quality with state-of-the-art classical solvers. In turn, for m = 2000, experiments with n = 17 trapped-ion qubits feature MaxCut approximation ratios estimated to be beyond the hardness threshold 0.941. Our findings offer an interesting heuristics for quantum-inspired solvers as well as a promising route towards solving commercially-relevant problems on near-term quantum devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

A fully non-linear multi-species Fokker–Planck–Landau collision operator for simulation of fusion plasma

Fusion edge plasmas can be far from thermal equilibrium and require the use of a non-linear collision operator for accurate numerical simulations. In this article, the non-linear single-species Fokker–Planck–Landau collision operator developed by Yoon and Chang (2014) [9] is generalized to include multiple particle species. The finite volume discretization used in this work naturally yields exact conservation of mass, momentum, and energy. The implementation of this new non-linear Fokker–Planck–Landau operator in the gyrokinetic particle-in-cell codes XGC1 and XGCa is described and results of a verification study are discussed. Finally, the numerical techniques that make our non-linear collision operator viable on high-performance computing systems are described, including specialized load balancing algorithms and nested OpenMP parallelization. The collision operator's good weak and strong scaling behavior are shown.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Acoustic logic gates and Boolean operation based on self-collimating acoustic beams

The reveal of self-collimation effect in two-dimensional (2D) photonic or acoustic crystals has opened up possibilities for signal manipulation. In this paper, we have proposed acoustic logic gates based on the linear interference of self-collimated beams in 2D sonic crystals (SCs) with line-defects. The line defects on the diagonal of the 2D square SCs are actually functioning as a 3 dB splitter. By adjusting the phase difference between two input signals, the basic Boolean logic functions such as XOR, OR, AND, and NOT are achieved both theoretically and experimentally. Due to the non-diffracting property of self-collimation beams, more complex Boolean logic and algorithms such as NAND, NOR, and XNOR can be realized by cascading the basic logic gates. The achievement of acoustic logic gates and Boolean operation provides a promising approach for acoustic signal computing and manipulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Heel effect adaptive flat field correction of digital x-ray detectors

Purpose: Anode heel effect renders large-scale background nonuniformities in digital radiographs. Conventional offset/gain calibration is performed at mono source-to-image distance (SID), and disregards the SID-dependent characteristic of heel effect. It results in a residual nonuniform background in the corrected radiographs when the SID settings for calibration and correction differ. In this work, the authors develop a robust and efficient computational method for digital x-ray detector gain correction adapted to SID-variant heel effect, without resorting to physical filters, phantoms, complicated heel effect models, or multiple-SID calibration and interpolation.Methods: The authors present the Duo-SID projection correction method. In our approach, conventional offset/gain calibrations are performed only twice, at the minimum and maximum SIDs of the system in typical clinical use. A fast iterative separation algorithm is devised to extract the detector gain and basis heel patterns from the min/max SID calibrations. The resultant detector gain is independent of SID, while the basis heel patterns are parameterized by the min- and max-SID. The heel pattern at any SID is obtained from the min-SID basis heel pattern via projection imaging principles. The system gain desired at a specific acquisition SID is then constructed using the projected heel pattern and detector gain map.Results: The method was evaluated for flat field and anatomical phantom image corrections. It demonstrated promising improvements over interpolation and conventional gain calibration/correction methods, lowering their correction errors by approximately 70% and 80%, respectively. The separation algorithm was able to extract the detector gain and heel patterns with less than 2% error, and the Duo-SID corrected images showed perceptually appealing uniform background across the detector.Conclusions: The Duo-SID correction method has substantially improved on conventional offset/gain corrections for digital x-ray imaging in an SID-variant environment. The technique is relatively simple, and can be easily incorporated into multiple-point gain calibration/correction techniques. It offers a potentially valuable tool for preprocessing digital x-ray images to boost image quality of mammography, chest and cardiac radiography, as well as automated computer aided diagnostic radiology.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2025

Dissipative ground state preparation in ab initio electronic structure theory

Dissipative engineering is a powerful tool for quantum state preparation, and has drawn significant attention in quantum algorithms and quantum many-body physics in recent years. In this work, we introduce a novel approach using the Lindblad dynamics to efficiently prepare the ground state for general ab initio electronic structure problems on quantum computers, without variational parameters. These problems often involve Hamiltonians that lack geometric locality or sparsity structures, which we address by proposing two generic types of jump operators for the Lindblad dynamics. Type-I jump operators break the particle number symmetry and should be simulated in the Fock space. Type-II jump operators preserves the particle number symmetry and can be simulated more efficiently in the full configuration interaction space. For both types of jump operators, we prove that in a simplified Hartree-Fock framework, the spectral gap of our Lindbladian is lower bounded by a universal constant. For physical observables such as energy and reduced density matrices, the convergence rate of our Lindblad dynamics with Type-I jump operators remains universal, while the convergence rate with Type-II jump operators only depends on coarse grained information such as the number of orbitals and the number of electrons. To validate our approach, we employ a Monte Carlo trajectory-based algorithm for simulating the Lindblad dynamics for full ab initio Hamiltonians, demonstrating its effectiveness on molecular systems amenable to exact wavefunction treatment.

Quantum chemistry↗
DOE OSTI2021

When and why PINNs fail to train: A neural tangent kernel perspective

Physics-informed neural networks (PINNs) have lately received great attention thanks to their flexibility in tackling a wide range of forward and inverse problems involving partial differential equations. However, despite their noticeable empirical success, little is known about how such constrained neural networks behave during their training via gradient descent. More importantly, even less is known about why such models sometimes fail to train at all. Here in this work, we aim to investigate these questions through the lens of the Neural Tangent Kernel (NTK); a kernel that captures the behavior of fully-connected neural networks in the infinite width limit during training via gradient descent. Specifically, we derive the NTK of PINNs and prove that, under appropriate conditions, it converges to a deterministic kernel that stays constant during training in the infinite-width limit. This allows us to analyze the training dynamics of PINNs through the lens of their limiting NTK and find a remarkable discrepancy in the convergence rate of the different loss components contributing to the total training error. To address this fundamental pathology, we propose a novel gradient descent algorithm that utilizes the eigenvalues of the NTK to adaptively calibrate the convergence rate of the total training error. Finally, we perform a series of numerical experiments to verify the correctness of our theory and the practical effectiveness of the proposed algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

Analytic treatment of source photon emission times to reduce noise in implicit Monte Carlo calculations

Statistical uncertainty is inherent to any Monte Carlo simulation of radiation transport problems. In space-angle-frequency independent radiative transfer calculations, the uncertainty in the solution is entirely due to random sampling of source photon emission times. We have developed a modification to the Implicit Monte Carlo algorithm that eliminates noise due to sampling of the emission time of source photons. In problems that are independent of space, angle, and energy, the new algorithm generates a smooth solution, while a standard implicit Monte Carlo solution is noisy. For space- and angle-dependent problems, the new algorithm exhibits reduced noise relative to standard implicit Monte Carlo in some cases, and comparable noise in all other cases. In conclusion, the improvements are limited to short time scales; over long time scales, noise due to random sampling of spatial and angular variables tends to dominate the noise reduction from the new algorithm.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A quantum encryption design featuring confusion, diffusion, and mode of operation

Abstract Quantum cryptography—the application of quantum information processing and quantum computing techniques to cryptography has been extensively investigated. Two major directions of quantum cryptography are quantum key distribution (QKD) and quantum encryption, with the former focusing on secure key distribution and the latter focusing on encryption using quantum algorithms. In contrast to the success of the QKD, the development of quantum encryption algorithms is limited to designs of mostly one-time pads (OTP) that are unsuitable for most communication needs. In this work we propose a non-OTP quantum encryption design utilizing a quantum state creation process to encrypt messages. As essentially a non-OTP quantum block cipher the method stands out against existing methods with the following features: 1. complex key-ciphertext relation (i.e. confusion) and complex plaintext-ciphertext relation (i.e. diffusion); 2. mode of operation design for practical encryption on multiple blocks. These features provide key reusability and protection against eavesdropping and standard cryptanalytic attacks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

A digitally reconstructed radiograph algorithm calculated from first principles

Purpose: To develop an algorithm for computing realistic digitally reconstructed radiographs (DRRs) that match real cone-beam CT (CBCT) projections with no artificial adjustments. Methods: The authors used measured attenuation data from cone-beam CT projection radiographs of different materials to obtain a function to convert CT number to linear attenuation coefficient (LAC). The effects of scatter, beam hardening, and veiling glare were first removed from the attenuation data. Using this conversion function the authors calculated the line integral of LAC through a CT along rays connecting the radiation source and detector pixels with a ray-tracing algorithm, producing raw DRRs. The effects of scatter, beam hardening, and veiling glare were then included in the DRRs through postprocessing. Results: The authors compared actual CBCT projections to DRRs produced with all corrections (scatter, beam hardening, and veiling glare) and to uncorrected DRRs. Algorithm accuracy was assessed through visual comparison of projections and DRRs, pixel intensity comparisons, intensity histogram comparisons, and correlation plots of DRR-to-projection pixel intensities. In general, the fully corrected algorithm provided a small but nontrivial improvement in accuracy over the uncorrected algorithm. The authors also investigated both measurement- and computation-based methods for determining the beam hardening correction, and found the computation-based method to be superior, as it accounted for nonuniform bowtie filter thickness. The authors benchmarked the algorithm for speed and found that it produced DRRs in about 0.35 s for full detector and CT resolution at a ray step-size of 0.5 mm. Conclusions: The authors have demonstrated a DRR algorithm calculated from first principles that accounts for scatter, beam hardening, and veiling glare in order to produce accurate DRRs. The algorithm is computationally efficient, making it a good candidate for iterative CT reconstruction techniques that require a data fidelity term based on the matching of DRRs and projections.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Quantum Testbeds Stakeholder Workshop (QTSW) Report meeting purpose and agenda.

Quantum computing (QC) is a promising early-stage technology with the potential to provide scientific computing capabilities far beyond what is possible with even an Exascale computer in specific problems of relevance to the Office of Science. These include (but are not limited to) materials modeling, molecular dynamics, and quantum chromodynamics. However, commercial QC systems are not yet available and the technical maturity of current QC hardware, software, algorithms, and systems integration is woefully incomplete. Thus, there is a significant opportunity for DOE to define the technology building blocks, and solve the system integration issues to enable a revolutionary tool. Once realized, QC will have world changing impact on economic competitiveness, the scientific enterprise, and citizen well-being. Prior to this workshop, DOE / Office of Advanced Scientific Computing Research (ASCR) hosted a workshop in 2015 to explore QC scientific applications. The goal of that workshop was to assess the viability of QC technologies to meet the computational requirements in support of DOE’s science and energy mission and to identify the potential impact of these technologies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Generalized Quantum Signal Processing

Quantum signal processing (QSP) and quantum singular value transformation (QSVT) currently stand as the most efficient techniques for implementing functions of block-encoded matrices, a central task that lies at the heart of most prominent quantum algorithms. However, current QSP approaches face several challenges, such as the restrictions imposed on the family of achievable polynomials and the difficulty of calculating the required phase angles for specific transformations. In this paper, we present a generalized quantum signal processing (GQSP) approach, employing general SU(2) rotations as our signal-processing operators, rather than relying solely on rotations in a single basis. Our approach lifts all practical restrictions on the family of achievable transformations, with the sole remaining condition being that | P | ≤ 1 , a restriction necessary due to the unitary nature of quantum computation. Furthermore, GQSP provides a straightforward recursive formula for determining the rotation angles needed to construct the polynomials in cases where P and Q are known. In cases where only P is known, we provide an efficient optimization algorithm capable of identifying in under a minute of GPU time, a corresponding Q for polynomials of degree on the order of 10 7 . We further illustrate GQSP simplifies QSP-based strategies for Hamiltonian simulation, offer an optimal solution to the ϵ -approximate fractional query problem that requires O ( ( 1 / δ ) + log ( 1 / ϵ ) ) queries to perform where O ( 1 / δ ) is a proved lower bound, and introduces novel approaches for implementing bosonic operators. Moreover, we propose a novel framework for the implementation of normal matrices, demonstrating its applicability through synthesis of diagonal matrices, as well as the development of a new algorithm for convolution through synthesis of circulant matrices using only O ( d log N + log 2 N ) 1 and 2-qubit gates for a filter of lengths d . Published by the American Physical Society 2024

Motlagh, Danial↗
DOE OSTI2023

Q-BEEP: Quantum Bayesian Error Mitigation Employing Poisson Modeling over the Hamming Spectrum

Quantum computing technology has grown rapidly in recent years, with new technologies being explored, error rates being reduced, and quantum processor’s qubit capacity growing. However, near-term quantum algorithms are still unable to be induced without compounding consequential levels of noise, leading to non-trivial erroneous results. Quantum Error Correction (in-situ error mitigation) and Quantum Error Mitigation (post-induction error mitigation) are promising fields of research within the quantum algorithm scene, aiming to alleviate quantum errors, increasing the overall fidelity and hence the overall quality of circuit induction. Earlier this year, a pioneering work, namely HAMMER, published in ASPLOS-22 demonstrated the existence of a latent structure regarding post-circuit induction errors when mapping to the Hamming spectrum. However, they intuitively assumed that errors occur in local clusters, and that at higher average Hamming distances this structure falls away. In this work, we show that such a correlation structure is not only local but extends certain non-local clustering patterns which can be precisely described by a Poisson distribution model taking the input circuit, the device run time status (i.e., calibration statistics) and qubit topology into consideration. Using this quantum error characterizing model, we developed an iterative algorithm over the generated Bayesian network state-graph for post-induction error mitigation. Thanks to more precise modeling of the error distribution latent structure and the new iterative method, our Q-Beep approach provides state of the art performance and can boost circuit execution fidelity by up to 234.6% on Bernstein-Vazirani circuits and on average 71.0% on QAOA solution quality, using 16 practical IBMQ quantum processors. For other benchmarks such as those in QASMBench, the fidelity improvement is up to 17.8%. Q-Beep is a light-weight post-processing technique that can be performed offline and remotely, making it a useful tool for quantum vendors to integrate and provide more reliable circuit induction results.

Stein, Samuel A.↗
DOE OSTI2024

Scaling whole-chip QAOA for higher-order ising spin glass models on heavy-hex graphs

Abstract We show that the quantum approximate optimization algorithm (QAOA) for higher-order, random coefficient, heavy-hex compatible spin glass Ising models has strong parameter concentration across problem sizes from 16 up to 127 qubits for p = 1 up to p = 5, which allows for computationally efficient parameter transfer of QAOA angles. Matrix product state (MPS) simulation is used to compute noise-free QAOA performance. Hardware-compatible short-depth QAOA circuits are executed on ensembles of 100 higher-order Ising models on noisy IBM quantum superconducting processors with 16, 27, and 127 qubits using QAOA angles learned from a single 16-qubit instance using the JuliQAOA tool. We show that the best quantum processors find lower energy solutions up to p = 2 or p = 3, and find mean energies that are about a factor of two off from the noise-free distribution. We show that p = 1 QAOA energy landscapes remain very similar as the problem size increases using NISQ hardware gridsearches with up to a 414 qubit processor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Data decomposition of Monte Carlo particle transport simulations via tally servers

An algorithm for decomposing large tally data in Monte Carlo particle transport simulations is developed, analyzed, and implemented in a continuous-energy Monte Carlo code, OpenMC. The algorithm is based on a non-overlapping decomposition of compute nodes into tracking processors and tally servers. The former are used to simulate the movement of particles through the domain while the latter continuously receive and update tally data. A performance model for this approach is developed, suggesting that, for a range of parameters relevant to LWR analysis, the tally server algorithm should perform with minimal overhead on contemporary supercomputers. An implementation of the algorithm in OpenMC is then tested on the Intrepid and Titan supercomputers, supporting the key predictions of the model over a wide range of parameters. We thus conclude that the tally server algorithm is a successful approach to circumventing classical on-node memory constraints en route to unprecedentedly detailed Monte Carlo reactor simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Resource-Optimized Fermionic Local-Hamiltonian Simulation on a Quantum Computer for Quantum Chemistry

The ability to simulate a fermionic system on a quantum computer is expected to revolutionize chemical engineering, materials design, nuclear physics, to name a few. Thus, optimizing the simulation circuits is of significance in harnessing the power of quantum computers. Here, we address this problem in two aspects. In the fault-tolerant regime, we optimize the R z and T gate counts along with the ancilla qubit counts required, assuming the use of a product-formula algorithm for implementation. We obtain a savings ratio of two in the gate counts and a savings ratio of eleven in the number of ancilla qubits required over the state of the art. In the pre-fault tolerant regime, we optimize the two-qubit gate counts, assuming the use of the variational quantum eigensolver (VQE) approach. Specific to the latter, we present a framework that enables bootstrapping the VQE progression towards the convergence of the ground-state energy of the fermionic system. This framework, based on perturbation theory, is capable of improving the energy estimate at each cycle of the VQE progression, by about a factor of three closer to the known ground-state energy compared to the standard VQE approach in the test-bed, classically-accessible system of the water molecule. The improved energy estimate in turn results in a commensurate level of savings of quantum resources, such as the number of qubits and quantum gates, required to be within a pre-specified tolerance from the known ground-state energy. We also explore a suite of generalized transformations of fermion to qubit operators and show that resource-requirement savings of up to more than 20 % , in small instances, is possible.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

A projected preconditioned conjugate gradient algorithm for computing many extreme eigenpairs of a Hermitian matrix

We present an iterative algorithm for computing an invariant subspace associated with the algebraically smallest eigenvalues of a large sparse or structured Hermitian matrix A. We are interested in the case in which the dimension of the invariant subspace is large (e.g., over several hundreds or thousands) even though it may still be small relative to the dimension of A. These problems arise from, for example, density functional theory (DFT) based electronic structure calculations for complex materials. The key feature of our algorithm is that it performs fewer Rayleigh–Ritz calculations compared to existing algorithms such as the locally optimal block preconditioned conjugate gradient or the Davidson algorithm. It is a block algorithm, and hence can take advantage of efficient BLAS3 operations and be implemented with multiple levels of concurrency. We discuss a number of practical issues that must be addressed in order to implement the algorithm efficiently on a high performance computer.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗