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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

A graphics processing unit accelerated sparse direct solver and preconditioner with block low rank compression

We present the GPU implementation efforts and challenges of the sparse solver package STRUMPACK. The code is made publicly available on github with a permissive BSD license. STRUMPACK implements an approximate multifrontal solver, a sparse LU factorization which makes use of compression methods to accelerate time to solution and reduce memory usage. Multiple compression schemes based on rank-structured and hierarchical matrix approximations are supported, including hierarchically semi-separable, hierarchically off-diagonal butterfly, and block low rank. Here, in this paper, we present the GPU implementation of the block low rank (BLR) compression method within a multifrontal solver. Our GPU implementation relies on highly optimized vendor libraries such as cuBLAS and cuSOLVER for NVIDIA GPUs, rocBLAS and rocSOLVER for AMD GPUs and the Intel oneAPI Math Kernel Library (oneMKL) for Intel GPUs. Additionally, we rely on external open source libraries such as SLATE (Software for Linear Algebra Targeting Exascale), MAGMA (Matrix Algebra on GPU and Multi-core Architectures), and KBLAS (KAUST BLAS). SLATE is used as a GPU-capable ScaLAPACK replacement. From MAGMA we use variable sized batched dense linear algebra operations such as GEMM, TRSM and LU with partial pivoting. KBLAS provides efficient (batched) low rank matrix compression for NVIDIA GPUs using an adaptive randomized sampling scheme. The resulting sparse solver and preconditioner runs on NVIDIA, AMD and Intel GPUs. Interfaces are available from PETSc, Trilinos and MFEM, or the solver can be used directly in user code. We report results for a range of benchmark applications, using the Perlmutter system from NERSC, Frontier from ORNL, and Aurora from ALCF. For a high frequency wave equation on a regular mesh, using 32 Perlmutter compute nodes, the factorization phase of the exact GPU solver is about 6.5× faster compared to the CPU-only solver. The BLR-enabled GPU solver is about 13.8× faster than the CPU exact solver. For a collection of SuiteSparse matrices, the STRUMPACK exact factorization on a single GPU is on average 1.9× faster than NVIDIA’s cuDSS solver.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

LANSCE CCL Performance Limits

This report summarizes the performance limits of the LANSCE Coupled-Cavity Linac (CCL). These results are captured or summarized directly from the references cited. This report was written in support of the LANSCE Modernization Project (LAMP). Many factors contribute to the performance limits of the CCL accelerator system. One performance limit is set by the CCL mechanical structure and available cooling. Heating of the structure is ultimately linked to the operating RF duty factor of the CCL. Another performance limit is set by the maximum RF and beam duty factors that can be supported by the 805-MHz klystrons and associated HVDC power supplies. The RF and HVDC systems also set limits for the maximum peak beam current that can be accelerated in the CCL. And finally, a maximum beam current limit is set by the beam dynamics determined by the details of the CCL physics design (number of cells per CCL tank, accelerating gradients, magnetic focusing lattice, beam losses, etc.). This limit can be informed by both simulation results and beam measurement data, if available. A detailed explanation of each performance limit is given in the sections below. The results are summarized in the table below. In all cases, it is assumed that the CCL and the RF system are operating in their nominal beam production configuration – nominal magnet set points and nominal cavity fields, unless otherwise specified.

43 PARTICLE ACCELERATORS↗
DOE OSTI2016

The M358R variant of α{sub 1}-proteinase inhibitor inhibits coagulation factor VIIa

The naturally occurring M358R mutation of the plasma serpin α{sub 1}-proteinase inhibitor (API) changes both its cleavable reactive centre bond to Arg–Ser and the efficacy with which it inhibits different proteases, reducing the rate of inhibition of neutrophil elastase, and enhancing that of thrombin, factor XIa, and kallikrein, by several orders of magnitude. Although another plasma serpin with an Arg–Ser reactive centre, antithrombin (AT), has been shown to inhibit factor VIIa (FVIIa), no published data are available with respect to FVIIa inhibition by API M358R. Recombinant bacterially-expressed API M358R and plasma-derived AT were therefore compared using gel-based and kinetic assays of FVIIa integrity and activity. Under pseudo-first order conditions of excess serpin over protease, both AT and API M358R formed denaturation-resistant inhibitory complexes with FVIIa in reactions accelerated by TF; AT, but not API M358R, also required heparin for maximal activity. The second order rate constant for heparin-independent API M358R-mediated FVIIa inhibition was determined to be 7.8 ± 0.8 × 10{sup 2} M{sup −1}sec{sup −1}. We conclude that API M358R inhibits FVIIa by forming inhibitory complexes of the serpin type more rapidly than AT in the absence of heparin. The likely 20-fold excess of API M358R over AT in patient plasma during inflammation raises the possibility that it could contribute to the hemorrhagic tendencies manifested by rare individuals expressing this mutant serpin. - Highlights: • The inhibitory specificity of the serpin alpha-1-proteinase inhibitor (API) is sharply altered in the M358R variant. • API M358R forms denaturation-resistant complexes with coagulation factor VIIa at a rate accelerated by tissue factor but unaffected by heparin. • Complex formation was shown by gel-based assays and quantified kinetically by inhibition of FVIIa-dependent amidolysis.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

A Statistical Perspective on Highly Accelerated Testing

Highly accelerated life testing has been heavily promoted at Sandia (and elsewhere) as a means to rapidly identify product weaknesses caused by flaws in the product's design or manufacturing process. During product development, a small number of units are forced to fail at high stress. The failed units are then examined to determine the root causes of failure. The identification of the root causes of product failures exposed by highly accelerated life testing can instigate changes to the product's design and/or manufacturing process that result in a product with increased reliability. It is widely viewed that this qualitative use of highly accelerated life testing (often associated with the acronym HALT) can be useful. However, highly accelerated life testing has also been proposed as a quantitative means for "demonstrating" the reliability of a product where unreliability is associated with loss of margin via an identified and dominating failure mechanism. It is assumed that the dominant failure mechanism can be accelerated by changing the level of a stress factor that is assumed to be related to the dominant failure mode. In extreme cases, a minimal number of units (often from a pre-production lot) are subjected to a single highly accelerated stress relative to normal use. If no (or, sufficiently few) units fail at this high stress level, some might claim that a certain level of reliability has been demonstrated (relative to normal use conditions). Underlying this claim are assumptions regarding the level of knowledge associated with the relationship between the stress level and the probability of failure. The primary purpose of this document is to discuss (from a statistical perspective) the efficacy of using accelerated life testing protocols (and, in particular, "highly accelerated" protocols) to make quantitative inferences concerning the performance of a product (e.g., reliability) when in fact there is lack-of-knowledge and uncertainty concerning the assumed relationship between the stress level and performance. In addition, this document contains recommendations for conducting more informative accelerated tests.

42 ENGINEERING↗
DOE OSTI2015

The Sirt1 activator SRT1720 attenuates angiotensin II-induced atherosclerosis in apoE{sup −/−} mice through inhibiting vascular inflammatory response

Activation of the silent mating type information regulation 2 homolog 1 (SIRT1) has been shown consistent antiinflammatory function. However, little information is available on the function of SIRT1 during Angiotensin II (AngII)-induced atherosclerosis. Here we report atheroprotective effects of sirt1 activation in a model of AngII-accelerated atherosclerosis, characterized by suppression pro-inflammatory transcription factors Nuclear transcription factor (NF)-κB and Signal Transducers and Activators of Transcription. (STAT) signaling pathway, and atherosclerotic lesion macrophage content. In this model, administration of the SIRT1 agonist SRT1720 substantially attenuated AngII-accelerated atherosclerosis with decreasing blood pressure and inhibited NF-κB and STAT3 activation, which was associated with suppression of inflammatory factor and atherogenic gene expression in the artery. In vitro studies demonstrated similar changes in AngII-treated VSMCs and macrophages: SIRT1 activation inhibited the expression levels of proinflammatory factor. These studies uncover crucial proinflammatory mechanisms of AngII and highlight actions of SIRT1 activation to inhibit AngII signaling, which is atheroprotective. - Highlights: • SRT1720 reduced atherosclerotic lesion size in aortic arches and atherosclerotic lesion macrophage content. • SRT1720 could inhibit the phosphorylation of STAT3 and p65 phosphorylation and translocation. • SRT1720 could inhibit the expression of proinflammatory factor.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2022

FY2022 Status Report: Cold Spray for Canister SCC Mitigation and Repair

This progress report describes work performed during FY22 at Sandia National Laboratories (SNL) to assess the corrosion performance of cold spray coatings to enable optimization of cold spray for the purposes of mitigation and/or repair of potentially susceptible regions, corrosion, or stress corrosion cracking (SCC) in austenitic stainless steel for spent nuclear fuel (SNF) storage. Of particular concern is SCC, by which a through-wall crack could potentially form in a canister outer wall over time intervals that may be shorter than possible dry storage times. In FY21, initial corrosion explorations of cold spray coating were evaluated and in FY22, an expanded set of cold spray coatings with in-depth analysis of post-exposure accelerated testing was explored. Additionally, relevant atmospheric exposure testing was carried out and initial results are presented herein. The corrosion attack from the accelerated testing and more realistic atmospheric exposures environments were compared to identify potentially deleterious factors for corrosion as well as help to understand the applicability of accelerated testing for cold spray optimization. This initial analysis will help to enable optimization of the corrosion resistance cold spray, one of the more promising coating and repair techniques, for potential application in an SNF environment. Learnings from both are summarized, and implications and future work are presented in this report.

36 MATERIALS SCIENCE↗
NASA NTRS2008

Magnetohydrodynamic Effects in Propagating Relativistic Ejecta: Reverse Shock and Magnetic Acceleration

We solve the Riemann problem for the deceleration of arbitrarily magnetized relativistic ejecta injected into a static unmagnetized medium. We find that for the same initial Lorentz factor, the reverse shock becomes progressively weaker with increasing magnetization s (the Poynting-to-kinetic energy flux ratio), and the shock becomes a rarefaction wave when s exceeds a critical value, sc, defined by the balance between the magnetic pressure in the ejecta and the thermal pressure in the forward shock. In the rarefaction wave regime, we find that the rarefied region is accelerated to a Lorentz factor that is significantly larger than the initial value. This acceleration mechanism is due to the strong magnetic pressure in the ejecta.

Mizuno, Y.↗
DOE OSTI2021

An Upgrade Path for the Fermilab Accelerator Complex

The completion of the PIP-II project and its superconducting linear accelerator will provide up to 1.2 MW of beam power to the LBNF/DUNE facility for neutrino physics. It will also be able to produce high-power beams directly from the linac that can be used for lower-energy particle physics experiments as well, such as directing beam toward the Muon Campus at Fermilab for example. Any further significant upgrade of the beam power to DUNE, however, will be impeded by the limitations of the present Booster synchrotron at the facility. To increase the power to DUNE by a factor of two would require a new accelerator arrangement to feed the Main Injector that does not include the Booster. In what follows, a path toward upgrading the Fermilab accelerator complex to bring the beam power for DUNE to 2.4 MW is presented, using a new rapid-cycling synchrotron plus an energy upgrade to the PIP-II linac. The path includes the ability to instigate a new lower-energy, very high-power beam delivery system for experiments that can address much of the science program presented by the Booster Replacement Science Working Group. It also allows for the future possibility to go beyond 2.4 MW up to roughly 4 MW from the Main Injector.

43 PARTICLE ACCELERATORS↗
NASA NTRS1984

A review of turbulent-boundary-layer heat transfer research at Stanford, 1958-1983

For the past 25 years, there has existed in the Thermosciences Laboratory of the Mechanical Engineering Department of Stanford University a research program, primarily experimental, concerned with heat transfer through turbulent boundary layers. In the early phases of the program, the topics considered were the simple zero-pressure-gradient turbulent boundary layer with constant and with varying surface temperature, and the accelerated boundary layer. Later equilibrium boundary layers were considered along with factors affecting the boundary layer, taking into account transpired flows, flows with axial pressure gradients, transpiration, acceleration, deceleration, roughness, full-coverage film cooling, surface curvature, free convection, and mixed convection. A description is provided of the apparatus and techniques used, giving attention to the smooth plate rig, the rough plate rig, the full-coverage film cooling rig, the curvature rig, the concave wall rig, the mixed convection tunnel, and aspects of data reduction and uncertainty analysis.

Moffat, R. J.↗
DOE OSTI2014

SU-E-T-533: Evaluation of Dose Calculation Accuracy for Small Elongated Targets On the Edge Linac

Purpose: To evaluate output factors and dose calculation accuracy on a novel SRS linear accelerator, the Edge (Varian), for treatments of small, elongated targets using flattening filter free (FFF) beam. Methods: Total scatter/output factors (OF’s) for 24 elongated, small, high definition multi-leaf collimator (HDMLC)-defined fields were measured on the Edge machine using 6X FFF beam. 3 detectors were used in water tank: CC01 ion chamber (active volume 10cc), stereotactic photon diode (SFD) (active diameter 0.6mm, active thickness 0.06mm), Edge detector (active volume 0.0019cc). The 24 MLC apertures have widths ranging from 5 to 20mm and length/width ratio from 0.25 to 5. Readings were cross calibrated with CC04 at field size 3×3 cm. A beam model was developed using commissioning measurements for treatment planning in Eclipse (AAA, version 11). One representative patient case (IMRT, target volume 0.2cc, 4×4×14mm) was calculated using AAA 11 and delivered on the Edge. Results: Due to volume averaging effects, CC01 readings were 11.2±0.9% lower than SFD readings for 5mm field sizes. The Edge diode showed a uniform over-response of 2.6±0.7% compared to SFD. Calculation using AAA v11 showed the best agreement with SFD measurements (2.4±1.7% lower than SFD). The largest difference between AAA v11 and SFD occurs at 5mm field sizes. For the patient plan, dose delivered on Edge was measured to be 2.2% higher than AAA v11 calculation. Conclusion: Cross-calibrated SFD output measurements presented the best agreement with commissioned AAA v11 beam model. Field sizes smaller than 1cm posed challenges to both the detectors and the calculation algorithm. For the representative patient with small elongated target, AAA v11 and measurements agreed within ~2% on the Edge linac. Although encouraging, a more comprehensive study is required to validate the overall algorithmic accuracy.

60 APPLIED LIFE SCIENCES↗
NASA NTRS2001

Spatiotemporal relationships between growth and microtubule orientation as revealed in living root cells of Arabidopsis thaliana transformed with green-fluorescent-protein gene construct GFP-MBD

Arabidopsis thaliana plants were transformed with GFP-MBD (J. Marc et al., Plant Cell 10: 1927-1939, 1998) under the control of a constitutive (35S) or copper-inducible promoter. GFP-specific fluorescence distributions, levels, and persistence were determined and found to vary with age, tissue type, transgenic line, and individual plant. With the exception of an increased frequency of abnormal roots of 35S GFP-MBD plants grown on kanamycin-containing media, expression of GFP-MBD does not appear to affect plant phenotype. The number of leaves, branches, bolts, and siliques as well as overall height, leaf size, and seed set are similar between wild-type and transgenic plants as is the rate of root growth. Thus, we conclude that the transgenic plants can serve as a living model system in which the dynamic behavior of microtubules can be visualized. Confocal microscopy was used to simultaneously monitor growth and microtubule behavior within individual cells as they passed through the elongation zone of the Arabidopsis root. Generally, microtubules reoriented from transverse to oblique or longitudinal orientations as growth declined. Microtubule reorientation initiated at the ends of the cell did not necessarily occur simultaneously in adjacent neighboring cells and did not involve complete disintegration and repolymerization of microtubule arrays. Although growth rates correlated with microtubule reorientation, the two processes were not tightly coupled in terms of their temporal relationships, suggesting that other factor(s) may be involved in regulating both events. Additionally, microtubule orientation was more defined in cells whose growth was accelerating and less stringent in cells whose growth was decelerating, indicating that microtubule-orienting factor(s) may be sensitive to growth acceleration, rather than growth per se.

NASA Discipline Plant Biology↗
DOE OSTI2013

Measurement of the axial and the strangeness magnetic form factor of the proton with a P2 backward angle setup

The P2 experiment at the future accelerator facility MESA in Mainz aims for a precise determination of the weak charge of the proton at low momentum transfer. The experimental method is a measurement of the parity violating asymmetry in elastic electron-proton scattering at forward angle. This asymmetry is dominated by the weak charge, but also the proton structure plays a role. Here we consider a back angle measurement, which is more sensitive to the proton structure, and present its possible implications on the main P2 measurement.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2013

Orion MPCV Touchdown Detection Threshold Development and Testing

A robust method of detecting Orion Multi-Purpose Crew Vehicle (MPCV) splashdown is necessary to ensure crew and hardware safety during descent and after touchdown. The proposed method uses a triple redundant system to inhibit Reaction Control System (RCS) thruster firings, detach parachute risers from the vehicle, and transition to the post-landing segment of the Flight Software (FSW). An in-depth trade study was completed to determine optimal characteristics of the touchdown detection method resulting in an algorithm monitoring filtered, lever-arm corrected, 200 Hz Inertial Measurement Unit (IMU) vehicle acceleration magnitude data against a tunable threshold using persistence counter logic. Following the design of the algorithm, high fidelity environment and vehicle simulations, coupled with the actual vehicle FSW, were used to tune the acceleration threshold and persistence counter value to result in adequate performance in detecting touchdown and sufficient safety margin against early detection while descending under parachutes. An analytical approach including Kriging and adaptive sampling allowed for a sufficient number of finite element analysis (FEA) impact simulations to be completed using minimal computation time. The combination of a persistence counter of 10 and an acceleration threshold of approximately 57.3 ft/s2 resulted in an impact performance factor of safety (FOS) of 1.0 and a safety FOS of approximately 2.6 for touchdown declaration. An RCS termination acceleration threshold of approximately 53.1 ft/s(exp)2 with a persistence counter of 10 resulted in an increased impact performance FOS of 1.2 at the expense of a lowered under-parachutes safety factor of 2.2. The resulting tuned algorithm was then tested on data from eight Capsule Parachute Assembly System (CPAS) flight tests, showing an experimental minimum safety FOS of 6.1. The formulated touchdown detection algorithm will be flown on the Orion MPCV FSW during the Exploration Flight Test 1 (EFT-1) mission in the second half of 2014.

Daum, Jared↗
DOE OSTI2015

SU-E-T-525: Ionization Chamber Perturbation in Flattening Filter Free Beams

Purpose: Changing the characteristic of a photon beam by mechanically removing the flattening filter may impact the dose response of ionization chambers. Thus, perturbation factors of cylindrical ionization chambers in conventional and flattening filter free photon beams were calculated by Monte Carlo simulations. Methods: The EGSnrc/BEAMnrc code system was used for all Monte Carlo calculations. BEAMnrc models of nine different linear accelerators with and without flattening filter were used to create realistic photon sources. Monte Carlo based calculations to determine the fluence perturbations due to the presens of the chambers components, the different material of the sensitive volume (air instead of water) as well as the volume effect were performed by the user code egs-chamber. Results: Stem, central electrode, wall, density and volume perturbation factors for linear accelerators with and without flattening filter were calculated as a function of the beam quality specifier TPR{sub 20/10}. A bias between the perturbation factors as a function of TPR{sub 20/10} for flattening filter free beams and conventional linear accelerators could not be observed for the perturbations caused by the components of the ionization chamber and the sensitive volume. Conclusion: The results indicate that the well-known small bias between the beam quality correction factor as a function of TPR20/10 for the flattening filter free and conventional linear accelerators is not caused by the geometry of the detector but rather by the material of the sensitive volume. This suggest that the bias for flattening filter free photon fields is only caused by the different material of the sensitive volume (air instead of water)

60 APPLIED LIFE SCIENCES↗
NASA NTRS1994

Focused interplanetary transport of approximately 1 MeV solar energetic protons through self-generated Alfven waves

We present a model of the focused transport of approximately 1 MeV solar energetic protons through interplanetary Alfven waves that the protons themselves amplify or damp. It is based on the quasi-linear theory but with a phenomenological pitch angle diffusion coefficient in the 'resonance gap.' For initial Alfven wave distributions that give mean free paths greater than approximately 0.5 AU for approximately 1 MeV protons in the inner heliosphere, the model predicts greater than roughly an order of magnitude amplification (damping) in the outward (inward) propagating resonant Alfven waves at less than or approximately equal to o.3 AU heliocentric distance. As the strength of proton source is increased, the peak differential proton intensity at approximately 1 MeV at 1 AU increases to a maximum of approximately 250 particles (/(sq cm)(s)(sr)(MeV)) and then decreases slowly. It may be attenuated by a factor of 5 or more relative to the case without wave evolution, provided that the proton source is sufficiently intense that the resulting peak differential intensity of approximately 1 MeV protons at 1 AU exceeds approximately 200 particles (/(sq cm)(s)(sr)(MeV)). Therefore, in large solar proton events, (1) one may have to take into account self-amplified waves in studying solar particle propagation, (2) the number of accelerated protons escaping from a flare or interplanetary shock may have been underestimated in past studies by a significant factor, and (3) accelerated protons escaping from a traveling interplanetary shock at r less than or approximately equal to 0.3 AU should amplify the ambient hydromagnetic waves siginificantly to make the shock an efficient accelerator, even if initially the mean free path is greater than or approximately equal to 1 AU.

Ng, C. K.↗
NASA NTRS2006

Low-gravity Orbiting Research Laboratory Environment Potential Impact on Space Biology Research

One of the major objectives of any orbital space research platform is to provide a quiescent low gravity, preferably a zero gravity environment, to perform fundamental as well as applied research. However, small disturbances exist onboard any low earth orbital research platform. The impact of these disturbances must be taken into account by space research scientists during their research planning, design and data analysis in order to avoid confounding factors in their science results. The reduced gravity environment of an orbiting research platform in low earth orbit is a complex phenomenon. Many factors, among others, such as experiment operations, equipment operation, life support systems and crew activity (if it is a crewed platform), aerodynamic drag, gravity gradient, rotational effects as well as the vehicle structural resonance frequencies (structural modes) contribute to form the overall reduced gravity environment in which space research is performed. The contribution of these small disturbances or accelerations is precisely why the environment is NOT a zero gravity environment, but a reduced acceleration environment. This paper does not discuss other factors such as radiation, electromagnetic interference, thermal and pressure gradient changes, acoustic and CO2 build-up to name a few that affect the space research environment as well, but it focuses solely on the magnitude of the acceleration level found on orbiting research laboratory used by research scientists to conduct space research. For ease of analysis this paper divides the frequency spectrum relevant to most of the space research disciplines into three regimes: a) quasi-steady, b) vibratory and c) transient. The International Space Station is used as an example to illustrate the point. The paper discusses the impact of these three regimes on space biology research and results from space flown experiments are used to illustrate the potential negative impact of these disturbances (accelerations) on space biology research.

Jules, Kenol↗
DOE OSTI2025

Implications of point defect accumulation on UO 2 thermal conductivity and fission gas release under accelerated fuel irradiation

Evaluation of thermal properties is a crucial factor for nuclear fuel performance. During reactor operation, the accumulation of fission products and irradiation-induced lattice defects are responsible for degradation in thermal conductivity. Consequently, it affects fuel temperature and fission gas release (FGR) among other Multiphysics processes important for economics and safety analysis. We analyze the implications of point defects (PD) accumulation described using a rate theory (RT) Model on lattice thermal conductivity of UO 2 . Here, we demonstrate that fission rate-dependent point defect concentrations have the largest impact on in-pile thermal conductivity in the periphery of light water reactor fuels below a temperature threshold governed by the migration barrier of defects. Our analysis provides a mechanistic description of this phenomena which current fuel performance codes treat empirically. The reduction of thermal conductivity in the low -temperature rim region acts as additional thermal resistance and leads to a temperature notably larger than suggested by Lucuta thermal conductivity correlation. These effects are anticipated to have notable impacts when fuels are exposed to accelerated radiation. The impact of such point defect-informed treatment of thermal conductivity on fuel performance is evaluated by a detailed analysis of fission gas behavior and its release. We consider several models capturing different stages of fission gas bubble evolution and fission gas release (FGR). Finally, a new fission rate-dependent correction to the Lucuta correlation is proposed. The results show a significant reduction in thermal conductivity at the fuels’ periphery and an increase in fuel centerline temperature specifically at low burnups. Ultimately a modified LC shows a higher FGR compared to the original LC, while the acceleration process results in a reduction in overall FGR.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Prime factorization using quantum variational imaginary time evolution

The road to computing on quantum devices has been accelerated by the promises that come from using Shor’s algorithm to reduce the complexity of prime factorization. However, this promise hast not yet been realized due to noisy qubits and lack of robust error correction schemes. Here we explore a promising, alternative method for prime factorization that uses well-established techniques from variational imaginary time evolution. We create a Hamiltonian whose ground state encodes the solution to the problem and use variational techniques to evolve a state iteratively towards these prime factors. We show that the number of circuits evaluated in each iteration scales as \(O(n^{5}d)\) , where n is the bit-length of the number to be factorized and d is the depth of the circuit. We use a single layer of entangling gates to factorize 36 numbers represented using 7, 8, and 9-qubit Hamiltonians. We also verify the method’s performance by implementing it on the IBMQ Lima hardware to factorize 55, 65, 77 and 91 which are greater than the largest number (21) to have been factorized on IBMQ hardware.

97 MATHEMATICS AND COMPUTING↗