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At least 199 records · Page 11

Critical analysis of velocimetry methods for particulate flows from synthetic data

Particle tracking methods that extract high-fidelity particle velocity data from high speed video of particle laden flows is a common experimental technique applied to chemical processes. These measurements are used to better understand the motion of particles and fluids in complex systems and create data against which computational models are validated. However, the methods, codes, and experimental setups all have limitations. It is imperative that practitioners verify the methods and their implementation as well as understand the limitations of experimental setups. This work focuses on quantifying the visible depth of field in a high particle concentration fluidized bed. Following a precedent set by the particle imaging velocimetry community, a particle velocity field is manufactured using a computational fluid dynamics and discrete element method simulation. Photo realistic high-speed videos are rendered based on the simulated data using the three-dimensional creation software Blender. Particle velocities are extracted from the synthetic high-speed videos using three variants of Particle Tracking Velocimetry and Optical Flow Velocimetry methodologies. Here, the tracked results are then compared to the known solution, quantifying the error associated with the assumed visible depth. The results indicate that at depth of one particle diameter, all three particle tracking codes give accurate measurements, largely within 5%. However, the error increases when the full bed video measurements are compared to the known solution at one particle diameter, i.e., mimicking a validation study. Finally, for some statistics the constant depth assumption only increases the error slightly, for others significantly.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Evaluation of an active magnetic resonance tracking system for interstitial brachytherapy

Purpose: In gynecologic cancers, magnetic resonance (MR) imaging is the modality of choice for visualizing tumors and their surroundings because of superior soft-tissue contrast. Real-time MR guidance of catheter placement in interstitial brachytherapy facilitates target coverage, and would be further improved by providing intraprocedural estimates of dosimetric coverage. A major obstacle to intraprocedural dosimetry is the time needed for catheter trajectory reconstruction. Herein the authors evaluate an active MR tracking (MRTR) system which provides rapid catheter tip localization and trajectory reconstruction. The authors assess the reliability and spatial accuracy of the MRTR system in comparison to standard catheter digitization using magnetic resonance imaging (MRI) and CT. Methods: The MRTR system includes a stylet with microcoils mounted on its shaft, which can be inserted into brachytherapy catheters and tracked by a dedicated MRTR sequence. Catheter tip localization errors of the MRTR system and their dependence on catheter locations and orientation inside the MR scanner were quantified with a water phantom. The distances between the tracked tip positions of the MRTR stylet and the predefined ground-truth tip positions were calculated for measurements performed at seven locations and with nine orientations. To evaluate catheter trajectory reconstruction, fifteen brachytherapy catheters were placed into a gel phantom with an embedded catheter fixation framework, with parallel or crossed paths. The MRTR stylet was then inserted sequentially into each catheter. During the removal of the MRTR stylet from within each catheter, a MRTR measurement was performed at 40 Hz to acquire the instantaneous stylet tip position, resulting in a series of three-dimensional (3D) positions along the catheter’s trajectory. A 3D polynomial curve was fit to the tracked positions for each catheter, and equally spaced dwell points were then generated along the curve. High-resolution 3D MRI of the phantom was performed followed by catheter digitization based on the catheter’s imaging artifacts. The catheter trajectory error was characterized in terms of the mean distance between corresponding dwell points in MRTR-generated catheter trajectory and MRI-based catheter digitization. The MRTR-based catheter trajectory reconstruction process was also performed on three gynecologic cancer patients, and then compared with catheter digitization based on MRI and CT. Results: The catheter tip localization error increased as the MRTR stylet moved further off-center and as the stylet’s orientation deviated from the main magnetic field direction. Fifteen catheters’ trajectories were reconstructed by MRTR. Compared with MRI-based digitization, the mean 3D error of MRTR-generated trajectories was 1.5 ± 0.5 mm with an in-plane error of 0.7 ± 0.2 mm and a tip error of 1.7 ± 0.5 mm. MRTR resolved ambiguity in catheter assignment due to crossed catheter paths, which is a common problem in image-based catheter digitization. In the patient studies, the MRTR-generated catheter trajectory was consistent with digitization based on both MRI and CT. Conclusions: The MRTR system provides accurate catheter tip localization and trajectory reconstruction in the MR environment. Relative to the image-based methods, it improves the speed, safety, and reliability of the catheter trajectory reconstruction in interstitial brachytherapy. MRTR may enable in-procedural dosimetric evaluation of implant target coverage.

60 APPLIED LIFE SCIENCES↗

SU-E-T-619: Comparison of CyberKnife Versus HDR (SAVI) for Partial Breast Irradiation

Purpose: Compare SAVI plans and CyberKnife (CK) plans for the same accelerated course. Methods and Materials: Three SAVI patients were selected. Pre-SAVI CTs were used for CK planning. All prescriptions are 3400cGy in 10 fractions BID. Max dose to skin and chestwall is 425cGy. For SAVI, PTV is a 1cm expansion of the cavity minus the cavity. For CK, CTV is a 1cm expansion of the seroma, with 2mm margin. CK plans are normalized to SAVI, so that in both cases the 323cGy isodose line covers the same percentage of PTV. For CK Fiducial/Synchrony tracking is used. Results: In the following, all doses are per fraction and results are averaged. The PTVs for the CK plans are 2.4 times larger than the corresponding SAVI PTVs. Nonetheless the CK plans meet all constraints and are superior to SAVI plans in several respects. Max skin dose for SAVI vs CK is 332cGy vs 337cGy. Max dose to chestwall is 252cGy vs 286cGy. The volume of lung over 125cGy is 6.4cc for SAVI and 2.5cc for CK. Max heart dose is 60cGy for SAVI and 83cGy for CK. The volume of PTV receiving over 425cGy is 49cc for SAVI and 1.3cc for CK. Max dose to contra-lateral breast is 16cGy for SAVI and 4.5cGy for CK. Conclusion: CK PTVs are directly derived from the seroma. Corresponding SAVI PTVs tend to be much smaller. Dosimetrically, CK plans are equivalent or superior to SAVI plans despite the larger PTVs. Interestingly, the dose delivered to the lung is higher in SAVI vs CK. Fiducial/Synchrony tracking employed by CK might reduce errors in delivery compared to errors associated with shifts of the SAVI implant. In conclusion, when CK is an option for partial breast irradiation it may preferable to SAVI.

60 APPLIED LIFE SCIENCES↗

SU-F-BRA-01: A Procedure for the Fast Semi-Automatic Localization of Catheters Using An Electromagnetic Tracker (EMT) for Image-Guided Brachytherapy

Purpose: To evaluate the feasibility of brachytherapy catheter localization through use of an EMT and 3D image set. Methods: A 15-catheter phantom mimicking an interstitial implantation was built and CT-scanned. Baseline catheter reconstruction was performed manually. An EMT was used to acquire the catheter coordinates in the EMT frame of reference. N user-identified catheter tips, without catheter number associations, were used to establish registration with the CT frame of reference. Two algorithms were investigated: brute-force registration (BFR), in which all possible permutation of N identified tips with the EMT tips were evaluated; and signature-based registration (SBR), in which a distance matrix was used to generate a list of matching signatures describing possible N-point matches with the registration points. Digitization error (average of the distance between corresponding EMT and baseline dwell positions; average, standard deviation, and worst-case scenario over all possible registration-point selections) and algorithm inefficiency (maximum number of rigid registrations required to find the matching fusion for all possible selections of registration points) were calculated. Results: Digitization errors on average <2 mm were observed for N ≥5, with standard deviation <2 mm for N ≥6, and worst-case scenario error <2 mm for N ≥11. Algorithm inefficiencies were: N = 5, 32,760 (BFR) and 9900 (SBR); N = 6, 360,360 (BFR) and 21,660 (SBR); N = 11, 5.45*1010 (BFR) and 12 (SBR). Conclusion: A procedure was proposed for catheter reconstruction using EMT and only requiring user identification of catheter tips without catheter localization. Digitization errors <2 mm were observed on average with 5 or more registration points, and in any scenario with 11 or more points. Inefficiency for N = 11 was 9 orders of magnitude lower for SBR than for BFR. Funding: Kaye Family Award.

60 APPLIED LIFE SCIENCES↗

SU-F-J-88: Comparison of Two Deformable Image Registration Algorithms for CT-To-CT Contour Propagation

Purpose: To compare the contour propagation accuracy of two deformable image registration (DIR) algorithms in the Raystation treatment planning system – the “Hybrid” algorithm based on image intensities and anatomical information; and the “Biomechanical” algorithm based on linear anatomical elasticity and finite element modeling. Methods: Both DIR algorithms were used for CT-to-CT deformation for 20 lung radiation therapy patients that underwent treatment plan revisions. Deformation accuracy was evaluated using landmark tracking to measure the target registration error (TRE) and inverse consistency error (ICE). The deformed contours were also evaluated against physician drawn contours using Dice similarity coefficients (DSC). Contour propagation was qualitatively assessed using a visual quality score assigned by physicians, and a refinement quality score (0 0.9 for lungs, > 0.85 for heart, > 0.8 for liver) and similar qualitative assessments (VQS < 0.35, RQS > 0.75 for lungs). When anatomical structures were used to control the deformation, the DSC improved more significantly for the biomechanical DIR compared to the hybrid DIR, while the VQS and RQS improved only for the controlling structures. However, while the inclusion of controlling structures improved the TRE for the hybrid DIR, it increased the TRE for the biomechanical DIR. Conclusion: The hybrid DIR was found to perform slightly better than the biomechanical DIR based on lower TRE while the DSC, VQS, and RQS studies yielded comparable results for both. The use of controlling structures showed considerable improvement in the hybrid DIR results and is recommended for clinical use in contour propagation.

60 APPLIED LIFE SCIENCES↗

Dynamic Aperture of the PIP-II Accumulator Ring (PAR)

The Proton Improvement Plan-II (PIP-II) will include a superconducting linear accelerator which will accelerate H- ions to 800MeV, at an intensity never seen before. A proposed PIP-II Accumulator Ring (PAR) can reduce the injection losses to the booster, enhance the ramp up of the Long Baseline Neutrino Facility (LBNF) and support experiments in Dark Sector Physics. When the beam is circulating in PAR at its full intensity, it will then be transferred to the Booster via single turn injection. Strong PAR focusing results in larger phase advances, shorter focal lengths and higher machine tunes, which creates robust beam envelope control. Particles will be able to survive modest excursions from the elliptical phase-space trajectories of linear optics, and any loss of particles would be due to reduced dynamic aperture. The values for tunes and chromaticities are flexible and will continue to evolve as the lattice matures. Since there will be non-linear terms impacting the particles’ trajectories, tracking will include realistic magnetic field errors and installation alignment errors to determine the dynamic aperture as a function of the machine tunes. This will allow us to determine the optimum operating point in phase-space.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

‘Universal Injector’ at LERF - Layout and Optics Architecture

Here, we present a next level design of a compact injector within the LERF vault, which would serve both the 22 GeV CEBAF and the positron program, while being compatible with the electron source required to produce positrons for Ce+BAF. The baseline design of a 3-pass recirculator features a main linac configured with three C-75 cryo-modules, five isochronous return arcs and three straight sections, facilitating electron beam acceleration up to 650 MeV. The Universal Injector offers flexibility of extraction 1-pass and 2-pass energy electrons, as needed for positron production, with a final 3-pass extraction required by the 650 MeV injector for 22 GeV CEBAF. This note provides an overview of the baseline optics design of the Universal Injector complex, including the 8 MeV injector merger and the recirculator racetrack, including individual extraction lines for all three passes. A comprehensive suite of beam dynamics studies to validate the design is under way; starting with the orbit correction scheme, followed by start-to-end tracking with lattice misalignments and magnet errors.

Bogacz, Alex [Thomas Jefferson National Accelerato↗

Application of Ensemble Kalman Filter in Power System State Tracking and Sensitivity

Ensemble Kalman Filter (EnKF) is proposed to track dynamic states of generators. The algorithm of EnKF and its application to generator state tracking are presented in detail. The accuracy and sensitivity of the method are analyzed with respect to initial state errors, measurement noise, unknown fault locations, time steps and parameter errors. It is demonstrated through simulation studies that even with some errors in the parameters, the developed EnKF can effectively track generator dynamic states using disturbance data.

dynamic state tracking↗

Real-time automatic fiducial marker tracking in low contrast cine-MV images

Purpose: To develop a real-time automatic method for tracking implanted radiographic markers in low-contrast cine-MV patient images used in image-guided radiation therapy (IGRT). Methods: Intrafraction motion tracking using radiotherapy beam-line MV images have gained some attention recently in IGRT because no additional imaging dose is introduced. However, MV images have much lower contrast than kV images, therefore a robust and automatic algorithm for marker detection in MV images is a prerequisite. Previous marker detection methods are all based on template matching or its derivatives. Template matching needs to match object shape that changes significantly for different implantation and projection angle. While these methods require a large number of templates to cover various situations, they are often forced to use a smaller number of templates to reduce the computation load because their methods all require exhaustive search in the region of interest. The authors solve this problem by synergetic use of modern but well-tested computer vision and artificial intelligence techniques; specifically the authors detect implanted markers utilizing discriminant analysis for initialization and use mean-shift feature space analysis for sequential tracking. This novel approach avoids exhaustive search by exploiting the temporal correlation between consecutive frames and makes it possible to perform more sophisticated detection at the beginning to improve the accuracy, followed by ultrafast sequential tracking after the initialization. The method was evaluated and validated using 1149 cine-MV images from two prostate IGRT patients and compared with manual marker detection results from six researchers. The average of the manual detection results is considered as the ground truth for comparisons. Results: The average root-mean-square errors of our real-time automatic tracking method from the ground truth are 1.9 and 2.1 pixels for the two patients (0.26 mm/pixel). The standard deviations of the results from the 6 researchers are 2.3 and 2.6 pixels. The proposed framework takes about 128 ms to detect four markers in the first MV images and about 23 ms to track these markers in each of the subsequent images. Conclusions: The unified framework for tracking of multiple markers presented here can achieve marker detection accuracy similar to manual detection even in low-contrast cine-MV images. It can cope with shape deformations of fiducial markers at different gantry angles. The fast processing speed reduces the image processing portion of the system latency, therefore can improve the performance of real-time motion compensation.

60 APPLIED LIFE SCIENCES↗

Space Charge Models for Particle Tracking on Long Time Scales

In order to efficiently track charged particles over long times, most tracking codes use either analytic charge distributions or particle-in-cell (PIC) methods based on fast Fourier transforms (FFTs). While useful for theoretical studies, analytic distribution models do not allow accurate simulation of real machines. PIC calculations can utilize realistic space charge distributions, but these methods suffer from the presence of discretization errors. We examine the situation for particle tracking with space charge over long times, and consider possible ideas to improve the accuracy of such calculations.

Holmes, Jeffrey A↗

Using Eye Tracking to Elucidate the Mechanisms Underlying Stimulation-Enhanced Visual Target Detection

Transcranial direct current stimulation (tDCS) is a noninvasive form of brain stimulation that involves passing a weak electrical current between electrodes on the scalp to modulate underlying neural tissue. TDCS has been shown to modulate cognition in a variety of domains, including memory, attention, and visual processing. Prior work from our laboratory has shown positive effects of tDCS on learning to detect target objects hidden in complex naturalistic visual scenes and learn rules for categorizing images, though the mechanism for these benefits remains unknown. One possibility is that tDCS optimizes visual search by modulating visual attention or via the reduction in search errors. One method of quantifying visual attention is to use eye tracking to record search patterns to determine if and how visual search is adjusted under verum stimulation conditions. Eye tracking data allows classification of errors into error types, including sampling errors (failing to look in the relevant region), recognition errors (looking at the critical portion of a scene, but failing to recognize it as such as evidenced by visual fixation), and decision-making errors (fixating on the relevant portion of a scene, but making the wrong determination). Our results indicate that the benefit tDCS confers on visual search for targets stems from the reduction in decision-making errors when targets are present (Cohen’s d = 0.86). Also reported is a replication of previous findings showing a tDCS-dependent improvement in learning this task, learning score (Cohen’s d = 0.88); d’ (Cohen’s d = 1.00). This provides support for moving tDCS into the application space by pairing it with analysts who are concerned with the type of search error that is corrected via stimulation.

attention↗

TH-AB-202-11: Spatial and Rotational Quality Assurance of 6DOF Patient Tracking Systems

Purpose: External tracking systems used for patient positioning and motion monitoring during radiotherapy are now capable of detecting both translations and rotations (6DOF). In this work, we develop a novel technique to evaluate the 6DOF performance of external motion tracking systems. We apply this methodology to an infrared (IR) marker tracking system and two 3D optical surface mapping systems in a common tumor 6DOF workspace. Methods: An in-house designed and built 6DOF parallel kinematics robotic motion phantom was used to follow input trajectories with sub-millimeter and sub-degree accuracy. The 6DOF positions of the robotic system were then tracked and recorded independently by three optical camera systems. A calibration methodology which associates the motion phantom and camera coordinate frames was first employed, followed by a comprehensive 6DOF trajectory evaluation, which spanned a full range of positions and orientations in a 20×20×16 mm and 5×5×5 degree workspace. The intended input motions were compared to the calibrated 6DOF measured points. Results: The technique found the accuracy of the IR marker tracking system to have maximal root mean square error (RMSE) values of 0.25 mm translationally and 0.09 degrees rotationally, in any one axis, comparing intended 6DOF positions to positions measured by the IR camera. The 6DOF RSME discrepancy for the first 3D optical surface tracking unit yielded maximal values of 0.60 mm and 0.11 degrees over the same 6DOF volume. An earlier generation 3D optical surface tracker was observed to have worse tracking capabilities than both the IR camera unit and the newer 3D surface tracking system with maximal RMSE of 0.74 mm and 0.28 degrees within the same 6DOF evaluation space. Conclusion: The proposed technique was effective at evaluating the performance of 6DOF patient tracking systems. All systems examined exhibited tracking capabilities at the sub-millimeter and sub-degree level within a 6DOF workspace.

60 APPLIED LIFE SCIENCES↗

SU-G-JeP3-01: A Method to Quantify Lung SBRT Target Localization Accuracy Based On Digitally Reconstructed Fluoroscopy

Purpose: To develop a methodology based on digitally-reconstructed-fluoroscopy (DRF) to quantitatively assess target localization accuracy of lung SBRT, and to evaluate using both a dynamic digital phantom and a patient dataset. Methods: For each treatment field, a 10-phase DRF is generated based on the planning 4DCT. Each frame is pre-processed with a morphological top-hat filter, and corresponding beam apertures are projected to each detector plane. A template-matching algorithm based on cross-correlation is used to detect the tumor location in each frame. Tumor motion relative beam aperture is extracted in the superior-inferior direction based on each frame’s impulse response to the template, and the mean tumor position (MTP) is calculated as the average tumor displacement. The DRF template coordinates are then transferred to the corresponding MV-cine dataset, which is retrospectively filtered as above. The treatment MTP is calculated within each field’s projection space, relative to the DRF-defined template. The field’s localization error is defined as the difference between the DRF-derived-MTP (planning) and the MV-cine-derived-MTP (delivery). A dynamic digital phantom was used to assess the algorithm’s ability to detect intra-fractional changes in patient alignment, by simulating different spatial variations in the MV-cine and calculating the corresponding change in MTP. Inter-and-intra-fractional variation, IGRT accuracy, and filtering effects were investigated on a patient dataset. Results: Phantom results demonstrated a high accuracy in detecting both translational and rotational variation. The lowest localization error of the patient dataset was achieved at each fraction’s first field (mean=0.38mm), with Fx3 demonstrating a particularly strong correlation between intra-fractional motion-caused localization error and treatment progress. Filtering significantly improved tracking visibility in both the DRF and MV-cine images. Conclusion: We have developed and evaluated a methodology to quantify lung SBRT target localization accuracy based on digitally-reconstructed-fluoroscopy. Our approach may be useful in potentially reducing treatment margins to optimize lung SBRT outcomes. R01-184173.

60 APPLIED LIFE SCIENCES↗

Polished diamond X-ray lenses

High-quality bi-concave 2D focusing diamond X-ray lenses of apex-radius R = 100 µm produced via laser-ablation and improved via mechanical polishing are presented here. Both for polished and unpolished individual lenses and for stacks of ten lenses, the remaining figure errors determined using X-ray speckle tracking are shown and these results are compared with those of commercial R = 50 µm beryllium lenses that have similar focusing strength and physical aperture. For two stacks of ten diamond lenses (polished and unpolished) and a stack of eleven beryllium lenses, this paper presents measured 2D beam profiles out of focus and wire scans to obtain the beam size in the focal plane. These results are complemented with small-angle X-ray scattering (SAXS) measurements of a polished and an unpolished diamond lens. Again, this is compared with the SAXS of a beryllium lens. The polished X-ray lenses show similar figure errors to commercially available beryllium lenses. While the beam size in the focal plane is comparable to that of the beryllium lenses, the SAXS signal of the polished diamond lenses is considerably lower.

47 OTHER INSTRUMENTATION↗

Design, analysis and testing of a parallel-kinematic high-bandwidth XY nanopositioning stage

This paper presents the design, analysis, and testing of a parallel-kinematic high-bandwidth XY nanopositioning stage driven by piezoelectric stack actuators. The stage is designed with two kinematic chains. In each kinematic chain, the end-effector of the stage is connected to the base by two symmetrically distributed flexure modules, respectively. Each flexure module comprises a fixed-fixed beam and a parallelogram flexure serving as two orthogonal prismatic joints. With the purpose to achieve high resonance frequencies of the stage, a novel center-thickened beam which has large stiffness is proposed to act as the fixed-fixed beam. The center-thickened beam also contributes to reducing cross-coupling and restricting parasitic motion. To decouple the motion in two axes totally, a symmetric configuration is adopted for the parallelogram flexures. Based on the analytical models established in static and dynamic analysis, the dimensions of the stage are optimized in order to maximize the first resonance frequency. Then finite element analysis is utilized to validate the design and a prototype of the stage is fabricated for performance tests. According to the results of static and dynamic tests, the resonance frequencies of the developed stage are over 13.6 kHz and the workspace is 11.2 μm × 11.6 μm with the cross-coupling between two axes less than 0.52%. It is clearly demonstrated that the developed stage has high resonance frequencies, a relatively large travel range, and nearly decoupled performance between two axes. For high-speed tracking performance tests, an inversion-based feedforward controller is implemented for the stage to compensate for the positioning errors caused by mechanical vibration. The experimental results show that good tracking performance at high speed is achieved, which validates the effectiveness of the developed stage.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Analysis of Prostate Patient Setup and Tracking Data: Potential Intervention Strategies

Purpose: To evaluate the setup, interfraction, and intrafraction organ motion error distributions and simulate intrafraction intervention strategies for prostate radiotherapy. Methods and Materials: A total of 17 patients underwent treatment setup and were monitored using the Calypso system during radiotherapy. On average, the prostate tracking measurements were performed for 8 min/fraction for 28 fractions for each patient. For both patient couch shift data and intrafraction organ motion data, the systematic and random errors were obtained from the patient population. The planning target volume margins were calculated using the van Herk formula. Two intervention strategies were simulated using the tracking data: the deviation threshold and period. The related planning target volume margins, time costs, and prostate position 'fluctuation' were presented. Results: The required treatment margin for the left-right, superoinferior, and anteroposterior axes was 8.4, 10.8, and 14.7 mm for skin mark-only setup and 1.3, 2.3, and 2.8 mm using the on-line setup correction, respectively. Prostate motion significantly correlated among the superoinferior and anteroposterior directions. Of the 17 patients, 14 had prostate motion within 5 mm of the initial setup position for {>=}91.6% of the total tracking time. The treatment margin decreased to 1.1, 1.8, and 2.3 mm with a 3-mm threshold correction and to 0.5, 1.0, and 1.5 mm with an every-2-min correction in the left-right, superoinferior, and anteroposterior directions, respectively. The periodic corrections significantly increase the treatment time and increased the number of instances when the setup correction was made during transient excursions. Conclusions: The residual systematic and random error due to intrafraction prostate motion is small after on-line setup correction. Threshold-based and time-based intervention strategies both reduced the planning target volume margins. The time-based strategies increased the treatment time and the in-fraction position fluctuation.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Efficient flexible characterization of quantum processors with nested error models

We present a simple and powerful technique for finding a good error model for a quantum processor. The technique iteratively tests a nested sequence of models against data obtained from the processor, and keeps track of the best-fit model and its wildcard error (a metric of the amount of unmodeled error) at each step. Each best-fit model, along with a quantification of its unmodeled error, constitutes a characterization of the processor. We explain how quantum processor models can be compared with experimental data and to each other. We demonstrate the technique by using it to characterize a simulated noisy two-qubit processor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗