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Young Electronics Company's new product is a testboard developed by the Jet Propulsion Laboratory as a tool for training and qualifying personnel in board assembly and in the art of soldering components without damaging boards or components. The boards are used for pre- employment testing and employee requalification.
Parameterized quantum circuits (PQCs) are fundamental to quantum machine learning (QML), quantum optimization, and variational quantum algorithms (VQAs). The expressibility of PQCs is a measure that determines their capability to harness the full potential of the quantum state space. It is thus a crucial guidepost to know when selecting a particular PQC ansatz. However, the existing technique for expressibility computation through statistical estimation requires a large number of samples, which poses significant challenges due to time and computational resource constraints. This paper introduces a novel approach for expressibility estimation of PQCs using Graph Neural Networks (GNNs). We demonstrate the predictive power of our GNN model with a dataset consisting of 25,000 samples from the noiseless IBM QASM Simulator and 12,000 samples from three distinct noisy quantum backends. The model accurately estimates expressibility, with root mean square errors (RMSE) of 0.05 and 0.06 for the noiseless and noisy backends, respectively. We compare our model’s predictions with reference circuits from Sim et al. and IBM Qiskit’s hardwareefficient ansatz sets to further evaluate our model’s performance. Our experimental evaluation in noiseless and noisy scenarios reveals a close alignment with ground truth expressibility values, highlighting the model’s efficacy. Moreover, our model exhibits promising extrapolation capabilities, predicting expressibility values with low RMSE for out-of-range qubit circuits trained solely on only up to 5-qubit circuit sets. This work thus provides a reliable means of efficiently evaluating the expressibility of diverse PQCs on noiseless simulators and hardware.
Variational training of parameterized quantum circuits (PQCs) underpins many workflows employed on near-term noisy intermediate scale quantum (NISQ) devices. It is a hybrid quantum-classical approach that minimizes an associated cost function in order to train a parameterized ansatz. In this work we adapt the qualitative loss landscape characterization for neural networks introduced in Goodfellow et al. (2014); Li et al. (2017) and tests for connectivity used in Draxler et al. (2018) to study the loss landscape features in PQC training. We present results for PQCs trained on a simple regression task, using the bilayer circuit ansatz, which consists of alternating layers of parameterized rotation gates and entangling gates. Multiple circuits are trained with 3 different batch gradient optimizers: stochastic gradient descent, the quantum natural gradient, and Adam. We identify large features in the landscape that can lead to faster convergence in training workflows.
Abstract Variational hybrid quantum–classical algorithms are powerful tools to maximize the use of noisy intermediate-scale quantum devices. While past studies have developed powerful and expressive ansatze, their near-term applications have been limited by the difficulty of optimizing in the vast parameter space. In this work, we propose a heuristic optimization strategy for such ansatze used in variational quantum algorithms, which we call ‘parameter-efficient circuit training (PECT)’. Instead of optimizing all of the ansatz parameters at once, PECT launches a sequence of variational algorithms, in which each iteration of the algorithm activates and optimizes a subset of the total parameter set. To update the parameter subset between iterations, we adapt the Dynamic Sparse Reparameterization scheme which was originally proposed for training deep convolutional neural networks. We demonstrate PECT for the Variational Quantum Eigensolver, in which we benchmark unitary coupled-cluster ansatze including UCCSD and k -UpCCGSD, as well as the Low-Depth Circuit Ansatz (LDCA), to estimate ground state energies of molecular systems. We additionally use a layerwise variant of PECT to optimize a hardware-efficient circuit for the Sycamore processor to estimate the ground state energy densities of the one-dimensional Fermi-Hubbard model. From our numerical data, we find that PECT can enable optimizations of certain ansatze that were previously difficult to converge and more generally can improve the performance of variational algorithms by reducing the optimization runtime and/or the depth of circuits that encode the solution candidate(s).
Transient stability assessment (TSA) is a cornerstone for resilient operations of todays interconnected power grids. This paper is a confluence of quantum computing, data science and machine learning to potentially address the power system TSA issue. Here, we devise a quantum TSA (QTSA) method to enable scalable and efficient data-driven transient stability prediction for bulk power systems, which is the first attempt to tackle the TSA issue with quantum computing. Our contributions are three-fold: 1) A high expressibility, low-depth (HELD) quantum circuit is designed for accurate and noise-resilient TSA; 2) A quantum natural gradient descent algorithm is developed for efficient HELD circuit training; 3) A systematical analysis on QTSAs performance under various quantum factors is per-formed. QTSA underpins a foundation of quantum-enabled and data-driven power grid stability analytics. It renders the intractable TSA straightforward and effortless in the Hilbert space, and therefore provides stability information for power system operations. Extensive experiments on quantum simulators and real quantum computers verify the accuracy, noise-resilience, scalability and universality of QTSA.
Error mitigation techniques are crucial to achieving near-term quantum advantage. Classical postprocessing of quantum computation outcomes is a popular approach for error mitigation, which includes methods, such as zero noise extrapolation, virtual distillation, and learning-based error mitigation. However, these techniques have limitations due to the propagation of uncertainty resulting from the finite shot number of a quantum measurement. In this work, we introduce general and unbiased methods for quantifying the uncertainty and error of error-mitigated observables based on the strategic sampling of error mitigation outcomes. We then extend our approach to demonstrate the optimization of performance and robustness of error mitigation under uncertainty. To illustrate our methods, we apply them to zero noise extrapolation and Clifford date regression in the ground state of the XY model simulated using depolarizing and International Business Machines Corporation (IBM) Toronto noise models, respectively. In particular, we optimize the choice of noise levels and the allocation of shots for zero noise extrapolation and the distribution of the training circuits for Clifford data regression. While our methods are readily applicable to any postprocessing-based error mitigation approach, in practice they must not be prohibitively expensive—even though they perform optimizations of the error mitigation hyperparameters requiring sampling of a statistical distribution of error mitigation outcomes. By leveraging surrogate-based optimization, we show that our methods can efficiently perform optimal design for a zero noise extrapolation implementation. We then further demonstrate the transferability of learned zero noise extrapolation hyperparameters to other similar circuits.
Separations between views adjusted precisely for best results. Simple jig adjusted to set precisely, distance between right and left positions of camera used to make stereoscopic photographs. Camera slides in slot between extreme positions, where it takes stereoscopic pictures. Distance between extreme positions set reproducibly with micrometer. In view of trend toward very-large-scale integration of electronic circuits, training method and jig used to make training photographs useful to many companies to reduce cost of training manufacturing personnel.
An engineering evaluation was performed on the ExerGenie(r) exercise device to quantify its capabilities and limitations to address questions from the Constellation Program. Three subjects performed rowing and circuit training sessions to assess the suitability of the device for aerobic exercise. Three subjects performed a resistive exercise session to assess the suitability of the device for resistive exercise. Since 1 subject performed both aerobic and resistive exercise sessions, a total of 5 subjects participated.
Practical success of quantum learning models hinges on having a suitable structure for the parameterized quantum circuit. Such structure is defined both by the types of gates employed and by the correlations of their parameters. While much research has been devoted to devising adequate gate-sets, typically respecting some symmetries of the problem, very little is known about how their parameters should be structured. In this work, we show that an ideal parameter structure naturally emerges when carefully considering spatial symmetries (i.e. the symmetries that are permutations of parts of the system under study). Namely, we consider the automorphism group of the problem Hamiltonian, leading us to develop a circuit construction that is equivariant under this symmetry group. The benefits of our novel circuitstructure, called ORB, are numerically probed in several ground-state problems. We find a consistent improvement (in terms of circuit depth, number of parameters required, and gradient magnitudes) compared to literature circuit constructions.
Abstract Practical success of quantum learning models hinges on having a suitable structure for the parameterized quantum circuit. Such structure is defined both by the types of gates employed and by the correlations of their parameters. While much research has been devoted to devising adequate gate-sets, typically respecting some symmetries of the problem, very little is known about how their parameters should be structured. In this work, we show that an ideal parameter structure naturally emerges when carefully considering spatial symmetries (i.e. the symmetries that are permutations of parts of the system under study). Namely, we consider the automorphism group of the problem Hamiltonian, leading us to develop a circuit construction that is equivariant under this symmetry group. The benefits of our novel circuitstructure, called ORB, are numerically probed in several ground-state problems. We find a consistent improvement (in terms of circuit depth, number of parameters required, and gradient magnitudes) compared to literature circuit constructions.
Circuit converts number represented as two level signal on n-bit lines to series of pulses on one of two lines, depending on sign of number. Converter accepts parallel binary input data and produces number of output pulses equal to number represented by input data.
As the size and ubiquity of artificial intelligence and computational machine learning models grow, the energy required to train and use them is rapidly becoming economically and environmentally unsustainable. Recent laboratory prototypes of self-learning electronic circuits, such as “physical learning machines,” open the door to analog hardware that directly employs physics to learn desired functions from examples at a low energy cost. In this work, we show that this hardware platform allows for an even further reduction in energy consumption by using good initial conditions and a new learning algorithm. Using analytical calculations, simulations, and experiments, we show that a trade-off emerges when learning dynamics attempt to minimize both the error and the power consumption of the solution—greater power reductions can be achieved at the cost of decreasing solution accuracy. Finally, we demonstrate a practical procedure to weigh the relative importance of error and power minimization, improving the power efficiency given a specific tolerance to error.
Optimization is a promising candidate for studying the utility of variational quantum algorithms (VQAs). However, evaluating cost functions using quantum hardware introduces runtime overheads that limit exploration. Surrogate-based methods can reduce calls to a quantum computer, yet existing approaches require hyperparameter pre-training and have been tested only on small problems. Here, we show that surrogate-based methods can enable successful optimization at scale, without pre-training, by using radial basis function interpolation (RBF) to construct an adaptive, hyperparameter-free surrogate. Using the surrogate as an acquisition function drives hardware queries to the vicinity of the true optima. For 16-qubit random 3-regular Max-Cut instances with the Quantum Approximate Optimization Algorithm (QAOA), our method outperforms state-of-the-art approaches, without considering their upfront training costs. Furthermore, we successfully optimize QAOA circuits for 127-qubit random Ising models on an IBM processor using 10 4 −10 5 measurements. Strong empirical performance demonstrates the promise of automated surrogate-based learning for large-scale VQA applications.
A power supply circuit for converting a first voltage to a second voltage where the first voltage is greater than the second voltage, and a power train having the same, are provided. The power supply circuit may have multiple stages and each stage of the power supply circuit may include a first circuit block configured to provide a start-up power to a second circuit block; a second circuit block configured to generate a Pulse-Width-Modulation (PWM) signal that controls a pulse duration of a transistor; a third circuit block configured to activate or deactivate the transistor based on the PWM signal; a fourth circuit block configured to reset a magnetic flux in a transformer to a zero state when the transistor is deactivated; and a fifth circuit block configured to maintain an output of a stage below a predetermined value by adjusting a voltage across the transformer.
Quantum compiling, where a parameterized quantum circuit is trained to learn a target unitary, is an important primitive for quantum computing that can be used as a subroutine to obtain optimal circuits or as a tomographic tool to study the dynamics of an experimental system. While much attention has been paid to quantum compiling on discrete-variable hardware, less has been paid to compiling in the continuous-variable paradigm. Here we motivate several, closely related, short-depth continuous-variable algorithms for quantum compilation. We analyze the trainability of our proposed cost functions and numerically demonstrate our algorithms by learning arbitrary Gaussian operations and Kerr nonlinearities. We further make connections between this framework and quantum learning theory in the continuous-variable setting by deriving no-free-lunch theorems. These generalization bounds demonstrate a linear resource reduction for learning Gaussian unitaries using entangled coherent-Fock states and an exponential resource reduction for learning arbitrary unitaries using two-mode-squeezed states.
Firefighters typically undergo a 16–24-week training academy during which they perform a variety of traditional exercise programs such as cardiovascular, resistance, and concurrent training. Because of limited facility access, some fire departments seek alternative exercise programs, such as multimodal high-intensity interval training (MM-HIIT), which essentially combines resistance and interval training. Here, the primary purpose of this study was to assess the effect of MM-HIIT on body composition and physical fitness in firefighter recruits who completed a training academy during the coronavirus (COVID-19) pandemic. A secondary purpose was to compare the effects of MM-HIIT to previous training academies that implemented traditional exercise programs. Healthy and recreationally-trained recruits (n=12) participated in 2-3 days/week of MM-HIIT for 12 weeks and had several components of body composition and physical fitness measured before and after the program. Because of COVID-19-related gym closures, all MM-HIIT sessions were performed outdoors at a fire station with minimal equipment. These data were retroactively compared to a control group (CG) that previously completed training academies with traditional exercise programs. Subjects in the MM-HIIT group significantly improved several components of body composition and fitness, including fat mass, fat-free mass, body fat percentage, aerobic capacity, and muscular endurance (p < 0.005). Moreover, there were no significant differences for any dependent variable when MM-HIIT was compared to the CG (p≥0.005). These results suggest that MM-HIIT may serve as an effective substitute for traditional concurrent training paradigms that are typically used for firefighter academies.
The primary objective of this project was to develop and demonstrate an integrated pilot-scale circuitry for recovering high-value rare earth elements (REEs) from coal and coal byproducts. The target performance was to produce a mixed REE product with content of at least two percent by weight on a dry mass basis in a cost-effective and environmentally benign manner. During the first nine months of the project period (Phase 2 Budget Period 2), pilot plant construction was completed including all field site startup activities such as permitting, engineering design, procurement/bidding, unit fabrication, site construction, equipment installation, module assembly, safety training, and circuit shakedown. During the remaining 21 months of project period (Phase 2 Budget Period 3), detailed field-testing activities were performed including feedstock sample collection and preparation, exploratory testing, circuit modification, detailed parametric study, and performance optimization. A detailed techno-economic analysis was performed based on the pilot plant testing findings which provided various scenarios for REE production. The project successfully accomplished the proposed target performance by producing mixed rare earth oxide (REO) with greater than 90% purity by weight in a continuous pilot scale operation from two distinctly different coarse refuse materials (i.e., West Kentucky No. 13 and Fire Clay coal seams), and at least three secondary sources (i.e., heap leach process and naturally formed acid mine drainage system). Project partners included the University of Kentucky, Virginia Tech, West Virginia University, Alliance Coal, Blackhawk Mining, Mineral Refining Company, and Mineral Separation Technologies. The pilot scale test facility was constructed at a former mining complex owned by Alliance Natural Resource Partners (Alliance Coal). The site was rehabilitated to accommodate the equipment installation, construction and fabrication, electrical power requirement, water line management and containment. The process units constructed and installed included X-ray sorting unit, crushing and grinding unit, physical separation unit, acid leaching unit, solvent extraction unit, and wastewater management unit. A rare earth mineral concentration unit was constructed as a standalone unit for flexible operation. A detailed environmental assessment and control plan was carried out to identify and quantify any potential impacts of the pilot-scale processing circuitry on the human and eco-system health and well-being. Corresponding mitigation strategies and control measures were provided. A conceptual flowsheet was developed to effectively remove thorium and uranium from high purity rare earth oxide mix or any potential radionuclide enriched stream. The two distinct feedstock materials were secured from the Blackhawk Mining Complex in eastern Kentucky where the Fire Clay (Hazard No. 4) seam is processed. The West Kentucky No. 13 (Baker) coarse refuse material was collected from an active process stream at an Alliance coal preparation plant located in western Kentucky. Characterization analysis indicated that both of feed materials generated from the two sources contained >300 ppm of TREEs on a dry whole mass basis which met the requirements for a qualified feed stock. The two feedstocks were further upgraded using a dual x-ray sorter to prepare the feed material for hydrometallurgical circuit. Thermal treatment on feed material prior to leaching was found to: 1) improve the leaching recovery of REEs, 2) increase the leaching kinetics, and 3) allow the leaching reaction to occur at lower acidity. Roasting at 600°C was selected as the pre-treatment condition for both West Kentucky No. 13 and Fire Clay coarse refuse material. Over 40% of leaching recovery was achieved by roasting West Kentucky No. 13 material having a top particle size of 3 mm in the pilot scale operation using 1.2M sulfuric acid leaching at 75OC. Initial pilot scale testing involved continuous operation of the pilot plant for 94 hours. The leaching unit was operated at solid-to-liquid ratio of 1 to 10 (w/v) using 0.5M sulfuric acid solution at a temperature of 75°C. The continuous solvent extraction circuit utilized rougher and cleaner units with DEHPA and TBP as the extractants. An innovative stripping circuit was developed to accumulate the REE concentration in the stripping solution to a level above 600 ppm. A bleed stream from the recycled strip solution was treated using oxalic acid precipitation which produced a high grade rare earth oxalate. The oxalate product was roasted to remove the oxalate which produced a rare earth oxide product having a purity greater 90%. Due to high concentrations of contaminant ions in the pregnant leach solution (PLS), a modified flowsheet was developed that involved pre-concentration of the REEs using multiple stages of precipitation and redissolution. The advantage of this process was improved removal of contamination before the downstream purification process and a significant cost reduction relative to the circuit that utilized the solvent extraction process. The modified circuitry included processes involving leaching, multistage precipitation, redissolution, and oxalate precipitation followed by roasting of the oxalate product. The circuit produced a mixed REO that was 92.96% pure from the initial test. A detailed parametric test plan was carried out which involved varying key parameters including solids feed rate, acid flowrate, acid concentration, multistage precipitation pH, redissolution pH, oxalate precipitation dosage and pH. The response variables included REE recovery, contaminant recovery, REO product grade and overall chemical consumption. Test results indicated that the acid-to-solid ratio is the key parameter to leaching efficiency as performance deteriorated with an increase in solids concentration. The optimal pH determined for REE precipitation and redissolution was 6.5 and 2.5, respectively. Additional tests were conducted to further improve the flowsheet. Recirculating a portion of the PLS to the feed of the leach tanks improved the leaching performance by lowering the pH of the leaching system and reducing the contamination recovery by shortening the residence time. Moreover, the removal of Al prior to REE precipitation significantly reduced the oxalic acid consumption in the oxalate precipitation circuit. The modified circuit produced over 90% grade REO by weight from both West Kentucky No. 13 and Fire Clay coarse refuse material in pilot scale continuous test programs. A case analysis model was developed to project the REE and major contaminants concentration in each PLS stream based on the leaching condition, pH cut point, and oxalic acid dosage. A correlation was established using empirical and semi-empirical models. Using the models, chemical consumption required for each stage was predicted based on the projected performance of the hydrometallurgy circuit. After identifying the optimum conditions, validation tests were carried out for the treatment of both West Kentucky No. 13 and Fire Clay coarse refuse materials in the pilot plant. The actual circuit performance and chemical consumptions were very close to the model predictions. Other than the two coarse refuse sources, several secondary feedstocks were also tested in the pilot plant facility. A “heap leach” system was constructed using the coarse refuse material generated from cleaning the West Kentucky No. 13 seam coal. Using the two stage SX rougher and cleaner circuit, a concentrate with a grade >90% REO was produced while recovering >97% of the REEs from the heap leach PLS. Naturally generated acid mine drainage (AMD) from West Kentucky No.13 mine was processed using the multistage precipitation circuit in the pilot plant in a test conducted for a period of 32 hours. The final grade of the mix RE oxide produced from the AMD was 90.84% with an overall circuit recovery of 64%. The primary source of REE was the selective precipitation steps involving iron and aluminum rejection. The hydrophobic-hydrophilic separation (HHS) process was proven to effectively recover coal from fine waste materials. For REM recovery, the HHS process was able to produce concentrates at grades of approximately 1.8% REE on an ash basis; however, recovery values were typically low, <10%, under the optimal conditions determined in the laboratory-scale testing. Staged testing of the pilot-scale HHS process for coal recovery and semi-continuous laboratory testing for REM testing showed that a total concentration ratio of more than 15x was observed for the REM recovery process. A circuit simulation package was developed for REE extraction and purification using a spreadsheet-based platform (Microsoft Excel). The REESim circuit simulation package is configured to track the mass and volume flows of components passing through a series of unit operations specified and configured by the user. The mass rates can then be utilized by the user to determine important performance indicators such as product mass yields, concentrate purity levels, element-by-element recoveries, and so forth. The techno-economic analysis showed that the roasting and leaching operations were the most expensive capital items, each contributing approximately 30% to the total capital cost. One notable contributor to the high production costs was the low REE recovery observed in the pilot scale trials. The product basket price was shown to have a strong influence on the economic viability of the scenarios, with the scandium price being the most significant influencer. Operating cost was shown to be extremely sensitive to REE recovery, REE feed grade, and leaching acid consumption. An analysis of ten different scenarios for a 500 t/h commercial operation revealed that three were economically favorable, producing internal rates of return varying from 27.7% to 33.1% and payback periods of 4 to 5 years. The project successfully developed and demonstrated a process to recover REEs from coal and coal byproducts in a pilot-plant operation which consistently produced over 90% grade REO mix from varies types of feedstocks. Commercialization analysis showed that the technology readiness level successfully achieved TRL 6 at the end of the project and demonstrated the need and the potential for scaling the process to further advance the technologies toward the goal of providing a domestic supply of REEs at a commercial scale.
Superconducting microwave circuits with Josephson junctions, the major platform for quantum computing, can only reach the full capability when connected. This requires an efficient protocol to distribute microwave entanglement. While quantum computers typically use discrete-variable (DV) methods for information encoding, the entire continuous-variable (CV) degree of freedom in electromagnetic fields must be utilized to achieve the highest entanglement distribution rate. Here, we propose a hybrid protocol to resolve the incompatibility between DV microwave quantum computers and CV quantum communications. CV microwave entanglement is distributed using optical swapping of optical-microwave entanglement pairs. To interface with DV microwave quantum computers, we further design a hybrid circuit to simultaneously convert and distill high-quality DV entanglement from noisy CV entanglement. The hybrid circuit is trained with machine-learning algorithms, ensuring high entanglement fidelity and generation rate. In conclusion, our work not only provides a practical method to realize efficient quantum links for superconducting microwave quantum computers, but also opens avenues to bridge the gap between DV and CV quantum systems.