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At least 541 records · Page 30

Hydrothermal Liquefaction: Path to Sustainable Aviation Fuel

A variety of technologies are currently under development for producing sustainable aviation fuel (SAF), and one of the most promising technologies is the hydrothermal liquefaction (HTL) of low-cost waste feedstocks. Organizations across the globe are conducting research and development on HTL technology at scales varying from the laboratory to demonstrations focused on various aspects of technology development. The identification of more advanced and sustainable solutions to maximize the fuel yield while optimizing fuel properties and achieving cost parity with conventional fuels is the major focus in developing HTL technology. This workshop on the application of HTL to produce SAF, coordinated by the U.S. Department of Energy Bioenergy Technologies Office, Commercial Aviation Alternative Fuels Initiative, and Pacific Northwest National Laboratory (PNNL), was held virtually on November 17–19, 2020. A broad spectrum of experts from industry, academia, national laboratories, and government from across the globe participated in the workshop, contributing their ideas, insights, and perspectives. A series of keynote presentations, plenary presentations, and breakout sessions provided an interdisciplinary framework for sharing information and building collaboration. This document provides an overview of the content discussed in the presentations as well as the breakout session discussion. Diverse stakeholder perspectives were gathered, and this wealth of information collectively provides an update on the current state of the field and identifies the key research opportunities.

09 BIOMASS FUELS↗

Efficient Implementation of Artificial Neural Networks for Sensor Data Analysis Based on a Genetic Algorithm

The reliability of many industrial processes depends on the sensor system. However, these sensors can be affected by noise, perturbations and failures. Hence, sensor monitoring and diagnosis are fundamental to guarantee the quality of an industrial process. Nowadays, artificial neural networks (ANN) are widely used in sensor signal processing and diagnosis. However, those ANNs usually require many artificial neurons, being difficult to implement in software and hardware due to their high computational costs. This paper presents an optimized implementation of artificial neurons in ANNs for sensor data analysis using a Genetic Algorithm (GA). The objective of GA is to find an adequate segmentation to reduce the activation function approximation error. One of the advantages of the proposed approach is that the cost function used in GA considers the effect of factors such as the ANN architecture or the number of bits used in arithmetic operations. The proposed ANN implementation technique aims to get the best possible approximation for a specific ANN architecture, making easier its implementation in software and hardware. Simulation and experimental results using FPGA (Field Programmable Gate Array) prove the advantages of the proposed approach for implementing sensor data analysis systems based on ANNs.

D estefani, André↗

Assessment of Technoeconomic Opportunities in Automation for Nuclear Microreactors

Achieving full decarbonization of all economic sectors remains a challenge, especially in niche markets. For example, remote communities and industrial or mining activities detached from the main electric grid heavily rely on fossil fuels, similar to urban and industrial microgrids with combined heat and power needs. A combination of renewables and energy storage is often not suitable due to cost, reliability, intermittency, and large storage requirements. Small nuclear reactors with a flexible purpose could serve these applications. Microreactors (MR) are a class of reactors that are compact, factory manufactured, transportable, and self-regulating. Typically, they generate much less power than their large reactor counterparts. The main advantages of microreactors include the versatile nature of the energy produced, the reliability of supply, and freedom from having to transport and store large quantities of fuels on-site, coupled with the absence of dependence on an electrical grid. A strong business case is needed to move from the microreactor prototype to the commercialization phase. In fact, fossil fuels are still relatively inexpensive, and in the near term, carbon credits will be available to virtually compensate for emissions. For microreactors, one of the main costs in operation and maintenance (O&M) is their staffing levels. In this study, we investigate how to optimize the number (and thus the cost) of workers, moving from a traditional, fully manned, on-site personnel approach to an unmanned, remote personnel approach. We examine four different staffing models that can be implemented as the technology matures and evolves. We estimate the staffing needs of each model and build a business case to justify the substitution of on-site personnel with adequate technologies. To do so, we propose a cost model to quantify potential cost reductions from automating O&M activities. The model accounts for both the reduction in cost derived from the reduced number of full-time-equivalent (FTE) employees and the increase in cost derived from the need to buy new control hardware as needed. Applying the cost model that we created to different scenarios, an on-site O&M cost reduction exceeding 80% can be expected. Additionally, we found that it is more impactful to focus on automating routine O&M tasks rather than attempting to automate transient management (shutdowns, restarts, monitoring condition deviations). In fact, transients typically account for less than 1% of the total FTE time spent on the reactors.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Optimized self-designing key-value storage engine

Embodiments of the invention utilize an optimized key-value storage engine to strike the optimal balance between cloud-cost and performance and supports queries, including updates, lookups, range queries, inserts, and read-modify-writes. Cloud cost is manifested in purchasing both storage and processing resources. The improved approach has the ability to self-design and instantiate holistic configurations given a workload, a cloud budget, and optionally performance goals and a set of Service Level Agreement (SLA) specifications. A configuration reflects an optimized storage engine design in terms of, for example, the individual data structures design (in-memory and on-disk) in the engine as well as their algorithms and interactions, a cloud provider, and the exact virtual machines to be used.

Idreos, Stratos↗

Global techno-economic and life cycle greenhouse gas emissions assessment of solar and wind based renewable hydrogen production

This study conducts a global assessment of renewable hydrogen production pathways, focusing on techno-economic performance and life cycle greenhouse gas (GHG) emissions. It evaluates standalone solar photovoltaic (PV), wind, and hybrid PV/wind systems, integrated with proton exchange membrane (PEM) electrolyzers, through multi-objective optimization and considering embodied emissions in manufacturing PV, wind and electrolyzers. Results identify optimal configurations to minimize levelized cost of hydrogen (LCOH) and carbon intensity (CI) of hydrogen, showing potential reductions of cost and CI by 2030. Standalone PV systems can achieve LCOH values smaller than 6.5 USD/kg H 2 and CI less than 2.5 kg CO 2 eq/kg H 2 in regions with high solar irradiance, such as North Africa, the Middle East and Chile. Wind systems in regions such as Middle East, North Africa, Australia and Central United States achieve LCOH below 5 USD/kg H 2 and CI under 1.5 kg CO 2 eq/kg H 2 . Hybrid systems emerge as the optimal solution for minimizing both the LCOH and CI by maximizing the use of renewable energy. Moreover, the results also indicate that, with the technological advancements, future reduction in the capital cost of renewable energy systems and the PEM electrolyzer as well as the trade of coproduct O 2 could drive the LCOH of all the RES-based hydrogen systems below 1 USD/kg H 2 and the CI below zero in different regions as Middle East, North Africa and Central United State

08 HYDROGEN↗

Models and Strategies for Optimal Demand Side Management in the Chemical Industries

Deregulation and the increase of renewable electricity generation from wind and solar photovoltaics have transformed the U.S. electricity market. Economic and environmental benefits notwithstanding, the presence of renewables has increased variability and uncertainty on the supply side of the grid. Managing demand, rather than generation – a strategy referred to as “demand response (DR)” – is an attractive approach for mitigating this imbalance. DR efforts aim to reduce electricity usage during peak demand times, lessening stress on the grid. Industrial users are particularly attractive entities for DR participation since they present large, localized loads that can provide significant relief on grid demand and –unlike other large loads, such as buildings – are minimally dependent on human needs and preferences. In this project, we accomplished three main objectives. (1) We developed data-driven low-order DR scheduling-relevant dynamic models of chemical processes. Concurrently, we studied the formulation and solution of the associated optimal DR production scheduling problems. (a) A prototype air separation unit (ASU) model was used to generate simulated operating data for initial modeling efforts, which enabled the later use of industrial data for data-driven modeling. (b) We utilized Hammerstein-Wiener (HW) and Finite Step Response (FSR) models to represent nonlinear plant dynamics. (c) The HW models were linearized using exact linearization so they could potentially be embedded in power system models, which are formulated as mixed integer linear programs (MILPs). (d) We solved DR optimization problems under uncertainty and found that even naïve predictions of electricity price and product demand led to significant cost savings benefits. (2) Our DR scheduling optimization problem formulations are amenable to real-time solution. (a) We utilized Lagrangian Relaxation (LR) to efficiently solve the optimization problem by decoupling subproblems linked by complicating constraints. (b) We have achieved computation times for the 3-day DR scheduling problem of an ASU as low as 1.88 minutes. (3) Our representations of the DR behavior of chemical process as grid-level batteries were embedded in power system models. (a) For a small-scale grid, we found that incorporating the dynamics of the chemical plant in the optimal power flow calculations resulted in better resource management leading to up to 15% and 46% cost reduction for the grid and chemical plant operations, respectively, during periods of power line congestion. We have published several works dedicated to modeling and solving DR optimization problems from the user side. These were published in top peer-reviewed journals and are summarized in this report. The most recent work (and papers in preparation) considers DR scheduling from the grid side. Future efforts will consider networked plants (e.g., air separation units operating on a common pipeline) for DR participation, which is expected to amplify the capabilities of industrial DR participants to perform load-shifting. Our consideration of uncertainty in DR has inspired future directions in this area as well: we plan to develop multistage methods to fully account for the effects of uncertainty in DR scheduling.

24 POWER TRANSMISSION AND DISTRIBUTION↗

RL-HEMS: Reinforcement Learning Based Home Energy Management System for HVAC Energy Optimization

Heating, ventilation, and air conditioning (HVAC) is one of the major energy consumers in the residential sector. It is important to be able to monitor and control the energy consumed to provide utility services such as load shaping while satisfying the comfort and economic constraints of the homeowner. The objective of this work is to create the optimal schedule for HVAC operation to reduce the cost while satisfying the home-owner and equipment’s constraints using a model-free Reinforcement Learning (RL)-based optimization. The specific goal is to find the right balance between reducing energy cost, consumption, and customer comfort level. Our research effort addresses this optimization problem using multiple components: the development of initial learning test-bed and implementation of RL techniques on a real home. This will enable the rapid evaluation of the RL techniques and provide an early baseline to train before implementation on site. The RL algorithm is designed to learn the energy use patterns and generate the optimized schedule for HVAC within an acceptable time-interval to satisfy the homeowner’s comfort and minimize the energy usage. Our preliminary results are promising and we have observed a 17% reduction in the total cost and a 15% reduction in the power utilization using our RL-based HVAC model—RL-HEMS.

Kotevska, Olivera↗

Quantum Annealing for Real-World Machine Learning Applications

Optimizing the training of a machine learning pipeline is important for reducing training costs and improving model performance. One such optimizing strategy is quantum annealing, which is an emerging computing paradigm that has shown potential in optimizing the training of a machine learning model. The implementation of a physical quantum annealer has been realized by D-Wave systems and is available to the research community for experiments. Recent experimental results on a variety of machine learning applications have shown interesting results especially under the conditions where the performance of classical machine learning techniques are limited such as limited training data and high dimensional features. This chapter explores the application of D-Wave’s quantum annealer for optimizing machine learning pipelines for real-world classification problems. We review the application domains on which a physical quantum annealer has been used to train machine learning classifiers. We discuss and analyze the experiments performed on the D-Wave quantum annealer for applications such as image recognition, remote sensing imagery, security, computational biology, biomedical sciences, and physics. We discuss the possible advantages and the problems for which quantum annealing is likely to be advantageous over classical computation.

Kumar nath, Rajdeep↗

Approximating a linear multiplicative objective in watershed management optimization

Implementing management practices in a cost-efficient manner is critical for regional efforts to reduce the amount of pollutants entering the Chesapeake Bay. We study the problem of selecting a subset of practices that minimizes pollutant load—subject to budgetary and environmental constraints—as simulated in a widely used regulatory watershed model. Mimicking the computation of pollutant load in the regulatory model, we formulate this problem as a continuous optimization model with a linear multiplicative objective function and linear constraints. To lay the groundwork for incorporating additional stakeholder requirements in the future, especially those that would require integer variables, we present and study a continuous linear optimization model that approximates the nonlinear model. The linear model, which requires an exponential number of variables, arises naturally as an alternative model for the same underlying physical process. We examine the theoretical behavior of these optimization models and investigate restrictions of the linear model to handle its large number of variables. Through extensive computational tests on real and randomly generated instances, we demonstrate that the linear model and its restrictions provide optimal solutions close to those of the nonlinear model in practice, despite poor approximation properties in the worst case. We conclude that the linear model—together with our approach to handling its large number of variables—provides a viable framework from which to extend the optimization model to better meet the needs of the Chesapeake Bay watershed management stakeholders.

54 ENVIRONMENTAL SCIENCES↗

Qubit Assignment Using Time Reversal

As quantum computers with large numbers of qubits become increasingly available, experiments executed on a given device may not utilize all available qubits. In this case, the outcome of executing a quantum program will depend on the ability to efficiently select a subset of high-performing physical qubits. For any given quantum program and device there are many ways to assign physical qubits for execution of the program, and assignments will differ in performance due to the variability in quality across qubits and entangling operations on a single device. Evaluating the performance of each assignment using fidelity estimation introduces significant experimental overhead and will be infeasible for many applications, while relying on standard device benchmarks provides incomplete information about the performance of any specific program. Furthermore, the number of possible assignments grows combinatorially in the number of qubits on the device and in the program, motivating the use of heuristic optimization techniques. We demonstrate a practical solution to the problem of qubit assignment by using simulated annealing with a cost function based on the Loschmidt echo, a diagnostic that measures the reversibility of a quantum process. We provide theoretical justification for this choice of cost function by demonstrating that the optimal qubit assignment coincides with the optimal qubit assignment based on state fidelity in the weak error limit, and we provide experimental justification using diagnostics performed on Google’s superconducting qubit devices. We then establish the performance of simulated annealing for qubit assignment using classical simulations of noisy devices as well as optimization experiments performed on a quantum processor. Our results demonstrate that the use of Loschmidt echoes and simulated annealing provides a scalable and flexible approach to optimizing qubit assignment on near-term hardware.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Opportunities for Hybrid Wind and Solar PV Plants in India

The share of variable renewable energy (VRE) on India's grid has surpassed 100 GW, and the government has ambitious plans reach 450 GW by 2030. One strategy to increase wind and solar PV deployment is through the co-location of wind and solar PV plants to form a single hybrid power plant. Hybrid plants have the potential to reduce transmission infrastructure costs and variability in the output power profile compared to a standalone plant with a single technology, and this resource analysis aims to take a first step towards quantifying the potential savings from hybridizing wind and solar PV plants in India and the size of this opportunity. We utilize a brute-force optimization to minimize the levelized cost of energy (LCOE) for standalone wind, standalone solar PV, and hybrid wind/solar PV plants across all of India. By comparing these LCOEs, we determine that locations where hybrid plants exhibit potential cost savings and grid benefits exhibit both; a high interconnection cost and; a wind capacity factor between roughly 34% and 38%. However, because our work does not capture the value of the electricity generated by looking at energy prices, nor does it quantify the potential of hybrids to provide other value streams such as firm capacity and reserves. Further, because the work does not compare solar PV and wind hybrids to alternative generation technologies or storage systems, it cannot be considered a holistic cost-benefit analysis.

14 SOLAR ENERGY↗

Design and analysis of optimal pre-cooling in residential buildings

Existing pre-cooling strategies provide a means of shifting or reducing the peak demand and/or energy cost in residential buildings. However, majority of them are rule-based and therefore may not be optimal in terms of cost saving, leaving room for improvement. In this paper, an integer linear programming problem that accounts for the thermal properties of a specific home, HVAC system capacity, utility rate structure, and weather conditions and makes use of a home thermal model is formulated. This problem determines the HVAC on/off control signal that minimizes the 24-h energy cost while maintaining thermal comfort and calculates the corresponding optimal indoor air temperature. The model is constructed using home thermal properties identified via data training in real-time. Through simulation, the energy performance of the proposed optimal pre-cooling strategy is investigated and compared with three rule-based operation strategies from the literature. It is found that the optimal strategy requires the least energy consumption without sacrificing thermal comfort. The superb energy performance of the optimal strategy is attributed to a longer runtime of the HVAC system in cool outdoor air conditions and to the elimination of deadband in HVAC operation, which is required by the rule-based strategies, to allow the indoor air temperature to stay near the thermal comfort upper bound as much as possible. In terms of energy cost, the rule-based operation strategies require 3.52, 1.90, and 2.79, respectively, while the optimal strategy only requires 1.52. These figures represent a saving of 56.82%, 20.00%, and 45.52%, respectively. The results suggest that the optimal strategy is indeed significantly more effective than the existing rule-based operation strategies.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Structural Optimization (Final Technical Report V.2.0)

The overall Project (Project) objective is to materially decrease the leveled cost of energy (LCOE) of the Columbia Power (CPwr) StingRAY utility-scale wave energy converter (WEC). This will be achieved by reducing structural material and manufacturing costs and increasing energy output. In this Project, improving the overall Power-to-Weight ratio (PWR) is accomplished through lowering design margins - allowing for weight reduction and more efficient, cost-effective WEC manufacturing and assembly - and by optimizing mass-related WEC performance parameters, such as center of gravity and system inertia. A mixed materials approach to further structural optimization was developed under this Project and validated with extensive laboratory structural testing. This approach substitutes fiber-reinforced plastic (FRP) for steel where appropriate. The benefits of steel are maintained where most useful, for instance at structural joints where the stiffness of steel is required, and the complex geometry is more readily fabricated with steel. However, there are structural spans whose simple shapes are readily fabricated with mandrel-wound FRP and where significant cost and weight savings can be found. An adhesive, double lap shear joint is used to join the FRP and steel subcomponents.

16 TIDAL AND WAVE POWER↗

Electrolyte and Cutoff Potential Effects on Cycle Life of Li4Ti5O12/LiNi0.9Mn0.1O2 Batteries for Behind-the-Meter Storage Applications

Behind-the-Meter Storage (BTMS) is a stationary battery energy storage system that is connected to the electrical distribution system on the customer's side of the utility's service meter. BTMS systems are used to store electrical energy from the grid as well as inconstant, renewable energy, such as local solar and wind generation. A successful BTMS system will allow the customer to pair their energy generation and storage to optimize electrical consumption from the grid, improving reliability and minimizing cost. For BTMS applications, batteries must be designed and optimized with different set of criteria from other leading segments of the Li-ion battery market, like transportation, due the system being stationary and proximal to the residential or commercial building it's benefitting. BTMS applications prioritize safety, cost (low/no-critical materials), reliability (20-year calendar life), and durability (10,000 cycle life), while having the ability to (minimally) compromise energy density and rate capability. Lithium titanate (Li4Ti5O12-, LTO) is a promising anode candidate for BTMS applications due to its high safety and capacity retention, while maintaining a reasonable 160 mAhg-1 reversable capacity and composition of relatively abundant materials. (1) Specifically, LTO has a high working voltage which helps to prevent Li dendrite formation, improving safety. Furthermore, LTO also has negligible lithiation-based volume change, leading to less mechanical pulverization, or loss of active material, upon cycling. For the cathode, materials with little or no Co are of high interest due to the high cost and low abundance of Co. LiMn2O4 (LMO) has been paired with LTO for BTMS applications in the past due to its safety, low cost (abundancy), and reasonably high operating voltage. (2-4) However, the low capacity of LMO limits energy density and specific energy. While not the highest priority for BTMS applications, increasing energy density will enable deployment in space constrained BTMS applications and decrease total cost. LiNi0.9Mn0.1O2 (LN-MO) is a recently developed material with promise due to its high operating voltage and relatively low price. (5) However, Ni-rich layered oxides, including LNMO, tend to struggle with capacity retention during high-voltage cycling due to mechanical pulverization, irreversible phase transitions, and unstable solid-electrolyte interphase. The study presented here focuses on building an understanding of how electrolyte solvent and varied cutoff potentials will impact the cycle life of LTO/LN-MO cells. Specifically, a comparison is provided between ethylene carbonate (EC), ethyl methyl carbonate (EMC), fluoroethylene carbonate (FEC), and Gen2 electrolyte solvents with 1M Lithium hexafluorophosphate (LiPF6) salt, cycling to two upper termination potentials, 2.6V and 2.7V. Electrochemical testing and diagnostics (e.g., differential capacity analysis, area specific impedance, constant voltage hold, and rate capability) and post-mortem characterization will be used to understand the aging behavior and failure mechanisms of the 8 cell combinations (four electrolytes and two voltage cutoffs). Cells with FEC electrolyte showed a lower initial capacity compared to cells with Gen2, EMC, and EC cycling at both voltages; however, the cells with FEC showed consistent trends in capacity retention with 2.6V and 2.7V termination potentials, while the cells with the other electrolytes showed much higher rates of capacity loss when cycling to the higher voltage. These results indicate that FEC may play a role in improving durability of high-voltage, Ni-rich electrode systems for use in high-cycle applications, such as BTMS.

electrolyte↗

Sensor System and Observer Algorithm Co-Design For Modern Internal Combustion Engine Air Management Based on H2 Optimization

This paper outlines a novel sensor selection and observer design algorithm for linear time-invariant systems with both process and measurement noise based on H 2 optimization to optimize the tradeoff between the observer error and the number of required sensors. The optimization problem is relaxed to a sequence of convex optimization problems that minimize the cost function consisting of the H 2 norm of the observer error and the weighted l 1 norm of the observer gain. An LMI formulation allows for efficient solution via semi-definite programing. The approach is applied here, for the first time, to a turbo-charged spark-ignited engine using exhaust gas circulation to determine the optimal sensor sets for real-time intake manifold burnt gas mass fraction estimation. Simulation with the candidate estimator embedded in a high fidelity engine GT-Power model demonstrates that the optimal sensor sets selected using this algorithm have the best H 2 estimation performance. Sensor redundancy is also analyzed based on the algorithm results. This algorithm is applicable for any type of modern internal combustion engines to reduce system design time and experimental efforts typically required for selecting optimal sensor sets.

Zhang, Xu↗

Techno-Economic Implications of Electrical Machine Scaling for Wave Energy Converters: Preprint

The sizing of an electrical machine for a Wave Energy Converter (WEC) can have a substantial impact on the overall sizing, cost, and rating of the device. An electrical generator is typically part of the power take-off (PTO) system, which is the mechanism by which the energy absorbed by the prime mover is transformed into useable electrical. For practically all WECs, the rate of change of actuation is predominantly determined by the wave resource (i.e., the wave height and frequency) and devices will see a sinusoidally varying velocity according to the wave conditions. The same can then be said for both directly and indirectly coupled PTOs with electrical generators. This techno-economic study investigates electrical machine scaling and associated cost implications through core machine design theory, manufacturer data, supporting literature, and the DOE sponsored Reference Model Project (RMP). The RMP was a partnered effort to develop open-source marine energy (ME) point designs as reference models (RMs) to benchmark ME technology performance and costs, methods for design and analysis of ME technologies, estimations for capital costs, operational costs, and levelized costs of energy (LCOE). The results from this study show torque is directly related to (1) the physical size of the machine required to increase the airgap sheer stresses, (2) the amount of active material, (3) the support structure, (4) bearing size and rating, and (5) offshore cable rating, all of which have a significant effect on overall system costs in terms of both CAPEX and OPEX. This paper aims to be a critical benchmark in helping determine an “optimal” nameplate rating for wave energy devices and their associated PTO. With an optimized rating and sizing process, WEC costs can be reduced, and overall performance can be improved.

cables↗

Techno-Economic Implications of Electrical Machine Scaling for Wave Energy Converters

The sizing of an electrical machine for a Wave Energy Converter (WEC) can have a substantial impact on the overall sizing, cost, and rating of the device. An electrical generator is typically part of the power take-off (PTO) system, which is the mechanism by which the energy absorbed by the prime mover is transformed into useable electrical. For practically all WECs, the rate of change of actuation is predominantly determined by the wave resource (i.e., the wave height and frequency) and devices will see a sinusoidally varying velocity according to the wave conditions. The same can then be said for both directly and indirectly coupled PTOs with electrical generators. This techno-economic study investigates electrical machine scaling and associated cost implications through core machine design theory, manufacturer data, supporting literature, and the DOE sponsored Reference Model Project (RMP). The RMP was a partnered effort to develop open-source marine energy (ME) point designs as reference models (RMs) to benchmark ME technology performance and costs, methods for design and analysis of ME technologies, estimations for capital costs, operational costs, and levelized costs of energy (LCOE). The results from this study show torque is directly related to (1) the physical size of the machine required to increase the airgap sheer stresses, (2) the amount of active material, (3) the support structure, (4) bearing size and rating, and (5) offshore cable rating, all of which have a significant effect on overall system costs in terms of both CAPEX and OPEX. This paper aims to be a critical benchmark in helping determine an “optimal” nameplate rating for wave energy devices and their associated PTO. With an optimized rating and sizing process, WEC costs can be reduced, and overall performance can be improved.

cables↗

Large gradients via correlation in random parameterized quantum circuits

Scaling of variational quantum algorithms to large problem sizes requires efficient optimization of random parameterized quantum circuits. For such circuits with uncorrelated parameters, the presence of exponentially vanishing gradients in cost function landscapes is an obstacle to optimization by gradient descent methods. In this work, we prove that reducing the dimensionality of the parameter space by utilizing circuit modules containing spatially or temporally correlated gate layers can allow one to circumvent the vanishing gradient phenomenon. Here, examples are drawn from random separable circuits and asymptotically optimal variational versions of Grover's algorithm based on the quantum alternating operator ansatz. In the latter scenario, our bounds on cost function variation imply a transition between vanishing gradients and efficient trainability as the number of layers is increased toward $\mathcal{O}\left({2}^{n/2}\right)$, the optimal oracle complexity of quantum unstructured search.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗