Quantum algorithms for generator coordinate methods
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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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97 MATHEMATICS AND COMPUTING↗
A comparative study of machine learning models for predicting the state of reactive mixing
Mixing phenomena are important mechanisms controlling flow, species transport, and reaction processes in fluids and porous media. Accurate predictions of reactive mixing are critical for many Earth and environmental science problems such as contaminant fate and remediation, macroalgae growth, and plankton biomass evolution. Here, to investigate the evolution of mixing dynamics under different scenarios (e.g., anisotropy, fluctuating velocity fields), a finite-element-based numerical model was built to solve the fast, irreversible bimolecular reaction-diffusion equations to simulate a range of reactive-mixing scenarios. A total of 2,315 simulations were performed using different sets of model input parameters comprising various spatial scales of vortex structures in the velocity field, time-scales associated with velocity oscillations, the perturbation parameter for the vortex-based velocity, anisotropic dispersion contrast (i.e., ratio of longitudinal-to-transverse dispersion), and molecular diffusion. The outputs comprised concentration profiles of reactants and products. The inputs to and outputs from these simulations were concatenated into feature and label matrices, respectively, to train 20 different machine learning (ML) models intended to emulate system behavior. These 20 ML emulators, based on linear methods, Bayesian methods, ensemble learning methods, and multilayer perceptrons (MLPs), were trained to classify the state of mixing and predict three quantities of interest (QoIs) characterizing species production, decay (i.e., average concentration, square of average concentration), and degree of mixing (i.e., variances of species concentration). Unsurprisingly, linear classifiers and regressors failed to reproduce the QoIs; however, ensemble methods (classifiers and regressors) and the MLP model accurately classified the state of reactive mixing and the QoIs. Among ensemble methods, random forest and decision-tree-based AdaBoost faithfully predicted the QoIs. At run time, trained ML emulators produced results times faster than the finite-element simulations. Due to their low computational expense and high accuracy, ensemble and MLP models are excellent emulators for these numerical simulations and great utilities in uncertainty quantification exercises, which can require 1,000s of forward model runs.
97 MATHEMATICS AND COMPUTING↗
Quantum computing and preconditioners for hydrological linear systems
Modeling hydrological fracture networks is a hallmark challenge in computational earth sciences. Accurately predicting critical features of fracture systems, e.g. percolation, can require solving large linear systems far beyond current or future high performance capabilities. Quantum computers can theoretically bypass the memory and speed constraints faced by classical approaches, however several technical issues must first be addressed. Chief amongst these difficulties is that such systems are often ill-conditioned, i.e. small changes in the system can produce large changes in the solution, which can slow down the performance of linear solving algorithms. We test several existing quantum techniques to improve the condition number, but find they are insufficient. We then introduce the inverse Laplacian preconditioner, which improves the scaling of the condition number of the system from O(N) to O($\sqrt{N}$) and admits a quantum implementation. These results are a critical first step in developing a quantum solver for fracture systems, both advancing the state of hydrological modeling and providing a novel real-world application for quantum linear systems algorithms.
97 MATHEMATICS AND COMPUTING↗
Numerical evidence against advantage with quantum fidelity kernels on classical data
Quantum machine learning techniques are commonly considered one of the most promising candidates for demonstrating practical quantum advantage. In particular, quantum kernel methods have been demonstrated to be able to learn certain classically intractable functions efficiently if the kernel is well aligned with the target function. In the more general case, quantum kernels are known to suffer from exponential “flattening” of the spectrum as the number of qubits grows, preventing generalization and necessitating the control of the inductive bias by hyperparameters. We show that the general-purpose hyperparameter-tuning techniques proposed to improve the generalization of quantum kernels lead to the kernel becoming well approximated by a classical kernel, removing the possibility of quantum advantage. We provide extensive numerical evidence for this phenomenon utilizing multiple previously studied quantum feature maps and both synthetic and real data. Our results show that unless novel techniques are developed to control the inductive bias of quantum kernels, they are unlikely to provide a quantum advantage on classical data that lacks special structure.
Quantum Information, Science & Technology↗
Preparing Precollege Students for the Second Quantum Revolution with Core Concepts in Quantum Information Science
After the passage of the U.S. National Quantum Initiative Act in December 2018, the National Science Foundation (NSF) and the Office of Science and Technology Policy (OSTP) recently assembled an interagency working group and conducted a workshop titled “Key Concepts for Future Quantum Information Science Learners” that focused on identifying core concepts for future curricular and educator activities to help precollege students engage with quantum information science (QIS). Helping precollege students learn these key concepts in QIS is an effective approach to introducing them to the second quantum revolution and inspiring them to become future contributors in the growing field of quantum information science and technology as leaders in areas related to quantum computing, communication, and sensing. This paper is a call to precollege educators to contemplate including QIS concepts into their existing courses at appropriate levels and get involved in the development of curricular materials suitable for their students. Also, research shows that compare-and-contrast activities can provide an effective approach to helping students learn. Therefore, we illustrate a pedagogical approach that contrasts the classical and quantum concepts so that educators can adapt them for their students in their lesson plans to help them learn the differences between key concepts in quantum and classical contexts.
Education & Educational Research↗
Increasing the Measured Effective Quantum Volume with Zero Noise Extrapolation
Quantum volume is a full-stack benchmark for near-term quantum computers. It quantifies the largest size of a square circuit which can be executed on the target device with reasonable fidelity. Error mitigation is a set of techniques intended to remove the effects of noise present in the computation of noisy quantum computers when computing an expectation value of interest. Effective quantum volume is a proposed metric that applies error mitigation to the quantum volume protocol to evaluate the effectiveness not only of the target device but also of the error mitigation algorithm. Digital zero-noise extrapolation is an error mitigation technique that estimates the noiseless expectation value using circuit folding to amplify errors by known scale factors and then extrapolating computed expectation values to the zero-noise limit. Here we demonstrate that zero-noise extrapolation, with global and local unitary folding with fractional scale factors, in conjunction with dynamical decoupling, can increase the effective quantum volume over the vendor-measured quantum volume. Specifically, we measure the effective quantum volume of four IBM Quantum superconducting processor units, obtaining values that are larger than the vendor-measured quantum volume on each device. This is the first such increase reported.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
LDRD 2022 Annual Report: Laboratory Directed Research and Development Program Activities
Each year, Brookhaven National Laboratory (BNL) is required to provide a report of its completed Laboratory Directed Research and Development Program (LDRD) projects to the Department of Energy (DOE) Office of Scientific and Technical Information in accordance with DOE Order 413.2C Chg1 (MinChg) dated August 2, 2018. This report provides a detailed look at the scientific and technical activities for each of the LDRD projects funded by BNL in FY 2022, in fulfillment of that requirement. In FY 2022, the BNL LDRD Program funded 70 projects, 30 of which were new starts, at a total cost of $17.2M. The investments that BNL makes in its LDRD program support the Laboratory’s strategic goals. BNL has identified seven scientific initiatives that define the Laboratory’s scientific future and that will enable it to realize its overall vision. This requires simultaneous excellence in all aspects of BNL’s work – from science and operations, to external partnerships with the local, state, and national communities, and beyond. This is enabled by safe, efficient, and secure operations; by an unwavering commitment to a diverse, equitable, and inclusive environment, including workforce development, both with staff and reaching out to the community; and by a strong focus on renewed infrastructure. The seven scientific initiatives are: 1) Nuclear Physics: uncover the structure of visible matter by constructing and operating the Electron-Ion Collider at BNL to maintain international leadership in nuclear physics for decades; 2) Clean Energy and Climate: support a net-zero U.S. economy through fundamental research in basic energy and climate sciences to revolutionize grid-scale storage, renewable integration, and the study of atmospheric processes with a new facility to improve climate predictability; 3) Quantum Information Science and Technology: discover new quantum materials to enhance quantum computers and develop an entanglement sharing quantum network as a prototype for the first quantum internet; 4) Discovery Science Driven by the Human-AI Facility Integration: revolutionize the operation of experiments across the sciences at user facilities and in core programs; 5) High Energy Physics: understand the origin of space and time with the ATLAS high luminosity upgrade at CERN and the future Long Baseline Neutrino Facility/Deep Underground Neutrino Experiment; 6) Isotope Production: accelerate and expand isotope production to ensure the security of the Nation’s supply; 7) Accelerator Science and Technology: harness the cross-cutting accelerator science expertise at BNL to develop new facilities, improve and expand its user facilities, and promote the use of accelerators in industry. The funded projects support BNL’s seven scientific initiatives and priority programs as well as new areas of research and competencies at the Laboratory that are consistent with the Laboratory’s vision and mission. In total, these LDRD investments supported 43 postdoctoral researchers in whole or in part and resulted in 138 publications and 7 awards. This Program Activities Report represents the future of BNL science; it is an impressive body of exploratory work that investigates many scientific and technical directions in support of the DOE and BNL missions.
99 GENERAL AND MISCELLANEOUS↗
Quantum complexity in gravity, quantum field theory, and quantum information science
Quantum complexity quantifies the difficulty of preparing a state or implementing a unitary transformation with limited resources. Applications range from quantum computation to condensed matter physics and quantum gravity. Here, we seek to bridge the approaches of these fields, which define and study complexity using different frameworks and tools. We describe several definitions of complexity, along with their key properties. In quantum information theory, we focus on complexity growth in random quantum circuits. In quantum many-body systems and quantum field theory (QFT), we discuss a geometric definition of complexity in terms of geodesics on the unitary group. In dynamical systems, we explore a definition of complexity in terms of state or operator spreading, as well as concepts from tensor-networks. We also outline applications to simple quantum systems, quantum many-body models, and QFTs including conformal field theories (CFTs). Finally, we explain the proposed relationship between complexity and gravitational observables within the holographic anti-de Sitter (AdS)/CFT correspondence.
Baiguera, Stefano [Istituto Nazionale di Fisica Nu↗
Implementation and analysis of quantum computing application to Higgs boson reconstruction at the large Hadron Collider
With the advent of the High-Luminosity Large Hadron Collider (HL-LHC) era, high energy physics (HEP) event selection will require new approaches to rapidly and accurately analyze vast databases. The current study addresses the enormity of HEP databases in an unprecedented manner—a quantum search using Grover’s Algorithm (GA) on an unsorted database, ATLAS Open Data, from the ATLAS detector. A novel method to identify rare events at 13 TeV in CERN’s LHC using quantum computing (QC) is presented. As indicated by the Higgs boson decay channel H→ZZ*→4l , the detection of four leptons in one event may be used to reconstruct the Higgs boson and, more importantly, evince Higgs boson decay to some new phenomena, such as H→ZZ d →4l . Searching the dataset for collisions resulting in detection of four leptons using a Jupyter Notebook, a classical simulation of GA, and several quantum computers with multiple qubits, the current application was found to make the proper selection in the unsorted dataset. Quantum search efficacy was analyzed for the incoming HL-LHC by implementing the QC method on multiple classical simulators and IBM’s quantum computers with the IBM Qiskit Open Source Software. The current QC application provides a novel, high-efficiency alternative to classical database searches, demonstrating its potential utility as a rapid and increasingly accurate search method in HEP.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Maximized Information Gain of Next Generation Pulsed Power Using Optimized Design of Z-Machine Experiments
This project develops a Bayesian optimization approach to extracting insights from Z Machine experimental data to determine if and how these insights can be used to extrapolate to a larger facility. The primary goal is to address the scientific challenge of informing how confidently experimental conditions can be predicted on a next generation facility, the design of which requires the reliable extrapolation of current high energy density technologies to regimes yet unobserved, except by costly high-fidelity computational models. Maximizing the use of presently available data and understanding how it informs future endeavors is critically important to enable transformative pulsed power and the science of extreme conditions. We explore a Bayesian optimization approach to experimental design which combines information theory, experimental data, and computational modeling to explore how information gain can be maximized.
97 MATHEMATICS AND COMPUTING↗
Theory of overparametrization in quantum neural networks
The prospect of achieving quantum advantage with quantum neural networks (QNNs) is exciting. Understanding how QNN properties (for example, the number of parameters $M$) affect the loss landscape is crucial to designing scalable QNN architectures. Here we rigorously analyze the overparametrization phenomenon in QNNs, defining overparametrization as the regime where the QNN has more than a critical number of parameters $M_c$ allowing it to explore all relevant directions in state space. In this study, our main results show that the dimension of the Lie algebra obtained from the generators of the QNN is an upper bound for $M_c$, and for the maximal rank that the quantum Fisher information and Hessian matrices can reach. Underparametrized QNNs have spurious local minima in the loss landscape that start disappearing when $M$ ≥ $M_c$. Thus, the overparametrization onset corresponds to a computational phase transition where the QNN trainability is greatly improved. We then connect the notion of overparametrization to the QNN capacity, so that when a QNN is overparametrized, its capacity achieves its maximum possible value.
97 MATHEMATICS AND COMPUTING↗
Remote operation of the DIII-D National Fusion Facility
Abstract Full remote scientific operation of the DIII-D National Fusion Facility is now possible through significant advances in the computer science hardware and software infrastructure made over the last decade. Capabilities around information visualization, data movement, and communication have all been enhanced. The level of capability deployed to remotely operate DIII-D required an infrastructure advancement over what had previously been achieved in the fusion community. The large quantity of real-time data that is automatically displayed on DIII-D’s control room screens can now be visualized by remote participants via web-based applications. New audio/video solutions using the VoIP and instant messaging application Discord have been implemented to mimic the dynamic and ad-hoc scientific conversations that are critical in successfully operating an experimental campaign. Discord’s ability for a user to rapidly move between audio channels, text with images, and share screens is a significant enhancement over traditional videoconferencing tools. In addition, multiple combinations of broadcast audio are made available via a web-based application to allow remote participants to simultaneously listen to general announcements/sounds while conducting their own specific conversations. Secure methodologies have been put into place to allow remote control of hardware including DIII-D’s plasma control system application. Secure methods also included the ability of the on-site team to closely coordinate their work with remote team members which has been enhanced through extensions to the wireless network and the use of tablet computers for audio/video/screen sharing. However, no amount of software can fully replace the need for ‘hands on hardware.’ This infrastructure was severely stress tested during the COVID-19 pandemic where occupancy of the DIII-D control room was restricted. Operational efficiency during the pandemic, measured in discharges per hour, remained high (3.8 ± 0.8) compared to values obtained pre-pandemic (3.7 ± 0.8).
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
A substitutional quantum defect in WS2 discovered by high-throughput computational screening and fabricated by site-selective STM manipulation
Abstract Point defects in two-dimensional materials are of key interest for quantum information science. However, the parameter space of possible defects is immense, making the identification of high-performance quantum defects very challenging. Here, we perform high-throughput (HT) first-principles computational screening to search for promising quantum defects within WS 2 , which present localized levels in the band gap that can lead to bright optical transitions in the visible or telecom regime. Our computed database spans more than 700 charged defects formed through substitution on the tungsten or sulfur site. We found that sulfur substitutions enable the most promising quantum defects. We computationally identify the neutral cobalt substitution to sulfur ( $${\rm{Co}}_{{{{{{{{\rm{S}}}}}}}}}^{0}$$ Co S 0 ) and fabricate it with scanning tunneling microscopy (STM). The $${\rm{Co}}_{{{{{{{{\rm{S}}}}}}}}}^{0}$$ Co S 0 electronic structure measured by STM agrees with first principles and showcases an attractive quantum defect. Our work shows how HT computational screening and nanoscale synthesis routes can be combined to design promising quantum defects.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Toward Mixed Analog-Digital Quantum Signal Processing: Quantum AD/DA Conversion and the Fourier Transform
Signal processing stands as a pillar of classical computation and modern information technology, applicable to both analog and digital signals. Recently, advancements in quantum information science have suggested that quantum signal processing (QSP) can enable more powerful signal processing capabilities. However, the developments in QSP have primarily leveraged digital quantum resources, such as discrete-variable (DV) systems like qubits, rather than analog quantum resources, such as continuous-variable (CV) systems like quantum oscillators. Consequently, there remains a gap in understanding how signal processing can be performed on hybrid CV-DV quantum computers. Here we address this gap by developing a new paradigm of mixed analog-digital QSP. We demonstrate the utility of this paradigm by showcasing how it naturally enables analog-digital conversion of quantum signals—specifically, the transfer of states between DV and CV quantum systems. We then show that such quantum analog-digital conversion enables new implementations of quantum algorithms on CV-DV hardware. This is exemplified by realizing the quantum Fourier transform of a state encoded on qubits via the free-evolution of a quantum oscillator, albeit with a runtime exponential in the number of qubits due to information theoretic arguments. Collectively, this work marks a significant step forward in hybrid CV-DV quantum computation, providing a foundation for scalable analog-digital signal processing on quantum processors.
42 ENGINEERING↗
Deep learning of free boundary and Stefan problems
Free boundary problems appear naturally in numerous areas of mathematics, science and engineering. These problems present a great computational challenge because they necessitate numerical methods that can yield an accurate approximation of free boundaries and complex dynamic interfaces. In this work, we propose a multi-network model based on physics-informed neural networks to tackle a general class of forward and inverse free boundary problems called Stefan problems. Specifically, we approximate the unknown solution as well as any moving boundaries by two deep neural networks. Besides, we formulate a new type of inverse Stefan problems that aim to reconstruct the solution and free boundaries directly from sparse and noisy measurements. We demonstrate the effectiveness of our approach in a series of benchmarks spanning different types of Stefan problems, and illustrate how the proposed framework can accurately recover solutions of partial differential equations with moving boundaries and dynamic interfaces. All code and data accompanying this manuscript are publicly available at https://github.com/PredictiveIntelligenceLab/DeepStefan.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Exponential concentration in quantum kernel methods
Kernel methods in Quantum Machine Learning (QML) have recently gained significant attention as a potential candidate for achieving a quantum advantage in data analysis. Among other attractive properties, when training a kernel-based model one is guaranteed to find the optimal model’s parameters due to the convexity of the training landscape. However, this is based on the assumption that the quantum kernel can be efficiently obtained from quantum hardware. In this work we study the performance of quantum kernel models from the perspective of the resources needed to accurately estimate kernel values. We show that, under certain conditions, values of quantum kernels over different input data can be exponentially concentrated (in the number of qubits) towards some fixed value. Thus on training with a polynomial number of measurements, one ends up with a trivial model where the predictions on unseen inputs are independent of the input data. We identify four sources that can lead to concentration including expressivity of data embedding, global measurements, entanglement and noise. For each source, an associated concentration bound of quantum kernels is analytically derived. Lastly, we show that when dealing with classical data, training a parametrized data embedding with a kernel alignment method is also susceptible to exponential concentration. Our results are verified through numerical simulations for several QML tasks. Altogether, we provide guidelines indicating that certain features should be avoided to ensure the efficient evaluation of quantum kernels and so the performance of quantum kernel methods.
97 MATHEMATICS AND COMPUTING↗
Parallelized telecom quantum networking with an ytterbium-171 atom array
The integration of quantum computers and sensors into a quantum network enables new capabilities in quantum information science. Most networks with atom-like qubits operate at visible or near-ultraviolet wavelengths and require conversion to the telecom band for long-distance communication, which reduces efficiency and potentially introduces noise. In this article we report high-fidelity entanglement between ytterbium-171 atoms and optical photons generated directly in the telecommunication band, where fibre loss is low. The nuclear spin of the atom is entangled with a single photon in the time-bin basis, yielding a high atom-measurement-corrected atom–photon Bell state fidelity. This can be further improved by addressing photon measurement errors. By imaging the atom array onto an optical fibre array, we also implement a parallelized networking protocol that can increase the remote entanglement rate proportionately with the number of channels. We also preserve coherence on a memory qubit during operations on communication qubits. These results support the integration of atomic systems into scalable quantum networks.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗