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High-dimensional multi-fidelity Bayesian optimization for quantum control

Abstract We present the first multi-fidelity Bayesian optimization (BO) approach for solving inverse problems in the quantum control of prototypical quantum systems. Our approach automatically constructs time-dependent control fields that enable transitions between initial and desired final quantum states. Most importantly, our BO approach gives impressive performance in constructing time-dependent control fields, even for cases that are difficult to converge with existing gradient-based approaches. We provide detailed descriptions of our machine learning methods as well as performance metrics for a variety of machine learning algorithms. Taken together, our results demonstrate that BO is a promising approach to efficiently and autonomously design control fields in general quantum dynamical systems.

Computer Science↗

Quantum machine learning with differential privacy

Abstract Quantum machine learning (QML) can complement the growing trend of using learned models for a myriad of classification tasks, from image recognition to natural speech processing. There exists the potential for a quantum advantage due to the intractability of quantum operations on a classical computer. Many datasets used in machine learning are crowd sourced or contain some private information, but to the best of our knowledge, no current QML models are equipped with privacy-preserving features. This raises concerns as it is paramount that models do not expose sensitive information. Thus, privacy-preserving algorithms need to be implemented with QML. One solution is to make the machine learning algorithm differentially private, meaning the effect of a single data point on the training dataset is minimized. Differentially private machine learning models have been investigated, but differential privacy has not been thoroughly studied in the context of QML. In this study, we develop a hybrid quantum-classical model that is trained to preserve privacy using differentially private optimization algorithm. This marks the first proof-of-principle demonstration of privacy-preserving QML. The experiments demonstrate that differentially private QML can protect user-sensitive information without signficiantly diminishing model accuracy. Although the quantum model is simulated and tested on a classical computer, it demonstrates potential to be efficiently implemented on near-term quantum devices [noisy intermediate-scale quantum (NISQ)]. The approach’s success is illustrated via the classification of spatially classed two-dimensional datasets and a binary MNIST classification. This implementation of privacy-preserving QML will ensure confidentiality and accurate learning on NISQ technology.

97 MATHEMATICS AND COMPUTING↗

Quantum graph learning and algorithms applied in quantum computer sciences and image classification

Graph and network theory play a fundamental role in quantum computer sciences, including quantum information and computation. Random graphs and complex network theory are pivotal in predicting novel quantum phenomena, where entangled links are represented by edges. Quantum algorithms have been developed to enhance solutions for various network problems, giving rise to quantum graph computing and quantum graph learning (QGL). Here, in this review, we explore graph theory and graph learning methods as powerful tools for quantum computers to generate efficient solutions to problems beyond the reach of classical systems. We delve into the development of quantum complex network theory and its applications in quantum computation, materials discovery, and research. We also discuss quantum machine learning (QML) methodologies for effective image classification using qubits, quantum gates, and quantum circuits. Additionally, the paper addresses the challenges of QGL and algorithms, emphasizing the steps needed to develop flexible QGL solvers. This review presents a comprehensive overview of the fields of QGL and QML, highlights recent advancements, and identifies opportunities for future research.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A Novel Spatial-Temporal Variational Quantum Circuit to Enable Deep Learning on NISQ Devices

Quantum computing presents a promising approach for machine learning with its capability for extremely parallel computation in high-dimension through superposition and entanglement. Despite its potential, existing quantum learning algorithms, such as Variational Quantum Circuits (VQCs), face challenges in handling more complex datasets, particularly those that are not linearly separable. What’s more, it encounters the deployability issue, making the learning models suffer a drastic accuracy drop after deploying them to the actual quantum devices. To overcome these limitations, this paper proposes a novel spatial-temporal design, namely “ST-VQC”, to integrate nonlinearity in quantum learning and improve the robustness of the learning model to noise. Specifically, ST-VQC can extract spatial features via a novel block-based encoding quantum sub-circuit coupled with a layer-wise computation quantum sub-circuit to enable temporal-wise deep learning. Additionally, a SWAP-Free physical circuit design is devised to improve robustness. These designs bring a number of hyperparameters. After a systematic analysis of the design space for each design component, an automated optimization framework is proposed to generate the ST-VQC quantum circuit. The proposed ST-VQC has been evaluated on two IBM quantum processors, ibm-cairo with 27 qubits and ibmq-lima with 7 qubits to assess its effectiveness. The results of the evaluation on the standard dataset for binary classification show that ST-VQC can achieve over 30% accuracy improvement compared with existing VQCs on actual quantum computers. Moreover, on a non-linear synthetic dataset, the STVQC outperforms a linear classifier by 27.9%, while the linear classifier using classical computing outperforms the existing VQC by 15.58%.

Li, Jinyang↗

Studying the hadron structure with PANDA and CLAS using machine learning techniques

The hadron spectroscopy and structure are currently very active fields of research to study the non-perturbative regime of quantum chronodynamics. The first one studies the complex structure of excited hadrons by looking at their decay products, while the latter uses lepton scattering on nucleons. Both methods require reconstruction algorithms with great efficiency and good particle identification and background rejection rates. This work aims to provide these by either improving the existing methods or developing new ones. The first part of this document presents a feasibility study of a predicted hybrid charmonium state for the PANDA experiment. Lattice QCD calculations predict the ground state hybrid charmonium to be a spin exotic with quantum numbers of JP C = 1?+ at a mass of around 4.3 GeV with a width to be around 20 MeV. A machine learning based data analysis scheme is proposed to further improve the signal efficiency and the background reduction, alongside with improvements of the analysis software (PandaRoot), that are vital for this study. These improvements include a reworked clustering algorithm for the electromagnetic calorimeter (EMC) and an optimized monte carlo matching for neutral particles. The second part of this document is about studying the proton structure. A multidimensional study of the structure function ratio Fsin(?)LU /FUU has been performed for K±, based on the measurement of beam-spin asymmetries. It uses the high statistics data recorded with the CLAS12 spectrometer at Jefferson Laboratory. Fsin(?)LU is a twist-3 quantity that provides information about the quark gluon correlations in the proton. This document will present for the first time a simultaneous analysis of two kaon channels over a large kinematic range of z, xB , PT and Q2 with virtualities Q2 ranging from 1 GeV2 up to 8 GeV2 using machine learning techniques for improved particle identification.

Kripko, Aron↗

High-Dimensional Similarity Search with Quantum-Assisted Variational Autoencoder

Recent progress in quantum algorithms and hardware indicates the potential importance of quantum computing in the near future. However, finding suitable application areas remains an active area of research. Quantum machine learning is touted as a potential approach to demonstrate quantum advantage within both the gate-model and the adiabatic schemes. For instance, the QVAE has been proposed as a quantum enhancement to the discrete VAE. We extend on previous work and study the real-world applicability of a QVAE by presenting a proof-of-concept for similarity search in large-scale high-dimensional datasets. While exact and fast similarity search algorithms are available for low dimensional datasets, scaling to high-dimensional data is non-trivial. We show how to construct a space-efficient search index based on the latent space representation of a QVAE. Our experiments show a correlation between the Hamming distance in the embedded space and the Euclidean distance in the original space on the MODIS dataset. Further, we find real-world speedups compared to linear search and demonstrate memory-efficient scaling to half a billion data points.

Data mining, similarity search, quantum machine le↗

TensorFlow Quantum: A Software Framework for Quantum Machine Learning

We introduce TensorFlow Quantum (TFQ), an open source library for the rapid prototyping of hybrid quantum-classical models for classical or quantum data. This framework offers high-level abstractions for the design and training of both discriminative and generative quantum models under TensorFlow and supports high-performance quantum circuit simulators. We provide an overview of the software architecture and building blocks through several examples and review the theory of hybrid quantum-classical neural networks. We illustrate TFQ functionalities via several basic applications including supervised learning for quantum classification, quantum control, simulating noisy quantum circuits, and quantum approximate optimization. Moreover, we demonstrate how one can apply TFQ to tackle advanced quantum learning tasks including meta-learning, layerwise learning, Hamiltonian learning, sampling thermal states, variational quantum eigensolvers, classification of quantum phase transitions, generative adversarial networks, and reinforcement learning. We hope this framework provides the necessary tools for the quantum computing and machine learning research communities to explore models of both natural and artificial quantum systems, and ultimately discover new quantum algorithms which could potentially yield a quantum advantage.

Broughton, Michael↗

Exploration of Quantum Machine Learning and AI Accelerators for Fusion Science

The dawn of the noisy intermediate-scale quantum (NISQ) era sparked rapid development in variational quantum algorithms. These algorithms, utilizing parameterized quantum circuit optimized by classical computers with feedback, are practical under the constraints of the current hardware and can potentially show quantum advantage. In recent years, these variational circuit are applied to neural networks, hoping to boost the triumphant success of deep learning. We simulate various of quantum-classical hybrid neural networks applied to scientific tasks, and seek to understand their capabilities and limitations. Specifically, we devise quantum convolutional layers and apply them to deep neural networks used for predicting plasma disruption in fusion reactors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Distributed quantum approximate optimization algorithm on a quantum-centric supercomputing architecture

Quantum approximate optimization algorithm (QAOA) has shown promise in solving combinatorial optimization problems by providing quantum speedup on near-term gate-based quantum computing systems. However, QAOA faces challenges for high-dimensional problems due to the large number of qubits required and the complexity of deep circuits, limiting its scalability for real-world applications. In this study, we present a distributed QAOA (DQAOA), which leverages distributed computing strategies to decompose a large computational workload into smaller tasks that require fewer qubits and shallower circuits than are necessary to solve the original problem. These sub-problems are processed using a combination of high-performance and quantum computing resources. The global solution is iteratively updated by aggregating sub-solutions, allowing convergence toward the optimal solution. We demonstrate that DQAOA can handle considerably large-scale optimization problems (e.g., 1000-bit problem), achieving a high solution quality and short time-to-solution, outperforming existing strategies. Furthermore, we realize DQAOA on a quantum-centric supercomputing architecture, paving the way for practical applications of gate-based quantum computers in real-world optimization tasks. To extend DQAOA’s applicability to materials science, we further develop an active learning algorithm integrated with our DQAOA (AL-DQAOA), which involves machine learning, DQAOA, and active data production in an iterative loop. We successfully optimize photonic structures using AL-DQAOA, indicating that solving real-world optimization problems using gate-based quantum computing is feasible. We expect the proposed DQAOA to be applicable to a wide range of optimization problems and AL-DQAOA to find broader applications in material design.

Kim, Seongmin [ORNL] (ORCID:0000000159063004)↗

Two-Tower Quantum Matrix Chain Multiplication: Trading Qubits for Depth

Matrix chain multiplication -- computing $\mathcal{W} = M^{(0)}\cdots M^{(K-1)}$ where $M^{(k)} \in \mathbb{R}^{P_k \times P_{k+1}}$-- arises in scientific computing, machine learning, and graph analysis. Despite the importance of this problem, for chains of distinct matrices, the classical number of operations grows linearly with the chain length $K$ and polynomially in the matrix dimensions. We present \emph{Two-Tower Matrix Multiplication}, a quantum subroutine that encodes the product $\mathcal{W}$ of the $K$ matrices into a quantum state in circuit depth $\mathcal{O}(\max_{k} \mathrm{polylog} (P_k P_{k+1}))$, which is independent of~$K$ within the QRAM-based state-preparation model, whereas the qubit count is $\mathcal{O}\bigl(\sum_{k} \log P_k \bigr)$; the total gate count remains linear in $K$, so the gain is in the circuit depth. The construction interleaves state-preparation operators across two layers; within each layer, all operators act on disjoint registers and execute in parallel. This subroutine can be specialized for the chain-vector case, which computes the product of $K-1$ matrices applied to a vector. We prove the correctness of the subroutine for all $K$ and provide two implementations using the Qiskit and QCLAB frameworks. The subroutine is applicable to any downstream quantum algorithm that operates on a matrix encoded in the statevector, including norm estimation, graph-matrix powers, linear system solving, and quantum machine learning kernels.

Antonioli, Giacomo [Pisa U.] (ORCID:00090000668703↗

Large-Scale Materials Modeling at Quantum Accuracy: Ab Initio Simulations of Quasicrystals and Interacting Extended Defects in Metallic Alloys

Ab initio electronic-structure has remained dichotomous between achievable accuracy and length-scale. Quantum many-body (QMB) methods realize quantum accuracy but fail to scale. Density functional theory (DFT) scales favorably but remains far from quantum accuracy. We present a framework that breaks this dichotomy by use of three interconnected modules: (i) invDFT: a methodological advance in inverse DFT linking QMB methods to DFT; (ii) MLXC: a machine-learned density functional trained with invDFT data, commensurate with quantum accuracy; (iii) DFT-FE-MLXC: an adaptive higher-order spectral finite-element (FE) based DFT implementation that integrates MLXC with efficient solver strategies and HPC innovations in FE-specific dense linear algebra, mixed-precision algorithms, and asynchronous compute-communication. Furthermore, we demonstrate a paradigm shift in DFT that not only provides an accuracy commensurate with QMB methods in ground-state energies, but also attains an unprecedented performance of 659.7 PFLOPS (43.1% peak FP64 performance) on 619,124 electrons using 8,000 GPU nodes of Frontier supercomputer.

density functional theory↗

High dimensional similarity search with quantum assisted variational autoencoder

Recent progress in quantum algorithms and hardware is indicator of the potential importance of quantum computing in the next future. However, finding suitable application areas remains an active area of research. Quantum machine learning [1] is touted as a potential approach to demonstrate quantum advantage within both the gate-model [2,3] and the adiabatic [4,5] schemes. For instance, the Quantum-assisted Variational Autoencoder (QVAE) [6] has been proposed as a quantum enhancement to the discrete VAE [7]. We extend on previous work and study the real-world applicability of a QVAE, specifically, for similarity search in large-scale high dimensional datasets. While similarity search algorithms are available for low dimensional datasets, scaling to billion-scale datasets with thousands of dimensions is non-trivial. We show how the latent-space representation of a QVAE can be used to construct a space-efficient search index. We back up our claims by experimental results which show a correlation between the Hamming distance in the embedded space and the Euclidean distance in the original space on the Moderate Resolution Imaging Spectroradiometer (MODIS) dataset. Further, we show real-world speedups compared to linear search and demonstrate memory efficient scaling to large-scale datasets.

Nicholas D Gao↗

Quantum-Compatible Variational Segmentation for Image-to-Image Wildfire Detection Using Satellite Data

Wildfire occurrences have been increasing for the past decade, leaving devastating traces across the world. In the recent efforts, remote sensing and airborne missions have been utilized to better understand and manage wildfires. This has resulted in an exponential increase in volume of remote sensing data, which has pushed the need for intelligent automation of data extraction for wildfire studies. Machine learning offers accurate automation in detecting such natural anomalies and enable decision-makers to take actions in a timely manner. Recent advances in machine learning algorithms, namely probabilistic generative methods, allow researchers and decisionmakers to step beyond detection and study “what-if” scenarios for wildfire occurrences. Additionally, they offer better imitations to the stochastic behavior of nature, and wildfire events. However, optimizing the performance of these probabilistic generative models is a computationally expensive process, specially using digital computers. On the other hand, quantum computers have recently shown a promise to reduce computationally costly training of such models and provide performance improvements. There is a body of research investigating the potential for improved machine learning methods in which key operations are performed on a quantum computer. In this study, we propose a probabilistic image-toimage segmentation approach combining a very well-known segmentation method, U-NET, with a Conditional Variational Auto-Encoder (CVAE) to not only detect wildfires but also describe the stochasticity of the phenomenon and be capable of running “what-if” scenarios. Our proposed model is compatible with training on quantum computers, which results in a quantum-assisted image-to-image segmentation approach and can be used to benchmark the potential benefit of quantum computing over the classical one.

quantum↗

Machine-learning accelerated geometry optimization in molecular simulation

Geometry optimization is an important part of both computational materials and surface science because it is the path to finding ground state atomic structures and reaction pathways. These properties are used in the estimation of thermodynamic and kinetic properties of molecular and crystal structures. This process is slow at the quantum level of theory because it involves an iterative calculation of forces using quantum chemical codes such as density functional theory (DFT), which are computationally expensive and which limit the speed of the optimization algorithms. It would be highly advantageous to accelerate this process because then one could do either the same amount of work in less time or more work in the same time. Here, we provide a neural network (NN) ensemble based active learning method to accelerate the local geometry optimization for multiple configurations simultaneously. We illustrate the acceleration on several case studies including bare metal surfaces, surfaces with adsorbates, and nudged elastic band for two reactions. In all cases, the accelerated method requires fewer DFT calculations than the standard method. In addition, we provide an Atomic Simulation Environment (ASE)-optimizer Python package to make the usage of the NN ensemble active learning for geometry optimization easier.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Parallel hybrid quantum-classical machine learning for kernelized time-series classification

Supervised time-series classification garners widespread interest because of its applicability throughout a broad application domain including finance, astronomy, biosensors, and many others. Here, in this work, we tackle this problem with hybrid quantum-classical machine learning, deducing pairwise temporal relationships between time-series instances using a timeseries Hamiltonian kernel (TSHK). A TSHK is constructed with a sum of inner products generated by quantum states evolved using a parameterized time evolution operator. This sum is then optimally weighted using techniques derived from multiple kernel learning. Because we treat the kernel weighting step as a differentiable convex optimization problem, our method can be regarded as an end-to-end learnable hybrid quantum-classical-convex neural network, or QCC-net, whose output is a data set-generalized kernel function suitable for use in any kernelized machine learning technique such as the support vector machine (SVM). Using our TSHK as input to a SVM, we classify univariate and multivariate time-series using quantum circuit simulators and demonstrate the efficient parallel deployment of the algorithm to 127-qubit superconducting quantum processors using quantum multi-programming.

97 MATHEMATICS AND COMPUTING↗

Dynamical simulation via quantum machine learning with provable generalization

Much attention has been paid to dynamical simulation and quantum machine learning (QML) independently as applications for quantum advantage, while the possibility of using QML to enhance dynamical simulations has not been thoroughly investigated. Here we develop a framework for using QML methods to simulate quantum dynamics on near-term quantum hardware. We use generalization bounds, which bound the error a machine learning model makes on unseen data, to rigorously analyze the training data requirements of an algorithm within this framework. Our algorithm is thus resource efficient in terms of qubit and data requirements. Furthermore, our preliminary numerics for the XY model exhibit efficient scaling with problem size, and we simulate 20 times longer than Trotterization on IBMQ-Bogota. Published by the American Physical Society 2024

97 MATHEMATICS AND COMPUTING↗

Materials genome innovation for computational software (magics) center

Functional layered material (LM) architectures will dominate nanomaterials science in this century. We have developed theory, modeling, simulation, and software and data tools that enhance understanding and AI guide synthesis, enable characterization of complex structures, and improve capabilities in the predictive design and growth of LMs. Research at the Center has focused on: Computational synthesis and characterization: AI guided synthesis and experimental synthesis of stacked LMs with tailored properties via optimized chemical vapor deposition (CVD) growth and liquid-phase exfoliation; study defects, edges, grain boundaries, wrinkling of atomic layers and their effects on chemical, mechanical, electrical, and optical properties. Far-from-equilibrium processes: Joint experimental and simulation based probe of electronic processes with NAQMD and ultrafast X-ray free-electron laser (XFEL) and ultrafast electron diffraction (UED) facilities at Stanford. Experimentally validate NAQMD by ultrafast electron diffraction and X-ray spectroscopy studies of structural and excited state dynamics, shape fluctuations, and phonon dynamics. Scalable software: Simulation engines for desktop-to-exascale platforms using low-overhead, linear-scaling QMD algorithms; divide-conquer-recombine NAQMD with electronic excitations; extended-Lagrangian reactive molecular dynamics (RMD), machine learning (ML) based neural-network quantum molecular dynamics (NNQMD), and super-state accelerated molecular dynamics (AMD) and kinetic Monte Carlo codes; thermal and electrical transport software; and design 3D architectures of LMs with desired functionality using scalable software. Distribution of software and data, and training: Software and simulation-experimental data generated within the Center are distributed to the materials science community via Berkeley Materials Project (MP) framework. We have also organized three workshops for software distribution and training at USC (Nov. 2017, Mar. 2018) and Gaithersburg, MD (Nov. 2018) to train researchers, with the last one in focused on underrepresented groups, in collaboration with Howard University which is one of the largest HBCUs. The Center supported a total of 46 personnel and 6 undergraduate students. These include 14 faculty, 11 postdoctoral research associates, 20 graduate research assistants, and mentored 6 undergraduate students. This resulted in the publications of 63 research papers that include 46 publications on Reactive and Quantum Dynamics Simulations, 13 publications on Machine Learning for Quantum Materials, and 4 publications on Quantum Computing.

2D Materials↗