Search NASA⌕ Search

SEARCH · Search NASA

Results for “quantum algorithms, quantum machine learning, quantum computing”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Coreset Clustering on Small Quantum Computers

Many quantum algorithms for machine learning require access to classical data in superposition. However, for many natural data sets and algorithms, the overhead required to load the data set in superposition can erase any potential quantum speedup over classical algorithms. Recent work by Harrow introduces a new paradigm in hybrid quantum-classical computing to address this issue, relying on coresets to minimize the data loading overhead of quantum algorithms. We investigated using this paradigm to perform k-means clustering on near-term quantum computers, by casting it as a QAOA optimization instance over a small coreset. We used numerical simulations to compare the performance of this approach to classical k-means clustering. We were able to find data sets with which coresets work well relative to random sampling and where QAOA could potentially outperform standard k-means on a coreset. However, finding data sets where both coresets and QAOA work well—which is necessary for a quantum advantage over k-means on the entire data set—appears to be challenging.

42 ENGINEERING↗
DOE OSTI2023

Measurement-induced entanglement phase transitions in variational quantum circuits

Variational quantum algorithms (VQAs), which classically optimize a parametrized quantum circuit to solve a computational task, promise to advance our understanding of quantum many-body systems and improve machine learning algorithms using near-term quantum computers. Prominent challenges associated with this family of quantum-classical hybrid algorithms are the control of quantum entanglement and quantum gradients linked to their classical optimization. Known as the barren plateau phenomenon, these quantum gradients may rapidly vanish in the presence of volume-law entanglement growth, which poses a serious obstacle to the practical utility of VQAs. Inspired by recent studies of measurement-induced entanglement transition in random circuits, we investigate the entanglement transition in variational quantum circuits endowed with intermediate projective measurements. Considering the Hamiltonian Variational Ansatz (HVA) for the XXZ model and the Hardware Efficient Ansatz (HEA), we observe a measurement-induced entanglement transition from volume-law to area-law with increasing measurement rate. Moreover, we provide evidence that the transition belongs to the same universality class of random unitary circuits. Importantly, the transition coincides with a “landscape transition” from severe to mild/no barren plateaus in the classical optimization. Our work may provide an avenue for improving the trainability of quantum circuits by incorporating intermediate measurement protocols in currently available quantum hardware.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

A multilayer multi-configurational approach to efficiently simulate large-scale circuit-based quantum computers on classical machines

Here, a multilayer multi-configurational theory framework is adapted to simulate circuit-based quantum computers. Quantum addition of superpositions of an exponential number of summands is performed in polynomial time with high accuracy. We demonstrate numerically accurate calculations including up to one million qubits for entangling benchmarks. Simulation cost can be assessed by entropy-based entanglement measures. For the considered systems, we show that the entanglement only grows weakly with the system size. The present simulations demonstrate how quantum algorithms in low-entropy regimes can be used efficiently on classically simulated quantum computers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Equivalence of quantum barren plateaus to cost concentration and narrow gorges

Optimizing parameterized quantum circuits (PQCs) is the leading approach to make use of near-term quantum computers. However, very little is known about the cost function landscape for PQCs, which hinders progress towards quantum-aware optimizers. In this work, we investigate the connection between three different landscape features that have been observed for PQCs: (1) exponentially vanishing gradients (called barren plateaus (BPs)), (2) exponential cost concentration about the mean, and (3) the exponential narrowness of minima (called narrow gorges). Here we analytically prove that these three phenomena occur together, i.e., when one occurs then so do the other two. A key implication of this result is that one can numerically diagnose BPs via cost differences rather than via the computationally more expensive gradients. More broadly, our work shows that quantum mechanics rules out certain cost landscapes (which otherwise would be mathematically possible), and hence our results could be interesting from a quantum foundations perspective.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Quantum Neural Networks: Issues, Training, and Applications

Our work in the field aims at explaining the limitations and expressive power of Quantum Machine Learning models, as well as finding feasible training algorithms that could be implemented in near-term Quantum Computers. The promise of Quantum Machine Learning is that by incorporating quantum effects, such as entanglement, into machine learning models researchers can improve model performance and understand more complex datasets. This pledge is particularly pronounced in the design of Quantum neural networks (QNNs), a promising framework for creating quantum algorithms, that promise to outperform classical models by combining the speedups of quantum computation with the widespread successes of deep learning. We show that applying this approach alone to quantum deep learning is problematic given that an excess of entanglement between the hidden and visible layers can destroy the predictive power of our QNN models. We address the barren plateau problem by suggesting the use of a generative, unbounded, nonlinear loss function with simple gradients. The loss function quantifies how much the quantum states generated by the QNNs differ from the data and the goal during training is to minimize it. Finally, we showcase how to use generative training to construct a "classical-quantum" neural network to accurately interpolate between the ground states of a Molecular Hamiltonian, a central question in Quantum Chemistry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Quantum model learning agent: characterisation of quantum systems through machine learning

Accurate models of real quantum systems are important for investigating their behaviour, yet are difficult to distil empirically. Here, we report an algorithm—the quantum model learning agent (QMLA)—to reverse engineer Hamiltonian descriptions of a target system. We test the performance of QMLA on a number of simulated experiments, demonstrating several mechanisms for the design of candidate Hamiltonian models and simultaneously entertaining numerous hypotheses about the nature of the physical interactions governing the system under study. QMLA is shown to identify the true model in the majority of instances, when provided with limited a priori information, and control of the experimental setup. Our protocol can explore Ising, Heisenberg and Hubbard families of models in parallel, reliably identifying the family which best describes the system dynamics. We demonstrate QMLA operating on large model spaces by incorporating a genetic algorithm to formulate new hypothetical models. The selection of models whose features propagate to the next generation is based upon an objective function inspired by the Elo rating scheme, typically used to rate competitors in games such as chess and football. In all instances, our protocol finds models that exhibit F 1 score ≥ 0.88 when compared with the true model, and it precisely identifies the true model in 72% of cases, whilst exploring a space of over 250 000 potential models. By testing which interactions actually occur in the target system, QMLA is a viable tool for both the exploration of fundamental physics and the characterisation and calibration of quantum devices.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Adiabatic quantum support vector machines

Adiabatic quantum computers can solve difficult optimization problems (e.g., the quadratic unconstrained binary optimization problem), and they seem well suited to train machine learning models. In this paper, we describe an adiabatic quantum approach for training support vector machines. We show that the time complexity of our quantum approach is an order of magnitude better than the classical approach. Next, we compare the test accuracy of our quantum approach against a classical approach that uses the Scikit-learn library in Python across five benchmark datasets (Iris, Wisconsin Breast Cancer (WBC), Wine, Digits, and Lambeq). We show that our quantum approach obtains accuracies on par with the classical approach. Finally, we perform a scalability study in which we compute the total training times of the quantum approach and the classical approach with an increasing number of features and an increasing number of data points in the training dataset. In conclusion, our scalability results show that the quantum approach obtains a 3.5–4.5x speedup over the classical approach on datasets with many (millions of) features.

Computational Complexity↗
DOE OSTI2023

Interactive Quantum Chemistry Enabled by Machine Learning, Graphical Processing Units, and Cloud Computing

Modern quantum chemistry algorithms are increasingly able to accurately predict molecular properties that are useful for chemists in research and education. Despite this progress, performing such calculations is currently unattainable to the wider chemistry community, as they often require domain expertise, computer programming skills, and powerful computer hardware. In this review, we outline methods to eliminate these barriers using cutting-edge technologies. We discuss the ingredients needed to create accessible platforms that can compute quantum chemistry properties in real time, including graphical processing units–accelerated quantum chemistry in the cloud, artificial intelligence–driven natural molecule input methods, and extended reality visualization. We end by highlighting a series of exciting applications that assemble these components to create uniquely interactive platforms for computing and visualizing spectra, 3D structures, molecular orbitals, and many other chemical properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Universal Compiling and (No-)Free-Lunch Theorems for Continuous-Variable Quantum Learning

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.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Towards provably efficient quantum algorithms for large-scale machine-learning models

Large machine learning models are revolutionary technologies of artificial intelligence whose bottlenecks include huge computational expenses, power, and time used both in the pre-training and fine-tuning process. In this work, we show that fault-tolerant quantum computing could possibly provide provably efficient resolutions for generic (stochastic) gradient descent algorithms, scaling as $\mathcal{O}$(T 2 x polylog($n$)), where n is the size of the models and T is the number of iterations in the training, as long as the models are both sufficiently dissipative and sparse, with small learning rates. Based on earlier efficient quantum algorithms for dissipative differential equations, we find and prove that similar algorithms work for (stochastic) gradient descent, the primary algorithm for machine learning. In practice, we benchmark instances of large machine learning models from 7 million to 103 million parameters. We find that, in the context of sparse training, a quantum enhancement is possible at the early stage of learning after model pruning, motivating a sparse parameter download and re-upload scheme. Our work shows solidly that fault-tolerant quantum algorithms could potentially contribute to most state-of-the-art, large-scale machine-learning problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Barren Plateaus Preclude Learning Scramblers

Scrambling processes, which rapidly spread entanglement through many-body quantum systems, are difficult to investigate using standard techniques, but are relevant to quantum chaos and thermalization. In this Letter, we ask if quantum machine learning (QML) could be used to investigate such processes. In this study we prove a no-go theorem for learning an unknown scrambling process with QML, showing that it is highly probable for any variational Ansatz to have a barren plateau landscape, i.e., cost gradients that vanish exponentially in the system size. This implies that the required resources scale exponentially even when strategies to avoid such scaling (e.g., from Ansatz -based barren plateaus or no-free-lunch theorems) are employed. Furthermore, we numerically and analytically extend our results to approximate scramblers. Hence, our work places generic limits on the learnability of unitaries when lacking prior information.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Building spatial symmetries into parameterized quantum circuits for faster training

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.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Quantum circuit fidelity estimation using machine learning

The computational power of real-world quantum computers is limited by errors. When using quantum computers to perform algorithms which cannot be efficiently simulated classically, it is important to quantify the accuracy with which the computation has been performed. In this work, we introduce a machine learning-based technique to estimate the fidelity between the state produced by a noisy quantum circuit and the target state corresponding to ideal noise-free computation. Our machine learning model is trained in a supervised manner, using smaller or simpler circuits for which the fidelity can be estimated using other techniques like direct fidelity estimation and quantum state tomography. Here we demonstrate that, for simulated random quantum circuits with a realistic noise model, the trained model can predict the fidelities of more complicated circuits for which such methods are infeasible. In particular, we show that the trained model may make predictions for circuits with higher degrees of entanglement than were available in the training set and that the model may make predictions for non-Clifford circuits even when the training set included only Clifford-reducible circuits. This empirical demonstration suggests classical machine learning may be useful for making predictions about beyond-classical quantum circuits for some non-trivial problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Resource frugal optimizer for quantum machine learning

Quantum-enhanced data science, also known as quantum machine learning (QML), is of growing interest as an application of near-term quantum computers. Variational QML algorithms have the potential to solve practical problems on real hardware, particularly when involving quantum data. However, training these algorithms can be challenging and calls for tailored optimization procedures. Specifically, QML applications can require a large shot-count overhead due to the large datasets involved. In this work, we advocate for simultaneous random sampling over both the dataset as well as the measurement operators that define the loss function. We consider a highly general loss function that encompasses many QML applications, and we show how to construct an unbiased estimator of its gradient. This allows us to propose a shot-frugal gradient descent optimizer called Refoqus (REsource Frugal Optimizer for QUantum Stochastic gradient descent). Our numerics indicate that Refoqus can save several orders of magnitude in shot cost, even relative to optimizers that sample over measurement operators alone.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Towards Redefining the Reproducibility in Quantum Computing: A Data Analysis Approach on NISQ Devices

Although the building of quantum computers has kept making rapid progress in recent years, noise is still the main challenge for any application to leverage the power of quantum computing. Existing works addressing noise in quantum devices proposed noise reduction when deploying a quantum algorithm to a specified quantum computer. The reproducibility issue of quantum algorithms has been raised since the noise levels vary on different quantum computers. Importantly, existing works largely ignore the fact that the noise of quantum devices varies as time goes by. Therefore, reproducing the results on the same hardware will even become a problem. We analyze the reproducibility of quantum machine learning (QML) algorithms based on daily model training and execution data collection. Our analysis shows a correlation between our QML models’ test accuracy and quantum computer hardware’s calibration features. We also demonstrate that noisy simulators for quantum computers are not a reliable tool for quantum machine learning applications.

Senapati, Priyabrata↗
DOE OSTI2022

Noisy intermediate-scale quantum algorithms

A universal fault-tolerant quantum computer that can efficiently solve problems such as integer factorization and unstructured database search requires millions of qubits with low error rates and long coherence times. While the experimental advancement toward realizing such devices will potentially take decades of research, noisy intermediate-scale quantum (NISQ) computers already exist. These computers are composed of hundreds of noisy qubits, i.e., qubits that are not error corrected, and therefore perform imperfect operations within a limited coherence time. In the search for achieving quantum advantage with these devices, algorithms have been proposed for applications in various disciplines spanning physics, machine learning, quantum chemistry, and combinatorial optimization. The overarching goal of such algorithms is to leverage the limited available resources to perform classically challenging tasks. In this review, a thorough summary of NISQ computational paradigms and algorithms is provided. The key structure of these algorithms and their limitations and advantages are discussed. Finally, a comprehensive overview of various benchmarking and software tools useful for programming and testing NISQ devices is additionally provided.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Subtleties in the trainability of quantum machine learning models

A new paradigm for data science has emerged, with quantum data, quantum models, and quantum computational devices. This field, called quantum machine learning (QML), aims to achieve a speedup over traditional machine learning for data analysis. However, its success usually hinges on efficiently training the parameters in quantum neural networks, and the field of QML is still lacking theoretical scaling results for their trainability. Some trainability results have been proven for a closely related field called variational quantum algorithms (VQAs). While both fields involve training a parametrized quantum circuit, there are crucial differences that make the results for one setting not readily applicable to the other. In this work, we bridge the two frameworks and show that gradient scaling results for VQAs can also be applied to study the gradient scaling of QML models. Our results indicate that features deemed detrimental for VQA trainability can also lead to issues such as barren plateaus in QML. Consequently, our work has implications for several QML proposals in the literature. In addition, we provide theoretical and numerical evidence that QML models exhibit further trainability issues not present in VQAs, arising from the use of a training dataset. We refer to these as dataset-induced barren plateaus. These results are most relevant when dealing with classical data, as here the choice of embedding scheme (i.e., the map between classical data and quantum states) can greatly affect the gradient scaling.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Localization in Energy Materials (Final Project Report)

The last year of this award we have continued our research on using quantum machine learning to identify phase transitions. By combining quantum machine learning with quantum computing, we extended a hybrid classical-quantum algorithm to capture the metal-insulator quantum phase transition of the Hubbard model. We have also continued our studies of non-equilibrium dynamics of interacting disordered systems. In particular, we studied the non-equilibrium transient dynamics of a system described by the Anderson-Hubbard model following an interaction and disorder quench, and the effect of disorder on the out-of-time-order correlator on the Hubbard model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗