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Results for “exponential advantage”

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.

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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Quantum approximate optimization of the long-range Ising model with a trapped-ion quantum simulator

Quantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly improving performance for solving exponentially hard problems, such as optimization and satisfiability. Here, we report the implementation of a low-depth Quantum Approximate Optimization Algorithm (QAOA) using an analog quantum simulator. We estimate the ground-state energy of the Transverse Field Ising Model with long-range interactions with tunable range, and we optimize the corresponding combinatorial classical problem by sampling the QAOA output with high-fidelity, single-shot, individual qubit measurements. We execute the algorithm with both an exhaustive search and closed-loop optimization of the variational parameters, approximating the ground-state energy with up to 40 trapped-ion qubits. We benchmark the experiment with bootstrapping heuristic methods scaling polynomially with the system size. We observe, in agreement with numerics, that the QAOA performance does not degrade significantly as we scale up the system size and that the runtime is approximately independent from the number of qubits. We finally give a comprehensive analysis of the errors occurring in our system, a crucial step in the path forward toward the application of the QAOA to more general problem instances.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Analytic solutions of the DGLAP evolution and theoretical uncertainties

The energy dependence for the singlet sector of Parton Distributions Functions (PDFs) is described by an entangled pair of ordinary linear differential equations. Although there are no exact analytic solutions, it is possible to provide approximated results depending on the assumptions and the methodology adopted. These results differ in their sub-leading, neglected terms and ultimately they are associated with different treatments of the theoretical uncertainties. In this work, a novel analytic approach in Mellin space is presented and a new methodology for obtaining closed and exponentiated analytic solutions is devised. Different results for the DGLAP evolution at Next-Leading-Order are compared, discussing advantages and disadvantages for each solution. The generalizations to higher orders are addressed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Theory for Equivariant Quantum Neural Networks

Quantum neural network architectures that have little to no inductive biases are known to face trainability and generalization issues. Inspired by a similar problem, recent breakthroughs in machine learning address this challenge by creating models encoding the symmetries of the learning task. This is materialized through the usage of equivariant neural networks the action of which commutes with that of the symmetry. In this work, we import these ideas to the quantum realm by presenting a comprehensive theoretical framework to design equivariant quantum neural networks (EQNNs) for essentially any relevant symmetry group. We develop multiple methods to construct equivariant layers for EQNNs and analyze their advantages and drawbacks. Our methods can find unitary or general equivariant quantum channels efficiently even when the symmetry group is exponentially large or continuous. As a special implementation, we show how standard quantum convolutional neural networks (QCNNs) can be generalized to group-equivariant QCNNs where both the convolution and pooling layers are equivariant to the symmetry group. We then numerically demonstrate the effectiveness of a S U ( 2 ) -equivariant QCNN over symmetry-agnostic QCNN on a classification task of phases of matter in the bond-alternating Heisenberg model. Our framework can be readily applied to virtually all areas of quantum machine learning. Lastly, we discuss about how symmetry-informed models such as EQNNs provide hopes to alleviate central challenges such as barren plateaus, poor local minima, and sample complexity. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

SPIKANs: separable physics-informed Kolmogorov–Arnold networks

Physics-Informed Neural Networks (PINNs) have emerged as a promising method for solving partial differential equations (PDEs) in scientific computing. While PINNs typically use multilayer perceptrons (MLPs) as their underlying architecture, recent advancements have explored alternative neural network structures. One such innovation is the Kolmogorov–Arnold Network (KAN), which has demonstrated benefits over traditional MLPs, including faster neural scaling and better interpretability. The application of KANs to physics-informed learning has led to the development of Physics-Informed KANs (PIKANs), enabling the use of KANs to solve PDEs. However, despite their advantages, KANs often suffer from slower training speeds, particularly in higher-dimensional problems where the number of collocation points grows exponentially with the dimensionality of the system. To address this challenge, we introduce Separable Physics-Informed Kolmogorov–Arnold Networks (SPIKANs). This novel architecture applies the principle of separation of variables to PIKANs, decomposing the problem such that each dimension is handled by an individual KAN. This approach drastically reduces the computational complexity of training without sacrificing accuracy, facilitating their application to higher-dimensional PDEs. Through a series of benchmark problems, we demonstrate the effectiveness of SPIKANs, showcasing their superior scalability and performance compared to PIKANs and highlighting their potential for solving complex, high-dimensional PDEs in scientific computing.

Kolmogorov-Arnold networks↗
DOE OSTI2021

Postselection-Free Entanglement Dynamics via Spacetime Duality

The dynamics of entanglement in 'hybrid' non-unitary circuits (for example, involving both unitary gates and quantum measurements) has recently become an object of intense study. A major hurdle toward experimentally realizing this physics is the need to apply postselection on random measurement outcomes in order to repeatedly prepare a given output state, resulting in an exponential overhead. We propose a method to sidestep this issue in a wide class of non-unitary circuits by taking advantage of spacetime duality. This method maps the purification dynamics of a mixed state under non-unitary evolution onto a particular correlation function in an associated unitary circuit. This translates to an operational protocol which could be straightforwardly implemented on a digital quantum simulator. We discuss the signatures of different entanglement phases, and demonstrate examples via numerical simulations. With minor modifications, the proposed protocol allows measurement of the purity of arbitrary subsystems, which could shed light on the properties of the quantum error correcting code formed by the mixed phase in this class of hybrid dynamics.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Certifying almost all quantum states with few single-qubit measurements

Certifying that an n -qubit state synthesized in the laboratory is close to a given target state is a fundamental task in quantum information science. However, existing rigorous protocols applicable to general target states have potentially prohibitive resource requirements in the form of either deep quantum circuits or exponentially many single-qubit measurements. Here we prove that almost all n -qubit target states, including those with exponential circuit complexity, can be certified from only O ( n 2 ) single-qubit measurements. Given access to the target state’s amplitudes, our protocol requires only O ( n 3 ) classical computation. This result is established by a technique that relates certification to the mixing time of a random walk. Our protocol has applications for benchmarking quantum systems, for optimizing quantum circuits to generate a desired target state and for learning and verifying neural networks, tensor networks and various other representations of quantum states using only single-qubit measurements. We show that such verified representations can be used to efficiently predict highly non-local properties of a synthesized state that would otherwise require an exponential number of measurements on the state. We demonstrate these applications in numerical experiments with up to 120 qubits and observe an advantage over existing methods such as cross-entropy benchmarking.

information theory and computation↗
DOE OSTI2022

Dynamic and single cell characterization of a CRISPR-interference toolset in Pseudomonas putida KT2440 for β-ketoadipate production from p -coumarate

We report Pseudomonas putida KT2440 is a well-studied bacterium for the conversion of lignin-derived aromatic compounds to bioproducts. The development of advanced genetic tools in P. putida has reduced the turnaround time for hypothesis testing and enabled the construction of strains capable of producing various products of interest. Here, we evaluate an inducible CRISPR-interference (CRISPRi) toolset on fluorescent, essential, and metabolic targets. Nuclease-deficient Cas9 (dCas9) expressed with the arabinose (8K)-inducible promoter was shown to be tightly regulated across various media conditions and when targeting essential genes. In addition to bulk growth data, single cell time lapse microscopy was conducted, which revealed intrinsic heterogeneity in knockdown rate within an isoclonal population. The dynamics of knockdown were studied across genomic targets in exponentially-growing cells, revealing a universal 1.75 ± 0.38 hour quiescent phase after induction where 1.5 ± 0.35 doublings occur before a phenotypic response is observed. To demonstrate application of this CRISPRi toolset, β-ketoadipate, a monomer for performance-advantaged nylon, was produced at a 4.39 ± 0.5 g/L and yield of 0.76 ± 0.10 mol/mol from p-coumarate, a hydroxycinnamic acid that can be derived from grasses. These cultivation metrics were achieved by using the higher strength IPTG (1K)-inducible promoter to knockdown the pcaIJ operon in the βKA pathway during early exponential phase. This allowed the majority of the carbon to be shunted into the desired product while eliminating the need for a supplemental carbon and energy source to support growth and maintenance.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Diagnosing Barren Plateaus with Tools from Quantum Optimal Control

Variational Quantum Algorithms (VQAs) have received considerable attention due to their potential for achieving near-term quantum advantage. However, more work is needed to understand their scalability. One known scaling result for VQAs is barren plateaus, where certain circumstances lead to exponentially vanishing gradients. It is common folklore that problem-inspired ansatzes avoid barren plateaus, but in fact, very little is known about their gradient scaling. In this work we employ tools from quantum optimal control to develop a framework that can diagnose the presence or absence of barren plateaus for problem-inspired ansatzes. Such ansatzes include the Quantum Alternating Operator Ansatz (QAOA), the Hamiltonian Variational Ansatz (HVA), and others. With our framework, we prove that avoiding barren plateaus for these ansatzes is not always guaranteed. Specifically, we show that the gradient scaling of the VQA depends on the degree of controllability of the system, and hence can be diagnosed through the dynamical Lie algebra $\mathfrak{g}$ obtained from the generators of the ansatz. We analyze the existence of barren plateaus in QAOA and HVA ansatzes, and we highlight the role of the input state, as different initial states can lead to the presence or absence of barren plateaus. Taken together, our results provide a framework for trainability-aware ansatz design strategies that do not come at the cost of extra quantum resources. Moreover, we prove no-go results for obtaining ground states with variational ansatzes for controllable system such as spin glasses. Our work establishes a link between the existence of barren plateaus and the scaling of the dimension of $\mathfrak{g}$.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

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↗
DOE OSTI2021

Progress toward favorable landscapes in quantum combinatorial optimization

The performance of variational quantum algorithms relies on the success of using quantum and classical computing resources in tandem. Here, we study how these quantum and classical components interrelate. In particular, we focus on algorithms for solving the combinatorial optimization problem MaxCut, and study how the structure of the classical optimization landscape relates to the quantum circuit used to evaluate the MaxCut objective function. In order to analytically characterize the impact of quantum features on the critical points of the landscape, we consider a family of quantum circuit ansätze composed of mutually commuting elements. We identify multiqubit operations as a key resource and show that overparameterization allows for obtaining favorable landscapes. Namely, we prove that an ansatz from this family containing exponentially many variational parameters yields a landscape free of local optima for generic graphs. However, we further prove that these ansätze do not offer superpolynomial advantages over purely classical MaxCut algorithms. Here, we then present a series of numerical experiments illustrating that noncommutativity and entanglement are important features for improving algorithm performance.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Observable-projected ensembles

Measurements in many-body quantum systems can generate non-trivial phenomena, such as preparation of long-range entangled states, dynamical phase transitions, or measurement-altered criticality. Here, we introduce a new measurement scheme that produces an ensemble of mixed states in a subsystem, obtained by measuring a local Hermitian observable on part of its complement. We refer to this as the observable-projected ensemble . Unlike standard projected ensembles-where pure states are generated by projective measurements on the complement-our approach involves projective partial measurements of specific observables. This setup has two main advantages: theoretically, it is amenable to analytical computations, especially within conformal field theories. Experimentally, it requires only a linear number of measurements, rather than an exponential one, to probe the properties of the ensemble. As a first step in exploring the observable-projected ensemble, we investigate its entanglement properties in conformal field theory and perform a detailed analysis of the free compact boson.

Milekhin, Alexey [California Institute of Technolo↗
DOE OSTI2024

Addressing quantum’s “fine print” with efficient state preparation and information extraction for quantum algorithms and geologic fracture networks

Abstract Quantum algorithms provide an exponential speedup for solving certain classes of linear systems, including those that model geologic fracture flow. However, this revolutionary gain in efficiency does not come without difficulty. Quantum algorithms require that problems satisfy not only algorithm-specific constraints, but also application-specific ones. Otherwise, the quantum advantage carefully attained through algorithmic ingenuity can be entirely negated. Previous work addressing quantum algorithms for geologic fracture flow has illustrated core algorithmic approaches while incrementally removing assumptions. This work addresses two further requirements for solving geologic fracture flow systems with quantum algorithms: efficient system state preparation and efficient information extraction. Our approach to addressing each is consistent with an overall exponential speed-up.

58 GEOSCIENCES↗
DOE OSTI2023

Physics‐Informed Machine Learning for Inverse Design of Optical Metamaterials

Optical metamaterials manipulate light through various confinement and scattering processes, offering unique advantages like high performance, small form factor and easy integration with semiconductor devices. However, designing metasurfaces with suitable optical responses for complex metamaterial systems remains challenging due to the exponentially growing computation cost and the ill‐posed nature of inverse problems. To expedite the computation for the inverse design of metasurfaces, a physics‐informed deep learning (DL) framework is used. A tandem DL architecture with physics‐based learning is used to select designs that are scientifically consistent, have low error in design prediction, and accurate reconstruction of optical responses. The authors focus on the inverse design of a representative plasmonic device and consider the prediction of design for the optical response of a single wavelength incident or a spectrum of wavelength in the visible light range. The physics‐based constraint is derived from solving the electromagnetic wave equations for a simplified homogenized model. The model converges with an accuracy up to 97% for inverse design prediction with the optical response for the visible light spectrum as input, and up to 96% for optical response of single wavelength of light as input, with optical response reconstruction accuracy of 99%.

Sarkar, Sulagna↗
DOE OSTI2025

Demonstration of Algorithmic Quantum Speedup for an Abelian Hidden Subgroup Problem

Simon’s problem is to find a hidden period (a bitstring) encoded into an unknown 2-to-1 function. It is one of the earliest problems for which an exponential quantum speedup was proven for ideal, noiseless quantum computers, albeit in the oracle model. Here, using two different 127-qubit IBM Quantum superconducting processors, we demonstrate an algorithmic quantum speedup for a variant of Simon’s problem where the hidden period has a restricted Hamming weight 𝑤. For sufficiently small values of 𝑤 and for circuits involving up to 58 qubits, we demonstrate an exponential speedup, albeit of a lower quality than the speedup predicted for the noiseless algorithm. The speedup exponent and the range of 𝑤 values for which an exponential speedup exists are significantly enhanced when the computation is protected by dynamical decoupling. Further enhancement is achieved with measurement error mitigation. This case constitutes a demonstration of a bona fide quantum advantage for an Abelian hidden subgroup problem.

computation↗
DOE OSTI2022

Performance Analysis and Optimization for Scientific Data Workloads

Scientific data generated at experimental and observational facilities are increasingly being processed on large-scale compute systems. Most of the experimental data analysis workflows are not designed or implemented to run on large scale environments and take full advantage of HPC compute and storage resources. These applications are unlike the traditional tightly-coupled scientific applications and hence face significant performance and scalability challenges as the volume of data increases exponentially. In this paper, we conduct a performance and scalability analysis for experimental analysis applications and workflows operating on data from light sources. Our analysis detects and quantifies I/O performance, scalability and runtime bottlenecks for three data analysis applications that run on NERSC resources. Based on our analysis we propose and implement a set of optimizations that lead to reducing the amount of time spent on I/O operations by almost 90%.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Block encoding of the three-dimensional heterogeneous Poisson equation with application to fracture flow

Quantum linear system (QLS) algorithms offer the potential to solve large-scale linear systems exponentially faster than classical methods. However, applying QLS algorithms to real-world problems remains challenging due to issues such as state preparation, data loading, and efficient information extraction. In this work, we study the feasibility of applying QLS algorithms to solve discretized three-dimensional (3D) heterogeneous Poisson equations, with specific examples relating to groundwater flow through geologic fracture networks. We explicitly construct a block encoding for the 3D heterogeneous Poisson matrix by leveraging the sparse local structure of the discretized operator. While classical solvers benefit from preconditioning, we show that block encoding the system matrix and preconditioner separately does not improve the effective condition number that dominates the QLS run-time. This differs from classical approaches where the preconditioner and the system matrix can often be implemented independently. Nevertheless, due to the structure of the problem in three dimensions, the quantum algorithm achieves a run-time of 𝑂⁡(𝑁 2/3 polylog 𝑁 ⋅log (1/𝜖)), outperforming the best classical methods (with run times of 𝑂⁡(𝑁⁢log 𝑁 ⋅log (1/𝜖))) and offering exponential memory savings. These results highlight both the promise and limitations of QLS algorithms for practical scientific computing, and point to effective condition-number reduction as a key barrier in achieving quantum advantages.

58 GEOSCIENCES↗
DOE OSTI2025

SpecSims: A Scalable Speculative Tree-based Simulation Cloning Framework for Finite Memory Machines

Simulation cloning is a technique in which cloned simulations whose state spaces differ partially from their parent simulation due to intervening events are spawned at runtime and concurrently advanced. It is a powerful method to carry out what-if analysis by speculatively exploring and evaluating the impact of various permutations of intervening cascade of events. Due to the exponential growth in the number of possible clones even for a small number of distinct intervening events, the practical efficacy of the approach is often severely limited by the maximum available memory of the computing host. In this paper, we introduce a novel speculative simulation cloning framework that executes a simulation cloning campaign capable of efficiently exploring an exponentially large space of clone simulations created by permutation of intervening events under a finite memory constraint. We provide a theoretical analysis of the runtime characteristics of our proposed approach and highlight its novel advantages such as memory-aware and as-long-as-needed execution. Furthermore, in support of our analytical findings and to demonstrate its practical feasibility, we implement a prototype of the cloning framework on a shared memory system and report its performance characteristics in the context of a heat diffusion simulation, and a power grid simulation subject to cascading disruptions from geomagnetic disturbances.

Simulation framework↗
DOE OSTI2025

Memristive linear algebra

The advent of memristive devices offers a promising avenue for efficient and scalable analog computing, particularly for linear algebra operations essential in various scientific and engineering applications. This paper investigates the potential of memristive crossbars in implementing matrix inversion algorithms. We explore both static and dynamic approaches, emphasizing the advantages of analog and in-memory computing for matrix operations beyond multiplication. In particular, we demonstrate that the electrical properties of memristive crossbars uniquely suit them for the evolution of a family of matrix exponentials, which can be exploited for the efficient computation of matrix inverses and online solutions for linear problems. Our results demonstrate that memristive arrays can reduce computational complexity. We also study power consumption and show a tradeoff between precision and energy. Furthermore, we address the challenges of device variability, precision, and scalability, providing insights into the practical implementation of these algorithms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗