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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 19 records
All sourcesNASA NTRSDOE OSTI
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 OSTI2021

Effect of barren plateaus on gradient-free optimization

Barren plateau landscapes correspond to gradients that vanish exponentially in the number of qubits. Such landscapes have been demonstrated for variational quantum algorithms and quantum neural networks with either deep circuits or global cost functions. For obvious reasons, it is expected that gradient-based optimizers will be significantly affected by barren plateaus. However, whether or not gradient-free optimizers are impacted is a topic of debate, with some arguing that gradient-free approaches are unaffected by barren plateaus. Here we show that, indeed, gradient-free optimizers do not solve the barren plateau problem. Our main result proves that cost function differences, which are the basis for making decisions in a gradient-free optimization, are exponentially suppressed in a barren plateau. Hence, without exponential precision, gradient-free optimizers will not make progress in the optimization. We numerically confirm this by training in a barren plateau with several gradient-free optimizers (Nelder-Mead, Powell, and COBYLA algorithms), and show that the numbers of shots required in the optimization grows exponentially with the number of qubits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Does provable absence of barren plateaus imply classical simulability?

A large amount of effort has recently been put into understanding the barren plateau phenomenon. In this perspective article, we face the increasingly loud elephant in the room and ask a question that has been hinted at by many but not explicitly addressed: Can the structure that allows one to avoid barren plateaus also be leveraged to efficiently simulate the loss classically? We collect evidence-on a case-by-case basis-that many commonly used models whose loss landscapes avoid barren plateaus can also admit classical simulation, provided that one can collect some classical data from quantum devices during an initial data acquisition phase. This follows from the observation that barren plateaus result from a curse of dimensionality, and that current approaches for solving them end up encoding the problem into some small, classically simulable, subspaces. Thus, while stressing that quantum computers can be essential for collecting data, our analysis sheds doubt on the information processing capabilities of many parametrized quantum circuits with provably barren plateau-free landscapes. We end by discussing the (many) caveats in our arguments including the limitations of average case arguments, the role of smart initializations, models that fall outside our assumptions, the potential for provably superpolynomial advantages and the possibility that, once larger devices become available, parametrized quantum circuits could heuristically outperform our analytic expectations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

AmeriFlux FLUXNET-1F US-Wi6 Pine barrens #1 (PB1)

This is the AmeriFlux Management Project (AMP) created FLUXNET-1F version of the carbon flux data for the site US-Wi6 Pine barrens #1 (PB1). This is the FLUXNET version of the carbon flux data for the site US-Wi6 Pine barrens #1 (PB1) produced by applying the standard ONEFlux (1F) software. Site Description - The Wisconsin Pine Barrens site is located in the Washburn Ranger District of the northeastern section of Chequamegon National Forest. A member of the northern coniferous-deciduous biome, surveys from the mid-19th century indicate the region consisted of a mixed stand of red, white, and jack pines. After extensive timber harvesting, wildfires, and farming activity, the region turned into a fragmented mosaic of stands of various ages and composition. As an assemblage, the ten Wisconsin sites are indicative of the successional stages of development in the predominant stand types of a physically homogeneous landscape. In order to establish and maintain both natural and plantation jack pine stands, pine barrens undergo prescribed burns and harvesting rotations. Pine Barrens occupy 17% of the region in 2001.

Chen, Jiquan↗
DOE OSTI2021

Noise-induced barren plateaus in variational quantum algorithms

Abstract Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers. A natural question is whether noise on NISQ devices places fundamental limitations on VQA performance. We rigorously prove a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau (i.e., vanishing gradient). Specifically, for the local Pauli noise considered, we prove that the gradient vanishes exponentially in the number of qubits n if the depth of the ansatz grows linearly with n . These noise-induced barren plateaus (NIBPs) are conceptually different from noise-free barren plateaus, which are linked to random parameter initialization. Our result is formulated for a generic ansatz that includes as special cases the Quantum Alternating Operator Ansatz and the Unitary Coupled Cluster Ansatz, among others. For the former, our numerical heuristics demonstrate the NIBP phenomenon for a realistic hardware noise model.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus

Abstract Variational quantum eigensolvers (VQEs) represent a powerful class of hybrid quantum-classical algorithms for computing molecular energies. Various numerical issues exist for these methods, however, including barren plateaus and large numbers of local minima. In this work, we consider the Adaptive, Problem-Tailored Variational Quantum Eiegensolver (ADAPT-VQE) ansätze, and examine how they are impacted by these local minima. We find that while ADAPT-VQE does not remove local minima, the gradient-informed, one-operator-at-a-time circuit construction accomplishes two things: First, it provides an initialization strategy that can yield solutions with over an order of magnitude smaller error compared to random initialization, and which is applicable in situations where chemical intuition cannot help with initialization, i.e., when Hartree-Fock is a poor approximation to the ground state. Second, even if an ADAPT-VQE iteration converges to a local trap at one step, it can still “burrow” toward the exact solution by adding more operators, which preferentially deepens the occupied trap. This same mechanism helps highlight a surprising feature of ADAPT-VQE: It should not suffer optimization problems due to barren plateaus and random initialization. Even if such barren plateaus appear in the parameter landscape, our analysis suggests that ADAPT-VQE avoids such regions by design.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Absence of Barren Plateaus and Scaling of Gradients in the Energy Optimization of Isometric Tensor Network States

Abstract Vanishing gradients can pose substantial obstacles for high-dimensional optimization problems. Here we consider energy minimization problems for quantum many-body systems with extensive Hamiltonians and finite-range interactions, which can be studied on classical computers or in the form of variational quantum eigensolvers on quantum computers. Barren plateaus correspond to scenarios where the average amplitude of the energy gradient decreases exponentially with increasing system size. This occurs, for example, for quantum neural networks and for brickwall quantum circuits when the depth increases polynomially in the system size. Here we prove that the variational optimization problems for matrix product states, tree tensor networks, and the multiscale entanglement renormalization ansatz are free of barren plateaus. The derived scaling properties for the gradient variance provide an analytical guarantee for the trainability of randomly initialized tensor network states (TNS) and motivate certain initialization schemes. In a suitable representation, unitary tensors that parametrize the TNS are sampled according to the uniform Haar measure. We employ a Riemannian formulation of the gradient based optimizations which simplifies the analytical evaluation.

Barthel, Thomas↗
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

Hamiltonian variational ansatz without barren plateaus

Variational quantum algorithms, which combine highly expressive parameterized quantum circuits (PQCs) and optimization techniques in machine learning, are one of the most promising applications of a near-term quantum computer. Despite their huge potential, the utility of variational quantum algorithms beyond tens of qubits is still questioned. One of the central problems is the trainability of PQCs. The cost function landscape of a randomly initialized PQC is often too flat, asking for an exponential amount of quantum resources to find a solution. This problem, dubbed barren plateaus , has gained lots of attention recently, but a general solution is still not available. In this paper, we solve this problem for the Hamiltonian variational ansatz (HVA), which is widely studied for solving quantum many-body problems. After showing that a circuit described by a time-evolution operator generated by a local Hamiltonian does not have exponentially small gradients, we derive parameter conditions for which the HVA is well approximated by such an operator. Based on this result, we propose an initialization scheme for the variational quantum algorithms and a parameter-constrained ansatz free from barren plateaus.

Physics↗
NASA NTRS1981

The Pennsylvania Barrens - A view from space

The presence of an anomalous cold area, the Pennsylvania Barrens, which consistently displays temperatures 10-15 C below those of a nearby college weather station on clear, dry, windless nights, was studied by means of IR images from the NASA Heat Capacity Mapping Mission satellite. The Barrens are surrounded by wooded ridges, which have a high thermal inertia, and it is concluded that the movement of cold air from high regions to lower valleys contributes significantly to the thermal differences between sites.

Carlson, T. N.↗
DOE OSTI2024

A Lie algebraic theory of barren plateaus for deep parameterized quantum circuits

Variational quantum computing schemes train a loss function by sending an initial state through a parametrized quantum circuit, and measuring the expectation value of some operator. Despite their promise, the trainability of these algorithms is hindered by barren plateaus (BPs) induced by the expressiveness of the circuit, the entanglement of the input data, the locality of the observable, or the presence of noise. Up to this point, these sources of BPs have been regarded as independent. In this work, we present a general Lie algebraic theory that provides an exact expression for the variance of the loss function of sufficiently deep parametrized quantum circuits, even in the presence of certain noise models. Our results allow us to understand under one framework all aforementioned sources of BPs. This theoretical leap resolves a standing conjecture about a connection between loss concentration and the dimension of the Lie algebra of the circuit’s generators.

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 OSTI2021

Cost function dependent barren plateaus in shallow parametrized quantum circuits

Variational quantum algorithms (VQAs) optimize the parameters θ of a parametrized quantum circuit V(θ) to minimize a cost function C. While VQAs may enable practical applications of noisy quantum computers, they are nevertheless heuristic methods with unproven scaling. Here, we rigorously prove two results, assuming V(θ) is an alternating layered ansatz composed of blocks forming local 2-designs. Our first result states that defining C in terms of global observables leads to exponentially vanishing gradients (i.e., barren plateaus) even when V(θ) is shallow. Hence, several VQAs in the literature must revise their proposed costs. On the other hand, our second result states that defining C with local observables leads to at worst a polynomially vanishing gradient, so long as the depth of V(θ) is Ο(logn). Our results establish a connection between locality and trainability. We illustrate these ideas with large-scale simulations, up to 100 qubits, of a quantum autoencoder implementation.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1987

Landsat classification of the barren hydrolittoral areas of Lake Yli-Kitka, north-eastern Finland

As a part of the project 'Landsat-studies for Mapping the Variables within Water Areas' this study deals with the classification possibilities of evaluating and mapping depth relations and bottom materials within the barren and clear-watered shores of Lake Yli-Kitka, North-Eastern Finland. It has been discovered that it is possible to distinguish open water areas with a water depth of more than about half of the Secchi disk depth from those of shallower hydrolittoral areas. The morainic, sandy and only slightly vegetated subareas of the shallow shores and shoals can possibly be identified by using a simple classification procedure. The data used were recorded by the coarse-resolution Landsat MSS imagery system, and better results are expected after the experiences of the Landsat TM data and the availability of the SPOT material.

Raitala, J.↗
NASA NTRS2017

Using High Spatial Resolution Satellite Imagery to Map Forest Burn Severity Across Spatial Scales in a Pine Barrens Ecosystem

As a primary disturbance agent, fire significantly influences local processes and services of forest ecosystems. Although a variety of remote sensing based approaches have been developed and applied to Landsat mission imagery to infer burn severity at 30 m spatial resolution, forest burn severity have still been seldom assessed at fine spatial scales (less than or equal to 5 m) from very-high-resolution (VHR) data. We assessed a 432 ha forest fire that occurred in April 2012 on Long Island, New York, within the Pine Barrens region, a unique but imperiled fire-dependent ecosystem in the northeastern United States. The mapping of forest burn severity was explored here at fine spatial scales, for the first time using remotely sensed spectral indices and a set of Multiple Endmember Spectral Mixture Analysis (MESMA) fraction images from bi-temporal - pre- and post-fire event - WorldView-2 (WV-2) imagery at 2 m spatial resolution. We first evaluated our approach using 1 m by 1 m validation points at the sub-crown scale per severity class (i.e. unburned, low, moderate, and high severity) from the post-fire 0.10 m color aerial ortho-photos; then, we validated the burn severity mapping of geo-referenced dominant tree crowns (crown scale) and 15 m by 15 m fixed-area plots (inter-crown scale) with the post-fire 0.10 m aerial ortho-photos and measured crown information of twenty forest inventory plots. Our approach can accurately assess forest burn severity at the sub-crown (overall accuracy is 84% with a Kappa value of 0.77), crown (overall accuracy is 82% with a Kappa value of 0.76), and inter-crown scales (89% of the variation in estimated burn severity ratings (i.e. Geo-Composite Burn Index (CBI)). This work highlights that forest burn severity mapping from VHR data can capture heterogeneous fire patterns at fine spatial scales over the large spatial extents. This is important since most ecological processes associated with fire effects vary at the less than 30 m scale and VHR approaches could significantly advance our ability to characterize fire effects on forest ecosystems.

Meng, Ran↗
NASA NTRS2018

Assessment of the Barren Ground Caribou Die-off During Winter 2015-2016 Using Passive Microwave Observations

In summer 2016, more than 50 Arctic Barren Ground caribous were found dead on Prince Charles Island (Nunavut, Canada), a species recently classified as threatened. Neither predator nor sign of diseases was observed and reported. The main hypothesis is that caribous were not able to access food due to a very dense snow surface, created by a strong storm system in spring. Using satellite microwave data, a significant increase in brightness temperature polarization ratio at 19 and 37 GHz was observed in spring 2016 (60% higher than previous two winter seasons). Based on microwave radiative transfer simulations, such anomaly can be explained with a very dense snow surface. This is consistent with the succession of storms and strong winds highlighted in ERA‐Interim over Prince Charles Island in spring 2016. Using several sources of data, this study shows that changes in snow conditions explain the caribou die‐off due to restricted foraging.

Dolant, C.↗