arXiv subjects

Tad Hogg

Publications and source records attributed to Tad Hogg.

At least 19 recordsLinked to original sources

arXiv2024

Chemical Power Variability among Microscopic Robots in Blood Vessels

Fuel cells using oxygen and glucose could power microscopic robots operating in blood vessels. Swarms of such robots can significantly reduce oxygen concentration, depending on the time between successive transits of the lung, hematocrit variation in vessels and tissue oxygen consumption. These factors differ among circulation paths through the body. This paper evaluates how these variations affect the minimum oxygen concentration due to robot consumption and where it occurs: mainly in moderate-sized veins toward the end of long paths prior to their merging with veins from shorter paths. This shows that tens of billions of robots can obtain hundreds of picowatts throughout the body with minor reduction in total oxygen. However, a trillion robots significantly deplete oxygen in some parts of the body. By storing oxygen or limiting their consumption in long circulation paths, robots can actively mitigate this depletion. The variation in behavior is illustrated in three cases: the portal system which involves passage through two capillary networks, the spleen whose slits significantly slow some of the flow, and large tissue consumption in coronary circulation.

cs.RO↗

arXiv2023

Quantum Alternating Operator Ansatz (QAOA) beyond low depth with gradually changing unitaries

The Quantum Approximate Optimization Algorithm and its generalization to Quantum Alternating Operator Ansatz (QAOA) is a promising approach for applying quantum computers to challenging problems such as combinatorial optimization and computational chemistry. In this paper, we study the underlying mechanisms governing the behavior of QAOA circuits beyond shallow depth in the practically relevant setting of gradually varying unitaries. We use the discrete adiabatic theorem, which complements and generalizes the insights obtained from the continuous-time adiabatic theorem primarily considered in prior work. Our analysis explains some general properties that are conspicuously depicted in the recently introduced QAOA performance diagrams. For parameter sequences derived from continuous schedules (e.g. linear ramps), these diagrams capture the algorithm's performance over different parameter sizes and circuit depths. Surprisingly, they have been observed to be qualitatively similar across different performance metrics and application domains. Our analysis explains this behavior as well as entails some unexpected results, such as connections between the eigenstates of the cost and mixer QAOA Hamiltonians changing based on parameter size and the possibility of reducing circuit depth without sacrificing performance.

quant-ph↗

arXiv2023

Chemical Power for Swarms of Microscopic Robots in Blood Vessels

Microscopic robots in the bloodstream could obtain power from fuel cells using glucose and oxygen. Previous studies of small numbers of such robots operating near each other showed how robots compete with their neighbors for oxygen. However, proposed applications involve billions of such robots operating throughout the body. With such large numbers, the robots can have systemic effects on oxygen concentration. This paper evaluates these effects and their consequences for robot power generation, oxygen available to tissue and heating as such robots move with the blood. When robots consume oxygen as fast as it diffuses to their surfaces, available power decreases significantly as robots move from the lungs, through arteries to capillaries and veins. Tens of billions of robots can obtain hundreds of picowatts throughout the circuit, while a trillion robots significantly deplete oxygen in the veins. Robots can mitigate this depletion by limiting their oxygen consumption, either overall or in specific locations or situations.

cs.RO↗

arXiv2022

Analytical Framework for Quantum Alternating Operator Ansätze

We develop a framework for analyzing layered quantum algorithms such as quantum alternating operator ansätze. Our framework relates quantum cost gradient operators, derived from the cost and mixing Hamiltonians, to classical cost difference functions that reflect cost function neighborhood structure. By considering QAOA circuits from the Heisenberg picture, we derive exact general expressions for expectation values as series expansions in the algorithm parameters, cost gradient operators, and cost difference functions. This enables novel interpretability and insight into QAOA behavior in various parameter regimes. For single-level QAOA1 we show the leading-order changes in the output probabilities and cost expectation value explicitly in terms of classical cost differences, for arbitrary cost functions. This demonstrates that, for sufficiently small positive parameters, probability flows from lower to higher cost states on average. By selecting signs of the parameters, we can control the direction of flow. We use these results to derive a classical random algorithm emulating QAOA1 in the small-parameter regime, i.e., that produces bitstring samples with the same probabilities as QAOA1 up to small error. For deeper QAOAp circuits we apply our framework to derive analogous and additional results in several settings. In particular we show QAOA always beats random guessing. We describe how our framework incorporates cost Hamiltonian locality for specific problem classes, including causal cone approaches, and applies to QAOA performance analysis with arbitrary parameters. We illuminate our results with a number of examples including applications to QUBO problems, MaxCut, and variants of MaxSat. We illustrate the application to QAOA circuits using mixing unitaries beyond the transverse-field mixer through two examples of constrained optimization, Max Independent Set and Graph Coloring.

quant-ph↗

arXiv2022

A Parameter Setting Heuristic for the Quantum Alternating Operator Ansatz

Parameterized quantum circuits are widely studied approaches for tackling optimization problems. A prominent example is the Quantum Alternating Operator Ansatz (QAOA), an approach that builds off the structure of the Quantum Approximate Optimization Algorithm. Finding high-quality parameters efficiently for QAOA remains a major challenge in practice. In this work, we introduce a classical strategy for parameter setting, suitable for common cases in which the number of distinct cost values grows only polynomially with the problem size. The crux of our strategy is that we replace the cost function expectation value step of QAOA with a parameterized model that can be efficiently evaluated classically. This model is based on empirical observations that QAOA states have large overlaps with states where variable configurations with the same cost have the same amplitude, which we define as Perfect Homogeneity. We thus define a Classical Homogeneous Proxy for QAOA in which Perfect Homogeneity holds exactly, and which yields information describing both states and expectation values. We classically determine high-quality parameters for this proxy, and use these parameters in QAOA, an approach we label the Homogeneous Heuristic for Parameter Setting. We numerically examine this heuristic for MaxCut on random graphs. For up to $3$ QAOA levels we are easily able to find parameters that match approximation ratios returned by previous globally optimized approaches. For levels up to $20$ we obtain parameters with approximation ratios monotonically increasing with depth, while a strategy that uses parameter transfer instead fails to converge with comparable classical resources. These results suggest that our heuristic may find good parameters in regimes that are intractable with noisy intermediate-scale quantum devices. Finally, we outline how our heuristic may be applied to wider classes of problems.

quant-ph↗

arXiv2022

Acoustic Power Management by Swarms of Microscopic Robots

Microscopic robots in the body could harvest energy from ultrasound to provide on-board control of autonomous behaviors such as measuring and communicating diagnostic information and precisely delivering drugs. This paper evaluates the acoustic power available to micron-size robots that collect energy using pistons. Acoustic attenuation and viscous drag on the pistons are the major limitations on the available power. Frequencies around 100kHz can deliver hundreds of picowatts to a robot in low-attenuation tissue within about 10cm of transducers on the skin, but much less in high-attenuation tissue such as a lung. However, applications of microscopic robots could involve such large numbers that the robots significantly increase attenuation, thereby reducing power for robots deep in the body. This paper describes how robots can collectively manage where and when they harvest energy to mitigate this attenuation so that a swarm of a few hundred billion robots can provide tens of picowatts to each robot, on average.

cs.RO↗

arXiv2021

Classical symmetries and the Quantum Approximate Optimization Algorithm

We study the relationship between the Quantum Approximate Optimization Algorithm (QAOA) and the underlying symmetries of the objective function to be optimized. Our approach formalizes the connection between quantum symmetry properties of the QAOA dynamics and the group of classical symmetries of the objective function. The connection is general and includes but is not limited to problems defined on graphs. We show a series of results exploring the connection and highlight examples of hard problem classes where a nontrivial symmetry subgroup can be obtained efficiently. In particular we show how classical objective function symmetries lead to invariant measurement outcome probabilities across states connected by such symmetries, independent of the choice of algorithm parameters or number of layers. To illustrate the power of the developed connection, we apply machine learning techniques towards predicting QAOA performance based on symmetry considerations. We provide numerical evidence that a small set of graph symmetry properties suffices to predict the minimum QAOA depth required to achieve a target approximation ratio on the MaxCut problem, in a practically important setting where QAOA parameter schedules are constrained to be linear and hence easier to optimize.

quant-ph↗

arXiv2021

Quantum Alternating Operator Ansatz (QAOA) Phase Diagrams and Applications for Quantum Chemistry

Determining Hamiltonian ground states and energies is a challenging task with many possible approaches on quantum computers. While variational quantum eigensolvers are popular approaches for near term hardware, adiabatic state preparation is an alternative that does not require noisy optimization of parameters. Beyond adiabatic schedules, QAOA is an important method for optimization problems. In this work we modify QAOA to apply to finding ground states of molecules and empirically evaluate the modified algorithm on several molecules. This modification applies physical insights used in classical approximations to construct suitable QAOA operators and initial state. We find robust qualitative behavior for QAOA as a function of the number of steps and size of the parameters, and demonstrate this behavior also occurs in standard QAOA applied to combinatorial search. To this end we introduce QAOA phase diagrams that capture its performance and properties in various limits. In particular we show a region in which non-adiabatic schedules perform better than the adiabatic limit while employing lower quantum circuit depth. We further provide evidence our results and insights also apply to QAOA applications beyond chemistry.

quant-ph↗

arXiv2021

Privacy and Data Balkanization: Circumventing the Barriers

The rapid growth in digital data forms the basis for a wide range of new services and research, e.g, large-scale medical studies. At the same time, increasingly restrictive privacy concerns and laws are leading to significant overhead in arranging for sharing or combining different data sets to obtain these benefits. For new applications, where the benefit of combined data is not yet clear, this overhead can inhibit organizations from even trying to determine whether they can mutually benefit from sharing their data. In this paper, we discuss techniques to overcome this difficulty by employing private information transfer to determine whether there is a benefit from sharing data, and whether there is room to negotiate acceptable prices. These techniques involve cryptographic protocols. While currently considered secure, these protocols are potentially vulnerable to the development of quantum technology, particularly for ensuring privacy over significant periods of time into the future. To mitigate this concern, we describe how developments in practical quantum technology can improve the security of these protocols.

cs.CR↗

arXiv2020

Origins of Algorithmic Instabilities in Crowdsourced Ranking

Crowdsourcing systems aggregate decisions of many people to help users quickly identify high-quality options, such as the best answers to questions or interesting news stories. A long-standing issue in crowdsourcing is how option quality and human judgement heuristics interact to affect collective outcomes, such as the perceived popularity of options. We address this limitation by conducting a controlled experiment where subjects choose between two ranked options whose quality can be independently varied. We use this data to construct a model that quantifies how judgement heuristics and option quality combine when deciding between two options. The model reveals popularity-ranking can be unstable: unless the quality difference between the two options is sufficiently high, the higher quality option is not guaranteed to be eventually ranked on top. To rectify this instability, we create an algorithm that accounts for judgement heuristics to infer the best option and rank it first. This algorithm is guaranteed to be optimal if data matches the model. When the data does not match the model, however, simulations show that in practice this algorithm performs better or at least as well as popularity-based and recency-based ranking for any two-choice question. Our work suggests that algorithms relying on inference of mathematical models of user behavior can substantially improve outcomes in crowdsourcing systems.

cs.SI↗

arXiv2020

Identifying Vessel Branching from Fluid Stresses on Microscopic Robots

Objects moving in fluids experience patterns of stress on their surfaces determined by the geometry of nearby boundaries. Flows at low Reynolds number, as occur in microscopic vessels such as capillaries in biological tissues, have relatively simple relations between stresses and nearby vessel geometry. Using these relations, this paper shows how a microscopic robot moving with such flows can use changes in stress on its surface to identify when it encounters vessel branches.

cs.RO↗

arXiv2020

Characterizing local noise in QAOA circuits

Recently Xue et al. [arXiv:1909.02196] demonstrated numerically that QAOA performance varies as a power law in the amount of noise under certain physical noise models. In this short note, we provide a deeper analysis of the origin of this behavior. In particular, we provide an approximate closed form equation for the fidelity and cost in terms of the noise rate, system size, and circuit depth. As an application, we show these equations accurately model the trade off between larger circuits which attain better cost values, at the expense of greater degradation due to noise.

quant-ph↗

arXiv2019

Quantifying the Impact of Cognitive Biases in Question-Answering Systems

Crowdsourcing can identify high-quality solutions to problems; however, individual decisions are constrained by cognitive biases. We investigate some of these biases in an experimental model of a question-answering system. In both natural and controlled experiments, we observe a strong position bias in favor of answers appearing earlier in a list of choices. This effect is enhanced by three cognitive factors: the attention an answer receives, its perceived popularity, and cognitive load, measured by the number of choices a user has to process. While separately weak, these effects synergistically amplify position bias and decouple user choices of best answers from their intrinsic quality. We end our paper by discussing the novel ways we can apply these findings to substantially improve how high-quality answers are found in question-answering systems.

cs.HC↗

arXiv2019

From Ansätze to Z-gates: a NASA View of Quantum Computing

For the last few years, the NASA Quantum Artificial Intelligence Laboratory (QuAIL) has been performing research to assess the potential impact of quantum computers on challenging computational problems relevant to future NASA missions. A key aspect of this research is devising methods to most effectively utilize emerging quantum computing hardware. Research questions include what experiments on early quantum hardware would give the most insight into the potential impact of quantum computing, the design of algorithms to explore on such hardware, and the development of tools to minimize the quantum resource requirements. We survey work relevant to these questions, with a particular emphasis on our recent work in quantum algorithms and applications, in elucidating mechanisms of quantum mechanics and their uses for quantum computational purposes, and in simulation, compilation, and physics-inspired classical algorithms. To our early application thrusts in planning and scheduling, fault diagnosis, and machine learning, we add thrusts related to robustness of communication networks and the simulation of many-body systems for material science and chemistry. We provide a brief update on quantum annealing work, but concentrate on gate-model quantum computing research advances within the last couple of years.

quant-ph↗

arXiv2019

Quantum-assisted associative adversarial network: Applying quantum annealing in deep learning

We present an algorithm for learning a latent variable generative model via generative adversarial learning where the canonical uniform noise input is replaced by samples from a graphical model. This graphical model is learned by a Boltzmann machine which learns low-dimensional feature representation of data extracted by the discriminator. A quantum annealer, the D-Wave 2000Q, is used to sample from this model. This algorithm joins a growing family of algorithms that use a quantum annealing subroutine in deep learning, and provides a framework to test the advantages of quantum-assisted learning in GANs. Fully connected, symmetric bipartite and Chimera graph topologies are compared on a reduced stochastically binarized MNIST dataset, for both classical and quantum annealing sampling methods. The quantum-assisted associative adversarial network successfully learns a generative model of the MNIST dataset for all topologies, and is also applied to the LSUN dataset bedrooms class for the Chimera topology. Evaluated using the Fréchet inception distance and inception score, the quantum and classical versions of the algorithm are found to have equivalent performance for learning an implicit generative model of the MNIST dataset.

cs.LG↗

arXiv2019

Mechanical Computing Systems Using Only Links and Rotary Joints

A new model for mechanical computing is demonstrated that requires only two basic parts: links and rotary joints. These basic parts are combined into two main higher level structures: locks and balances, which suffice to create all necessary combinatorial and sequential logic required for a Turing-complete computational system. While working systems have yet to be implemented using this new approach, the mechanical simplicity of the systems described may lend themselves better to, e.g., microfabrication, than previous mechanical computing designs. Additionally, simulations indicate that if molecular-scale implementations could be realized, they would be far more energy-efficient than conventional electronic computers.

cs.ET↗

arXiv2018

Stress-Based Navigation for Microscopic Robots in Viscous Fluids

Objects moving in fluids experience patterns of stress on their surfaces determined by their motion and the geometry of nearby boundaries. Fish and underwater robots can use these patterns for navigation. This paper extends this stress-based navigation to microscopic robots in tiny vessels, where robots can exploit the physics of fluids at low Reynolds number. This applies, for instance, in vessels with sizes and flow speeds comparable to those of capillaries in biological tissues. We describe how a robot can use simple computations to estimate its motion, orientation and distance to nearby vessel walls from fluid-induced stresses on its surface. Numerically evaluating these estimates for a variety of vessel sizes and robot positions shows they are most accurate when robots are close to vessel walls.

cs.RO↗

arXiv2017

Evaluating the Friction of Rotary Joints in Molecular Machines

A computationally-efficient method for evaluating friction in molecular rotary bearings is presented. This method estimates drag from fluctuations in molecular dynamics simulations via the fluctuation-dissipation theorem. This is effective even for simulation times short compared to a bearing's energy damping time and for rotation speeds comparable to or below typical thermal values. We apply this method to two molecular rotary bearings of similar size at 300K: previously studied nested (9,9)/(14,14) double-walled carbon nanotubes and a hypothetical rotary joint consisting of single acetylenic bonds in a rigid diamondoid housing. The acetylenic joint has a rotational frictional drag coefficient of $2 \times 10^{-35}\,\mbox{kg m${}^2$/s}$. The friction for the nested nanotubes is 120 times larger, comparable to values reported by previous studies. This fluctuation-based method could evaluate dissipation in a variety of molecular systems with similarly rigid and symmetric bearings.

cond-mat.soft↗