Out-of-distribution generalization for learning quantum dynamics.

Generalization bounds are a critical tool to assess the training data requirements of Quantum Machine Learning (QML). Recent work has established guarantees for in-distribution generalization of quantum neural networks (QNNs), where training and testing data are drawn from the same data distribution. However, there are currently no results on out-of-distribution generalization in QML, where we require a trained model to perform well even on data drawn from a different distribution to the training distribution. Here, we prove out-of-distribution generalization for the task of learning an unknown unitary. In particular, we show that one can learn the action of a unitary on entangled states having trained only product states. Since product states can be prepared using only single-qubit gates, this advances the prospects of learning quantum dynamics on near term quantum hardware, and further opens up new methods for both the classical and quantum compilation of quantum circuits.

Inference-Based Quantum Sensing.

In a standard quantum sensing (QS) task one aims at estimating an unknown parameter θ, encoded into an n-qubit probe state, via measurements of the system. The success of this task hinges on the ability to correlate changes in the parameter to changes in the system response R(θ) (i.e., changes in the measurement outcomes). For simple cases the form of R(θ) is known, but the same cannot be said for realistic scenarios, as no general closed-form expression exists. In this Letter, we present an inference-based scheme for QS. We show that, for a general class of unitary families of encoding, R(θ) can be fully characterized by only measuring the system response at 2n+1 parameters. This allows us to infer the value of an unknown parameter given the measured response, as well as to determine the sensitivity of the scheme, which characterizes its overall performance. We show that inference error is, with high probability, smaller than δ, if one measures the system response with a number of shots that scales only as Ω(log^{3}(n)/δ^{2}). Furthermore, the framework presented can be broadly applied as it remains valid for arbitrary probe states and measurement schemes, and, even holds in the presence of quantum noise. We also discuss how to extend our results beyond unitary families. Finally, to showcase our method we implement it for a QS task on real quantum hardware, and in numerical simulations.

Generalization in quantum machine learning from few training data.

Modern quantum machine learning (QML) methods involve variationally optimizing a parameterized quantum circuit on a training data set, and subsequently making predictions on a testing data set (i.e., generalizing). In this work, we provide a comprehensive study of generalization performance in QML after training on a limited number N of training data points. We show that the generalization error of a quantum machine learning model with T trainable gates scales at worst as [Formula: see text]. When only K ≪ T gates have undergone substantial change in the optimization process, we prove that the generalization error improves to [Formula: see text]. Our results imply that the compiling of unitaries into a polynomial number of native gates, a crucial application for the quantum computing industry that typically uses exponential-size training data, can be sped up significantly. We also show that classification of quantum states across a phase transition with a quantum convolutional neural network requires only a very small training data set. Other potential applications include learning quantum error correcting codes or quantum dynamical simulation. Our work injects new hope into the field of QML, as good generalization is guaranteed from few training data.

Quantum simulation of operator spreading in the chaotic Ising model.

There is great interest in using near-term quantum computers to simulate and study foundational problems in quantum mechanics and quantum information science, such as the scrambling measured by an out-of-time-ordered correlator (OTOC). Here we use an IBM Q processor, quantum error mitigation, and weaved Trotter simulation to study high-resolution operator spreading in a four-spin Ising model as a function of space, time, and integrability. Reaching four spins while retaining high circuit fidelity is made possible by the use of a physically motivated fixed-node variant of the OTOC, allowing scrambling to be estimated without overhead. We find clear signatures of a ballistic operator spreading in a chaotic regime, as well as operator localization in an integrable regime. The techniques developed and demonstrated here open up the possibility of using cloud-based quantum computers to study and visualize scrambling phenomena, as well as quantum information dynamics more generally.

Reformulation of the No-Free-Lunch Theorem for Entangled Datasets.

The no-free-lunch (NFL) theorem is a celebrated result in learning theory that limits one's ability to learn a function with a training dataset. With the recent rise of quantum machine learning, it is natural to ask whether there is a quantum analog of the NFL theorem, which would restrict a quantum computer's ability to learn a unitary process with quantum training data. However, in the quantum setting, the training data can possess entanglement, a strong correlation with no classical analog. In this Letter, we show that entangled datasets lead to an apparent violation of the (classical) NFL theorem. This motivates a reformulation that accounts for the degree of entanglement in the training set. As our main result, we prove a quantum NFL theorem whereby the fundamental limit on the learnability of a unitary is reduced by entanglement. We employ Rigetti's quantum computer to test both the classical and quantum NFL theorems. Our Letter establishes that entanglement is a commodity in quantum machine learning.

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. 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.

A Mechanism for Synaptic Copy Between Neural Circuits.

Cortical oscillations are central to information transfer in neural systems. Significant evidence supports the idea that coincident spike input can allow the neural threshold to be overcome and spikes to be propagated downstream in a circuit. Thus, an observation of oscillations in neural circuits would be an indication that repeated synchronous spiking may be enabling information transfer. However, for memory transfer, in which synaptic weights must be being transferred from one neural circuit (region) to another, what is the mechanism? Here, we present a synaptic transfer mechanism whose structure provides some understanding of the phenomena that have been implicated in memory transfer, including nested oscillations at various frequencies. The circuit is based on the principle of pulse-gated, graded information transfer between neural populations.

Variational consistent histories as a hybrid algorithm for quantum foundations.

Although quantum computers are predicted to have many commercial applications, less attention has been given to their potential for resolving foundational issues in quantum mechanics. Here we focus on quantum computers' utility for the Consistent Histories formalism, which has previously been employed to study quantum cosmology, quantum paradoxes, and the quantum-to-classical transition. We present a variational hybrid quantum-classical algorithm for finding consistent histories, which should revitalize interest in this formalism by allowing classically impossible calculations to be performed. In our algorithm, the quantum computer evaluates the decoherence functional (with exponential speedup in both the number of qubits and the number of times in the history) and a classical optimizer adjusts the history parameters to improve consistency. We implement our algorithm on a cloud quantum computer to find consistent histories for a spin in a magnetic field and on a simulator to observe the emergence of classicality for a chiral molecule.

Imaging neural events in zebrafish larvae with linear structured illumination light sheet fluorescence microscopy.

Light sheet fluorescence microscopy (LSFM) is a powerful tool for investigating model organisms including zebrafish. However, due to scattering and refractive index variations within the sample, the resulting image often suffers from low contrast. Structured illumination (SI) has been combined with scanned LSFM to remove out-of-focus and scattered light using square-law detection. Here, we demonstrate that the combination of LSFM with linear reconstruction SI can further increase resolution and contrast in the vertical and axial directions compared to the widely adopted root-mean square reconstruction method while using the same input images. We apply this approach to imaging neural activity in 7-day postfertilization zebrafish larvae. We imaged two-dimensional sections of the zebrafish central nervous system in two colors at an effective frame rate of 7 frames per second.

Mutual Information and Information Gating in Synfire Chains.

Coherent neuronal activity is believed to underlie the transfer and processing of information in the brain. Coherent activity in the form of synchronous firing and oscillations has been measured in many brain regions and has been correlated with enhanced feature processing and other sensory and cognitive functions. In the theoretical context, synfire chains and the transfer of transient activity packets in feedforward networks have been appealed to in order to describe coherent spiking and information transfer. Recently, it has been demonstrated that the classical synfire chain architecture, with the addition of suitably timed gating currents, can support the graded transfer of mean firing rates in feedforward networks (called synfire-gated synfire chains-SGSCs). Here we study information propagation in SGSCs by examining mutual information as a function of layer number in a feedforward network. We explore the effects of gating and noise on information transfer in synfire chains and demonstrate that asymptotically, two main regions exist in parameter space where information may be propagated and its propagation is controlled by pulse-gating: a large region where binary codes may be propagated, and a smaller region near a cusp in parameter space that supports graded propagation across many layers.

MiCASA is a new method for quantifying cellular organization.

While many tools exist for identifying and quantifying individual cell types, few methods are available to assess the relationships between cell types in organs and tissues and how these relationships change during aging or disease states. We present a quantitative method for evaluating cellular organization, using the mouse thymus as a test organ. The thymus is the primary lymphoid organ responsible for generating T cells in vertebrates, and its proper structure and organization is essential for optimal function. Our method, Multitaper Circularly Averaged Spectral Analysis (MiCASA), identifies differences in the tissue-level organization with high sensitivity, including defining a novel type of phenotype by measuring variability as a specific parameter. MiCASA provides a novel and easily implemented quantitative tool for assessing cellular organization.

Late Effects of Exposure to Ionizing Radiation and Age on Human Thymus Morphology and Function.

The thymus is essential for proper development and maintenance of a T-cell repertoire that can respond to newly encountered antigens, but its function can be adversely affected by internal factors such as pregnancy and normal aging or by external stimuli such as stress, infection, chemotherapy and ionizing radiation. We have utilized a unique archive of thymus tissues, obtained from 165 individuals, exposed to the 1945 atomic bomb blast in Hiroshima, to study the long-term effects of receiving up to ∼3 Gy dose of ionizing radiation on human thymus function. A detailed morphometric analysis of thymus activity and architecture in these subjects at the time of their natural deaths was performed using bright-field immunohistochemistry and dual-color immunofluorescence and compared to a separate cohort of nonexposed control subjects. After adjusting for age-related effects, increased hallmarks of thymic involution were observed histologically in individuals exposed to either low (5-200 mGy) or moderate-to-high (>200 mGy) doses of ionizing radiation compared to unirradiated individuals (<5 mGy). Sex-related differences were seen when the analysis was restricted to individuals under 60 years of attained age at sample collection, but were not observed when comparing across the entire age range. This indicates that while females undergo slower involution than males, they ultimately attain similar phenotypes. These findings suggest that even low-dose-radiation exposure can accelerate thymic aging, with decreased thymopoiesis relative to nonexposed controls evident years after exposure. These data were used to develop a model that can predict thymic function during normal aging or in individuals therapeutically or accidentally exposed to radiation.

Cusps enable line attractors for neural computation.

Line attractors in neuronal networks have been suggested to be the basis of many brain functions, such as working memory, oculomotor control, head movement, locomotion, and sensory processing. In this paper, we make the connection between line attractors and pulse gating in feed-forward neuronal networks. In this context, because of their neutral stability along a one-dimensional manifold, line attractors are associated with a time-translational invariance that allows graded information to be propagated from one neuronal population to the next. To understand how pulse-gating manifests itself in a high-dimensional, nonlinear, feedforward integrate-and-fire network, we use a Fokker-Planck approach to analyze system dynamics. We make a connection between pulse-gated propagation in the Fokker-Planck and population-averaged mean-field (firing rate) models, and then identify an approximate line attractor in state space as the essential structure underlying graded information propagation. An analysis of the line attractor shows that it consists of three fixed points: a central saddle with an unstable manifold along the line and stable manifolds orthogonal to the line, which is surrounded on either side by stable fixed points. Along the manifold defined by the fixed points, slow dynamics give rise to a ghost. We show that this line attractor arises at a cusp catastrophe, where a fold bifurcation develops as a function of synaptic noise; and that the ghost dynamics near the fold of the cusp underly the robustness of the line attractor. Understanding the dynamical aspects of this cusp catastrophe allows us to show how line attractors can persist in biologically realistic neuronal networks and how the interplay of pulse gating, synaptic coupling, and neuronal stochasticity can be used to enable attracting one-dimensional manifolds and, thus, dynamically control the processing of graded information.

Graded, Dynamically Routable Information Processing with Synfire-Gated Synfire Chains.

Coherent neural spiking and local field potentials are believed to be signatures of the binding and transfer of information in the brain. Coherent activity has now been measured experimentally in many regions of mammalian cortex. Recently experimental evidence has been presented suggesting that neural information is encoded and transferred in packets, i.e., in stereotypical, correlated spiking patterns of neural activity. Due to their relevance to coherent spiking, synfire chains are one of the main theoretical constructs that have been appealed to in order to describe coherent spiking and information transfer phenomena. However, for some time, it has been known that synchronous activity in feedforward networks asymptotically either approaches an attractor with fixed waveform and amplitude, or fails to propagate. This has limited the classical synfire chain's ability to explain graded neuronal responses. Recently, we have shown that pulse-gated synfire chains are capable of propagating graded information coded in mean population current or firing rate amplitudes. In particular, we showed that it is possible to use one synfire chain to provide gating pulses and a second, pulse-gated synfire chain to propagate graded information. We called these circuits synfire-gated synfire chains (SGSCs). Here, we present SGSCs in which graded information can rapidly cascade through a neural circuit, and show a correspondence between this type of transfer and a mean-field model in which gating pulses overlap in time. We show that SGSCs are robust in the presence of variability in population size, pulse timing and synaptic strength. Finally, we demonstrate the computational capabilities of SGSC-based information coding by implementing a self-contained, spike-based, modular neural circuit that is triggered by streaming input, processes the input, then makes a decision based on the processed information and shuts itself down.

A Multitaper, Causal Decomposition for Stochastic, Multivariate Time Series: Application to High-Frequency Calcium Imaging Data.

Neural data analysis has increasingly incorporated causal information to study circuit connectivity. Dimensional reduction forms the basis of most analyses of large multivariate time series. Here, we present a new, multitaper-based decomposition for stochastic, multivariate time series that acts on the covariance of the time series at all lags, C(τ), as opposed to standard methods that decompose the time series, X(t), using only information at zero-lag. In both simulated and neural imaging examples, we demonstrate that methods that neglect the full causal structure may be discarding important dynamical information in a time series.

A mechanism for graded, dynamically routable current propagation in pulse-gated synfire chains and implications for information coding.

Neural oscillations can enhance feature recognition (Azouz and Gray Proceedings of the National Academy of Sciences of the United States of America, 97, 8110-8115 2000), modulate interactions between neurons (Womelsdorf et al. Science, 316, 1609-01612 2007), and improve learning and memory (Markowska et al. The Journal of Neuroscience, 15, 2063-2073 1995). Numerical studies have shown that coherent spiking can give rise to windows in time during which information transfer can be enhanced in neuronal networks (Abeles Israel Journal of Medical Sciences, 18, 83-92 1982; Lisman and Idiart Science, 267, 1512-1515 1995, Salinas and Sejnowski Nature Reviews. Neuroscience, 2, 539-550 2001). Unanswered questions are: 1) What is the transfer mechanism? And 2) how well can a transfer be executed? Here, we present a pulse-based mechanism by which a graded current amplitude may be exactly propagated from one neuronal population to another. The mechanism relies on the downstream gating of mean synaptic current amplitude from one population of neurons to another via a pulse. Because transfer is pulse-based, information may be dynamically routed through a neural circuit with fixed connectivity. We demonstrate the transfer mechanism in a realistic network of spiking neurons and show that it is robust to noise in the form of pulse timing inaccuracies, random synaptic strengths and finite size effects. We also show that the mechanism is structurally robust in that it may be implemented using biologically realistic pulses. The transfer mechanism may be used as a building block for fast, complex information processing in neural circuits. We show that the mechanism naturally leads to a framework wherein neural information coding and processing can be considered as a product of linear maps under the active control of a pulse generator. Distinct control and processing components combine to form the basis for the binding, propagation, and processing of dynamically routed information within neural pathways. Using our framework, we construct example neural circuits to 1) maintain a short-term memory, 2) compute time-windowed Fourier transforms, and 3) perform spatial rotations. We postulate that such circuits, with automatic and stereotyped control and processing of information, are the neural correlates of Crick and Koch's zombie modes.

The Effect of Examiner Variability on Multiple Canine Stifle Kinematic Gait Collections in a 3-Dimensional Model.

OBJECTIVE: To evaluate examiner variability in a superficial skin marker model of canine stifle kinematics. STUDY DESIGN: Experimental. ANIMALS: Six clinically normal dogs. METHODS: Dogs had 11 retroreflective markers fixed to the skin on the right hindlimb. Dogs were trotted 5 times through the calibrated testing space and this was repeated on 4 different testing days. Examiner A applied all markers to a dog and collected 6 good trials for analysis. The markers were then removed and Examiner B immediately repeated the process on the same dog. This was repeated for each dog on the 4 testing days. The dogs were trotted at a velocity of 1.70-2.10 m/s through the testing space to obtain the dynamic data sets. Comparisons were performed with Fourier analysis and Generalized Indicator Function Analysis (GIFA). Significance was set at P < .05 for all comparisons. RESULTS: Fourier analysis and GIFA found differences within and between examiners. Fourier analysis found no differences in sagittal and transverse planes for the experienced (A) and novice examiner (B), respectively. Fourier analysis detected fewer differences for the experienced examiner (A). CONCLUSION: Variability occurs within and between examiners using the same kinematic model. Transverse and frontal plane kinematics produce variable results between examiners. Prior experience with the model reduces the amount of variability and results in consistent and repeatable sagittal plane kinematic data collection.

Electrophysiological recording in the brain of intact adult zebrafish.

Previously, electrophysiological studies in adult zebrafish have been limited to slice preparations or to eye cup preparations and electrorentinogram recordings. This paper describes how an adult zebrafish can be immobilized, intubated, and used for in vivo electrophysiological experiments, allowing recording of neural activity. Immobilization of the adult requires a mechanism to deliver dissolved oxygen to the gills in lieu of buccal and opercular movement. With our technique, animals are immobilized and perfused with habitat water to fulfill this requirement. A craniotomy is performed under tricaine methanesulfonate (MS-222; tricaine) anesthesia to provide access to the brain. The primary electrode is then positioned within the craniotomy window to record extracellular brain activity. Through the use of a multitube perfusion system, a variety of pharmacological compounds can be administered to the adult fish and any alterations in the neural activity can be observed. The methodology not only allows for observations to be made regarding changes in neurological activity, but it also allows for comparisons to be made between larval and adult zebrafish. This gives researchers the ability to identify the alterations in neurological activity due to the introduction of various compounds at different life stages.

Quantum simulation of tunneling in small systems.

A number of quantum algorithms have been performed on small quantum computers; these include Shor's prime factorization algorithm, error correction, Grover's search algorithm and a number of analog and digital quantum simulations. Because of the number of gates and qubits necessary, however, digital quantum particle simulations remain untested. A contributing factor to the system size required is the number of ancillary qubits needed to implement matrix exponentials of the potential operator. Here, we show that a set of tunneling problems may be investigated with no ancillary qubits and a cost of one single-qubit operator per time step for the potential evolution, eliminating at least half of the quantum gates required for the algorithm and more than that in the general case. Such simulations are within reach of current quantum computer architectures.

Improved dimensionally-reduced visual cortical network using stochastic noise modeling.

In this paper, we extend our framework for constructing low-dimensional dynamical system models of large-scale neuronal networks of mammalian primary visual cortex. Our dimensional reduction procedure consists of performing a suitable linear change of variables and then systematically truncating the new set of equations. The extended framework includes modeling the effect of neglected modes as a stochastic process. By parametrizing and including stochasticity in one of two ways we show that we can improve the systems-level characterization of our dimensionally reduced neuronal network model. We examined orientation selectivity maps calculated from the firing rate distribution of large-scale simulations and stochastic dimensionally reduced models and found that by using stochastic processes to model the neglected modes, we were able to better reproduce the mean and variance of firing rates in the original large-scale simulations while still accurately predicting the orientation preference distribution.