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A central roadblock to analyzing quantum algorithms on quantum states is the lack of a comparable input model for classical algorithms. Inspired by recent work of the author [E. Tang, STOC'19], we introduce such a model, where we assume we…
We introduce a framework for uncertainty estimation that both describes and extends many existing methods. We consider typical hyperparameters involved in classical training as random variables and marginalise them out to capture various…
Existing abstract models of quantum computation make reference to circuit elements, much in contrast to their classical counterparts. Circuits, as a model of computation, substantially limit algorithmic expression and obscure high-level…
We prove that quantum computation is polynomially equivalent to classical probabilistic computation with an oracle for estimating the value of simple sums, quadratically signed weight enumerators. The problem of estimating these sums can be…
We study the computational complexity of certain integrable quantum theories in 1+1 dimensions. We formalize a model of quantum computation based on these theories. In this model, distinguishable particles start out with known momenta and…
We study the utility of a complex Langevin (CL) equation as an alternative for the Monte Carlo (MC) procedure in the evaluation of expectation values occurring in fermionic many-body problems. We find that a CL approach is natural in cases…
For ordinary differential equations in the complex domain, a central problem is to understand, in a given equation or class of equations, those whose solutions do not present multivaluedness. We consider autonomous, first-order, quadratic…
We consider a class of pseudodifferential operators with a doubly characteristic point, where the quadratic part of the symbol fails to be elliptic but obeys an averaging assumption. Under suitable additional assumptions, semiclassical…
We consider a coherent-classical estimation scheme for a class of linear quantum systems. It comprises an estimator that is a mixed quantum-classical system without involving coherent feedback. The estimator yields a classical estimate of a…
Computation of observables and their gradients on near-term quantum hardware is a central aspect of any quantum algorithm. In this work, we first review standard approaches to the estimation of observables with and without quantum amplitude…
Machine learning algorithms based on parametrized quantum circuits are prime candidates for near-term applications on noisy quantum computers. In this direction, various types of quantum machine learning models have been introduced and…
This paper studies the numerical computation of integrals, representing estimates or predictions, over the output $f(x)$ of a computational model with respect to a distribution $p(\mathrm{d}x)$ over uncertain inputs $x$ to the model. For…
A quantum particle on a circle in a quadratic potential exhibits a spectrum that is not harmonic, despite having all algebraic properties of the quantum harmonic oscillator. This raises the question where the usual algebraic argument --…
We describe an algorithm for using a quantum computer to calculate mean values of observables and the partition function of a quantum system. Our algorithm includes two sub-algorithms. The first sub-algorithm is for calculating, with…
This study addresses the predictive limitation of probabilistic circuits and introduces transformations as a remedy to overcome it. We demonstrate this limitation in robotic scenarios. We motivate that independent component analysis is a…
We discuss the classical statistics of isolated subsystems. Only a small part of the information contained in the classical probability distribution for the subsystem and its environment is available for the description of the isolated…
Gaussian building blocks are essential for photonic quantum information processing, and universality can be practically achieved by equipping Gaussian circuits with adaptive measurement and feedforward. The number of adaptive steps then…
The class of problems in causal inference which seeks to isolate causal correlations solely from observational data even without interventions has come to the forefront of machine learning, neuroscience and social sciences. As new large…
A non-Euclidean generalization of conditional expectation is introduced and characterized as the minimizer of expected intrinsic squared-distance from a manifold-valued target. The computational tractable formulation expresses the…
Statistical inference on the explained variation of an outcome by a set of covariates is of particular interest in practice. When the covariates are of moderate to high-dimension and the effects are not sparse, several approaches have been…