Related papers: Fine-Grained Complexity via Quantum Natural Proofs
Bayesian inference requires specification of a single, precise prior distribution, whereas frequentist inference only accommodates a vacuous prior. Since virtually every real-world application falls somewhere in between these two extremes,…
In this paper, we focus on the links between Boolean function theory and quantum computing. In particular, we study the notion of what we call fully-balanced functions and analyse the Fourier--Hadamard and Walsh supports of those functions…
From the ancient Einstein-Podolsky-Rosen paradox to the recent Sorkin-type impossible measurements problem, the contradictions between relativistic causality, quantum non-locality, and quantum measurement have persisted. Based on quantum…
One perspective on quantum algorithms is that they are classical algorithms having access to a special kind of memory with exotic properties. This perspective suggests that, even in the case of quantum algorithms, the control flow notions…
The quantum Bruhat graph, which is an extension of the graph formed by covering relations in the Bruhat order, is naturally related to the quantum cohomology ring of G/B. We enhance a result of Fulton and Woodward by showing that the…
Previously, Bennet and Feynman asked if Heisenberg's uncertainty principle puts a limitation on a quantum computer (Quantum Mechanical Computers, Richard P. Feynman, Foundations of Physics, Vol. 16, No. 6, p597-531, 1986). Feynman's answer…
Quantum neural networks have emerged as promising quantum machine learning models, leveraging the properties of quantum systems and classical optimization to solve complex problems in physics and beyond. However, previous studies have…
Solving the ground state and the ground-state properties of quantum many-body systems is generically a hard task for classical algorithms. For a family of Hamiltonians defined on an $m$-dimensional space of physical parameters, the ground…
Quantum coherence characterizes the non-classical feature of a single party system with respect to a local basis. Based on a recently introduced resource framework, coherence can be regarded as a resource and be systematically manipulated…
Quantum Boltzmann machines (QBMs) are generative models with potential advantages in quantum machine learning, yet their training is fundamentally limited by the barren plateau problem, where gradients vanish exponentially with system size.…
Most of physical experiments are usually described as repeated measurements of some random variables. The experimental data registered by on-line computers form time series of outcomes. The frequencies of different outcomes are compared…
The emerging field of quantum machine learning has the potential of revolutionizing our perspectives of quantum computing and artificial intelligence. In the predominantly empirical realm of quantum machine learning, a theoretical void…
We present a hybrid quantum-classical framework for simulating generic matrix functions more amenable to early fault-tolerant quantum hardware than standard quantum singular-value transformations. The method is based on randomization over…
We develop a quenched thermodynamic formalism for open random dynamical systems generated by finitely branched, piecewise-monotone mappings of the interval. The openness refers to the presence of holes in the interval, which terminate…
We establish fundamental and general techniques for formal verification of quantum protocols. Quantum protocols are novel communication schemes involving the use of quantum-mechanical phenomena for representation, storage and transmission…
It is well known that artificial neural networks initialized from independent and identically distributed priors converge to Gaussian processes in the limit of a large number of neurons per hidden layer. In this work we prove an analogous…
Bayes' rule plays a crucial piece of logical inference in information and physical sciences alike. Its extension into the quantum regime has been the object of several recent works. These quantum versions of Bayes' rule have been expressed…
In the second paper of this series we extend our Bayesian reanalysis of the evidence for a cosmic variation of the fine structure constant to the semi-parametric modelling regime. By adopting a mixture of Dirichlet processes prior for the…
Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g. in computation, communication and control. Fully random transformations require exponential time for either classical or quantum…
We propose a robust Q-learning algorithm for Markov decision processes under model uncertainty when each state-action pair is associated with a finite ambiguity set of candidate transition kernels. This finite-measure framework enables…