Related papers: Quantum algorithmic randomness
We show algorithmic randomness versions of the two classical theorems on subsequences of normal numbers. One is Kamae-Weiss theorem (Kamae 1973) on normal numbers, which characterize the selection function that preserves normal numbers.…
The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems: nuclear…
An overarching milestone of quantum machine learning (QML) is to demonstrate the advantage of QML over all possible classical learning methods in accelerating a common type of learning task as represented by supervised learning with…
Is quantum mechanics about 'states'? Or is it basically another kind of probability theory? It is argued that the elementary formalism of quantum mechanics operates as a well-justified alternative to 'classical' instantiations of a…
We present a no-go theorem for the distinguishability between quantum random numbers (i.e., random numbers generated quantum mechanically) and pseudo-random numbers (i.e., random numbers generated algorithmically). The theorem states that…
We develop a fundamental framework for the quantum mechanics of stochastic systems (QMSS), showing that classical discrete stochastic processes emerge naturally as perturbations of the quantum harmonic oscillator (QHO). By constructing…
The problem of generating random quantum states is of a great interest from the quantum information theory point of view. In this paper we present a package for Mathematica computing system harnessing a specific piece of hardware, namely…
Neural networks have achieved impressive breakthroughs in both industry and academia. How to effectively develop neural networks on quantum computing devices is a challenging open problem. Here, we propose a new quantum neural network model…
We propose an effective approach to rapid estimation of the energy spectrum of quantum systems with the use of machine learning (ML) algorithm. In the ML approach (back propagation), the wavefunction data known from experiments is…
Recent work has exposed the idea that interesting quantum-like probability laws, including interference effects, can be manifest in classical systems. Here we propose a model for quantum-like (QL) states and QL bits. We suggest a way that…
Applying probabilistic techniques we study regularity properties of quantum master equations (QMEs) in the Lindblad form with unbounded coefficients; a density operator is regular if, roughly speaking, it describes a quantum state with…
A new interpretation of quantum mechanics is proposed according to which precedence, freedom and novelty play central roles. This is based on a modification of the postulates for quantum theory given by Masanes and Muller. We argue that…
Due to the strong correlations present in quantum systems, classical machine learning algorithms like stochastic gradient descent are often insufficient for the training of neural network quantum states (NQSs). These difficulties can be…
This paper describes an algorithm for selecting a consistent set within the consistent histories approach to quantum mechanics and investigates its properties. The algorithm select from among the consistent sets formed by projections…
The quantum state of a light beam can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We describe quantum tomography as an inverse statistical problem in which…
Conventional quantum mechanics with a complex Hilbert space and the Born Rule is derived from five axioms describing properties of probability distributions for the outcome of measurements. Axioms I,II,III are common to quantum mechanics…
We consider classical and quantum algorithms which have a duality property: roughly, either the algorithm provides some nontrivial improvement over random or there exist many solutions which are significantly worse than random. This enables…
We show how to efficiently generate pseudo-random states suitable for quantum information processing via cluster-state quantum computation. By reformulating pseudo-random algorithms in the cluster-state picture, we identify a strategy for…
A result of Shen says that if $F\colon2^{\mathbb{N}}\rightarrow2^{\mathbb{N}}$ is an almost-everywhere computable, measure-preserving transformation, and $y\in2^{\mathbb{N}}$ is Martin-L\"of random, then there is a Martin-L\"of random…
In this note, we present the formalism to start a quantum analysis for the recent billiard representation introduced by Damour, Henneaux and Nicolai in the study of the cosmological singularity. In particular we use the theory of Maass…