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The original motivation to build a quantum computer came from Feynman who envisaged a machine capable of simulating generic quantum mechanical systems, a task that is believed to be intractable for classical computers. Such a machine would…
Sampling from complicated probability distributions is a hard computational problem arising in many fields, including statistical physics, optimization, and machine learning. Quantum computers have recently been used to sample from…
The Markov Chain Monte Carlo method is at the heart of efficient approximation schemes for a wide range of problems in combinatorial enumeration and statistical physics. It is therefore very natural and important to determine whether…
I generalize the well-known classical Metropolis-Hastings algorithm into a quantum algorithm that can equilibrate, measure, and mix a quantum thermal state on a quantum computer. It performs non-symmetric transitions on labels of state…
Increasingly sophisticated programmable quantum simulators and quantum computers are opening unprecedented opportunities for exploring and exploiting the properties of highly entangled complex quantum systems. The complexity of large…
Bayesian inference is a widely used technique for real-time characterization of quantum systems. It excels in experimental characterization in the low data regime, and when the measurements have degrees of freedom. A decisive factor for its…
Quantum technologies offer a promising route to the efficient sampling and analysis of stochastic processes, with potential applications across the sciences. Such quantum advantages rely on the preparation of a quantum sample state of the…
Efficient sampling from a classical Gibbs distribution is an important computational problem with applications ranging from statistical physics over Monte Carlo and optimization algorithms to machine learning. We introduce a family of…
Rejection sampling is a well-known method to sample from a target distribution, given the ability to sample from a given distribution. The method has been first formalized by von Neumann (1951) and has many applications in classical…
This is the documentation for generating random samples from the quantum state space in accordance with a specified distribution, associated with this webpage: http://tinyurl.com/QSampling . Ready-made samples (each with at least a million…
We propose digitized counterdiabatic quantum sampling (DCQS), a hybrid quantum-classical algorithm for efficient sampling from energy-based models, such as low-temperature Boltzmann distributions. The method utilizes counterdiabatic…
Stochastic modelling of complex systems plays an essential, yet often computationally intensive role across the quantitative sciences. Recent advances in quantum information processing have elucidated the potential for quantum simulators to…
Quantum mechanics predicts correlation between spacelike separated events which is widely argued to violate the principle of Local Causality. By contrast, here we shall show that the Schr\"odinger equation with Born's statistical…
As quantum machine learning continues to develop at a rapid pace, the importance of ensuring the robustness and efficiency of quantum algorithms cannot be overstated. Our research presents an analysis of quantum randomized smoothing, how…
Stochastic mechanics (SM), as proposed by Edward Nelson and others in the 20th century, aims to reconstruct quantum mechanics (QM) from a more fundamental theory of classical point particles interacting with a classical-like ether, where…
Drawing independent samples from a probability distribution is an important computational problem with applications in Monte Carlo algorithms, machine learning, and statistical physics. The problem can in principle be solved on a quantum…
Quantum computers are known for their potential to achieve up-to-exponential speedup compared to classical computers for certain problems. To exploit the advantages of quantum computers, we propose quantum algorithms for linear stochastic…
We demonstrate the application of the Metropolis-Hastings algorithm to sampling of classical thermal states of one-dimensional Bose-Einstein quasicondensates in the classical fields approximation, both in untrapped and harmonically trapped…
We construct a simple quantum version of the classical Metropolis algorithm to prepare and observe quantum thermal states. It induces both a quantum Markov chain that mixes the quantum thermal state and a classical Markov chain that mixes…
Quantum stochastic differential equations have been used to describe the dynamics of an atom interacting with the electromagnetic field via absorption/emission processes. Here, by using the full quantum stochastic Schroedinger equation…