Related papers: Sampling and the complexity of nature
This thesis is intended in part to summarize and also to contribute to the newest developments in passive linear optics that have resulted, directly or indirectly, from the somewhat shocking discovery in 2010 that the BosonSampling problem…
Quantum computation and quantum information are of great current interest in computer science, mathematics, physical sciences and engineering. They will likely lead to a new wave of technological innovations in communication, computation…
Random samples of quantum states with specific properties are useful for various applications, such as Monte Carlo integration over the state space. In the high-dimensional situations that one encounters already for a few qubits, the…
The paper gives a systematic review of the basic ideas of (non-relativistic) quantum mechanics including all changes that result from previous work of the authors. This shows that the new theory is self-consistent and (in certain sense)…
Neural networks are being used to improve the probing of the state spaces of many particle systems as approximations to wavefunctions and in order to avoid the recurring sign problem of quantum monte-carlo. One may ask whether the usual…
A defining signature of classical systems is "in principle measurability" without disturbance: a feature manifestly violated by quantum systems. We describe a multi-interferometer experimental setup that can, in principle, reveal the…
Coherence and entanglement are fundamental properties of quantum systems, promising to power the near future quantum computers, sensors and simulators. Yet, their experimental detection is challenging, usually requiring full reconstruction…
One of the most fundamental problems in distribution testing is the identity testing problem: given samples $x_1,\ldots,x_s$, the goal is to determine whether the samples are drawn from a target distribution $\mathcal{D}$. When…
The descriptions of the quantum realm and the macroscopic classical world differ significantly not only in their mathematical formulations but also in their foundational concepts and philosophical consequences. When and how physical systems…
In this paper we provide a general account of the causal models which attempt to provide a solution to the famous measurement problem of Quantum Mechanics (QM). We will argue that --leaving aside instrumentalism which restricts the physical…
Interest in problems of statistical inference connected to measurements of quantum systems has recently increased substantially, in step with dramatic new developments in experimental techniques for studying small quantum systems.…
Quantum measurement is a fundamental concept in the field of quantum mechanics. The action of quantum measurement, leading the superposition state of the measured quantum system into a definite output state, not only reconciles…
Fast quantum algorithms can solve important computational problems more efficiently than classical algorithms. However, little is known about whether quantum computing can speed up solving geometric problems. This article explores quantum…
Experimental demonstration of the quantum advantage over classical simulations with Boson Sampling is currently under intensive investigation. There seems to be a scalability issue to the necessary number of bosons on the linear optical…
Quantum computers promise to efficiently solve not only problems believed to be intractable for classical computers, but also problems for which verifying the solution is also considered intractable. This raises the question of how one can…
The boson sampling problem has triggered a lot of interest in the scientific community because of its potential of demonstrating the computational power of quantum interference without the need of non-linear processes. However, the…
Boson sampling is a mathematical problem that is strongly believed to be intractable for classical computers, whereas passive linear interferometers can produce samples efficiently. So far, the problem remains a computational curiosity, and…
Involving only the measurements of commuting observables - the problem-setting and the corresponding solution - quantum algorithms should be subject to classical logic. This would allow flanking their customary quantum description with a…
In contrast with software-generated randomness (called pseudo-randomness), quantum randomness is provable incomputable, i.e.\ it is not exactly reproducible by any algorithm. We provide experimental evidence of incomputability --- an…
In classical statistical learning theory, one of the most well studied problems is that of binary classification. The information-theoretic sample complexity of this task is tightly characterized by the Vapnik-Chervonenkis (VC) dimension. A…