Related papers: Classical Statistical simulation of Quantum Field …
Classical field theories coupled to stochastic noise provide an extremely powerful tool for modeling phenomena as diverse as turbulence, pattern-formation, and the structural development of the universe itself. In this Letter we sketch a…
A fundamental problem with attempting to quantize general relativity is its perturbative non-renormalizability. However, this fact does not rule out the possibility that non-perturbative effects can be computed, at least in some…
We address the use of a single qubit as a quantum probe to characterize the properties of classical noise. In particular, we focus on the characterization of classical noise arising from the interaction with a stochastic field described by…
A nonlocal method of extracting the positive (or the negative) frequency part of a field, based on knowledge of a 2-point function, leads to certain natural generalizations of the normal ordering of quantum fields in classical gravitational…
One of the core research questions in the theory of quantum computing is to find out to what precise extent the classical simulation of a noisy quantum circuits is possible and where potential quantum advantages can set in. In this work, we…
An approach to field theory is studied in which fields are comprised of $N$ constituent random neurons. Gaussian theories arise in the infinite-$N$ limit when neurons are independently distributed, via the Central Limit Theorem, while…
In classical mechanics, a natural way to simplify a many-body problem is to ``replace'' some of the elements of the composite system with surrogate \textit{force fields}. In the realm of quantum mechanics, however, such a description is…
The main goal of these notes is to give an introduction to the mathematics of quantum noise and some of its applications in non-equilibrium statistical mechanics. We start with some reminders from the theory of classical stochastic…
The practice of setting quantum fields as sources for classical general relativity is examined. Several conceptual problems are identified which invalidate apparently innocuous equations. Alternative ways to links classical general…
Traditional quantum field theory can lead to enormous zero-point energy, which markedly disagrees with experiment. Unfortunately, this situation is built into conventional canonical quantization procedures. For identical classical theories,…
We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the…
Perturbation theory is an important technique for reducing computational cost and providing physical insights in simulating quantum systems with classical computers. Here, we provide a quantum algorithm to obtain perturbative energies on…
We argue that the quantized non-Abelian gauge theory can be obtained as the infrared limit of the corresponding classical gauge theory in a higher dimension. We show how the transformation from classical to quantum field theory emerges and…
For classical field theories with probabilistic initial conditions the classical field observables are an idealization. Their arbitrarily precise values poorly reflect the characteristic uncertainty in the presence of substantial…
All quantum field theories that describe interacting bosonic elementary particles, share the feature that the zeroth order perturbation expansion describes non-interacting harmonic oscillators. This is explained in the paper. We then…
An effective formalism for white noise analysis, conceptually equivalent to Wilsonian renormalization theory, is introduced. Space-time gets represented by a boolean lattice of coarse regions, energy scales become space-time partitions by…
Variational quantum algorithms (VQAs) are expected to become a practical application of near-term noisy quantum computers. Although the effect of the noise crucially determines whether a VQA works or not, the heuristic nature of VQAs makes…
We address two basic issues in the theory of galaxy formation from fluctuations of quantum fields: 1) the nature and origin of noise and fluctuations and 2) the conditions for using a classical stochastic equation for their description. On…
We study quantum mechanics in the stochastic formulation, using the functional integral approach. The noise term enters the classical action as a local contribution of anticommuting fields. The partition function is not invariant under…
The quantum theory of a harmonic oscillator with a time dependent frequency arises in several important physical problems, especially in the study of quantum field theory in an external background. While the mathematics of this system is…