Related papers: A generic tool to evaluate second quantization
We apply general difference calculus in order to obtain solutions to the functional equations of the second order. We show that factorization method can be successfully applied to the functional case. This method is equivariant under the…
Quantum mechanics is well known to accelerate statistical sampling processes over classical techniques. In quantitative finance, statistical samplings arise broadly in many use cases. Here we focus on a particular one of such use cases,…
Usual quantum mechanics predicts probabilities for the outcomes of measurements carried out at definite moments of time. However, realistic measurements do not take place in an instant, but are extended over a period of time. The assumption…
Recently people started to understand that applications of the mathematical formalism of quantum theory are not reduced to physics. Nowadays, this formalism is widely used outside of quantum physics, in particular, in cognition, psychology,…
A second quantization procedure for the field-theoretic description of interactive games is analyzed. Its relation to the dynamical inverse problem of representation theory is emphasized.
Alongside the development of quantum algorithms and quantum complexity theory in recent years, quantum techniques have also proved instrumental in obtaining results in classical (non-quantum) areas. In this paper we survey these results and…
Quantum computers have the potential to provide an advantage over classical computers in a number of areas. Numerous metrics to benchmark the performance of quantum computers, ranging from their individual hardware components to entire…
Classical particle mechanics on curved spaces is related to the flow of ideal fluids, by a dual interpretation of the Hamilton-Jacobi equation. As in second quantization, the procedure relates the description of a system with a finite…
Here we will give a perspective on new possible interplays between Machine Learning and Quantum Physics, including also practical cases and applications. We will explore the ways in which machine learning could benefit from new quantum…
Generalized quantum master equations (GQMEs) are an important tool in modeling chemical and physical processes. For a large number of problems it has been shown that exact and approximate quantum dynamics methods can be made dramatically…
A notion of generalized quantifier in computational complexity theory is explored and used to give a unified treatment of leaf language definability, oracle separations, type 2 operators, and circuits with monoidal gates. Relations to…
Recently Quantum Computation has generated a lot of interest due to the discovery of a quantum algorithm which can factor large numbers in polynomial time. The usefulness of a quantum com puter is limited by the effect of errors. Simulation…
This article provides an accessible illustration of the measurement approach to the study of the quantum-classical transition suitable for beginning graduate students. As an example, we apply it to a quantum system with a general quadratic…
It is suggested that the individual outcomes of a measurement process can be understood within standard quantum mechanics in terms of the measuring apparatus, treated as a quantum computer, executing Grover's search algorithm.
Dirac notation is widely used in quantum physics and quantum programming languages to define, compute and reason about quantum states. This paper considers Dirac notation from the perspective of automated reasoning. We prove two main…
Derivatives play a critical role in computational statistics, examples being Bayesian inference using Hamiltonian Monte Carlo sampling and the training of neural networks. Automatic differentiation is a powerful tool to automate the…
Natural language processing models have emerged that can generate usable software and automate a number of programming tasks with high fidelity. These tools have yet to have an impact on the chemistry community. Yet, our initial testing…
The reduction paradigm of quantum interferometry is reanalyzed. In contrast to widespread opinion it is shown to be amenable to straightforward mathematical treatment within ``every-users'' simple-minded single particle quantum mechanics…
As quantum technologies advance, the ability to generate increasingly large quantum states has experienced rapid development. In this context, the verification and estimation of large entangled systems represents one of the main challenges…
Quantum coherence is the key resource for quantum technology, with applications in quantum optics, information processing, metrology and cryptography. Yet, there is no universally efficient method for quantifying coherence either in…