相关论文: Non-linear Quantization of Integrable Classical Sy…
We discuss a classical reinterpretation of quantum-mechanics-based analysis of classical Markov chains with detailed balance, that is based on the quantum-classical correspondence. The classical reinterpretation is then used to demonstrate…
In an effort to provide an alternative method to represent a quantum spin, a precise nonlinear dynamics semi-classical model is used to show that standard quantum spin analysis can be obtained. The model includes a multi-body,…
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 information science provides powerful technologies beyond the scope of classical physics. In practice, accurate control of quantum operations is a challenging task with current quantum devices. The implementation of high fidelity…
The purpose of this work is to present a method based on the factorizations used in one dimensional quantum mechanics in order to find the symmetries of quantum and classical superintegrable systems in higher dimensions. We apply this…
We propose a classical-quantum hybrid algorithm for machine learning on near-term quantum processors, which we call quantum circuit learning. A quantum circuit driven by our framework learns a given task by tuning parameters implemented on…
In cosmology minisuperspace models are described by nonlinear time-reparametrization invariant systems with a finite number of degrees of freedom. Often these models are not explicitly integrable and cannot be quantized exactly. Having this…
We introduce a general statistical learning theory for processes that take as input a classical random variable and output a quantum state. Our setting is motivated by the practical situation in which one desires to learn a quantum process…
Viewed as approximations to quantum mechanics, classical evolutions can violate the positive-semidefiniteness of the density matrix. The nature of this violation suggests a classification of dynamical systems based on classical-quantum…
We show on the example of the Arnold cat map that classical chaotic systems can be simulated with exponential efficiency on a quantum computer. Although classical computer errors grow exponentially with time, the quantum algorithm with…
The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic…
We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the…
Quantum canonical transformations are defined in analogy to classical canonical transformations as changes of the phase space variables which preserve the Dirac bracket structure. In themselves, they are neither unitary nor non-unitary. A…
If we admit that quantum mechanics (QM) is universal theory, then QM should contain also some description of classical mechanical systems. The presented text contains description of two different ways how the mathematical description of…
Indistinguishability of particles is normally considered to be an inherently quantum property which cannot be possessed by a classical theory. However, Saunders has argued that this is incorrect, and that classically indistinguishable…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
I argue that the linearity of quantum mechanics is an emergent feature at the Planck scale, along with the manifold structure of space-time. In this regime the usual causality violation objections to nonlinearity do not apply, and nonlinear…
Here is considered a specific detection loophole, that is relevant not only to testing of quantum nonlocality, but also to some other applications of quantum computations and communications. It is described by a simple affine relation…
By quantum calibration we name an experimental procedure apt to completely characterize an unknown measurement apparatus by comparing it with other calibrated apparatuses. Here we show how to achieve the calibration of an arbitrary…
Linear quantum mechanics can be regarded as a particular example of a nonlinear Nambu-type theory. Some elements of this approach are presented.