相关论文: Quantum "Pathfinder"
The interface between classical physics and quantum physics is explained from the point of view of quantum information theory (Feynman Processes). The interpretation depends on a hefty sacrifice: the classical determinism or the arrow of…
We consider classical and quantum algorithms which have a duality property: roughly, either the algorithm provides some nontrivial improvement over random or there exist many solutions which are significantly worse than random. This enables…
Classical machine learning theory and theory of quantum computations are among of the most rapidly developing scientific areas in our days. In recent years, researchers investigated if quantum computing can help to improve classical machine…
p-Adic generalization of the Feynman path integrals in quantum mechanics is considered. The probability amplitude for a particle in a constant field is calculated. Path integrals over p-adic space have the same form as those over R.
A quantum measurement model based upon restricted path-integrals allows us to study measurements of generalized position in various one-dimensional systems of phenomenological interest. After a general overview of the method we discuss the…
Quantum computers provide a fundamentally new computing paradigm that promises to revolutionize our ability to solve broad classes of problems. Surprisingly, the basic mathematical structures of gate-based quantum computing, such as unitary…
The Feynman path integral formalism has inspired the development of memory-efficient and parallelizable classical algorithms for simulating quantum computers. We adapt this approach for the calculation of probability amplitudes of…
The mathematical similarities between non-relativistic wavefunction propagation in quantum mechanics and image propagation in scalar diffraction theory are used to develop a novel understanding of time and paths through spacetime as a…
Quantum computers hold great promise, but it remains a challenge to find efficient quantum circuits that solve interesting computational problems. We show that finding optimal quantum circuits is essentially equivalent to finding the…
This course of lectures has been taught for several years at the Lomonosov Moscow State University; its modified version in 2021 is read in the Zhejiang University (Hangzhou), in the framework of summer school on quantum computing. The…
We describe a simple formalism for generating classes of quantum circuits that are classically efficiently simulatable and show that the efficient simulation of Clifford circuits (Gottesman-Knill theorem) and of matchgate circuits…
I assume a universe whereby the speed of light and the planck constant are not constants but instead parameters that vary locally in time-and space. When describing motion, I am able to derive a modified path integral description at the…
Even the uninitiated will know that Quantum Field Theory cannot be introduced systematically in just four lectures. I try to give a reasonably connected outline of part of it, from second quantization to the path-integral technique in…
In this work we present an algorithm to perform algorithmic differentiation in the context of quantum computing. We present two versions of the algorithm, one which is fully quantum and one which employees a classical step (hybrid…
Providing an optimal path to a quantum annealing algorithm is key to finding good approximate solutions to computationally hard optimization problems. Reinforcement is one of the strategies that can be used to circumvent the exponentially…
Quantum algorithm involves the manipulation of amplitudes and computational basis, of which manipulating basis is largely a quantum analogue of classical computing that is always a major contributor to the complexity. In order to make full…
It is wellknown that the Feynman kernel for the free particle on the half-line can be expressed as a sum over classical paths if we take the contribution from the reflected path into account. The minus sign for the reflected path needs to…
Quantum transition amplitudes are formulated for a model system with local internal time, using path integrals. The amplitudes are shown to be more regular near a turning point of internal time than could be expected based on existing…
Complex (semi-)classical paths, or instantons, form an integral part of our understanding of quantum physics. Whereas real classical paths describe classically allowed transitions in the real-time Feynman path integral, classically…
In this paper, I consider the issue of how two mathematical models of modern physics, the variational principles and the quantum path integral formalism, relate to reality. I assume that the observed phenomena are consistent with the…