Related papers: Perfect simulation for the Feynman-Kac law on the …
A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable…
We consider some important computational aspects of the long-step path-following algorithm developed in our previous work and show that a broad class of complicated optimization problems arising in quantum information theory can be solved…
Picard--Lefschetz theory is applied to path integrals of quantum mechanics, in order to compute real-time dynamics directly. After discussing basic properties of real-time path integrals on Lefschetz thimbles, we demonstrate its…
It is apparent to anyone who thinks about it that, to a large degree, the basic concepts of Newtonian physics are quite intuitive, but quantum mechanics is not. My purpose in this talk is to introduce you to a new, much more intuitive way…
Richard Feynman's method of path integrals is based on the fundamental assumption that a system starting at a point A and arriving at a point B takes all possible paths from A to B, with each path contributing its own (complex) probability…
In this paper, we present a novel path planning algorithm to achieve fast path planning in complex environments. Most existing path planning algorithms are difficult to quickly find a feasible path in complex environments or even fail.…
Very much as its classical counterpart, quantum cellular automata are expected to be a great tool for simulating complex quantum systems. Here we introduce a partitioned model of quantum cellular automata and show how it can simulate, with…
In this paper, we propose a deterministic algorithm that approximates the optimal path cover on weighted undirected graphs. Based on the 1/2-Approximation Path Cover Algorithm by Moran et al., we add a procedure to remove the redundant…
We design a particle interpretation of Feynman-Kac measures on path spaces based on a backward Markovian representation combined with a traditional mean field particle interpretation of the flow of their final time marginals. In contrast to…
This paper introduces a graph-based, potential-guided method for path planning problems in unknown environments, where obstacles are unknown until the robots are in close proximity to the obstacle locations. Inspired by optimal transport…
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…
We describe, for the first time, a completely rigorous homotopy (path--following) algorithm (in the Turing machine model) to find approximate zeros of systems of polynomial equations. If the coordinates of the input systems and the initial…
This article introduces quantum computation by analogy with probabilistic computation. A basic description of the quantum search algorithm is given by representing the algorithm as a C program in a novel way.
We present the calculation of the Feynman path integral in real time for tunneling in quantum mechanics and field theory, including the first quantum corrections. For this purpose, we use the well-known fact that Euclidean saddle points in…
Nowadays, quantum simulation schemes come in two flavours. Either they are continuous-time discrete-space models (a.k.a Hamiltonian-based), pertaining to non-relativistic quantum mechanics. Or they are discrete-spacetime models (a.k.a…
A discrete formulation of the real-time path integral as the expectation value of a functional of paths with respect to a complex probability on a sample space of discrete valued paths is explored. The formulation in terms of complex…
This chapter is a short pedagogical introduction to the use of quantum logic for the simulation of complex quantum systems, including a simulation example on actual quantum hardware.
Although the path-integral formalism is known to be equivalent to conventional quantum mechanics, it is not generally obvious how to implement path-based calculations for multi-qubit entangled states. Whether one takes the formal view of…
In this paper we construct a path integral formulation of quantum mechanics on noncommutative phase-space. We first map the system to an equivalent system on the noncommutative plane. Then by applying the formalism of representing a quantum…
We consider a suboptimal solution path algorithm for the Support Vector Machine. The solution path algorithm is an effective tool for solving a sequence of a parametrized optimization problems in machine learning. The path of the solutions…