Related papers: Exponential Gain in Quantum Computing of Quantum C…
We investigate a quantum algorithm which simulates efficiently the quantum kicked rotator model, a system which displays rich physical properties, and enables to study problems of quantum chaos, atomic physics and localization of electrons…
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…
Quantum computing promises the ability to compute properties of quantum systems exponentially faster than classical computers. Quantum advantage is achieved when a practical problem is solved more efficiently on a quantum computer than on a…
We study numerically the imperfection effects in the quantum computing of the kicked rotator model in the regime of quantum chaos. It is shown that there are two types of physical characteristics: for one of them the quantum computation…
We construct an oracular (i.e., black box) problem that can be solved exponentially faster on a quantum computer than on a classical computer. The quantum algorithm is based on a continuous time quantum walk, and thus employs a different…
A central task in the field of quantum computing is to find applications where quantum computer could provide exponential speedup over any classical computer. Machine learning represents an important field with broad applications where…
In the past decade quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests…
By employing a nonlinear quantum kicked rotor model, we investigate the transport of energy in multidimensional quantum chaos. Parallel numerical simulations and analytic theory demonstrate that the interplay between nonlinearity and…
We discuss the simulation of a complex dynamical system, the so-called quantum sawtooth map model, on a quantum computer. We show that a quantum computer can be used to efficiently extract relevant physical information for this model. It is…
The simulation of large-scale classical systems in exponentially small space on quantum computers has gained attention. The prior work demonstrated that a quantum algorithm offers an exponential speedup over any classical algorithm in…
This paper reviews the physics of quantum disorder in relation with a series of experiments using laser-cooled atoms exposed to "kicks" of a standing wave, realizing a paradigmatic model of quantum chaos, the kicked rotor. This dynamical…
We consider whether trainable quantum unitaries can be used to discover quantum speed-ups for classical problems. Using methods recently developed for training quantum neural nets, we consider Simon's problem, for which there is a known…
We show how a quantum computer may efficiently simulate a disordered Hamiltonian, by incorporating a pseudo-random number generator directly into the time evolution circuit. This technique is applied to quantum simulation of few-body…
The simulation of complex quantum systems on a quantum computer is studied, taking the kicked Harper model as an example. This well-studied system has a rich variety of dynamical behavior depending on parameters, displays interesting…
Quantum computers facing chaos. Quantum parallelism allows to perform computation in a radically new manner. A quantum computer based on these new principles may resolve certain problems exponentially faster than a classical computer. We…
Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same…
In this paper, we present efficient quantum algorithms that are exponentially faster than classical algorithms for solving the quantum optimal control problem. This problem involves finding the control variable that maximizes a physical…
It is known that quantum computers yield a speed-up for certain discrete problems. Here we want to know whether quantum computers are useful for continuous problems. We study the computation of the integral of functions from the classical…
Although quantum algorithms realizing an exponential time speed-up over the best known classical algorithms exist, no quantum algorithm is known performing computation using less space resources than classical algorithms. In this paper, we…
A central problem in quantum computation is to understand which quantum circuits are useful for exponential speed-ups over classical computation. We address this question in the setting of query complexity and show that for almost any…