اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدMonte Carlo simulation of stoquastic Hamiltonians
98
0
0.0
(
0
)
تأليف
Sergey Bravyi
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Stoquastic Hamiltonians are characterized by the property that their off-diagonal matrix elements in the standard product basis are real and non-positive. Many interesting quantum models fall into this class including the Transverse field Ising Model (TIM), the Heisenberg model on bipartite graphs, and the bosonic Hubbard model. Here we consider the problem of estimating the ground state energy of a local stoquastic Hamiltonian $H$ with a promise that the ground state of $H$ has a non-negligible correlation with some `guiding state that admits a concise classical description. A formalized version of this problem called Guided Stoquastic Hamiltonian is shown to be complete for the complexity class MA (a probabilistic analogue of NP). To prove this result we employ the Projection Monte Carlo algorithm with a variable number of walkers. Secondly, we show that the ground state and thermal equilibrium properties of the ferromagnetic TIM can be simulated in polynomial time on a classical probabilistic computer. This result is based on the approximation algorithm for the classical ferromagnetic Ising model due to Jerrrum and Sinclair (1993).
قيم البحث
اقرأ أيضاً
Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection method, and
Markov chain Monte Carlo to sample a probability distribution function, and methods for variance reduction to evaluate numerical integrals using the Monte Carlo simulation. We will also briefly introduce the quasi-Monte Carlo sampling at the end of this lecture.
There is a tremendous interest in fabricating superconducting flux circuits that are nonstoquastic---i.e., have positive off-diagonal matrix elements---in their qubit representation, as these circuits are thought to be unsimulable by classical approa
ches and thus could play a key role in the demonstration of speedups in quantum annealing protocols. We show however that the efficient simulation of these systems is possible by the direct simulation of the flux circuits. Our approach not only obviates the reduction to a qubit representation but also produces results that are more in the spirit of the experimental setup. We discuss the implications of our work. Specifically we argue that our results cast doubt on the conception that superconducting flux circuits represent the correct avenue for universal adiabatic quantum computers.
The algorithm for Monte Carlo simulation of parton-level events based on an Artificial Neural Network (ANN) proposed in arXiv:1810.11509 is used to perform a simulation of $Hto 4ell$ decay. Improvements in the training algorithm have been implemented
to avoid numerical instabilities. The integrated decay width evaluated by the ANN is within 0.7% of the true value and unweighting efficiency of 26% is reached. While the ANN is not automatically bijective between input and output spaces, which can lead to issues with simulation quality, we argue that the training procedure naturally prefers bijective maps, and demonstrate that the trained ANN is bijective to a very good approximation.
Several models for the Monte Carlo simulation of Compton scattering on electrons are quantitatively evaluated with respect to a large collection of experimental data retrieved from the literature. Some of these models are currently implemented in gen
eral purpose Monte Carlo systems; some have been implemented and evaluated for possible use in Monte Carlo particle transport for the first time in this study. Here we present first and preliminary results concerning total and differential Compton scattering cross sections.
Comptonization is the process in which photon spectrum changes due to multiple Compton scatterings in the electronic plasma. It plays an important role in the spectral formation of astrophysical X-ray and gamma-ray sources. There are several intrinsi
c limitations for the analytical method in dealing with the Comptonization problem and Monte Carlo simulation is one of the few alternatives. We describe an efficient Monte Carlo method that can solve the Comptonization problem in a fully relativistic way. We expanded the method so that it is capable of simulating Comptonization in the media where electron density and temperature varies discontinuously from one region to the other and in the isothermal media where density varies continuously along photon paths. The algorithms are presented in detail to facilitate computer code implementation. We also present a few examples of its application to the astrophysical research.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
