اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدClassical spin systems and the quantum stabilizer formalism: general mappings and applications
97
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We present general mappings between classical spin systems and quantum physics. More precisely, we show how to express partition functions and correlation functions of arbitrary classical spin models as inner products between quantum stabilizer states and product states, thereby generalizing mappings for some specific models established in [Phys. Rev. Lett. 98, 117207 (2007)]. For Ising- and Potts-type models with and without external magnetic field, we show how the entanglement features of the corresponding stabilizer states are related to the interaction pattern of the classical model, while the choice of product states encodes the details of interaction. These mappings establish a link between the fields of classical statistical mechanics and quantum information theory, which we utilize to transfer techniques and methods developed in one field to gain insight into the other. For example, we use quantum information techniques to recover well known duality relations and local symmetries of classical models in a simple way, and provide new classical simulation methods to simulate certain types of classical spin models. We show that in this way all inhomogeneous models of q-dimensional spins with pairwise interaction pattern specified by a graph of bounded tree-width can be simulated efficiently. Finally, we show relations between classical spin models and measurement-based quantum computation.
قيم البحث
اقرأ أيضاً
We explore a field theoretical approach to quantum computing and control. This book consists of three parts. The basics of systems theory and field theory are reviewed in Part I. In Part II, a gauge theory is reinterpreted from a systems theoretical
perspective and applied to the formulation of quantum gates. Then quantum systems are defined by introducing feedback to the gates. In Part III, quantum gates and systems are reformulated from a quantum field theoretical perspective using S-matrices. We also discuss how gauge fields are related to feedback.
Reliable models of a large variety of open quantum systems can be described by Lindblad master equation. An important property of some open quantum systems is the existence of decoherence-free subspaces. In this paper, we develop tools for constructi
ng stabilizer codes over open quantum systems governed by Lindblad master equation. We apply the developed stabilizer code formalism to the area of quantum metrology. In particular, a strategy to attain the Heisenberg limit scaling is proposed.
Representation of classical dynamics by unitary transformations has been used to develop unified description of hybrid classical-quantum systems with particular type of interaction, and to formulate abstract systems interpolating between classical an
d quantum ones. We solved the problem of unitary description of two interpolating systems with general potential interaction. The general solution is used to show that with arbitrary potential interaction between the two interpolating systems the evolution of the so called unobservable variables is decoupled from that of the observable ones if and only if the interpolation parameters in the two interpolating systems are equal.
We derive a sequence of measures whose corresponding Jacobi matrices have special properties and a general mapping of an open quantum system onto 1D semi infinite chains with only nearest neighbour interactions. Then we proceed to use the sequence of
measures and the properties of the Jacobi matrices to derive an expression for the spectral density describing the open quantum system when an increasing number of degrees of freedom in the environment have been embedded into the system. Finally, we derive convergence theorems for these residual spectral densities.
We develop a general framework to analyze the two important and much discussed questions concerning (a) `orbital and `spin angular momentum carried by light and (b) the paraxial approximation of the free Maxwell system both in the classical as well a
s quantum domains. After formulating the classical free Maxwell system in the transverse gauge in terms of complex analytical signals we derive expressions for the constants of motion associated with its Poincar{e} symmetry. In particular, we show that the constant of motion corresponding to the total angular momentum ${bf J}$ naturally splits into an `orbital part ${bf L}$ and a `spin part ${bf S}$ each of which is a constant of motion in its own right. We then proceed to discuss quantization of the free Maxwell system and construct the operators generating the Poincar{e} group in the quantum context and analyze their algebraic properties and find that while the quantum counterparts $hat{{bf L}}$ and $hat{{bf S}}$ of ${bf L}$ and ${bf S}$ go over into bona fide observables, they fail to satisfy the angular momentum algebra precluding the possibility of their interpretation as `orbital and `spin operators at the classical level. On the other hand $hat{{bf J}}=hat{{bf L}}+ hat{{bf S}}$ does satisfy the angular momentum algebra and together with $hat{{bf S}}$ generates the group $E(3)$. We then present an analysis of single photon states, paraxial quantization both in the scalar as well as vector cases, single photon states in the paraxial regime. All along a close connection is maintained with the Hilbert space $mathcal{M}$ that arises in the classical context thereby providing a bridge between classical and quantum descriptions of radiation fields.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
