اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدReplay to Comment on Quantum phase for an arbitrary system with finite-dimensional Hilbert space
119
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We point out the crucial difference between the relative and absolute phase observables treated in our contribution cite{1} and in the Comment by Hall and Pegg cite{HP} respectively. The main contribution of our work is to show that the quantum expectation of the relative phase is highly discontinuous function of the frequency and to point out interesting dependence of the phase on the number-theoretic nature of the frequencies.
قيم البحث
اقرأ أيضاً
A new purification scheme is proposed which applies to arbitrary dimensional bipartite quantum systems. It is based on the repeated application of a special class of nonlinear quantum maps and a single, local unitary operation. This special class of
nonlinear quantum maps is generated in a natural way by a hermitian generalized XOR-gate. The proposed purification scheme offers two major advantages, namely it does not require local depolarization operations at each step of the purification procedure and it purifies more efficiently than other know purification schemes.
The ability to manipulate quantum systems lies at the heart of the development of quantum technology. The ultimate goal of quantum control is to realize arbitrary quantum operations (AQuOs) for all possible open quantum system dynamics. However, the
demanding extra physical resources impose great obstacles. Here, we experimentally demonstrate a universal approach of AQuO on a photonic qudit with minimum physical resource of a two-level ancilla and a $log_{2}d$-scale circuit depth for a $d$-dimensional system. The AQuO is then applied in quantum trajectory simulation for quantum subspace stabilization and quantum Zeno dynamics, as well as incoherent manipulation and generalized measurements of the qudit. Therefore, the demonstrated AQuO for complete quantum control would play an indispensable role in quantum information science.
Dual-unitary quantum circuits can be used to construct 1+1 dimensional lattice models for which dynamical correlations of local observables can be explicitly calculated. We show how to analytically construct classes of dual-unitary circuits with any
desired level of (non-)ergodicity for any dimension of the local Hilbert space, and present analytical results for thermalization to an infinite-temperature Gibbs state (ergodic) and a generalized Gibbs ensemble (non-ergodic). It is shown how a tunable ergodicity-inducing perturbation can be added to a non-ergodic circuit without breaking dual-unitarity, leading to the appearance of prethermalization plateaux for local observables.
We argue in a model-independent way that the Hilbert space of quantum gravity is locally finite-dimensional. In other words, the density operator describing the state corresponding to a small region of space, when such a notion makes sense, is define
d on a finite-dimensional factor of a larger Hilbert space. Because quantum gravity potentially describes superpo- sitions of different geometries, it is crucial that we associate Hilbert-space factors with spatial regions only on individual decohered branches of the universal wave function. We discuss some implications of this claim, including the fact that quantum field theory cannot be a fundamental description of Nature.
We present a systematic study of quantum system compression for the evolution of generic many-body problems. The necessary numerical simulations of such systems are seriously hindered by the exponential growth of the Hilbert space dimension with the
number of particles. For a emph{constant} Hamiltonian system of Hilbert space dimension $n$ whose frequencies range from $f_{min}$ to $f_{max}$, we show via a proper orthogonal decomposition, that for a run-time $T$, the dominant dynamics are compressed in the neighborhood of a subspace whose dimension is the smallest integer larger than the time-bandwidth product $delf=(f_{max}-f_{min})T$. We also show how the distribution of initial states can further compress the system dimension. Under the stated conditions, the time-bandwidth estimate reveals the emph{existence} of an effective compressed model whose dimension is derived solely from system properties and not dependent on the particular implementation of a variational simulator, such as a machine learning system, or quantum device. However, finding an efficient solution procedure emph{is} dependent on the simulator implementation{color{black}, which is not discussed in this paper}. In addition, we show that the compression rendered by the proper orthogonal decomposition encoding method can be further strengthened via a multi-layer autoencoder. Finally, we present numerical illustrations to affirm the compression behavior in time-varying Hamiltonian dynamics in the presence of external fields. We also discuss the potential implications of the findings for machine learning tools to efficiently solve the many-body or other high dimensional Schr{o}dinger equations.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
