Optimal control theory is a promising candidate for a drastic improvement of the performance of quantum information tasks. We explore its ultimate limit in paradigmatic cases, and demonstrate that it coincides with the maximum speed limit allowed by quantum evolution.

In this work we describe in detail the Chopped RAndom Basis (CRAB) optimal control technique recently introduced to optimize t-DMRG simulations [1]. Here we study the efficiency of this control technique in optimizing different quantum processes and we show that in the considered cases we obtain results equivalent to those obtained via different optimal control methods while using less resources. We propose the CRAB optimization as a general and versatile optimal control technique. PACS numbers:Realizing artificial, controllable quantum systems has represented one of the most promising challenge in physics for the last thirty years [2]. On one side such systems could unveil unexplored features of Nature, when employed as universal quantum simulators [3]; on the other side this technology could be exploited to realize a new generation of extremely powerful devices, like quantum computers [4]. Along with the impressive progress marked recently in the construction of tunable quantum systems [5,6], there is a renewed and increasing interest in quantum optimal control (OC) theory, the study of the optimization techniques aimed at improving the outcome of a quantum process [2]. Indeed OC can prove to be crucial under several respects for the development of quantum devices: first, it can be generally employed to speed up a quantum process to make it less prone to decoherence or noise effects induced by the unavoidable interaction with the external environment. Second, considering a realistic experimental setup in which just few parameters are tunable or, in the most difficult situations, only partially tunable, OC can provide an answer about the optimal use of the available resources.Traditionally OC has been exploited in atomic and molecular physics [7][8][9]. More recently, with the advent of quantum information, the requirement of accurate control of quantum systems has become unavoidable to build quantum information processors [10][11][12][13][14][15][16]. However, the above mentioned methods often result in optimal driving fields that require a level of tunability incompatible with current experimental capabilities and in general, the calculation of the optimal fields requires an exact description of the system (either analytical or numerical). The field of application of these methods is severely limited also by the need to have access to huge amount of information about the system, e.g. computing gradients of the control fields, expectation values of observables as a function of time. Moreover, standard OC algorithms define a set of Euler-Lagrange equations that have to be solved to find the optimal control pulse [2], where the equation for the correction to the driving field is highly dependent on the constraints imposed on the system and on the figures of merit considered. This implies that considering different figures of merit and/or constraints on the system needs a redefinition of the corresponding Euler-Lagrange equations, hindering a straightforward adaptation of the optimization procedure to different s...

There has been rapid development of systems that yield strong interactions between freely propagating photons in one-dimension via controlled coupling to quantum emitters. This raises interesting possibilities such as quantum information processing with photons or quantum many-body states of light, but treating such systems generally remains a difficult task theoretically. Here, we describe a novel technique in which the dynamics and correlations of a few photons can be exactly calculated, based upon knowledge of the initial photonic state and the solution of the reduced effective dynamics of the quantum emitters alone. We show that this generalized 'input-output' formalism allows for a straightforward numerical implementation regardless of system details, such as emitter positions, external driving, and level structure. As a specific example, we apply our technique to show how atomic systems with infinite-range interactions and under conditions of electromagnetically induced transparency enable the selective transmission of correlated multi-photon states.from other emitters appears to be a difficult task. An exception is the weak excitation limit, in which atoms can be treated as linear scatterers and the powerful transfer matrix method of linear optics can be employed [18,19].The full quantum case has been solved exactly in a limited number of situations in which nonlinear systems are coupled to 1D waveguides [20][21][22][23][24][25][26][27][28][29][30]. The formalism employed in [21] is particularly elegant, because it establishes an input-output relation to determine the nonlinear scattering from a two-level atom. Here, we show that this technique can be efficiently generalized to many atoms, chiral or bi-directional waveguides, and arbitrary atomic configurations, providing a powerful tool to investigate nonlinear optical dynamics in all systems of interest.This paper is organized in the following way: first, we present a generalized input-output formalism to treat few-photon propagation in waveguides coupled to many atoms. We show that the infinite degrees of freedom associated with the photonic modes can be effectively integrated out, yielding an open, interacting 'spin' model that involves only the internal degrees of freedom of the atoms. This open system can be solved using a number of conventional, quantum optical techniques. Then, we show that the solution of the spin problem can be used to re-construct the optical fields. In particular, we provide a prescription to map spin correlations to S-matrix elements, which contain full information about the photon dynamics, and give explicit closed-form expressions for the one-and two-photon cases. Importantly, in analogy with the cavity QED case, our technique enables analytical solutions under some scenarios, but in general allows for simple numerical implementation under a wide variety of circumstances of interest, such as different level structures, external driving, atomic positions, atomic motion, etc. Finally, to illustrate the ease of usage, we apply ...

We present here our study of the adiabatic quantum dynamics of a random Ising chain across its quantum critical point. The model investigated is an Ising chain in a transverse field with disorder present both in the exchange coupling and in the transverse field. The transverse field term is proportional to a function Γ(t) which, as in the Kibble-Zurek mechanism, is linearly reduced to zero in time with a rate τ −1 , Γ(t) = −t/τ , starting at t = −∞ from the quantum disordered phase (Γ = ∞) and ending at t = 0 in the classical ferromagnetic phase (Γ = 0). We first analyze the distribution of the gaps, occurring at the critical point Γc = 1, which are relevant for breaking the adiabaticity of the dynamics. We then present extensive numerical simulations for the residual energy Eres and density of defects ρ k at the end of the annealing, as a function of the annealing inverse rate τ . Both the average Eres(τ ) and ρ k (τ ) are found to behave logarithmically for large τ , but with different exponents, [Eres(τ )/L]av ∼ 1/ ln ζ (τ ) with ζ ≈ 3.4, and [ρ k (τ )]av ∼ 1/ ln 2 (τ ). We propose a mechanism for 1/ ln 2 τ -behavior of [ρ k ]av based on the Landau-Zener tunneling theory and on a Fisher's type real-space renormalization group analysis of the relevant gaps. The model proposed shows therefore a paradigmatic example of how an adiabatic quantum computation can become very slow when disorder is at play, even in absence of any source of frustration.PACS numbers:

The adiabatic quantum evolution of the Lipkin-Meshkov-Glick (LMG) model across its quantum critical point is studied. The dynamics is realized by linearly switching the transverse field from an initial large value towards zero and considering different transition rates. We concentrate our attention on the residual energy after the quench in order to estimate the level of diabaticity of the evolution. We discuss a Landau-Zener approximation of the finite size LMG model, that is successful in reproducing the behavior of the residual energy as function of the transition rate in the most part of the regimes considered. We also support our description through the analysis of the entanglement entropy of the evolved state. The system proposed is a paradigm of infinite-range interaction or high-dimensional models.Comment: 8 pages, 7 figures. (v2) minor revisions, published versio