Operator Formulation of Green-Schwarz Superstring in the Semi-Light-Cone Conformal Gauge

In this article we present a comprehensive account of the operator formulation of the Green-Schwarz superstring in the semi-light-cone (SLC) gauge, where the worldsheet conformal invariance is preserved. Starting from the basic action, we systematically study the symmetry structure of the theory in the SLC gauge both in the Lagrangian and the phase space formulations. After quantizing the theory in the latter formulation we construct the quantum Virasoro and the super-Poincare generators and clarify the closure properties of these symmetry algebras. Then by making full use of this knowledge we will be able to construct the BRST-invariant vertex operators which describe the emission and the absorption of the massless quanta and show that they form the appropriate representation of the quantum symmetry algebras. Furthermore, we will construct an exact quantum similarity transformation which connects the SLC gauge and the familiar light-cone (LC) gauge. As an application BRST-invariant DDF operators in the SLC gauge are obtained starting from the corresponding physical oscillators in the LC gauge.Comment: 88 pages, ptptex, no figure. Some clarifications are made and a reference is added in section 6. Published versio

Sampling-based learning control of inhomogeneous quantum ensembles

Compensation for parameter dispersion is a significant challenge for control of inhomogeneous quantum ensembles. In this paper, we present a systematic methodology of sampling-based learning control (SLC) for simultaneously steering the members of inhomogeneous quantum ensembles to the same desired state. The SLC method is employed for optimal control of the state-to-state transition probability for inhomogeneous quantum ensembles of spins as well as $\Lambda$ type atomic systems. The procedure involves the steps of (i) training and (ii) testing. In the training step, a generalized system is constructed by sampling members according to the distribution of inhomogeneous parameters drawn from the ensemble. A gradient flow based learning and optimization algorithm is adopted to find the control for the generalized system. In the process of testing, a number of additional ensemble members are randomly selected to evaluate the control performance. Numerical results are presented showing the success of the SLC method.Comment: 8 pages, 9 figure

The source-lens clustering effect in the context of lensing tomography and its self-calibration

Cosmic shear can only be measured where there are galaxies. This source-lens clustering (SLC) effect has two sources, intrinsic source clustering and cosmic magnification (magnification/size bias). Lensing tomography can suppress the former. However, this reduction is limited by the existence of photo-z error and nonzero redshift bin width. Furthermore, SLC induced by cosmic magnification cannot be reduced by lensing tomography. Through N-body simulations, we quantify the impact of SLC on the lensing power spectrum in the context of lensing tomography. We consider both the standard estimator and the pixel-based estimator. We find that none of them can satisfactorily handle both sources of SLC. (1) For the standard estimator, SLC induced by both sources can bias the lensing power spectrum by O(1)-O(10)%. Intrinsic source clustering also increases statistical uncertainties in the measured lensing power spectrum. However, the standard estimator suppresses intrinsic source clustering in the cross-spectrum. (2) In contrast, the pixel-based estimator suppresses SLC through cosmic magnification. However, it fails to suppress SLC through intrinsic source clustering and the measured lensing power spectrum can be biased low by O(1)-O(10)%. In short, for typical photo-z errors (sigma_z/(1+z)=0.05) and photo-z bin sizes (Delta_z^P=0.2), SLC alters the lensing E-mode power spectrum by 1-10%, with ell~10^3$ and z_s~1 being of particular interest to weak lensing cosmology. Therefore the SLC is a severe systematic for cosmology in Stage-IV lensing surveys. We present useful scaling relations to self-calibrate the SLC effect.Comment: 13 pages, 10 figures, Accepted by AP

Sampling-based Learning Control for Quantum Systems with Uncertainties

Robust control design for quantum systems has been recognized as a key task in the development of practical quantum technology. In this paper, we present a systematic numerical methodology of sampling-based learning control (SLC) for control design of quantum systems with uncertainties. The SLC method includes two steps of "training" and "testing". In the training step, an augmented system is constructed using artificial samples generated by sampling uncertainty parameters according to a given distribution. A gradient flow based learning algorithm is developed to find the control for the augmented system. In the process of testing, a number of additional samples are tested to evaluate the control performance where these samples are obtained through sampling the uncertainty parameters according to a possible distribution. The SLC method is applied to three significant examples of quantum robust control including state preparation in a three-level quantum system, robust entanglement generation in a two-qubit superconducting circuit and quantum entanglement control in a two-atom system interacting with a quantized field in a cavity. Numerical results demonstrate the effectiveness of the SLC approach even when uncertainties are quite large, and show its potential for robust control design of quantum systems.Comment: 11 pages, 9 figures, in press, IEEE Transactions on Control Systems Technology, 201

Robust manipulation of superconducting qubits in the presence of fluctuations

Superconducting quantum systems are promising candidates for quantum information processing due to their scalability and design flexibility. However, the existence of defects, fluctuations, and inaccuracies is unavoidable for practical superconducting quantum circuits. In this paper, a sampling-based learning control (SLC) method is used to guide the design of control fields for manipulating superconducting quantum systems. Numerical results for one-qubit systems and coupled two-qubit systems show that the "smart" fields learned using the SLC method can achieve robust manipulation of superconducting qubits, even in the presence of large fluctuations and inaccuracies.Comment: 10 pages, 6 figure