Sampled-data design for robust control of a single qubit

This paper presents a sampled-data approach for the robust control of a single qubit (quantum bit). The required robustness is defined using a sliding mode domain and the control law is designed offline and then utilized online with a single qubit having bounded uncertainties. Two classes of uncertainties are considered involving the system Hamiltonian and the coupling strength of the system-environment interaction. Four cases are analyzed in detail including without decoherence, with amplitude damping decoherence, phase damping decoherence and depolarizing decoherence. Sampling periods are specifically designed for these cases to guarantee the required robustness. Two sufficient conditions are presented for guiding the design of unitary control for the cases without decoherence and with amplitude damping decoherence. The proposed approach has potential applications in quantum error-correction and in constructing robust quantum gates.Comment: 33 pages, 5 figures, minor correction

A microbiological assay method for p-aminobenzoic acid

Since the establishment of p-aminobenzoic acid as a member of the B vitamin group, a considerable interest has been shown in methods of determination in natural materials. Since known chemical methods are not sufficiently sensitive, it became evident that microbiological tests should be the most practicable. The organism Clostridium acetobutylicum has been used (1) but no general assay procedure has been presented. Several bacterial strains which respond to p-aminobenzoic acid have been investigated in this laboratory, but satisfactory assay procedures with these organisms have not yet been devised. For the discovery of the test organism used in the procedure described in this paper, we are indebted to Dr. Beadle and Dr. Tatum who kindly furnished us with a culture of their p-aminobenzoic acid requiring a mutant strain of Neurospora crassa, designated by them as Neurospora crassa p-aminobenzoicless No. 1633 (2). This mold will grow optimally on a medium consisting of inorganic salts, ammonium tartrate, sucrose, biotin, and p-aminobenzoic acid. For purposes of assay, however, it has proved advantageous to supplement this basal medium with natural extracts which are either naturally low in p-aminobenzoic acid or have been treated to remove it. With such a complex medium, the possibility of interference by toxic substances or stimulatory substances other than p-aminobenzoic acid which might be present in samples to be assayed is reduced to a minimum. Since the completion of a considerable part of the experimental work described in this paper, microbiological assay methods for p-aminobenzoic acid have been published by Landy and Dicken (3) utilizing the organism Acetobacter suboxydans and by Lewis (4) using Lactobacillus arabinosus 17-5

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

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

Direct Observation of the Fourth Star in the Zeta Cancri System

Direct imaging of the zeta Cnc system has resolved the fourth star in the system, which is in orbit around zeta Cnc C. The presence of the fourth star has been inferred for many years from irregularities in the motion of star C, and recently from C's spectroscopic orbit. However, its mass is close to that of C, making its non-detection puzzling. Observing at wavelengths of 1.2, 1.7, and 2.2 microns with the adaptive-optics system of the CFHT, we have obtained images which very clearly reveal star D and show it to have the color of an M2 star. Its brightness is consonant with its being two M stars, which are not resolved in our observations but are likely to be in a short-period orbit, thereby accounting for the large mass and the difficulty of detection at optical wavelengths, where the magnitude difference is much larger. The positions and colors of all four stars in the system are reported and are consistent with the most recent astrometric observations.Comment: 7 pages including 3 tables, 1 figure; To appear in PAS

A Simplified Approach to Optimally Controlled Quantum Dynamics

A new formalism for the optimal control of quantum mechanical physical observables is presented. This approach is based on an analogous classical control technique reported previously[J. Botina, H. Rabitz and N. Rahman, J. chem. Phys. Vol. 102, pag. 226 (1995)]. Quantum Lagrange multiplier functions are used to preserve a chosen subset of the observable dynamics of interest. As a result, a corresponding small set of Lagrange multipliers needs to be calculated and they are only a function of time. This is a considerable simplification over traditional quantum optimal control theory[S. shi and H. Rabitz, comp. Phys. Comm. Vol. 63, pag. 71 (1991)]. The success of the new approach is based on taking advantage of the multiplicity of solutions to virtually any problem of quantum control to meet a physical objective. A family of such simplified formulations is introduced and numerically tested. Results are presented for these algorithms and compared with previous reported work on a model problem for selective unimolecular reaction induced by an external optical electric field.Comment: Revtex, 29 pages (incl. figures

Optimal Control Theory for Continuous Variable Quantum Gates

We apply the methodology of optimal control theory to the problem of implementing quantum gates in continuous variable systems with quadratic Hamiltonians. We demonstrate that it is possible to define a fidelity measure for continuous variable (CV) gate optimization that is devoid of traps, such that the search for optimal control fields using local algorithms will not be hindered. The optimal control of several quantum computing gates, as well as that of algorithms composed of these primitives, is investigated using several typical physical models and compared for discrete and continuous quantum systems. Numerical simulations indicate that the optimization of generic CV quantum gates is inherently more expensive than that of generic discrete variable quantum gates, and that the exact-time controllability of CV systems plays an important role in determining the maximum achievable gate fidelity. The resulting optimal control fields typically display more complicated Fourier spectra that suggest a richer variety of possible control mechanisms. Moreover, the ability to control interactions between qunits is important for delimiting the total control fluence. The comparative ability of current experimental protocols to implement such time-dependent controls may help determine which physical incarnations of CV quantum information processing will be the easiest to implement with optimal fidelity.Comment: 39 pages, 11 figure