Continuous quantum error correction for non-Markovian decoherence

We study the effect of continuous quantum error correction in the case where each qubit in a codeword is subject to a general Hamiltonian interaction with an independent bath. We first consider the scheme in the case of a trivial single-qubit code, which provides useful insights into the workings of continuous error correction and the difference between Markovian and non-Markovian decoherence. We then study the model of a bit-flip code with each qubit coupled to an independent bath qubit and subject to continuous correction, and find its solution. We show that for sufficiently large error-correction rates, the encoded state approximately follows an evolution of the type of a single decohering qubit, but with an effectively decreased coupling constant. The factor by which the coupling constant is decreased scales quadratically with the error-correction rate. This is compared to the case of Markovian noise, where the decoherence rate is effectively decreased by a factor which scales only linearly with the rate of error correction. The quadratic enhancement depends on the existence of a Zeno regime in the Hamiltonian evolution which is absent in purely Markovian dynamics. We analyze the range of validity of this result and identify two relevant time scales. Finally, we extend the result to more general codes and argue that the performance of continuous error correction will exhibit the same qualitative characteristics.Comment: 16 pages, 4 figures, minor typos corrected, references update

Distributed Quantum Computation Based-on Small Quantum Registers

We describe and analyze an efficient register-based hybrid quantum computation scheme. Our scheme is based on probabilistic, heralded optical connection among local five-qubit quantum registers. We assume high fidelity local unitary operations within each register, but the error probability for initialization, measurement, and entanglement generation can be very high (~5%). We demonstrate that with a reasonable time overhead our scheme can achieve deterministic non-local coupling gates between arbitrary two registers with very high fidelity, limited only by the imperfections from the local unitary operation. We estimate the clock cycle and the effective error probability for implementation of quantum registers with ion-traps or nitrogen-vacancy (NV) centers. Our new scheme capitalizes on a new efficient two-level pumping scheme that in principle can create Bell pairs with arbitrarily high fidelity. We introduce a Markov chain model to study the stochastic process of entanglement pumping and map it to a deterministic process. Finally we discuss requirements for achieving fault-tolerant operation with our register-based hybrid scheme, and also present an alternative approach to fault-tolerant preparation of GHZ states.Comment: 22 Pages, 23 Figures and 1 Table (updated references

Stochastic stimulated electronic x-ray Raman spectroscopy

Resonant inelastic x-ray scattering (RIXS) is a well-established tool for studying electronic, nuclear and collective dynamics of excited atoms, molecules and solids. An extension of this powerful method to a time-resolved probe technique at x-ray free electron lasers (XFELs) to ultimately unravel ultrafast chemical and structural changes on a femtosecond time scale is often challenging, due to the small signal rate in conventional implementations at XFELs that rely on the usage of a monochromator set up to select a small frequency band of the broadband, spectrally incoherent XFEL radiation. Here, we suggest an alternative approach, based on stochastic spectroscopy, that uses the full bandwidth of the incoming XFEL pulses. Our proposed method is relying on stimulated resonant inelastic x-ray scattering, where in addition to a pump pulse that resonantly excites the system a probe pulse on a specific electronic inelastic transition is provided, that serves as seed in the stimulated scattering process. The limited spectral coherence of the XFEL radiation defines the energy resolution in this process and stimulated RIXS spectra of high resolution can be obtained by covariance analysis of the transmitted spectra. We present a detailed feasibility study and predict signal strengths for realistic XFEL parameters for the CO molecule resonantly pumped at the O1s-{\pi}* transition. Our theoretical model describes the evolution of the spectral and temporal characteristics of the transmitted x-ray radiation, by solving the equation of motion for the electronic and vibrational degrees of freedom of the system self consistently with the propagation by Maxwell's equations

Synchronization of spatiotemporal semiconductor lasers and its application in color image encryption

Optical chaos is a topic of current research characterized by high-dimensional nonlinearity which is attributed to the delay-induced dynamics, high bandwidth and easy modular implementation of optical feedback. In light of these facts, which adds enough confusion and diffusion properties for secure communications, we explore the synchronization phenomena in spatiotemporal semiconductor laser systems. The novel system is used in a two-phase colored image encryption process. The high-dimensional chaotic attractor generated by the system produces a completely randomized chaotic time series, which is ideal in the secure encoding of messages. The scheme thus illustrated is a two-phase encryption method, which provides sufficiently high confusion and diffusion properties of chaotic cryptosystem employed with unique data sets of processed chaotic sequences. In this novel method of cryptography, the chaotic phase masks are represented as images using the chaotic sequences as the elements of the image. The scheme drastically permutes the positions of the picture elements. The next additional layer of security further alters the statistical information of the original image to a great extent along the three-color planes. The intermediate results during encryption demonstrate the infeasibility for an unauthorized user to decipher the cipher image. Exhaustive statistical tests conducted validate that the scheme is robust against noise and resistant to common attacks due to the double shield of encryption and the infinite dimensionality of the relevant system of partial differential equations.Comment: 20 pages, 11 figures; Article in press, Optics Communications (2011

Large thermal biasing of individual gated nanostructures

We demonstrate a novel nanoheating scheme that yields very large and uniform temperature gradients up to about 1K every 100nm, in an architecture which is compatible with the field-effect control of the nanostructure under test. The temperature gradients demonstrated largely exceed those typically obtainable with standard resistive heaters fabricated on top of the oxide layer. The nanoheating platform is demonstrated in the specific case of a short-nanowire device.Comment: 6 pages, 6 figure

Optimal tracking for pairs of qubit states

In classical control theory, tracking refers to the ability to perform measurements and feedback on a classical system in order to enforce some desired dynamics. In this paper we investigate a simple version of quantum tracking, namely, we look at how to optimally transform the state of a single qubit into a given target state, when the system can be prepared in two different ways, and the target state depends on the choice of preparation. We propose a tracking strategy that is proved to be optimal for any input and target states. Applications in the context of state discrimination, state purification, state stabilization and state-dependent quantum cloning are presented, where existing optimality results are recovered and extended.Comment: 15 pages, 8 figures. Extensive revision of text, optimality results extended, other physical applications include