Degrees of controllability for quantum systems and applications to atomic systems

Precise definitions for different degrees of controllability for quantum systems are given, and necessary and sufficient conditions are discussed. The results are applied to determine the degree of controllability for various atomic systems with degenerate energy levels and transition frequencies.Comment: 20 pages, IoP LaTeX, revised and expanded versio

Quantum Control of Two-Qubit Entanglement Dissipation

We investigate quantum control of the dissipation of entanglement under environmental decoherence. We show by means of a simple two-qubit model that standard control methods - coherent or open-loop control - will not in general prevent entanglement loss. However, we propose a control method utilising a Wiseman-Milburn feedback/measurement control scheme which will effectively negate environmental entanglement dissipation.Comment: 11 pages,4 figures, minor correctio

Implementation of Fault-tolerant Quantum Logic Gates via Optimal Control

The implementation of fault-tolerant quantum gates on encoded logic qubits is considered. It is shown that transversal implementation of logic gates based on simple geometric control ideas is problematic for realistic physical systems suffering from imperfections such as qubit inhomogeneity or uncontrollable interactions between qubits. However, this problem can be overcome by formulating the task as an optimal control problem and designing efficient algorithms to solve it. In particular, we can find solutions that implement all of the elementary logic gates in a fixed amount of time with limited control resources for the five-qubit stabilizer code. Most importantly, logic gates that are extremely difficult to implement using conventional techniques even for ideal systems, such as the T-gate for the five-qubit stabilizer code, do not appear to pose a problem for optimal control.Comment: 18 pages, ioptex, many figure

Quantum System Identification by Bayesian Analysis of Noisy Data: Beyond Hamiltonian Tomography

We consider how to characterize the dynamics of a quantum system from a restricted set of initial states and measurements using Bayesian analysis. Previous work has shown that Hamiltonian systems can be well estimated from analysis of noisy data. Here we show how to generalize this approach to systems with moderate dephasing in the eigenbasis of the Hamiltonian. We illustrate the process for a range of three-level quantum systems. The results suggest that the Bayesian estimation of the frequencies and dephasing rates is generally highly accurate and the main source of errors are errors in the reconstructed Hamiltonian basis.Comment: 6 pages, 3 figure

Optimal Control of One-Qubit Gates

We consider the problem of carrying an initial Bloch vector to a final Bloch vector in a specified amount of time under the action of three control fields (a vector control field). We show that this control problem is solvable and therefore it is possible to optimize the control. We choose the physically motivated criteria of minimum energy spent in the control, minimum magnitude of the rate of change of the control and a combination of both. We find exact analytical solutions.Comment: 5 page

Quantum Control Theory for State Transformations: Dark States and their Enlightenment

For many quantum information protocols such as state transfer, entanglement transfer and entanglement generation, standard notions of controllability for quantum systems are too strong. We introduce the weaker notion of accessible pairs, and prove an upper bound on the achievable fidelity of a transformation between a pair of states based on the symmetries of the system. A large class of spin networks is presented for which this bound can be saturated. In this context, we show how the inaccessible dark states for a given excitation-preserving evolution can be calculated, and illustrate how some of these can be accessed using extra catalytic excitations. This emphasises that it is not sufficient for analyses of state transfer in spin networks to restrict to the single excitation subspace. One class of symmetries in these spin networks is exactly characterised in terms of the underlying graph properties.Comment: 14 pages, 3 figures v3: rewritten for increased clarit

An analytic approach to number counts of weak-lensing peak detections

We develop and apply an analytic method to predict peak counts in weak-lensing surveys. It is based on the theory of Gaussian random fields and suitable to quantify the level of spurious detections caused by chance projections of large-scale structures as well as the shape and shot noise contributed by the background galaxies. We compare our method to peak counts obtained from numerical ray-tracing simulations and find good agreement at the expected level. The number of peak detections depends substantially on the shape and size of the filter applied to the gravitational shear field. Our main results are that weak-lensing peak counts are dominated by spurious detections up to signal-to-noise ratios of 3--5 and that most filters yield only a few detections per square degree above this level, while a filter optimised for suppressing large-scale structure noise returns up to an order of magnitude more.Comment: 9 pages, 5 figures, submitted to A&

Complete controllability of quantum systems

Sufficient conditions for complete controllability of $N$-level quantum systems subject to a single control pulse that addresses multiple allowed transitions concurrently are established. The results are applied in particular to Morse and harmonic-oscillator systems, as well as some systems with degenerate energy levels. Morse and harmonic oscillators serve as models for molecular bonds, and the standard control approach of using a sequence of frequency-selective pulses to address a single transition at a time is either not applicable or only of limited utility for such systems.Comment: 8 pages, expanded and revised versio