A dynamical decoupling method is presented which is based on embedding a deterministic decoupling scheme into a stochastic one. This way it is possible to combine the advantages of both methods and to increase the suppression of undesired perturbations of quantum systems significantly even for long interaction times. As a first application the stabilization of a quantum memory is discussed which is perturbed by one- and two-qubit interactions.

A general error correction method is presented which is capable of correcting coherent errors originating from static residual inter-qubit couplings in a quantum computer. It is based on a randomization of static imperfections in a many-qubit system by the repeated application of Pauli operators which change the computational basis. This Pauli-Random-Error-Correction (PAREC)-method eliminates coherent errors produced by static imperfections and increases significantly the maximum time over which realistic quantum computations can be performed reliably. Furthermore, it does not require redundancy so that all physical qubits involved can be used for logical purposes.PACS numbers: 03.67. Lx,03.67.Pp,05.45.Mt Current developments in quantum physics demonstrate in an impressive way its technological potential [1]. In quantum computation, e.g., characteristic quantum phenomena, such as interference and entanglement, are exploited for solving computational tasks more efficiently than by classical means [2,3,4,5,6]. However, these quantum phenomena are affected easily by unknown residual inter-qubit couplings or by interactions with an uncontrolled environment [7]. In order to protect quantum algorithms against such undesired influences powerful methods of error correction have been developed over the last years.So far techniques of quantum error correction have concentrated predominantly on decoherence caused by uncontrolled couplings to environments [8,9]. In these cases appropriate syndrome measurements and recovery operations can reverse errors. However, up to now much less is known about the correction of coherent, unitary errors. Even if a quantum information processor (QIP) is isolated entirely from its environment and if all quantum gates are performed perfectly, there may still be residual inter-qubit couplings affecting its performance. Recently, it was demonstrated that static imperfections, i.e. random inter-qubit couplings which remain unchanged during a quantum computation, restrict the computational capabilities of a many-qubit QIP significantly as they cause quantum chaos and quantum phase transitions [10]. Furthermore, in addition to a usual exponential decay such static imperfections also cause a Gaussian decrease of the fidelity with time. At sufficiently long times this Gaussian decrease dominates the decay of the fidelity thus limiting significantly the maximum reliable computation times of many-qubit QIPs [11,12].In this Letter a general error correcting method is presented for overcoming these disastrous consequences of static imperfections. It is based on the repeated random application of Pauli operators to all the qubits of a QIP. The resulting random changes of the computational basis together with appropriate compensating changes of the quantum gates slow down the rapid Gaussian decay of the fidelity and change it to a linear-in-time exponential one. As a result this Pauli-Random-Error-Correction (PAREC)-method increases significantly the maximum time scale of reliable quantum computation....

We present a construction method for complete sets of cyclic mutually unbiased bases (MUBs) in Hilbert spaces of even prime power dimensions. In comparison to usual complete sets of MUBs, complete cyclic sets possess the additional property of being generated by a single unitary operator. The construction method is based on the idea of obtaining a partition of multi-qubit Pauli operators into maximal commuting sets of orthogonal operators with the help of a suitable element of the Clifford group. As a consequence, we explicitly obtain complete sets of cyclic MUBs generated by a single element of the Clifford group in dimensions 2 m for m = 1, 2, . . . , 24.

An embedded selective recoupling method is proposed which is based on the idea of embedding the recently proposed deterministic selective recoupling scheme of Yamaguchi et al.[1] into a stochastic dynamical decoupling method, such as the recently proposed Pauli-random-error-correction-(PAREC) scheme [2]. The recoupling scheme enables the implementation of elementary quantum gates in a quantum information processor by partial suppression of the unwanted interactions. The random dynamical decoupling method cancels a significant part of the residual interactions. Thus the time scale of reliable quantum computation is increased significantly. Numerical simulations are presented for a conditional two-qubit swap gate and for a complex iterative quantum algorithm.

We study the advantages to be gained in quantum key distribution (QKD) protocols by combining the techniques of local randomization, or noisy preprocessing, and structured (nonrandom) block codes. Extending the results of [Smith, Renes, and Smolin, {\em Physical Review Letters}, 100:170502] pertaining to BB84, we improve the best-known lower bound on the error rate for the 6-state protocol from 14.11% for local randomization alone to at least 14.59%. Additionally, we also study the effects of iterating the combined preprocessing scheme and find further improvements to the BB84 protocol already at small block lengths.