Fault-tolerant quantum computation with cluster states

The one-way quantum computing model introduced by Raussendorf and Briegel [Phys. Rev. Lett. 86 (22), 5188-5191 (2001)] shows that it is possible to quantum compute using only a fixed entangled resource known as a cluster state, and adaptive single-qubit measurements. This model is the basis for several practical proposals for quantum computation, including a promising proposal for optical quantum computation based on cluster states [M. A. Nielsen, arXiv:quant-ph/0402005, accepted to appear in Phys. Rev. Lett.]. A significant open question is whether such proposals are scalable in the presence of physically realistic noise. In this paper we prove two threshold theorems which show that scalable fault-tolerant quantum computation may be achieved in implementations based on cluster states, provided the noise in the implementations is below some constant threshold value. Our first threshold theorem applies to a class of implementations in which entangling gates are applied deterministically, but with a small amount of noise. We expect this threshold to be applicable in a wide variety of physical systems. Our second threshold theorem is specifically adapted to proposals such as the optical cluster-state proposal, in which non-deterministic entangling gates are used. A critical technical component of our proofs is two powerful theorems which relate the properties of noisy unitary operations restricted to act on a subspace of state space to extensions of those operations acting on the entire state space.Comment: 31 pages, 54 figure

Entanglement Sharing and Decoherence in the Spin-Bath

The monogamous nature of entanglement has been illustrated by the derivation of entanglement sharing inequalities - bounds on the amount of entanglement that can be shared amongst the various parts of a multipartite system. Motivated by recent studies of decoherence, we demonstrate an interesting manifestation of this phenomena that arises in system-environment models where there exists interactions between the modes or subsystems of the environment. We investigate this phenomena in the spin-bath environment, constructing an entanglement sharing inequality bounding the entanglement between a central spin and the environment in terms of the pairwise entanglement between individual bath spins. The relation of this result to decoherence will be illustrated using simplified system-bath models of decoherence.Comment: 5 pages, 1 figure v2: 6 pages 2 figures, additional example and reference

Noise thresholds for optical quantum computers

In this Letter we numerically investigate the fault-tolerant threshold for optical cluster-state quantum computing. We allow both photon loss noise and depolarizing noise (as a general proxy for all local noise), and obtain a threshold region of allowed pairs of values for the two types of noise. Roughly speaking, our results show that scalable optical quantum computing is possible for photon loss probabilities < 3x10(-3), and for depolarization probabilities < 10(-4)

Noise thresholds for optical cluster-state quantum computation

In this paper we do a detailed numerical investigation of the fault-tolerant threshold for optical cluster-state quantum computation. Our noise model allows both photon loss and depolarizing noise, as a general proxy for all types of local noise other than photon loss noise. We obtain a threshold region of allowed pairs of values for the two types of noise. Roughly speaking, our results show that scalable optical quantum computing is possible for photon loss probabilities less than 0.003, and for depolarization probabilities less than 0.0001. Our fault-tolerant protocol involves a number of innovations, including a method for syndrome extraction known as telecorrection, whereby repeated syndrome measurements are guaranteed to agree. This paper is an extended version of [Dawson et al., Phys. Rev. Lett. 96, 020501].Comment: 28 pages. Corrections made to Table I

Non-perturbative improvement of operators with Wilson fermions

We outline two methods of constructing improved composite operators using Wilson fermions

A practical scheme for quantum computation with any two-qubit entangling gate

Which gates are universal for quantum computation? Although it is well known that certain gates on two-level quantum systems (qubits), such as the controlled-not (CNOT), are universal when assisted by arbitrary one-qubit gates, it has only recently become clear precisely what class of two-qubit gates is universal in this sense. Here we present an elementary proof that any entangling two-qubit gate is universal for quantum computation, when assisted by one-qubit gates. A proof of this important result for systems of arbitrary finite dimension has been provided by J. L. and R. Brylinski [arXiv:quant-ph/0108062, 2001]; however, their proof relies upon a long argument using advanced mathematics. In contrast, our proof provides a simple constructive procedure which is close to optimal and experimentally practical [C. M. Dawson and A. Gilchrist, online implementation of the procedure described herein (2002), http://www.physics.uq.edu.au/gqc/].Comment: 3 pages, online implementation of procedure described can be found at http://www.physics.uq.edu.au/gqc

Aggressive shadowing of a low-dimensional model of atmospheric dynamics

Predictions of the future state of the Earth's atmosphere suffer from the consequences of chaos: numerical weather forecast models quickly diverge from observations as uncertainty in the initial state is amplified by nonlinearity. One measure of the utility of a forecast is its shadowing time, informally given by the period of time for which the forecast is a reasonable description of reality. The present work uses the Lorenz 096 coupled system, a simplified nonlinear model of atmospheric dynamics, to extend a recently developed technique for lengthening the shadowing time of a dynamical system. Ensemble forecasting is used to make forecasts with and without inflation, a method whereby the ensemble is regularly expanded artificially along dimensions whose uncertainty is contracting. The first goal of this work is to compare model forecasts, with and without inflation, to a true trajectory created by integrating a modified version of the same model. The second goal is to establish whether inflation can increase the maximum shadowing time for a single optimal member of the ensemble. In the second experiment the true trajectory is known a priori, and only the closest ensemble members are retained at each time step, a technique known as stalking. Finally, a targeted inflation is introduced to both techniques to reduce the number of instances in which inflation occurs in directions likely to be incommensurate with the true trajectory. Results varied for inflation, with success dependent upon the experimental design parameters (e.g. size of state space, inflation amount). However, a more targeted inflation successfully reduced the number of forecast degradations without significantly reducing the number of forecast improvements. Utilized appropriately, inflation has the potential to improve predictions of the future state of atmospheric phenomena, as well as other physical systems.Comment: 14 pages, 16 figure

Supported bimetallic nano-alloys as highly active catalysts for the one-pot tandem synthesis of imines and secondary amines from nitrobenzene and alcohols

The synthesis and functionalization of imines and amines are key steps in the preparation of many fine chemicals and for pharmaceuticals in particular. Traditionally, metal complexes are used as homogeneous catalysts for these organic transformations. Here we report gold-palladium and ruthenium-palladium nano-alloys supported on TiO2 acting as highly efficient heterogeneous catalysts for the one-pot synthesis of the imine N-benzylideneaniline and the secondary amine N-benzylaniline directly from the easily available and stable nitrobenzene and benzyl alcohol precursors using a hydrogen auto-transfer strategy. These reactions were carried out without any added external hydrogen, sacrificial hydrogen donor or a homogeneous base. The bimetallic catalysts were prepared by the recently developed modified impregnation strategy, giving efficient control of size and nano-alloy composition. Both bimetallic catalysts were found to be far more active than their monometallic analogues due to a synergistic effect. Based on the turnover numbers the catalytic activities follow the order Ru < Pd < Au << Au-Pd < Ru-Pd. Aberration corrected scanning transmission electron microscopy (AC-STEM) and X-ray absorption spectroscopy (XAFS) studies of these catalysts revealed that the reason for the observed synergistic effect is the electronic modification of the metal sites in the case of the Au-Pd system and a size stabilisation effect in the case of the Ru-Pd catalyst

The interaction of PRC2 with RNA or chromatin is mutually antagonistic

Polycomb repressive complex 2 (PRC2) modifies chromatin to maintain genes in a repressed state during development. PRC2 is primarily associated with CpG islands at repressed genes and also possesses RNA binding activity. However, the RNAs that bind PRC2 in cells, the subunits that mediate these interactions, and the role of RNA in PRC2 recruitment to chromatin all remain unclear. By performing iCLIP for PRC2 in comparison with other RNA binding proteins, we show here that PRC2 binds nascent RNA at essentially all active genes. Although interacting with RNA promiscuously, PRC2 binding is enriched at specific locations within RNAs, primarily exon-intron boundaries and the 3'UTR. Deletion of other PRC2 subunits reveals that SUZ12 is sufficient to establish this RNA binding profile. Contrary to prevailing models, we also demonstrate that the interaction of PRC2 with RNA or chromatin is mutually antagonistic in cells and in vitro. RNA degradation in cells triggers PRC2 recruitment to CpG islands at active genes. Correspondingly, release of PRC2 from chromatin in cells increases RNA binding. Consistent with this, RNA and nucleosomes compete for PRC2 binding in vitro. We propose that RNA prevents PRC2 recruitment to chromatin at active genes and that mutual antagonism between RNA and chromatin underlies the pattern of PRC2 chromatin association across the genome