Quantum process tomography of a controlled-NOT gate

We demonstrate complete characterization of a two-qubit entangling process - a linear optics controlled-NOT gate operating with coincident detection - by quantum process tomography. We use maximum-likelihood estimation to convert the experimental data into a physical process matrix. The process matrix allows accurate prediction of the operation of the gate for arbitrary input states, and calculation of gate performance measures such as the average gate fidelity, average purity and entangling capability of our gate, which are 0.90, 0.83 and 0.73, respectively.Comment: 4 pages, 2 figures. v2 contains new data corresponding to improved gate operation. Figure quality slightly reduced for arXi

Manipulating biphotonic qutrits

Quantum information carriers with higher dimension than the canonical qubit offer significant advantages. However, manipulating such systems is extremely difficult. We show how measurement induced non-linearities can be employed to dramatically extend the range of possible transforms on biphotonic qutrits; the three level quantum systems formed by the polarisation of two photons in the same spatio-temporal mode. We fully characterise the biphoton-photon entanglement that underpins our technique, thereby realising the first instance of qubit-qutrit entanglement. We discuss an extension of our technique to generate qutrit-qutrit entanglement and to manipulate any bosonic encoding of quantum information.Comment: 4 pages, 4 figure

Demonstration of a simple entangling optical gate and its use in Bell-state analysis

We demonstrate a new architecture for an optical entangling gate that is significantly simpler than previous realisations, using partially-polarising beamsplitters so that only a single optical mode-matching condition is required. We demonstrate operation of a controlled-Z gate in both continuous-wave and pulsed regimes of operation, fully characterising it in each case using quantum process tomography. We also demonstrate a fully-resolving, nondeterministic optical Bell-state analyser based on this controlled-Z gate. This new architecture is ideally suited to guided optics implementations of optical gates.Comment: 4 pages, 3 figures. v2: additional author, improved data and figures (low res), some other minor changes. Accepted for publication in PR

Linear Optical CNOT Gate in the Coincidence Basis

We describe the operation and tolerances of a non-deterministic, coincidence basis, quantum CNOT gate for photonic qubits. It is constructed solely from linear optical elements and requires only a two-photon source for its demonstration.Comment: Submitted to Physical Review

Experimental demonstration of Shor's algorithm with quantum entanglement

Shor's powerful quantum algorithm for factoring represents a major challenge in quantum computation and its full realization will have a large impact on modern cryptography. Here we implement a compiled version of Shor's algorithm in a photonic system using single photons and employing the non-linearity induced by measurement. For the first time we demonstrate the core processes, coherent control, and resultant entangled states that are required in a full-scale implementation of Shor's algorithm. Demonstration of these processes is a necessary step on the path towards a full implementation of Shor's algorithm and scalable quantum computing. Our results highlight that the performance of a quantum algorithm is not the same as performance of the underlying quantum circuit, and stress the importance of developing techniques for characterising quantum algorithms.Comment: 4 pages, 5 figures + half-page additional online materia

Measuring Entangled Qutrits and Their Use for Quantum Bit Commitment

We produce and holographically measure entangled qudits encoded in transverse spatial modes of single photons. With the novel use of a quantum state tomography method that only requires two-state superpositions, we achieve the most complete characterisation of entangled qutrits to date. Ideally, entangled qutrits provide better security than qubits in quantum bit-commitment: we model the sensitivity of this to mixture and show experimentally and theoretically that qutrits with even a small amount of decoherence cannot offer increased security over qubits.Comment: Paper updated to match published version; 5 pages, 4 figures, images have been included at slightly lower quality for the archiv

Investigation of two qubit quantum gates in linear optics

We discuss progress towards implementing two qubit quantum gates in optics. We review the operation of an optical quantum gate which performs all the operations of a control-NOT (CNOT) gate in the coincidence basis with two, unentangled photons as the input and discuss its implementation

Distributed Coordinate Descent for L1-regularized Logistic Regression

Solving logistic regression with L1-regularization in distributed settings is an important problem. This problem arises when training dataset is very large and cannot fit the memory of a single machine. We present d-GLMNET, a new algorithm solving logistic regression with L1-regularization in the distributed settings. We empirically show that it is superior over distributed online learning via truncated gradient

Whole-genome microarrays of fission yeast: characteristics, accuracy, reproducibility, and processing of array data

Background: The genome of the fission yeast Schizosaccharomyces pombe has recently been sequenced, setting the stage for the post-genomic era of this increasingly popular model organism. We have built fission yeast microarrays, optimised protocols to improve array performance, and carried out experiments to assess various characteristics of microarrays.|Results: We designed PCR primers to amplify specific probes (180-500 bp) for all known and predicted fission yeast genes, which are printed in duplicate onto separate regions of glass slides together with control elements (similar to13,000 spots/slide). Fluorescence signal intensities depended on the size and intragenic position of the array elements, whereas the signal ratios were largely independent of element properties. Only the coding strand is covalently linked to the slides, and our array elements can discriminate transcriptional direction. The microarrays can distinguish sequences with up to 70% identity, above which cross-hybridisation contributes to the signal intensity. We tested the accuracy of signal ratios and measured the reproducibility of array data caused by biological and technical factors. Because the technical variability is lower, it is best to use samples prepared from independent biological experiments to obtain repeated measurements with swapping of fluorochromes to prevent dye bias. We also developed a script that discards unreliable data and performs a normalization to correct spatial artefacts.|Conclusions: This paper provides data for several microarray properties that are rarely measured. The results define critical parameters for microarray design and experiments and provide a framework to optimise and interpret array data. Our arrays give reproducible and accurate expression ratios with high sensitivity. The scripts for primer design and initial data processing as well as primer sequences and detailed protocols are available from our website