Efficient Toffoli Gates Using Qudits

The simplest decomposition of a Toffoli gate acting on three qubits requires {\em five} 2-qubit gates. If we restrict ourselves to controlled-sign (or controlled-NOT) gates this number climbs to six. We show that the number of controlled-sign gates required to implement a Toffoli gate can be reduced to just {\em three} if one of the three quantum systems has a third state that is accessible during the computation, i.e. is actually a qutrit. Such a requirement is not unreasonable or even atypical since we often artificially enforce a qubit structure on multilevel quantums systems (eg. atoms, photonic polarization and spatial modes). We explore the implementation of these techniques in optical quantum processing and show that linear optical circuits could operate with much higher probabilities of success

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

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

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

ensity and spectral measurements using a 34 GHz interferometry system

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76380/1/AIAA-1999-2718-743.pd

Understanding images in biological and computer vision

yesThis issue of Interface Focus is a collection of papers arising out of a Royal Society Discussion meeting entitled ‘Understanding images in biological and computer vision’ held at Carlton Terrace on the 19th and 20th February, 2018. There is a strong tradition of inter-disciplinarity in the study of visual perception and visual cognition. Many of the great natural scientists including Newton [1], Young [2] and Maxwell (see [3]) were intrigued by the relationship between light, surfaces and perceived colour considering both physical and perceptual processes. Brewster [4] invented both the lenticular stereoscope and the binocular camera but also studied the perception of shape-from-shading. More recently, Marr's [5] description of visual perception as an information processing problem led to great advances in our understanding of both biological and computer vision: both the computer vision and biological vision communities have a Marr medal. The recent successes of deep neural networks in classifying the images that we see and the fMRI images that reveal the activity in our brains during the act of seeing are both intriguing. The links between machine vision systems and biology may at sometimes be weak but the similarity of some of the operations is nonetheless striking [6]. This two-day meeting brought together researchers from the fields of biological and computer vision, robotics, neuroscience, computer science and psychology to discuss the most recent developments in the field. The meeting was divided into four themes: vision for action, visual appearance, vision for recognition and machine learning

Optimal discrete stopping times for reliability growth tests

Often, the duration of a reliability growth development test is specified in advance and the decision to terminate or continue testing is conducted at discrete time intervals. These features are normally not captured by reliability growth models. This paper adapts a standard reliability growth model to determine the optimal time for which to plan to terminate testing. The underlying stochastic process is developed from an Order Statistic argument with Bayesian inference used to estimate the number of faults within the design and classical inference procedures used to assess the rate of fault detection. Inference procedures within this framework are explored where it is shown the Maximum Likelihood Estimators possess a small bias and converges to the Minimum Variance Unbiased Estimator after few tests for designs with moderate number of faults. It is shown that the Likelihood function can be bimodal when there is conflict between the observed rate of fault detection and the prior distribution describing the number of faults in the design. An illustrative example is provided

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

Ample consumption period available until use-by dates: a potential, marketing position for store brands

Traditionally store brands in Australia are viewed with suspicion in regard to their quality and are usually purchased because of the "value for money" that they offer. Australian supermarket majors are considering introducing a new suite of store brands in the higher price brackets. The danger of moving upscale however is that these store brands are relinquishing their value for money appeal and will come head to head with the manufactured brands. Store brands will now require some quality dimension to compete. This paper after studying the attitudes and behavioural response of grocery shoppers to use by dates, is proposing that that the promise of "generous" use-by dates as a surrogate for quality, could be considered as a positioning plank to promote store brands as alternatives to manufactured brands. Logit analysis is employed to explain shoppers' perception and response to use-by dates, of products that they regularly buy, and of alternative products which they have never bought before if the use-by dates of their regular items are perceived to be too shor