Multi-copy programmable discrimination of general qubit states

Quantum state discrimination is a fundamental primitive in quantum statistics where one has to correctly identify the state of a system that is in one of two possible known states. A programmable discrimination machine performs this task when the pair of possible states is not a priori known, but instead the two possible states are provided through two respective program ports. We study optimal programmable discrimination machines for general qubit states when several copies of states are available in the data or program ports. Two scenarios are considered: one in which the purity of the possible states is a priori known, and the fully universal one where the machine operates over generic mixed states of unknown purity. We find analytical results for both, the unambiguous and minimum error, discrimination strategies. This allows us to calculate the asymptotic performance of programmable discrimination machines when a large number of copies is provided, and to recover the standard state discrimination and state comparison values as different limiting cases.Comment: Based on version published in Physical Review A, some errors in appendix A corrected. 13 pages, 4 figure

Quantum Bootstrap Aggregation

We set out a strategy for quantizing attribute bootstrap aggregation to enable variance-resilient quantum machine learning. To do so, we utilise the linear decomposability of decision boundary parameters in the Rebentrost et al. Support Vector Machine to guarantee that stochastic measurement of the output quantum state will give rise to an ensemble decision without destroying the superposition over projective feature subsets induced within the chosen SVM implementation. We achieve a linear performance advantage, O(d), in addition to the existing O(log(n)) advantages of quantization as applied to Support Vector Machines. The approach extends to any form of quantum learning giving rise to linear decision boundaries

Quantum learning: optimal classification of qubit states

Pattern recognition is a central topic in Learning Theory with numerous applications such as voice and text recognition, image analysis, computer diagnosis. The statistical set-up in classification is the following: we are given an i.i.d. training set $(X_{1},Y_{1}),... (X_{n},Y_{n})$ where $X_{i}$ represents a feature and $Y_{i}\in \{0,1\}$ is a label attached to that feature. The underlying joint distribution of $(X,Y)$ is unknown, but we can learn about it from the training set and we aim at devising low error classifiers $f:X\to Y$ used to predict the label of new incoming features. Here we solve a quantum analogue of this problem, namely the classification of two arbitrary unknown qubit states. Given a number of `training' copies from each of the states, we would like to `learn' about them by performing a measurement on the training set. The outcome is then used to design mesurements for the classification of future systems with unknown labels. We find the asymptotically optimal classification strategy and show that typically, it performs strictly better than a plug-in strategy based on state estimation. The figure of merit is the excess risk which is the difference between the probability of error and the probability of error of the optimal measurement when the states are known, that is the Helstrom measurement. We show that the excess risk has rate $n^{-1}$ and compute the exact constant of the rate.Comment: 24 pages, 4 figure

Quantum computing for pattern classification

It is well known that for certain tasks, quantum computing outperforms classical computing. A growing number of contributions try to use this advantage in order to improve or extend classical machine learning algorithms by methods of quantum information theory. This paper gives a brief introduction into quantum machine learning using the example of pattern classification. We introduce a quantum pattern classification algorithm that draws on Trugenberger's proposal for measuring the Hamming distance on a quantum computer (CA Trugenberger, Phys Rev Let 87, 2001) and discuss its advantages using handwritten digit recognition as from the MNIST database.Comment: 14 pages, 3 figures, presented at the 13th Pacific Rim International Conference on Artificial Intelligenc

Towards Privacy Compliant and Anytime Recommender Systems

The original publication is available at www.springerlink.comInternational audienceRecommendation technologies have traditionally been used in domains such as E-commerce and Web navigation to recommend resources to customers so as to help them to get the pertinent resources. Among the possible approaches is collaborative filtering that does not take into account the content of the resources: only the traces of usage of the resources are considered. State of the art models, such as sequential association-rules and Markov models, that can be used in the frame of privacy concerns, are usually studied in terms of performance, state space complexity and time complexity. Many of them have a large time complexity and require a long time to compute recommendations. However, there are domains of application of the models where recommendations may be required quickly. This paper focuses on the study of how these state of the art models can be adapted so as to be anytime. In that case recommendations can be proposed to the user whatever is the computation time available, the quality of the recommendations increases according to the computation time. We show that such models can be adapted so as to be anytime and we propose several strategies to compute recommendations iteratively. We also show that the computation time needed by these new models is not increased compared to classical ones; even so, it sometimes decreases

Robust Online Hamiltonian Learning

In this work we combine two distinct machine learning methodologies, sequential Monte Carlo and Bayesian experimental design, and apply them to the problem of inferring the dynamical parameters of a quantum system. We design the algorithm with practicality in mind by including parameters that control trade-offs between the requirements on computational and experimental resources. The algorithm can be implemented online (during experimental data collection), avoiding the need for storage and post-processing. Most importantly, our algorithm is capable of learning Hamiltonian parameters even when the parameters change from experiment-to-experiment, and also when additional noise processes are present and unknown. The algorithm also numerically estimates the Cramer-Rao lower bound, certifying its own performance.Comment: 24 pages, 12 figures; to appear in New Journal of Physic

A Novel Clustering Algorithm Based on Quantum Games

Enormous successes have been made by quantum algorithms during the last decade. In this paper, we combine the quantum game with the problem of data clustering, and then develop a quantum-game-based clustering algorithm, in which data points in a dataset are considered as players who can make decisions and implement quantum strategies in quantum games. After each round of a quantum game, each player's expected payoff is calculated. Later, he uses a link-removing-and-rewiring (LRR) function to change his neighbors and adjust the strength of links connecting to them in order to maximize his payoff. Further, algorithms are discussed and analyzed in two cases of strategies, two payoff matrixes and two LRR functions. Consequently, the simulation results have demonstrated that data points in datasets are clustered reasonably and efficiently, and the clustering algorithms have fast rates of convergence. Moreover, the comparison with other algorithms also provides an indication of the effectiveness of the proposed approach.Comment: 19 pages, 5 figures, 5 table

Can dissonance engineering improve risk analysis of human–machine systems?

The paper discusses dissonance engineering and its application to risk analysis of human–machine systems. Dissonance engineering relates to sciences and technologies relevant to dissonances, defined as conflicts between knowledge. The richness of the concept of dissonance is illustrated by a taxonomy that covers a variety of cognitive and organisational dissonances based on different conflict modes and baselines of their analysis. Knowledge control is discussed and related to strategies for accepting or rejecting dissonances. This acceptability process can be justified by a risk analysis of dissonances which takes into account their positive and negative impacts and several assessment criteria. A risk analysis method is presented and discussed along with practical examples of application. The paper then provides key points to motivate the development of risk analysis methods dedicated to dissonances in order to identify the balance between the positive and negative impacts and to improve the design and use of future human–machine system by reinforcing knowledge