Quantitative functional analysis of the left ventricle plays a very important role in the diagnosis of heart diseases. While in standard two-dimensional echocardiography this quantification is limited to rather crude volume estimation, three-dimensional (3-D) echocardiography not only significantly improves its accuracy but also makes it possible to derive valuable additional information, like various wall-motion measurements. In this paper, we present a new efficient method for the functional evaluation of the left ventricle from 3-D echographic sequences. It comprises a segmentation step that is based on the integration of 3-D deformable surfaces and a four-dimensional statistical heart motion model. The segmentation results in an accurate 3-D + time left ventricle discrete representation. Functional descriptors like local wall-motion indexes are automatically derived from this representation. The method has been successfully tested both on electrocardiography-gated and real-time 3-D data. It has proven to be fast, accurate, and robust.

In quantum computing the decoherence time of the qubits determines the computation time available and this time is very limited when using current hardware. In this paper we minimize the execution time (the depth) for a class of circuits referred to as linear reversible circuits, which has many applications in quantum computing (e.g., stabilizer circuits, "CNOT+T" circuits, etc.). We propose a practical formulation of a divide and conquer algorithm that produces quantum circuits that are twice as shallow as those produced by existing algorithms. We improve the theoretical upper bound of the depth in the worst case for some range of qubits. We also propose greedy algorithms based on cost minimization to find more optimal circuits for small or simple operators. Overall, we manage to consistently reduce the total depth of a class of reversible functions, with up to 92% savings in an ancilla-free case and up to 99% when ancillary qubits are available.

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Linear reversible circuits represent a subclass of reversible circuits with many applications in quantum computing. These circuits can be efficiently simulated by classical computers and their size is polynomially bounded by the number of qubits, making them a good candidate to deploy efficient methods to reduce computational costs. We propose a new algorithm for synthesizing any linear reversible operator by using an optimized version of the Gaussian elimination algorithm coupled with a tuned LU factorization. We also improve the scalability of purely greedy methods. Overall, on random operators, our algorithms improve the state-of-the-art methods for specific ranges of problem sizes: The custom Gaussian elimination algorithm provides the best results for large problem sizes (n > 150), while the purely greedy methods provide quasi optimal results when n < 30. On a benchmark of reversible functions, we manage to significantly reduce the CNOT count and the depth of the circuit while keeping other metrics of importance (T-count, T-depth) as low as possible.