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We introduce an open source software package UniversalQCompiler written in Mathematica that allows the decomposition of arbitrary quantum operations into a sequence of single-qubit rotations (with arbitrary rotation angles) and controlled-NOT (C-NOT) gates. Together with the existing package QI, this allows quantum information protocols to be analysed and then compiled to quantum circuits. Our decompositions are based on Phys. Rev. A 93, 032318 (2016), and hence, for generic operations, they are near optimal in terms of the number of gates required. UniversalQCompiler allows the compilation of any isometry (in particular, it can be used for unitaries and state preparation), quantum channel, positive-operator valued measure (POVM) or quantum instrument, although the run time becomes prohibitive for large numbers of qubits. The resulting circuits can be displayed graphically within Mathematica or exported to LaTeX. We also provide functionality to translate the circuits to OpenQASM, the quantum assembly language used, for instance, by the IBM Q Experience.
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Boson-sampling is a simplified model for quantum computing that may hold the key to implementing the first ever post-classical quantum computer. Boson-sampling is a non-universal quantum computer that is significantly more straightforward to build than any universal quantum computer proposed so far. We begin this chapter by motivating boson-sampling and discussing the history of linear optics quantum computing. We then summarize the boson-sampling formalism, discuss what a sampling problem is, explain why boson-sampling is easier than linear optics quantum computing, and discuss the Extended Church-Turing thesis. Next, sampling with other classes of quantum optical states is analyzed. Finally, we discuss the feasibility of building a boson-sampling device using existing technology.
The following notes are based on lectures delivered at the research school Modeling and Control of Open Quantum Systems (Mod{e}lisation et contr^{o}le des syst`{e}mes quantiques ouverts) at CIRM, Marseille, 16-20 April, 2018, as part of the Trimester textit{Measurement and Control of Quantum Systems: Theory and Experiments} organized at Institut Henri Poincar{e}, Paris, France. The aim is to introduce quantum filtering to an audience with a background in either quantum theory or classical filtering.
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A concise introduction to quantum entanglement in multipartite systems is presented. We review entanglement of pure quantum states of three--partite systems analyzing the classes of GHZ and W states and discussing the monogamy relations. Special attention is paid to equivalence with respect to local unitaries and stochastic local operations, invariants along these orbits, momentum map and spectra of partial traces. We discuss absolutely maximally entangled states and their relation to quantum error correction codes. An important case of a large number of parties is also analysed and entanglement in spin systems is briefly reviewed.
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