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Introduction to Quantum Computing and Description of entanglement space in terms of polynomial invariants: challenges for computer algebra

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时间:2017-09-13  来源:数学机械化重点实验室

题目:          Introduction to Quantum Computing and Description of entanglement space in terms of polynomial invariants: challenges for computer algebra

报告人:     Vladimir P. Gerdt (Joint Institute for Nuclear Research,Russia)

时间地点:   2017.09.15  09:00am  N202

摘要:       The talk consisists of two parts. In the first part we give an introduction to quantum computing. In the second part we consider some computation aspects of the rigorous description of quantum entanglement in terms of polynomial invariants. The entanglement of qubits (quantum bits) provided by their quantum correlations is the main resource of quantum computation and quantum information processes, e.g., superdense coding, teleportation and cryptography. By this reason a qualitative and quantative characterization of entanglement is a topical research problem. We consider computational features of characterising the entanglement space of pure states of a few qubits and qutrits (3-level quantum objects) in terms of hyperdeterminants and some related challenging problems. Then we analyse two qubit mixed states via the polynomial invariants of local unitary group SU(2)xSU(2). Although in the literature a number of computer algebra based algorithms has been designed for construction of the ring of invariant polynomials, the underlying symbolic computation, even for the smallest nontrivial quantum system consisting of two qubits, is intractable for those algorithms and is a challenge for polynomial computer algebra. In this context we restrict ourselves with a subset of the two qubit states containing so-called X-states and present our computation of its invariant ring.
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