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Simulating quantum systems

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Presented by: Katie Barr

Quantum theory is famously difficult and paradoxical, but exploring quantum systems numerically in high level languages such as Python is surprisingly easy. In this talk I will describe, step by step, how to simulate a particular system, the discrete time quantum walk. This is the quantum analogue of a classical random walk, and has some interesting properties which I will briefly describe. The simulation can be performed with just 15 lines of Python code, using no external modules. I will then indicate how simple variations on this simulation are used to perform current research into the discrete time quantum walk, as the example I give is a variation of Grover's algorithm, which is asymptotically the fastest possible quantum search algorithm. By the end of the talk listeners should be able to go away and perform their own simulations of this system. I will also indicate further motivations for using Python to investigate quantum mechanical systems, in particular using numpy support for linear algebra, which is one of the types of mathematics used by quantum theorists. There will be no mention of the trickier aspects of quantum systems, but, for those interested, I will provide materials describing how to measure entanglement and explore the effects of measurement in the quantum walk I have presented. I do not expect listeners to have any background in mathematics and physics, and will keep technical discussion which would require such background to a minimum.

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