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Transcript
Simulating higher transcendental mathematical functions with quantum mechanics J. Twamley and G.J. Milburn Quantum Information Science, Centre for Quantum Computer Technology Physics Department, Division of Information and Communication Sciences Macquarie University, NSW 2109 Australia Tel: +61-2-9850-8908 Fax: +61-2-9850-8115 Room: E7A 328 http://www.ics.mq.edu.au/qis In quantum mechanics one can, via the Fourier transform, simulate the so-called, "lower" transcendental functions, sine and cosine. We show how to derive a new type of unitary transform, like the Fourier transform, in quantum mechanics which yields quantum wavefunctions whose amplitude matches many types of "higher transcendental functions". In particular we give details on how to engineer quantum wavefunctions whose amplitude approximates to the Riemann Zeta function on the critical line s=1/2+it.
