An Algorithm for Constructing Polynomial Systems Whose Solution Space Characterizes Quantum Circuits

Details An Algorithm for Constructing Polynomial Systems Whose Solution Space Characterizes Quantum Circuits An Algorithm for Constructing Polynomial Systems Whose Solution Space Characterizes Quantum Circuits

2005-12-08

arxiv.org/abs/quant-ph/0512064v1

Physics

Quantum Physics

10 pages, 9 Postscript figures, report presented on QI 2005

Scientific paper

An algorithm and its first implementation in C# are presented for assembling arbitrary quantum circuits on the base of Hadamard and Toffoli gates and for constructing multivariate polynomial systems over the finite field Z_2 arising when applying the Feynman's sum-over-paths approach to quantum circuits. The matrix elements determined by a circuit can be computed by counting the number of common roots in Z_2 for the polynomial system associated with the circuit. To determine the number of solutions in Z_2 for the output polynomial system, one can use the Groebner bases method and the relevant algorithms for computing Groebner bases.

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