An Algorithm for Constructing Polynomial Systems Whose Solution Space Characterizes Quantum Circuits
量子物理
2015-06-26 v1
摘要
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.
引用
@article{arxiv.quant-ph/0512064,
title = {An Algorithm for Constructing Polynomial Systems Whose Solution Space Characterizes Quantum Circuits},
author = {Vladimir P. Gerdt and Vasily M. Severyanov},
journal= {arXiv preprint arXiv:quant-ph/0512064},
year = {2015}
}
备注
10 pages, 9 Postscript figures, report presented on QI 2005