Vasily M. Severyanov | Searcharxiv

arXiv2005

A Software Package to Construct Polynomial Sets over Z_2 for Determining the Output of Quantum Computations

A C# package is presented that allows a user for an input quantum circuit to generate a set of multivariate polynomials over the finite field Z_2 whose total number of solutions in Z_2 determines the output of the quantum computation defined by the circuit. The generated polynomial system can further be converted to the canonical Groebner basis form which provides a universal algorithmic tool for counting the number of common roots of the polynomials.

quant-ph↗

arXiv2005

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

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.

quant-ph↗