Bases for quantum circuits

Vladimir P. Gerdt, Vasily M. Severyanov

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.

Margareta Vamos

François Chapeau‐Blondeau

Juan M. Romero, Emiliano Montoya-González, Oscar Velazquez-Alvarado

Bell's states are among the most useful in quantum computing. These state are an orthonormal base of entagled states with two qubits. We propose alternative bases of entangled states. Some of these states depend on a continuous parameter. We present the quantum circuit and code of these alternative bases. In addition, we study quantum teleportation with these entangled states and present their quantum circuits and codes associated.

Anonymous

Liu Rong, Pla Uni

Quantum teleportation can realize quantum cryptography communication which can not be deciphered in the physical layer using quantum entangled state.Described characteristics of the quantum entangled state,given out physics gate circuit which can realize quantum entangled;used the quantum circuit,analysised communication model of teleportation,gived out a quantum circuit to realize quantum teleportation base on Bell State which has simpler structure,proved the quantum circuit is feasible,laied the foundations to study quantum cryptography communication further.