QUANTUM CIRCUIT OPTIMIZATION (FOR 3 QUBITS)

Abstract

Logic gates like AND, OR, XOR are example of irreversible gates for which no input is calculated from each
output. But in case of reversible gates like NOT, CNOT, HADAMARD, TOFFOLI, V, V+, etc. each input is calculated
from each output, because no energy(information) loss is the best feature of reversible gates. And hence more
researchers focus on reversible circuits, which are used in quantum circuits or networks. Quantum computing is a
process that incorporates interacting physical systems that represent quantum bits and quantum gates. We present the
quantum bit(qubit), the quantum register and the quantum gates. The qubit is described as a vector in a two dimensional
Hilbert space and the quantum register, which comprises a number of qubits, as a vector in a multidimensional Hilbert
space. Any gates transform the input bits to the output bits in some deterministic fashion according to the definition of
the logic gate. Quantum gates are Hilbert space operators that rotate the qubit or the quantum register vectors. We
present the currently used two optimization methods one is template based and second is window based for reversible
and quantum circuits. Finally, we have implemented our method using the benefits of above two. Quantum circuit
optimization is useful to reduce the quantum cost for those circuits, where optimization is applicable. Response time is
reduced for complex computations.