ESTIMATING PI USING HIGH-DIMENSIONAL SINGLE AND MULTI-GLOBAL QUANTUM PHASE ESTIMATION ALGORITHM ON CIRQ

Quantum computing is carried out based on the working principles of quantum mechanics. Current 2-dimensional quantum computing techniques face major problems such as noise and information capacity. As such, high-dimensional quantum computing is leveraged to solve these problems. This study attempts to approximate the pi number through the multi-global and single-global Quantum Phase Estimation (QPE) algorithms in high-dimension. This study reveals that pi can be calculated by using fewer quantum resources in high dimension with at least equal or higher precision than that obtained by 2-dimensional QPE. In addition, when the number of qudits or the number of dimensions is kept constant, the multi-global QPE in high dimensions yields at least equal or better results than the single-global QPE. All calculations performed in this study are implemented on Cirq.