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Estimating pi using high-dimensional single and multi-global Quantum Phase Estimation algorithm on Cirq
(pp0425-0437)
Osman Semi Ceylan, Sabri Gündüz, Furkan Kaya, and
İhsan Yılmaz
doi:
https://doi.org/10.26421/QIC24.5-6-3
Abstracts:
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.
Key Words:
Pi, Quantum Computation,
High-Dimension |