  Quantum Computing is making significant advancements toward creating machines
capable of implementing quantum algorithms in various fields, such as quantum
cryptography, quantum image processing, and optimization. The development of
quantum arithmetic circuits for modulo addition is vital for implementing these
quantum algorithms. While it is ideal to use quantum circuits based on
fault-tolerant gates to overcome noise and decoherence errors, the current
Noisy Intermediate Scale Quantum (NISQ) era quantum computers cannot handle the
additional computational cost associated with fault-tolerant designs. Our
research aims to minimize circuit depth, which can reduce noise and facilitate
the implementation of quantum modulo addition circuits on NISQ machines. This
work presents quantum carry-lookahead modulo $(2^n - 1)$ adder (QCLMA), which
is designed to receive two n-bit numbers and perform their addition with an
O(log n) depth. Compared to existing work of O(n) depth, our proposed QCLMA
reduces the depth and helps increase the noise fidelity. In order to increase
error resilience, we also focus on creating a tree structure based Carry path,
unlike the chain based Carry path of the current work. We run experiments on
Quantum Computer IBM Cairo to evaluate the performance of the proposed QCLMA
against the existing work and define Quantum State Fidelity Ratio (QSFR) to
quantify the closeness of the correct output to the top output. When compared
against existing work, the proposed QCLMA achieves a 47.21% increase in QSFR
for 4-qubit modulo addition showcasing its superior noise fidelity.
