  The "Noisy intermediate-scale quantum" NISQ machine era primarily focuses on
mitigating noise, controlling errors, and executing high-fidelity operations,
hence requiring shallow circuit depth and noise robustness. Approximate
computing is a novel computing paradigm that produces imprecise results by
relaxing the need for fully precise output for error-tolerant applications
including multimedia, data mining, and image processing. We investigate how
approximate computing can improve the noise resilience of quantum adder
circuits in NISQ quantum computing. We propose five designs of approximate
quantum adders to reduce depth while making them noise-resilient, in which
three designs are with carryout, while two are without carryout. We have used
novel design approaches that include approximating the Sum only from the inputs
(pass-through designs) and having zero depth, as they need no quantum gates.
The second design style uses a single CNOT gate to approximate the SUM with a
constant depth of O(1). We performed our experimentation on IBM Qiskit on noise
models including thermal, depolarizing, amplitude damping, phase damping, and
bitflip: (i) Compared to exact quantum ripple carry adder without carryout the
proposed approximate adders without carryout have improved fidelity ranging
from 8.34% to 219.22%, and (ii) Compared to exact quantum ripple carry adder
with carryout the proposed approximate adders with carryout have improved
fidelity ranging from 8.23% to 371%. Further, the proposed approximate quantum
adders are evaluated in terms of various error metrics.
