Noise-Resilient and Reduced Depth Approximate Adders for NISQ Quantum Computing

TL;DR

This paper introduces five novel approximate quantum adder designs that reduce circuit depth and enhance noise resilience in NISQ quantum computers, demonstrating significant fidelity improvements across various noise models.

Contribution

It proposes new approximate quantum adder architectures with reduced depth and noise robustness, including pass-through and zero-depth designs, validated on IBM Qiskit with multiple noise models.

Findings

Approximate adders without carryout improve fidelity by up to 219.22%.

Approximate adders with carryout improve fidelity by up to 371%.

Proposed designs outperform exact adders under various noise conditions.

Abstract

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.