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

TL;DR

This work addresses noise and depth limitations of NISQ quantum computing by introducing five approximate adders that reduce carry-propagation dependence and enable parallel, shallow arithmetic. Two adders operate without carryout (including a zero-depth pass-through and a single-CNOT-depth design), while three with carryout use carry logic that preserves outputs with minimal depth (including Toffoli-based implementations). IBM Qiskit simulations across multiple noise models show substantial fidelity gains, with up to $371 ext{\%}$ improvement for carryout designs and significant gains for non-carryout designs, alongside quantitative error metrics such as NMED and ER. The findings suggest that approximate quantum adders can provide robust, low-depth arithmetic suitable for error-tolerant NISQ applications, including quantum image processing, and offer practical guidance on selecting an appropriate adder variant for a given noise profile.

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.

Figures (5)

• Figure 1: The CNOT and Toffoli gates.
• Figure 2: Exact quantum adder by Cuccaro et al cuccaro2004new. The inputs are in range a0 to a4 and b0 to b4 while S0 to S4 represent Sum bits. The Carry generation path extends from c0 to c4, creating higher depth and longer carrypath, increasing the noise susceptibility of carryout. LSB qubits spend much more time idling than MSB, making Sum vulnerable to noise jayashankar2022achieving.
• Figure 3: Proposed 2-Qubit Adders without Carryout. a) AQA1 needs no hardware to pass input A to Sum. b) Single CNOT gate in AQA2 reduces error distance.
• Figure 4: Error Metrics of Proposed Adders without Carryout for: (a) Normalized Mean Error Deviation. (b) Error Rate.
• Figure 6: Error Metrics of Proposed Adders with Carryout for: (a) Normalized Mean Error Deviation (b) Error Rate.