Approximate quantum adders are gaining traction in NISQ-era computing for their potential to reduce quantum resource usage while preserving computational accuracy. In this work, we evaluate two 8-qubit hybrid approximate quantum adders that combine a 2-qubit approximate block, either a pass-through Copy Adder or a CNOT-based design, with a 6-qubit Cuccaro ripple-carry adder. Simulations are conducted using IBM's Qiskit framework under realistic noise models, including bit-flip, depolarizing, and thermal noise. Compared to the exact 8-bit Cuccaro adder, our designs reduce quantum cost and circuit depth by over 20 percent and achieve up to 79.3 percent higher output probability under noisy conditions. These results highlight the robustness and efficiency of approximate logic in noisy quantum environments and confirm its practicality for near-term quantum hardware.
Approximate quantum adders are gaining traction in NISQ-era computing for their potential to reduce quantum resource usage while preserving computational accuracy. In this work, we evaluate two 8-qubit hybrid approximate quantum adders that combine a 2-qubit approximate block, either a pass-through Copy Adder or a CNOT-based design, with a 6-qubit Cuccaro ripple-carry adder. Simulations are conducted using IBM's Qiskit framework under realistic noise models, including bit-flip, depolarizing, and thermal noise. Compared to the exact 8-bit Cuccaro adder, our designs reduce quantum cost and circuit depth by over 20 percent and achieve up to 79.3 percent higher output probability under noisy conditions. These results highlight the robustness and efficiency of approximate logic in noisy quantum environments and confirm its practicality for near-term quantum hardware.
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.
The basic components of both quantum and quantum-inspired arithmetic systems are quantum adders. Traditional direct quantum adders like the Vedral and Cuccaro ripple-carry adders provide accurate computation but have higher circuit depth, longer propagation delay and complexity of hardware implementation based upon extensive usage of Toffoli gates. This article brings about a comparison analysis of the current quantum adder designs, and it suggests an Approximate Toffoli Adder in order to enhance performance and hardware efficiency. The suggested design is designed with the help of Verilog HDL and run with Xilinx Vivado 2025.2. As can be seen from experimental results, the Vedral and Cuccaro adders have a critical path delay of 7.999 ns and 7.979 ns, respectively, and the total on-chip power consumption of 2.945 W. Conversely, the Approximate Toffoli Adder proposed has a low critical path delay of 7.261 ns, lower power consumption of 2.442 W and less hardware consumption with 18 logic cells than the current designs with 20 logic cells. Analysis of errors ensures that there is a minimal difference in the accuracy of the output. It is proven that approximate arithmetic offers a successful trade-off between precision, speed, and power efficiency to use in quantum-inspired computing.
The state of the art of quantum circuits using the ripple-carry strategy for the addition and comparison of two n-bit numbers is presented, as well as optimizations in the Clifford+ <?TeX T?> Math 1 gate set, both in terms of <?TeX CNOT?> Math 2 -depth and <?TeX T?> Math 3 -depth, or <?TeX CNOT?> Math 4 -count and <?TeX T?> Math 5 -count. In particular, we consider the adders presented by Cuccaro et al. and Takahashi et al., and exhibit an adder with a <?TeX T?> Math 6 -depth of 3n and a <?TeX CNOT?> Math 7 -depth of 8n, while without optimization of the original circuits, a <?TeX T?> Math 8 -depth of 6n is expected. Note that we have focused here on quantum ripple-carry adders using at most one ancilla, without any approximation of the 3-qubit gates involved (Toffoli, Peres and TR) or any strategy involving a measurement.
Abstract Quantum arithmetic circuits, such as adders and multipliers, are essential for many quantum algorithms, but their practical deployment on noisy intermediate-scale quantum (NISQ) devices remains challenging due to limited coherence times and high gate error rates. In this paper, we propose Qaradox, a configurable approximate quantum multiplier architecture that achieves higher computation accuracy than its exact counterpart under realistic quantum noise. The proposed architecture introduces a novel class of controlled quantum adders that enable flexible combinations of exact, approximate, and truncated operations, allowing the quantum circuit to be tailored to hardware-specific noise characteristics. Experimental results using IBM’s 127-qubit Brisbane noise model show that Qaradox reduces the error rate (ER), normalized mean error distance (NMED), and mean relative error distance (MRED) by up to 23.7%, 80.3%, and 88.1%, respectively, compared to the fully exact multiplier. Furthermore, when applied to image sharpening, the proposed architecture improves peak signal-to-noise ratio (PSNR) by more than three times and increases structural similarity index measure (SSIM) from 0.00 to 0.83, effectively recovering visual quality lost in exact designs. These results demonstrate that approximation, when applied structurally and selectively, can enhance both robustness and correctness in quantum arithmetic for NISQ-era systems.
With the rise of Noisy Intermediate-Scale Quantum (NISQ) computing, the selection of suitable adders becomes more crucial for optimizing quantum computations. The ripple carry adder (RCA) and carry lookahead adder (CLA) are fundamental quantum adder architectures, yet, their performance under NISQ environments remains to be largely unexplored. In this paper, we extensively compare the RCA and CLA designs through a systematic analysis in NISQ computing. Our results reveal that the proposed quantum RCA has a 29.7% lower error rate than the existing quantum CLA, highlighting the importance of simple exact quantum adder designs tailored for specific noisy quantum hardware constraints. These findings offer the crucial insights for designing efficient quantum algorithms and optimizing quantum circuits for practical NISQ systems.
Quantum addition is a vital building block for many quantum applications, yet exact adder architectures exhibit long carry paths and higher depth, increasing their exposure to quantum attacks. This paper presents a security driven evaluation of quantum approximate adders with carryout, having constant depth approximation and benchmarks them against two exact quantum adders. We evaluate resilience against four attack models: (1) Stuck-at∣0⟩/∣1⟩qubit attack, (2) State preparation attack, (3) Gate attack, and (4) Crosstalk attack in multi-tenant scenario. We use an emulator provided by Quantinuum that models its H1 ion trap-based 20-qubit quantum computer to conduct attacks. Our results indicate that approximate adders show higher resilience to noise, state preparation, gate, and crosstalk attacks, with AQA3 outperforming AQA4, which outperforms AQA5, due to increasing gate counts across zero, single CNOT layer, and one Toffoli gate respectively. Exact adders remain more robust against stuck-at∣0⟩/∣1⟩qubit attacks, as their carry propagation structure acts as an error absorbing mechanism, highlighting a security accuracy trade off for selecting adders in error-tolerant quantum applications.