In quantum computing, quantum multiplier circuits serve as fundamental building blocks for a wide range of algorithms. Although numerous exact quantum multiplier designs have been presented so far, their practical implementation remains limited, as today's quantum computers are still in the noisy intermediate-scale quantum (NISQ) era, lacking full fault tolerance. This paper presents a comparative analysis of errors characteristics in exact quantum multiplier circuits under NISQ conditions. Our experimental results demonstrate that, under identical noise conditions, error rate (ER), normalized mean error distance (NMED), and mean relative error distance (MRED) vary by up to 1.95×, 4.40×, and 6.53×, respectively, across different multipliers. Furthermore, each multiplier exhibits distinct sensitivity patterns depending on the type of noise.
In quantum computing, quantum multiplier circuits serve as fundamental building blocks for a wide range of algorithms. Although numerous exact quantum multiplier designs have been presented so far, their practical implementation remains limited, as today's quantum computers are still in the noisy intermediate-scale quantum (NISQ) era, lacking full fault tolerance. This paper presents a comparative analysis of errors characteristics in exact quantum multiplier circuits under NISQ conditions. Our experimental results demonstrate that, under identical noise conditions, error rate (ER), normalized mean error distance (NMED), and mean relative error distance (MRED) vary by up to 1.95×, 4.40×, and 6.53×, respectively, across different multipliers. Furthermore, each multiplier exhibits distinct sensitivity patterns depending on the type of noise.
Since the advent of quantum computing, the accuracy performance of quantum adders in Noisy Intermediate-Scale Quantum (NISQ) computing has received significant attention. This paper analyzes the accuracy of exact quantum adders in the NISQ environment. Our results show the impacts of noise vary significantly on the quantum circuits, reaching up to 86%, 0.23, and 0.66 in error rate (ER), normalized mean error distance (NMED), and mean relative error distance (MRED), respectively. Furthermore, the bitflip noise model impacts the greatest on quantum adders, showing, on average, 12.20, 11.30, and 11.62 times higher values in ER, NMED, and MRED, respectively. These findings highlight that the accuracy of exact quantum adders is affected by NISQ computing.
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.
Quantum devices in the noisy intermediate-scale quantum (NISQ) era are highly susceptible to different types of quantum noise, which directly impact the reliability of experimental results. This work provides a characterization of error behavior arising from quantum noises on IBM's superconducting quantum processor, offering practical insights for algorithm design, benchmarking, and error-mitigation strategies on a real superconducting quantum processor in the NISQ era. The study begins with the measurement of the basis state, without applying any gate, to quantify state-preparation and measurement (SPAM) errors. Additionally, the errors are further quantified due to the application of single-qubit Pauli-X, two-qubit CNOT gate and other multi-qubit Controlled-X gates. Each circuit was executed with 1024 shots, and the percentage error between the expected and observed outputs was computed. The results show that the single-qubit Pauli-X gate exhibits relatively low errors in comparison with the two-qubit CNOT gate, whereas other multi-qubit Controlled-X gates lead to significantly higher deviations. This work also analyzes the noise effect of a fourqubit Controlled-X gate being implemented using a three-qubit Controlled-X gate with an extra auxiliary qubit, and the result shows a significant reduction in the error rate.
Quantum systems operate using quantum bits (qubits), which are highly sensitive to external noises and disturbances and they are easily prone to errors. In the Noisy Intermediate-Scale Quantum (NISQ) era, these errors make difficult to build reliable, fault tolerant quantum circuits for real world deployment. This work provides an overview of need for Quantum Error Correction (QEC) in NISQ devices, as qubits commonly get affected by bit-flip, phase-flip, and combined errors that degrades system performance and examines Quantum Error Correction Code (QECC) techniques usage in communication, computation, and quantum multimedia applications such as image and video transmission. In addition, a simple three-qubit repetition circuit is introduced to demonstrate an error-mitigation approach. These findings, also show how QEC improves fidelity, reduces logical errors, and improves noise tolerance. The analysis also identifies challenges and outlines the future research direction aimed at achieving efficient and scalable fault tolerant quantum circuits.
Quantum systems operate using quantum bits (qubits), which are highly sensitive to external noises and disturbances and they are easily prone to errors. In the Noisy Intermediate-Scale Quantum (NISQ) era, these errors make difficult to build reliable, fault tolerant quantum circuits for real world deployment. This work provides an overview of need for Quantum Error Correction (QEC) in NISQ devices, as qubits commonly get affected by bit-flip, phase-flip, and combined errors that degrades system performance and examines Quantum Error Correction Code (QECC) techniques usage in communication, computation, and quantum multimedia applications such as image and video transmission. In addition, a simple three-qubit repetition circuit is introduced to demonstrate an error-mitigation approach. These findings, also show how QEC improves fidelity, reduces logical errors, and improves noise tolerance. The analysis also identifies challenges and outlines the future research direction aimed at achieving efficient and scalable fault tolerant quantum circuits.
Recent developments in quantum computers have been pushing up the number of qubits. However, the state-of-the-art Noisy Intermediate Scale Quantum (NISQ) computers still do not have enough qubits to accommodate the error correction circuit. Noise in quantum gates limits the reliability of quantum circuits. To characterize the noise effects, prior methods such as process tomography, gateset tomography and randomized benchmarking have been proposed. However, the challenge is that these methods do not scale well with the number of qubits. Noise models based on the understanding of underneath physics have also been proposed to study different kinds of noise in quantum computers. The difficulty is that there is no widely accepted noise model that incorporates all different kinds of errors. The realworld errors can be very complicated and it remains an active area of research to produce accurate noise models. In this paper, instead of using noise models to estimate the reliability, which is measured with success rates or inference strength, we treat the NISQ quantum computer as a black box. We use several quantum circuit characteristics such as the number of qubits, circuit depth, the number of CNOT gates, and the connection topology of the quantum computer as inputs to the black box and derive a reliability estimation model using (1) polynomial fitting and (2) a shallow neural network. We propose randomized benchmarks with random numbers of qubits and basic gates to generate a large data set for neural network training. We show that the estimated reliability from our black-box model outperforms the noise models from Qiskit. We also showcase that our black-box model can be used to guide quantum circuit optimization at compile time.