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.
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 crucial operation for the implementation of quantum algorithms. For this reason, many researchers focused their attention on the design of quantum adders. The two main schemes for adders are the Ripple Carry Adder (RCA), which is considered slow because its execution time depends on the length of the operands, and the Carry Look-ahead Adder, which can reduce the execution time anticipating the computation of the carry, but is more complex and expensive in terms of quantum cost. A good alternative to the slow ripple carry adder and the complex carry-lookahead adder is represented by the Carry Select Adder (CSA), which divides the addition execution into subgroups of qubits and exploits the simplicity of the RCA. In this work, we propose a new quantum version of the CSA, based on an efficient realization of the RCA, chosen among the possible RCAs proposed in the literature. To this end, we show how to design the quantum CSA blocks and how to concatenate them to produce the result. The proposed quantum CSA has been simulated on the DDSIM tool of Munich Quantum Toolkit (MQT) to check its correctness, and the performance has been analyzed using the three conventional parameters for quantum circuits: number of qubits, quantum cost and delay. For each of these parameters, a formula is given as a function of the size of the operand length and the number of blocks in the quantum CSA. The CSA proposed shows a speedup variable from 2.5 to 6 for operands up to 64 qubits and a block size that goes from 2 to n/2.
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.
Progress in quantum hardware design is progressing toward machines of sufficient size to begin realizing quantum algorithms in disciplines such as encryption and physics. Quantum circuits for addition are crucial to realize many quantum algorithms on these machines. Ideally, quantum circuits based on fault-tolerant gates and error-correcting codes should be used as they tolerant environmental noise. However, current machines called Noisy Intermediate Scale Quantum (NISQ) machines cannot support the overhead associated with faulttolerant design. In response, low depth circuits such as quantum carry lookahead adders (QCLA)s have caught the attention of researchers. The risk for noise errors and decoherence increase as the number of gate layers (or depth) in the circuit increases. This work presents an out-of-place QCLA based on Clifford+T gates. The QCLAs optimized for T gate count and make use of a novel uncomputation gate to save T gates. We base our QCLAs on Clifford+T gates because they can eventually be made faulttolerant with error-correcting codes once quantum hardware that can support fault-tolerant designs becomes available. We focus on T gate cost as the T gate is significantly more costly to make faulttolerant than the other Clifford+T gates. The proposed QCLAs are compared and shown to be superior to existing works in terms of T-count and therefore the total number of quantum gates. Finally, we illustrate the application of the proposed QCLAs in quantum image processing by presenting quantum circuits for bilinear interpolation.
Progress in quantum hardware design is progressing toward machines of sufficient size to begin realizing quantum algorithms in disciplines such as encryption and physics. Quantum circuits for addition are crucial to realize many quantum algorithms on these machines. Ideally, quantum circuits based on fault-tolerant gates and error-correcting codes should be used as they tolerant environmental noise. However, current machines called Noisy Intermediate Scale Quantum (NISQ) machines cannot support the overhead associated with fault-tolerant design. In response, low depth circuits such as quantum carry lookahead adders (QCLA)s have caught the attention of researchers. The risk for noise errors and decoherence increase as the number of gate layers (or depth) in the circuit increases. This work presents an out-of-place QCLA based on Clifford+T gates. The QCLAs optimized for T gate count and make use of a novel uncomputation gate to save T gates. We base our QCLAs on Clifford+T gates because they can eventually be made fault-tolerant with error-correcting codes once quantum hardware that can support fault-tolerant designs becomes available. We focus on T gate cost as the T gate is significantly more costly to make fault-tolerant than the other Clifford+T gates. The proposed QCLAs are compared and shown to be superior to existing works in terms of T-count and therefore the total number of quantum gates. Finally, we illustrate the application of the proposed QCLAs in quantum image processing by presenting quantum circuits for bilinear interpolation.
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.
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.