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.
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.
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.
This paper presents the design, optimization, and simulation of arithmetic circuits using reversible logic for quantum computing applications. The motivation behind this work is to achieve resource-efficient computation through reduced quantum cost, minimized garbage outputs, and lower ancilla requirements. The methodology involves implementing Half Adders, Full Adders, Multiplexers, and Ripple Carry Adders (RCAs) using Toffoli and Peres gates. The proposed 8-bit RCA achieves a quantum cost of 58 using 24 qubits, 8 garbage outputs, and 6 ancilla inputs—showing a significant improvement over conventional Toffoli-based designs that require higher quantum cost and resources. Simulations were conducted on IBM Qiskit and Google Colab using the Qiskit SDK to validate circuit correctness and scalability. The obtained results demonstrate superior resource efficiency and confirm the feasibility of reversible-logic-based quantum arithmetic as a foundation for scalable quantum arithmetic logic units (ALUs) and processors.
Addition is the most basic operation of computing based on a bit system. There are various addition algorithms considering multiple number systems and hardware, and studies for a more efficient addition are still ongoing. Quantum computing based on qubits as the information unit asks for the design of a new addition because it is, physically, wholly different from the existing frequency-based computing in which the minimum information unit is a bit. In this paper, we propose an efficient quantum circuit of modular addition, which reduces the number of gates and the depth. The proposed modular addition is for the Galois Field GF(2n−1), which is important as a finite field basis in various domains, such as cryptography. Its design principle was from the ripple carry addition (RCA) algorithm, which is the most widely used in existing computers. However, unlike conventional RCA, the storage of the final carry is not needed due to modifying existing diminished-1 modulo 2n−1 adders. Our proposed adder can produce modulo sum within the range 0,2n−2 by fewer qubits and less depth. For comparison, we analyzed the proposed quantum addition circuit over GF(2n−1) and the previous quantum modular addition circuit for the performance of the number of qubits, the number of gates, and the depth, and simulated it with IBM’s simulator ProjectQ.
Compared to classical computing implementations, reversible arithmetic adders offer a valuable platform for implementing quantum computation models in digital systems and specific applications, such as cryptography and natural language processing. Reversible logic efficiently prevents energy wastage through thermal dissipation. This study presents a comprehensive exploration introducing new carry-select adders (CSLA) based on quantum and reversible logic. Five reversible CSLA designs are proposed and compared, evaluating various criteria, including speed, quantum cost, and area, compared to previously published schemes. These comparative metrics are formulated for arbitrary n-bit size blocks. Each design type is described generically, capable of implementing carry-select adders of any size. As the best outcome, this study proposes an optimized reversible adder circuit that addresses quantum propagation delay, achieving an acceptable trade-off with quantum cost compared to its counterparts. This article reduces calculation delay by 66%, 73%, 82%, and 87% for 16, 32, 64, and 128 bits, respectively, while maintaining a lower quantum cost in all cases.
In this paper, we propose an efficient quantum carry-lookahead adder based on the higher radix structure. For the addition of two n-bit numbers, our adder uses [Formula: see text] qubits and [Formula: see text] T gates to get the correct answer in T-depth [Formula: see text], where r is the radix. Quantum carry-lookahead adder has already attracted some attention because of its low T-depth. Our work further reduces the overall cost by introducing a higher radix layer. By analyzing the performance in T-depth, T-count, and qubit count, it is shown that the proposed adder is superior to existing quantum carry-lookahead adders. Even compared to the Draper out-of-place adder which is very compact and efficient, our adder is still better in terms of T-count.
Quantum computing (Q-computing) is a revolutionary technology that applies quantum mechanics (QM) to implement calculations significantly quicker than traditional computers. Q-computing employs Q-bits (qubits) rather than classical bits, which can take on a superposition state, making it possible to represent both 0 and 1 at once. This distinctive property allows qubits to perform multiple calculations simultaneously, making Q computers exponentially more powerful as more qubits are added, compared to the linear scaling of classical computers. However, challenges such as qubit instability and error rates remain significant obstacles to fully realizing this potential. A vital aspect of this technology is the development of Q arithmetic circuits, which act as the foundational blocks for efficiently executing Q algorithms. Q half-adder and full-adder circuits are integral to performing fundamental arithmetic operations within Q computers. In contrast to classical adders, Q adders rely on Q gates such as Controlled NOT (CNOT) and Toffoli gates. These gates exploit Q phenomena like entanglement and superposition, allowing for more efficient computations. The Q half-adder consists of two qubits and adds two single bits, producing a carry and sum output. It utilizes the CNOT gate to compute the sum and the Toffoli gate (controlled-controlled-NOT [CCNOT]) to compute the carry. The Q full-adder builds on this, adding three qubits to produce a sum and a carry output, further increasing computational capacity. Through the entanglement of qubits, these circuits allow for more parallelism and speed compared to classical adders. Q carry-look-ahead adders (QCLAs) and Q ripple-carry adders (QRCAs) are used to perform more complex arithmetic operations based on these half-adder and full-adder structures. Q arithmetic circuits have broad applications, boosting secure key generation in cryptography, speeding up matrix operations for faster model training in machine learning, and enabling more precise, efficient image transformations in Q image processing, benefiting fields like medical imaging and computer vision.