Abstract Reversible logic is used increasingly to design digital circuits with lower power consumption. The parity preserving (PP) property contributes to detect permanent and transient faults in reversible circuits by comparing the input and output parity. Multiplication is also considered one of the primary operations in both digital and analog circuits due to its wide applications in digital signal processing and computer arithmetic operations. Accordingly, Vedic mathematics, as a set of techniques sutras, has become popular and is extensively used to solve mathematical problems more efficiently and faster. This work proposes three PP reversible blocks, N1, N2, and N3, which are used to develop a novel effective 2‐bit PP reversible Vedic multiplier and 4‐bit ripples carry adders (RCAs). Moreover, 2‐bit Vedic multiplier and RCA are used to develop the 4‐bit PP reversible Vedic multiplier. The proposed designs outperform the most relevant state‐of‐the‐art structures in terms of garbage output (GO), constant input (CI), gate count (GC), and quantum cost (QC). Average savings of 22.37%, 35.44%, 35.44%, and 34.76%, and 17.76%, 26.60%, 24.52%, and 27.27% respectively, are observed for two‐bit and four‐bit PP reversible Vedic multipliers in terms of QC, GO, CI and GC as compared to previous works.
Abstract Reversible logic is used increasingly to design digital circuits with lower power consumption. The parity preserving (PP) property contributes to detect permanent and transient faults in reversible circuits by comparing the input and output parity. Multiplication is also considered one of the primary operations in both digital and analog circuits due to its wide applications in digital signal processing and computer arithmetic operations. Accordingly, Vedic mathematics, as a set of techniques sutras, has become popular and is extensively used to solve mathematical problems more efficiently and faster. This work proposes three PP reversible blocks, N1, N2, and N3, which are used to develop a novel effective 2‐bit PP reversible Vedic multiplier and 4‐bit ripples carry adders (RCAs). Moreover, 2‐bit Vedic multiplier and RCA are used to develop the 4‐bit PP reversible Vedic multiplier. The proposed designs outperform the most relevant state‐of‐the‐art structures in terms of garbage output (GO), constant input (CI), gate count (GC), and quantum cost (QC). Average savings of 22.37%, 35.44%, 35.44%, and 34.76%, and 17.76%, 26.60%, 24.52%, and 27.27% respectively, are observed for two‐bit and four‐bit PP reversible Vedic multipliers in terms of QC, GO, CI and GC as compared to previous works.
Abstract Quantum computing has attracted increased attention in recent years owing to substantial advancements in quantum algorithms and system architecture. Quantum algorithms are implemented using quantum circuits. These circuits include an intrinsic reversibility and often have a substantial Boolean component that requires synthesis. A crucial characteristic of reversible circuits is the preservation of parity. Parity-preserving logic is a category that maintains the parity of both inputs and outputs, facilitating the detection of permanent and transient errors. Multiplier circuits are essential components in digital computing systems, playing a crucial role in the development of various hardware, including arithmetic circuits. This paper first introduces a novel block based on a transformationbased synthesis technique from the elementary quantum gates. Then it proposes a distinctive 2×2 parity-preserving reversible quantum Vedic multiplier based on the recommended block and prior gates. In addition, further designs of Vedic multipliers are provided, encompassing 4-bit, 8-bit, and 16-bit configurations. We illustrate that our design brings superior outcomes regarding quantum cost (QC), constant inputs (CI) count, CNOT-V/V + count, garbage outputs (GO) count, and gate count (GC) in comparison to earlier designs. This study achieves an average decrease of 23.09%, 37.51%, 37.51%, 54.89%, and 19.38% in QC, CI, GO, GC, and CNOT-V/V + count, respectively. Furthermore, all suggested circuits undergo appraisal and validation within the IBM quantum laboratory.
Quantum computers provide considerable potential to enhance computing technology, anticipated to surpass conventional computers by resolving intricate challenges that existing systems cannot tackle. They use quantum algorithms for improved performance and depend on reversible computations based on quantum physics and linear algebra. In contrast to traditional computing, which may include irreversible processes, quantum computing relies on unitary operations that are fundamentally reversible. The parity-preserving feature enables the identification of both permanent and transient defects within circuits. The parity-preserving feature ensures that the input and output states are equal in reversible circuits. Vedic multipliers offer a crucial foundation in the design and implementation of digital circuits, recognized for their speed, efficiency, ease of calculations, reduction of errors, and broad applicability. Prior investigations of quantum Vedic multipliers have faced obstacles like elevated Quantum Cost (QC), substantial Garbage Output (GO), Constant Input (CI), augmented Gate Count (GC), and CNOT-V/V+ count, resulting in more resource use and implementation intricacy. These inefficiencies hinder the scalability and feasibility of quantum multipliers in high-performance computing applications. A proposed solution to these issues is to introduce a cost-effective, parity-preserving reversible quantum block synthesized through an established method that produces a network list of multi-controlled Toffoli (MCT) gates. This Toffoli-based network is then optimized using various techniques, ultimately transforming it into a network of fundamental quantum gates. This approach decreases quantum expenses, eliminates unnecessary outputs, and enhances quantum gate efficiency. Integrating this innovative technique into the reversible quantum Vedic multipliers offers a more efficient, cost-effective, and scalable solution than current approaches. All proposed designs, such as a half adder-subtractor, a ripple carry adder (RCA), and two-bit and four-bit Vedic multipliers, are suggested based on functional blocks and pre-existing components. The suggested structures undergo evaluation in comparison to existing state-of-the-art procedures, demonstrating their cost-effectiveness. The observed average savings for two-bit and four-bit Vedic multipliers, with respect to QC, number of CNOT-V/V+ count, GO, CI, and GC, are 20.01%, 19.38%, 37.51%, 37.51%, and 54.89%, and 22.71%, 18.78%, 27.23%, 31.10%, and 42.38%, respectively when compared to previous studies. Furthermore, all suggested circuits are evaluated and confirmed using the IBM quantum laboratory.
Reversible logic, by enabling computations without loss of information, offers a promising approach to significantly reducing energy dissipation, making it a key technology for low-power and quantum computing systems. Parity-preserving reversible circuits further enhance reliability, enabling fault detection in nanoscale systems. Multiplication, a fundamental operation in computing and signal processing, benefits significantly from efficient reversible designs. However, existing reversible Vedic multipliers often suffer from excessive Quantum Cost (QC), Garbage Outputs (GO), and Constant Inputs (CI). This paper proposes two new 2-bit parity-preserving reversible quantum Vedic multipliers, serving as the foundational block for scalable n-bit multipliers, that are enhanced to reduce quantum metrics without compromising performance. The proposed circuits are simulated using the Quirk tool to test their correct functionality. Comparative analysis shows that the best proposed design outperforms existing architectures on average by 34%, 53%, and 9% in constant inputs, garbage outputs, and quantum cost, respectively, providing a fault-tolerant, cost-efficient, and scalable solution for next-generation quantum computing systems.
In recent years, there has been an increasing tendency towards designing circuits based on reversible logic, and has received much attention because of preventing internal power dissipation. In digital computing systems, multiplier circuits are one of the most fundamental and practical circuits used in the development of a wide range of hardware such as arithmetic circuits and Arithmetic Logic Unit (ALU). Vedic multiplier, which is based on Urdhva Tiryakbhayam (UT) algorithm, has many applications in circuit designing because of its high speed in performing multiplication compared to other multipliers. In Vedic multipliers, partial products are obtained through vertical and cross multiplication. In this paper, we propose four [Formula: see text] reversible Vedic multiplier blocks and use each one of them in its right place. Then, we propose a [Formula: see text] reversible Vedic multiplier using the four aforementioned multipliers. We prove that our design leads to better results in terms of quantum cost, number of constant inputs and number of garbage outputs, compared to the previous ones. We also expand our proposed design to [Formula: see text] multipliers which enable us to develop our proposed design in every dimension. Moreover, we propose a formula in order to calculate the quantum cost of our proposed [Formula: see text] reversible Vedic multiplier, which allows us to calculate the quantum cost even before designing the multiplier.
Arithmetic units constitute fundamental components of reversible-computing architectures, where circuit complexity, resource utilization, and hardware realizability are critical design considerations. This work presents a parity-preserving reversible 2 × 2 Vedic multiplier architecture constructed using existing N1, RF, A, and N3 reversible logic blocks and hierarchically extended to realize a 4 × 4 multiplier through a parity-preserving 4-bit ripple-carry adder structure. Comparative evaluation demonstrates competitive performance relative to representative reversible multiplier architectures. To evaluate implementation-oriented characteristics, the proposed architecture was mapped to the Clifford+T gate set and analyzed using hardware-aware resource metrics. The resulting realization exhibits a T-count of 35, a T-depth of 19, and a transpiled circuit depth of 55 without requiring SWAP operations. The proposed 2 × 2 multiplier core was experimentally validated on the IBM Quantum ibm_kingston superconducting processor based on the Heron r2 architecture through complete truth-table verification across all sixteen input combinations using 1024 measurement shots per experiment. The dominant measured output matched the expected multiplication result in every case, yielding an average success probability of 70.12% and an average Bhattacharyya fidelity of 0.7012. Calibration-based fidelity estimation using backend-reported gate fidelities yielded an estimated circuit fidelity of 0.7485, which is consistent with the experimentally observed average success probability of 70.12%. Hardware-aware circuit characterization, noise-model evaluation, and fidelity analysis were performed to assess implementation behavior under practical execution conditions. In addition, application-level arithmetic demonstrations involving Low-bit-width image-processing arithmetic examples were used solely as application-level demonstrations of multiplier functionality and do not constitute a complete quantum image-processing framework. The obtained results confirm the functional correctness, hardware compatibility, and resource efficiency of the proposed architecture and provide practical insights for future reversible arithmetic and quantum-computing applications.
One kind of logic architecture, known as reversible logic, maps the output and input vectors one-to-one. According to the Landauer’s principle from 1961, if a device is irreversible in its characteristics, then deleting a small amount will cause the release of heat energy of the order of kTln2 joules. Here, T represents the absolute temperature of the environment, and k is referred to as the Boltzmann constant. Quantum logic gates, which each carry out a fundamental unitary operation on 1, 2, or more qubits–two-state quantum systems–can be conceived of as the building blocks of a quantum computer, or as kinfolk’s networks of quantum. Quantum networks need the use of reversible logic components. The multiplication procedure in this study makes use of KMD gates. The KMD gate can be used to create a variety of logic circuits, including AND, half adder, and full adder. The criteria for reversibility, fault tolerance, and universality are satisfied by these gates. This research presents the design and simulation of a unique reversible fault-tolerant Wallace multiplier, Baugh-Wooley multiplier, Vedic multiplier, and minimal complexity multiplier. The above multipliers are designed to obtain the addition and product terms with the least amount of delay and optimal slice utilization for sustainable technology. The complete design of the fundamental reversible logic gates was confirmed using the QCADesigner software version 2.0.3. The current designs of several multipliers are compared in this paper based on a number of parameters, such as garbage output (GO), gate count (GC), quantum cost (QC), area, and constant input (CI). The simulation results show improvements in area, delay, CIs, GO, QC, and GC over currently available architectures.