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.
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.
One of the elementary operations in computing systems is multiplication. Therefore, high-speed and low-power multipliers design is mandatory for efficient computing systems. In designing low-energy dissipation circuits, reversible logic is more efficient than irreversible logic circuits but at the cost of higher complexity. This paper introduces an efficient signed/unsigned 4 × 4 reversible Vedic multiplier with minimum quantum cost. The Vedic multiplier is considered fast as it generates all partial product and their sum in one step. This paper proposes two reversible Vedic multipliers with optimized quantum cost and garbage output. First, the unsigned Vedic multiplier is designed based on the Urdhava Tiryakbhyam (UT) Sutra. This multiplier consists of bitwise multiplication and adder compressors. Compared with Vedic multipliers in the literature, the proposed design has a quantum cost of 111 with a reduction of 94% compared to the previous design. It has a garbage output of 30 with optimization of the best-compared design. Second, the proposed unsigned multiplier is expanded to allow the multiplication of signed numbers as well as unsigned numbers. Two signed Vedic multipliers are presented with the aim of obtaining more optimization in performance parameters. DesignI has separate binary two’s complement (B2C) and MUX circuits, while DesignII combines binary two’s complement and MUX circuits in one circuit. DesignI shows the lowest quantum cost, 231, regarding state-of-the-art. DesignII has a quantum cost of 199, reducing to 86.14% of DesignI. The functionality of the proposed multiplier is simulated and verified using XILINX ISE 14.2.
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.
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.
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 ternary circuit design is now being taken into consideration for its application within the quantum computer and other technologies associated with the nanotechnology domain, in addition to the advantages of the ternary logic application as opposed to binary logic. Multiplier circuit is one of the most important computing circuit in the ALU. Therefore, the circuit optimization for the multiplication will lead to efficient processor. In this paper, the reversible circuit for multiplication of two unsigned two-digit ternary numbers has been proposed. To construct reversible ternary multiplier, a new component termed TPPG with the quantum cost of 13 for partial product generation was proposed. In addition, we have introduced four new blocks of reversible ternary adder with the quantum cost of 11, 10, 7, 5 and one constant input, which can be used in the proposed multiplier circuit. We attempted to optimize the design of the circuits in terms of quantum cost, a number of primitive gates, constant inputs, and garbage outputs as far as possible. To realize all proposed circuits, one-qutrit shift gates and two-qutrit Muthukrishnan-Stroud gates were used.