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International Journal of Electronics

Computational analysis and comparison of reversible gates for design and test of logic circuits

Hari Mohan Gaur, Ashutosh Kumar Singh, Anand Mohan, Dhiraj K. Pradhan

Published Apr 18, 2019• 16 citations
Publisher

Abstract

Quantum computing is one of the most significant anticipation towards the accomplishment of interminable consumer demands of small, high speed, and low-power operable electronics devices. As reversible logic circuits have direct applicability to quantum circuits, design and synthesis of these circuits are finding grounds for emerging nano-technologies of quantum computing. Multiple Controlled Toffoli (MCT) and Multiple Controlled Fredkin (MCF) are the fundamental reversible gates that playing key role in this phase of development. A number of special reversible gates have also been presented so far, which were claimed superior for providing certain purposes like logic development and testing. This paper critically analyses a range of these gates to procure an optimal solution for design, synthesis and testing of reversible circuits. The experimentation is facilitated at three subsequent levels, i.e. gates properties, quantum cost and design & testability. MCT and MCF gates are found up to 50% more cost-effective than special gates at design level and 34.4% at testability level. Maximum reversibility depth (MRD) is included as a new measurement parameter for comparison. Special gates exhibit MRD up to 7 which ideally should be 1 for a system to be physically reversible as that of MCT and MCF gates.

DOI
10.1080/00207217.2019.1608587

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Quantum computing is one of the most significant anticipation towards the accomplishment of interminable consumer demands of small, high speed, and low-power operable electronics devices. As reversible logic circuits have direct applicability to quantum circuits, design and synthesis of these circuits are finding grounds for emerging nano-technologies of quantum computing. Multiple Controlled Toffoli (MCT) and Multiple Controlled Fredkin (MCF) are the fundamental reversible gates that playing key role in this phase of development. A number of special reversible gates have also been presented so far, which were claimed superior for providing certain purposes like logic development and testing. This paper critically analyses a range of these gates to procure an optimal solution for design, synthesis and testing of reversible circuits. The experimentation is facilitated at three subsequent levels, i.e. gates properties, quantum cost and design & testability. MCT and MCF gates are found up to 50% more cost-effective than special gates at design level and 34.4% at testability level. Maximum reversibility depth (MRD) is included as a new measurement parameter for comparison. Special gates exhibit MRD up to 7 which ideally should be 1 for a system to be physically reversible as that of MCT and MCF gates.
Reversible logic is expanding grounds with its applicability to various upcoming technologies and quantum computation. Numerous reversible gates has also been proposed for designing logic circuits apart of basic quantum controlled Toffoli and Fredkin gates. A comparative study and analysis of a range of reversible gates from the literature is presented in this paper to obtain an optimal solution for designing these circuits. The gates are synthesized and implemented to obtain equivalent quantum circuits and operating cost in terms of number of inputs, gate cost, quantum cost, garbage output and ancilla input. The comparison is done at two subsequent levels i.e. gates structural level and circuit design level, providing a better solution for designing logic circuits. It is calculated that, basic gates are 50% efficient at gate level and 33% at design level analysis in terms of gate cost, as compared to the most efficient gates proposed in the literature.
Quantum cost is the most important criteria to evaluate reversible and quantum circuits. Also the fundamental building blocks of reversible and quantum circuits are Multiple-Control Toffoli (MCT) gates. The synthesis of MCT based reversible circuits are usually conducted into two steps. First, MCT circuits are decomposed into quantum circuits and then they are optimized using various techniques such as template matching, moving rules to reduce the quantum cost of reversible circuits. In this paper, we propose new techniques to decompose the Toffoli gates, in which MCT based circuits are mapped into a corresponding quantum realization. The main improvement is that the resulting quantum realization of MCT based circuits makes significantly better realization than those achieved in the earlier approaches and further reduction is possible using some other optimization techniques. Experimental results show that our new techniques enable to get sub-optimal realization of the MCT based reversible circuits in decomposition stage and quantum cost reduction of the reversible circuits is achieved by using that sub-optimal realization.
Quantum computing is the latest computing concept that can substantially reduce the computational burden of some difficult NP problems. Boolean reversible logic is frequently used as a key component in many quantum algorithms. This study proposes an approach based on a mixed integer programming model for reversible circuit synthesis. The proposed optimization model maps a given reversible function into a multiple-control Toffoli (MCT) circuit with minimum quantum costs. Our model exploits the relationship between MCT gate patterns and the operations on qubit states. We also report our experience in computational experiments on the circuit synthesis of reversible benchmark problems.
As quantum technology advances, the efficient design of quantum circuits has become an important area of research. This paper provides an introduction to the MCT quantum circuit design problem for reversible Boolean functions with the necessary background in quantum computing to comprehend the problem. While this is a well-studied problem, optimization models that minimize the true objective have only been explored recently. This paper introduces a new optimization model and symmetry-breaking constraints that improve solving time by up to two orders of magnitude compared to earlier work when a Constraint Programming solver is used. Experiments with up to seven qubits and using up to 15 quantum gates result in several new best-known circuits, obtained by any method, for well-known benchmarks. Several in-depth analyses are presented to validate the effectiveness of the symmetry-breaking constraints from multiple perspectives. Finally, an extensive comparison with other approaches shows that optimization models may require more time but can provide superior circuits with optimality guarantees.
Abstract As quantum technology advances, the efficient design of quantum circuits has become an important area of research. This paper provides an introduction to the MCT quantum circuit design problem for reversible Boolean functions with the necessary background in quantum computing to comprehend the problem. While this is a well-studied problem, optimization models that minimize the true objective have only been explored recently. This paper introduces a new optimization model and symmetry-breaking constraints that improve solving time by up to two orders of magnitude compared to earlier work when a Constraint Programming solver is used. Experiments with up to seven qubits and using up to 15 quantum gates result in several new best-known circuits, obtained by any method, for well-known benchmarks. Several in-depth analyses are presented to validate the effectiveness of the symmetry-breaking constraints from multiple perspectives. Finally, an extensive comparison with other approaches shows that optimization models may require more time but can provide superior circuits with optimality guarantees.
Reversible logic, also known as information lossless logic, is a promising technology that allows embedded data within circuits to be retrieved in case of failure.This study explores the use of reversible gates, such as Feynman gates, Toffoli gates, Fredkin gates, Peres gates, Double Feynman gates, NFT gates, DKG gates, and DFT gates, to construct logic circuits.These reversible logic gates can be effectively used for the implementation of any higher logic circuits-based applications.In the proposed paper the Arithmetic logic unit based on reversible logic hates is implemented in Verilog as well as IBM quantum software.The major applications of reversible logic gates include quantum computing, low power circuits, nano and CMOS technologies, photonics.In the last part of the paper the circuits implemented using Verilog and IBM quantum a chip level design using Cadance layout is implemented.