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IEEE Annual Ubiquitous Computing, Electronics & Mobile Communication Conference (UEMCON)

A Novel Reversible Four Bit One’s Complement Quantum Gate (OCQG-4B)

Thomas F. Arciuolo, Muhammad Wasimuddin, Sushant Kumar Singh, Khaled M. Elleithy

Published Nov 1, 2018• 0 citations
Publisher

Abstract

The emerging field of Quantum Computing is still in its infancy stage. Much research has been done to develop application specific quantum gates for combinational and arithmetic logic. Still, there are shortcomings in this inventory of designs. In this paper, a Toffoli representation is provided for quantum implementation in both simulation as well as execution on an IBM quantum computer. Quantum metrics are provided for analysis of the proposed quantum gate design. The work presented here is an attempt to fill a single deficiency in this repertoire with the proposal of a Four Bit, One's Complement, Quantum Gate (OCQG-4B). This quantum gate design is both novel and reversible.

DOI
10.1109/uemcon.2018.8796690

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Reversible Logic has been an emerging topic of research for the last decade and has witnessed a substantial amount of work related to synthesis algorithms, optimization techniques and Boolean circuits. Considerable amount of reversible binary arithmetic designs have been proposed. 2's complement addition forms a fundamental arithmetic operation. This present communication proposes a novel reversible Two's Complement Gate (TCG) which can directly constitute a reversible adder/subtractor design. We provide the Toffoli representation of the gate for its plausible quantum realization. We also provide the quantum metric analysis for evaluation of our proposed gate. The proposed gate has also been implemented using Quantum-Dot Cellular Automata. Comparison with an existing proposal in literature has been done and the TCG gate has been observed to excel over the counterpart.
Abstract Reversible gates have been one of the emerging research areas in these days. The reversible gates have several applications in the fields of low power CMOS, DNA computing, optical, nanotechnology etc. Quantum computing is one of the fastest and upcoming nanotechnologies that can implement the digital logical circuits using reversible logic gates. In this paper, CNOT, TOFFOLI, FREDKIN and PERES reversible logic gates have been implemented on IBM quantum computer. An efficient one-bit full adder is going to be proposed using the reversible gates like CNOT and TOFFOLI. Later, a 4x4 multiplier will be developed using the proposed one-bit full adder. The proposed multiplier is proved to perform faster calculations compared to the earlier multipliers. The simulation of the presented modules will be done on IBM Quantum computer and the respective probabilities can be observed for different inputs.
Quantum is an emerging technology in future computers. Reversibility is the main advantage of quantum computers. In conventional computers, the computation is irreversible i.e. the input bits are lost once the logic block generates the output and input bits cannot be restored but it can be done in reversible computation because in reversible computation the inputs and outputs have a one-to-one correspondence. Therefore, a reversible gate input could even be uniquely determined from their output which leads to less power consumption. Hence the complexity of the digital circuits can be reduced by using reversible computing. In quantum computer to perform reversible operations, we need to implement the reversible gates using quantum gates. In this paper, we discussed various reversible logic gates like Feynman, Toffoli, R, Peres and TR gates using basic quantum gates like CNOT, Pauli, Swap gates and their implementation using IBM quantum experience.
Throughout the last decade, reversible logic has been an emerging research topic. Over the years, a considerable number of application specific new reversible gates with varied characteristics have been proposed. Barring few, most of the gates lack fundamental quantum mapping in contemporary literature. This paper takes into account the four variable reversible gates those have been proposed and provides the Toffoli mapping using positive control lines. The authors optimize the designs using negative control lines wherever possible. The quantum cost, quantum gate count and two-qubit gate count required to implement those reversible gates have been provided which will set a benchmark for optimized gate choice for complex Boolean realizations. The authors also provide Hamming Distance based Complexity analysis.
Quantum computing is an emerging computational paradigm that represents and processes information using quantum states. This paper presents the implementation and simulation of a Quantum Half Adder using the IBM Qiskit framework. The proposed circuit performs one-bit binary addition and produces two outputs, SUM and CARRY, through reversible quantum operations. Classical input values are encoded into quantum states using Pauli-X gates. Controlled-NOT (CNOT) gates are used to realize the XOR relationship required for SUM generation, while a Toffoli (CCNOT) gate realizes the AND relationship required for CARRY generation. The complete design is implemented in Python and executed using the Qiskit Aer Simulator. Four possible input combinations are evaluated and the measured outputs are compared with the expected Half Adder truth table. Circuit visualization, terminal output, and measurement histograms are used to verify the operation. The results show that the simulated circuit produces the expected SUM and CARRY values for all input combinations. The work provides a simple practical model for understanding reversible quantum computation, quantum gates, and Qiskit-based quantum circuit simulation.
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.