Application of quantum computing for cost reduction technology using reversible logic synthesis

Dipal Shah, Marek A. Perkowski

Reversible logic has many applications such as Quantum computing, low power CMOS circuit design, Optical computing. Hence reversible logic synthesis has attracted attention especially in quantum computing community. A logic function is reversible if it is a one-to-one mapping between input and output vectors. In this paper we present a new approach to synthesis of reversible circuits using Kronecker Functional Lattice Diagrams. Unlike other contemporary algorithms for synthesis of reversible function that use n × n Toffoli gates, our method invariably synthesizes functions using only 3×3 Toffoli gates, Feynman gates and NOT gates. This reduces the quantum cost. Our method adds small cost by adding extra ancilla bits. Moreover, our circuits are always (4-neighbors) regular, which is an asset when they are mapped to 2-Dimensional arrays in Ion Trap (quantum) technology.

Saleem Mohammed Ridha Taha

N. Vidhya, V. Seethalakshmi, A Arul +2 more

Shaveta Thakral, Dipali Bansal

Heuristic algorithms play a significant role in synthesize and optimization of digital circuits based on reversible logic yet suffer with multiple disadvantages for multiqubit functions like scalability, run time and memory space. Synthesis of reversible logic circuit ends up with trade off between number of gates, quantum cost, ancillary inputs and garbage outputs. Research on optimization of quantum cost seems intractable. Therefore post synthesis optimization needs to be done for reduction of quantum cost. Many researchers have proposed exact synthesis approaches in reversible logic but focussed on reduction of number of gates yet quantum cost remains undefined. The main goal of this paper is to propose improved Ant Colony Optimization (ACO) algorithm for quantum cost reduction. The research efforts reported in this paper represent a significant contribution towards synthesis and optimization of high complexity reversible function via swarm intelligence based approach. The improved ACO algorithm provides low quantum cost based toffoli synthesis of reversible logic function without long computation overhead.

Anupam Chattopadhyay, Pal, Nilanjan, Soumajit Majumder

Emerging technologies with asymptotic zero power dissipation, such as quantum computing, require the logical operations to be done in a reversible manner. In recent years, the problem of synthesizing Boolean functions in the reversible logic domain has gained significant research attention. The efficiency of the synthesis methods is measured in terms of quantum cost, gate cost, garbage lines, logic depth and speed of synthesis. In this paper, we present an approach based on Exclusive sum-of-Products (ESOP), which allows the user to explore the trade-off between quantum cost and garbage lines. The proposed technique adds a new dimension to the reversible logic synthesis solutions. We demonstrate by detailed experiments that controlled improvement in quantum cost and gate count by increasing garbage count can be achieved. In some cases, improved quantum cost and gate count compared to state-of-the-art synthesis methods are reported. Furthermore, we propose a novel rule-based approach to achieve ancilla-free reversible logic synthesis starting from an ESOP formulation.

Anirban Basak, Arindam Sadhu, Kunal Das +1 more