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Trends in logic

From Quantum Circuits to Quantum Computational Logics

María Luisa Dalla Chiara, Roberto Giuntini, Roberto Leporini, Giuseppe Sergioli

Published Jan 1, 2018• 0 citations
Publisher
DOI
10.1007/978-3-030-04471-8_4

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Reversible logic is emerging as a promising computing paradigm with applications in ultralow power nanocomputing and emerging nanotechnologies such as quantum computing, quantum dot cellular automata (QCA), optical computing, etc. Reversible circuits are similar to conventional logic circuits except that they are built from reversible gates. In reversible gates, there is a unique, one-to-one mapping between the inputs and outputs, not the case with conventional logic. One of the primary motivations for adopting reversible logic lies in the fact that it can provide a logic design methodology for designing ultra-low power circuits beyond KTln2 limit for those emerging nanotechnologies in which the energy dissipated due to information destruction will be a significant factor of the overall heat dissipation. Further, logic circuits for quantum computers must be built from reversible logic components. Several important metrics need to be considered in the design of reversible circuits the importance of which needs to be discussed. Quantum computers of many qubits are extremely difficult to realize thus the number of qubits in the quantum circuits needs to be minimized. This sets the major objective of optimizing the number of ancilla inputs and the number of the garbage outputs in the reversible logic based quantum circuits. The constant input in the reversible quantum circuit is called the ancilla input, while the garbage output refers to the output which exists in the circuit just to maintain one-to-one mapping but is not a primary or a useful output. The reversible circuit has other important parameters of quantum cost and delay which need to be optimized.
Abstract-Quantum theory of computation establishes that there are problems for which quantum algorithms are far more efficient than their classical counterpart. Advances in quantum computing have initiated the design of systems based on quantum logic gates. Quantum computer hardware being primarily available in research laboratories at present, it mandates the ability to design, develop and test quantum logic operations by simulation of quantum logic circuits on classical computers. In this paper, we have defined a programming model for the design of a quantum circuit simulator, which can simulate a given quantum circuit obeying the rules of quantum gate operations. The quantum gate operations on both pure and superposed quantum states are being done with the help of effective data structures. The proposed quantum circuit simulator also incorporates the simulation of quantum circuit error under the action of certain quantum faults.
Algorithms specifically designed for quantum computers have been developed. In quantum circuits, the Feynman, Toffoli, and Fredkin gates are employed instead of traditional inputs such as AND, OR, NAND, NOR, XOR, and XNOR in combinational logic gates. The ability to convert quantum circuits into combinational logic circuits, or vice versa, is of utmost importance. This essay study (or paper) aims to demonstrates the process of deriving combinational logic circuits from reversible quantum circuits. To achieve this, the Quine-McCluskey technique was utilized along with state tables generated from the quantum circuits to obtain an optimal logic expression that serves as the basis for constructing the combinational logic circuit. The resultant obtained combinational logic circuit was implemented within the MATLAB Simulink environment, and state tables were obtained. A comparison was made between the state tables derived from the quantum circuit and the combinational circuit, yielding successful results.