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Abstract:
This paper shows how to design efficient quantum multiplexer circuit borrowed from classical computer design. The design will show that it is composed of some Toffole gates or C^sup 2^NOT gate and some two input CNOT gates. Every C^sup 2^NOT gate is synthesized and optimized by applying the genetic algorithm to get the best possible combination for the design of these gate circuits.
Keywords:
Qubit, Toffole gate, Quantum Multiplexer Circuit, Circuit Synthesis, Quantum Half adder Circuit,Genetic Algorithm.
1. INTRODUCTION
Introduction: As the ever-shrinking transistor approaches atomic proportions, Moore's law must confront the small-scale granularity of the world: we can't build wires thinner than atoms. Theoretically, quantum computers could outperform their classical counterparts when solving certain discrete problems [15, 8].
The logical properties of qubits also differ significantly from those of classical bits[2]. Bits and their manipulation can be described using two constants (0 and 1) and the tools of Boolean algebra. Qubits [13], on the other hand, must be discussed in terms of vectors, matrices, and other linear algebraic constructions.
Quantum logic circuits [1,4,5,6,14], from a high level perspective, exhibit many similarities with their classical counterparts. They consist of quantum gates, connected by quantum wires which carry quantum bits. Moreover, logic synthesis for quantum circuits is as important as the classical case.
In this work, we focus on identifying useful quantum circuit blocks. we analyze quantum conditions and designing quantum multiplexor that engage CNOT[3] and Toffole gates. Here we synthesize and optimize each and every Toffole gate by applying genetic algorithm [7, 10, 11, 12].
2. Controlled Quantum Gate Operations:
Here we have engaged two controlled quantum gates i.e. C^sup 2^NOT and CNOT. C^sup 2^NOT is also known as Toffole gate. It is a three input gate. The first two inputs are the controlled inputs and the third one is the target input. This gate has a 3-bit input and output. If the first two bits are set, it flips the third bit. Following is a table over the input and output bits:
3. Quantum Half Adder:
In order to construct an efficient Quantum multiplexer circuit we'll need the quantum equivalent to the classical "half adder". This is a 2-input, 2-output device with the following truth table:
Classical Half Adder.
The sum output...