Ahmed Younes

Representation of Boolean Quantum Circuits as Reed-Muller Expansions

In this paper we show that there is a direct correspondence between Boolean quantum operations and certain forms of classical (non-quantum) logic known as Reed–Muller expansions. This allows us to readily convert Boolean circuits into their quantum equivalents. A direct result of this is that the problem of synthesis and optimization of Boolean quantum circuits can be tackled within the field of Reed–Muller logic.

Quantum Search Algorithm with more Reliable Behaviour using Partial Diffusion

In this paper, we will use a quantum operator which performs the inversion about the mean operation only on a subspace of the system (Partial Diffusion Operator) to propose a quantum search algorithm runs in O( p N/M) for searching unstructured list of size N with M matches such that, 1 ≤ M ≤ N. We will show that the performance of the algorithm is more reliable than known quantum search algorithms especially for multiple matches within the search space. A performance comparison with Grover’s algorithm will be provided.

Improving the quantum cost of reversible Boolean functions using reorder algorithm

This paper introduces a novel algorithm to synthesize a low-cost reversible circuits for any Boolean function with n inputs represented as a Positive Polarity Reed–Muller expansion. The proposed algorithm applies a predefined rules to reorder the terms in the function to minimize the multi-calculation of common parts of the Boolean function to decrease the quantum cost of the reversible circuit. The paper achieves a decrease in the quantum cost and/or the circuit length, on average, when compared with relevant work in the literature.

Using Reed-Muller Expansions in the Synthesis and Optimization of Boolean Quantum Circuits

There have been efforts to find an automatic way to create efficient Boolean quantum circuits, because of their wide range of applications. This chapter shows how to build efficient Boolean quantum circuits. A direct synthesis method can be used to implement any Boolean function as a quantum circuit using its truth table, where the generated circuits are more efficient than ones generated using methods proposed by others. The chapter shows, using another method, that there is a direct correspondence between Boolean quantum operations and the classical Reed-Muller expansions. This relation makes it possible for the problem of synthesis and optimization of Boolean quantum circuits to be tackled within the domain of Reed-Muller logic under manufacturing constraints, for example, the interaction between qubits of the system.