Superposed Quantum State Initialization Using Disjoint Prime Implicants (SQUID)

Abstract

The problem of initializing a quantum superposition is important for Grover's algorithm, quantum neural networks and other applications. The purpose of the algorithm presented here is to generate a quantum array that initializes a desired quantum superposition on n qubits. The SQUID algorithm almost always creates quantum arrays that perform better than those created by existing algorithms such as the Ventura-Martinez and Long-Sun algorithms. The best case performance for the quantum arrays created by the SQUID algorithm is O(n) when the superposition contains all possible states which is an exponential improvement over all existing algorithms. Also, the worst case performance of the quantum array created by the SQUID algorithm is never worse than the performance of existing algorithms. The SQUID algorithm represents a vast improvement over previous quantum superposition initialization algorithms and allows quantum superpositions to be initialized much more efficiently than with other algorithms.