Collapsing a perfect superposition to a chosen quantum state without measurement

Abstract

Given a perfect superposition of 2n states on a quantum system of n qubits. We propose a fast quantum algorithm for collapsing the perfect superposition to a chosen quantum state |xs〉 without applying any measurements. The basic idea is to use a phase destruction mechanism. Two operators are used, the first operator applies a phase shift and a temporary entanglement to mark |xs〉 in the superposition, and the second operator applies selective phase shifts on the states in the superposition according to their Hamming distance with |xs〉. The generated state can be used as an excellent input state for testing quantum memories and linear optics quantum computers. We make no assumptions about the used operators and applied quantum gates, but our result implies that for this purpose the number of qubits in the quantum register offers no advantage, in principle, over the obvious measurement-based feedback protocol. © 2014 Younes, Abdel-Aty.