Uncertainty In Quantum Computation

TL;DR

This paper investigates the challenge of initializing quantum registers to a specific superposition state without phase uncertainty, revealing that such a task is generally computationally impossible.

Contribution

It demonstrates the fundamental computational limitations in preparing quantum states with precise phase control from arbitrary initial states.

Findings

Preparing a specific superposition state without phase uncertainty is generally impossible.

The result highlights intrinsic limitations in quantum state initialization.

This work clarifies the boundaries of feasible quantum state preparation.

Abstract

We examine the effect of previous history on starting a computation on a quantum computer. Specifically, we assume that the quantum register has some unknown state on it, and it is required that this state be cleared and replaced by a specific superposition state without any phase uncertainty, as needed by quantum algorithms. We show that, in general, this task is computationally impossible.