Efficient scheme for initializing a quantum register with an arbitrary superposed state

TLDR

Preparing a quantum register is crucial for quantum computation, yet while simple basis states are easy to construct, creating arbitrary superpositions remains nontrivial. The authors propose a general scheme to initialize a quantum register into any desired superposition of basis states. The scheme uses O(N n²) standard one‑ and two‑bit gates and does not require extra qubits. The authors illustrate the scheme’s application in several special cases.

Abstract

Preparation of a quantum register is an important step in quantum computation and quantum information processing. It is straightforward to build a simple quantum state such as $|{i}_{1}{i}_{2}\ensuremath{\cdots}{i}_{n}〉$ with ${i}_{j}$ being either 0 or 1, but it is a nontrivial task to construct an arbitrary superposed quantum state. We present a scheme that can most generally initialize a quantum register with an arbitrary superposition of basis states. Implementation of this scheme requires ${O(Nn}^{2})$ standard 1- and 2-bit gate operations, without introducing additional quantum bits. Application of the scheme in some special cases is discussed.