Fast Black-Box Quantum State Preparation Based on Linear Combination of Unitaries

TL;DR

This paper introduces two new algorithms for black-box quantum state preparation using linear combination of unitaries, significantly reducing resource requirements and demonstrating feasibility on IBM Quantum hardware.

Contribution

The paper presents novel algorithms based on LCU that lower qubit and gate complexity for quantum state preparation, advancing practical implementation.

Findings

Reduced additional qubits to 2log(n)

Lowered Toffoli gates to n

Successfully demonstrated on IBM Quantum Experience

Abstract

Black-box quantum state preparation is a fundamental primitive in quantum algorithms. Starting from Grover, a series of techniques have been devised to reduce the complexity. In this work, we propose to perform black-box state preparation using the technique of linear combination of unitaries (LCU). We provide two algorithms based on a different structure of LCU. Our algorithms improve upon the existed best results by reducing the required additional qubits and Toffoli gates to 2log(n) and n, respectively, in the bit precision n. We demonstrate the algorithms using the IBM Quantum Experience cloud services. The further reduced complexity of the present algorithms brings the black-box quantum state preparation closer to reality.