Efficient state preparation for a register of quantum bits

TL;DR

This paper presents a quantum algorithm leveraging Grover's search to efficiently prepare arbitrary pure states in a quantum register with high fidelity, especially effective for states with bounded amplitudes.

Contribution

The paper introduces a novel quantum state preparation algorithm based on Grover's search, optimized for states with bounded amplitudes, requiring polynomial resources.

Findings

Algorithm achieves high fidelity state preparation.

Resource requirements are polynomial for certain state sequences.

Applicable to encoding classical distributions in quantum registers.

Abstract

We describe a quantum algorithm to prepare an arbitrary pure state of a register of a quantum computer with fidelity arbitrarily close to 1. Our algorithm is based on Grover's quantum search algorithm. For sequences of states with suitably bounded amplitudes, the algorithm requires resources that are polynomial in the number of qubits. Such sequences of states occur naturally in the problem of encoding a classical probability distribution in a quantum register.