Quantum state preparation protocol for encoding classical data into the amplitudes of a quantum information processing register's wave function

Sahel Ashhab

doi:10.1103/physrevresearch.4.013091

Abstract

We present a protocol for encoding $N$ real numbers stored in $N$ memory registers into the amplitudes of the quantum superposition that describes the state of $\log_2N$ qubits. This task is one of the main steps in quantum machine learning algorithms applied to classical data. The protocol combines partial CNOT gate rotations with probabilistic projection onto the desired state. The number of additional ancilla qubits used during the implementation of the protocol, as well as the number of quantum gates, scale linearly with the number of qubits in the processing register and hence logarithmically with $N$. The average time needed to successfully perform the encoding scales logarithmically with the number of qubits, in addition to being inversely proportional to the acceptable error in the encoded amplitudes. It also depends on the structure of the data set in such a way that the protocol is most efficient for non-sparse data.

Highlights

Quantum computing devices have made great progress toward the construction of a quantum computer whose computing power exceeds that of any existing classical computer [1,2,3]
New algorithms are continually being developed for future quantum computers [6,7]
As machine learning techniques become increasingly prevalent, researchers are exploring the potential for quantum computers to offer a computational advantage using similar techniques [8,9]

Summary

INTRODUCTION

Quantum computing devices have made great progress toward the construction of a quantum computer whose computing power exceeds that of any existing classical computer [1,2,3]. A clear quantum advantage over classical computers was recently demonstrated using superconducting devices [4,5]. There have been many proposals for using quantum computers to perform machine learning tasks. The data could be a quantum state that results from reproducible quantum dynamics, e.g., a quantum simulation of a physical system. In this case, it could be practically. CN−1}, one first needs to encode these data into the quantum state of a quantum register In this case, the step of encoding the classical data into the quantum processor can be the most challenging step in running the machine learning algorithm

AMPLITUDE ENCODING

PREVIOUS WORK

OUR PROTOCOL

RESOURCE SCALING

DISCUSSION

CONCLUSION