Calculating Unknown Eigenvalues with a Quantum Algorithm

TL;DR

This paper demonstrates a complete quantum phase estimation algorithm for a single qubit unitary, enabling calculation of unknown eigenvalues without prior knowledge, which advances quantum simulation and metrology.

Contribution

Introduces a new, efficient method for implementing controlled-unitary operations that does not require prior eigenvalue knowledge, improving quantum algorithm practicality.

Findings

Successfully implemented quantum phase estimation for unknown eigenvalues

Developed a more efficient controlled-unitary operation approach

Applicable across different quantum computing architectures

Abstract

Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct the algorithm. We have implemented the complete quantum phase estimation algorithm for a single qubit unitary in which the answer is calculated by the algorithm. We use a new approach to implementing the controlled-unitary operations that lie at the heart of the majority of quantum algorithms that is more efficient and does not require the eigenvalues of the unitary to be known. These results point the way to efficient quantum simulations and quantum metrology applications in the near term, and to factoring large numbers in the longer term. This approach is architecture independent and thus can be used in other physical implementations.