QPE is a quantum algorithm used to estimate a qubit's eigenvalue given an eigenvector and the unitary operation it has been affected by (eg. rotation). It is often used as a subroutine in other quantum algorithms such as HHL and Shor's algorithm.
First, we coded QPE in Q#, a language used to simulate qubits. We ran unit tests on multiple unitary operations such as rotations and their controlled variants. After confirming that our implementation of QPE worked, we migrated it to Python. Using the Qiskit library and IBM's quantum machines, we were able to implement and run our algorithm on actual quantum computers. Below is a circuit diagram of our implementation of QPE.
QPE is not practical for smaller quantum systems but is for larger, less error-prone ones. As the number of qubits and quantum volume increases in quantum computers, QPE's accuracy and precision will also increase, making it one of the fundamental "building block" algorithms of the quantum world.
- Understanding quantum papers is difficult. Initially we had trouble learning and understanding how eigenvalues, eigenvectors, and other mathematical concepts applied to QPE
- Endianness discrepancy between papers caused us to initially implement QPE incorrectly
- Unfortunately we were not able to run our algorithm on large quantum computers so some of our conclusions are speculative
Thank you to BWSI, our instructors, Joe Clapis and Richard Preston, and our TAs, Filip Aronshtein, Mridul Sarkar, and Christopher Um for putting together and guiding this program. None of this would have been possible otherwise.