GAPs for Shallow Implementation of Quantum Finite Automata

Mansur Ziiatdinov
Aliya Khadieva
Abuzer Yakaryılmaz

Quantum fingerprinting is a technique that maps classical input word to a quantum state. The obtained quantum state is much shorter than the original word, and its processing uses less resources, making it useful in quantum algorithms, communication, and cryptography. One of the examples of quantum fingerprinting is quantum automata algorithms for MOD_p languages, where p is a prime number.

However, implementing such an automaton on the current quantum hardware is not efficient. Quantum fingerprinting maps a word of length N to a state of O(log N) qubits, and uses O(N) unitary operations. Computing quantum fingerprint using all available qubits of the current quantum computers is infeasible due to a large number of quantum operations.

To make quantum fingerprinting practical, we should optimize the circuit for depth instead of width in contrast to the previous works. We propose explicit methods of quantum fingerprinting based on tools from additive combinatorics, such as generalized arithmetic progressions (GAPs), and prove that these methods provide circuit depth comparable to a probabilistic method. We also compare our method to prior work on explicit quantum fingerprinting methods.

In Zsolt Gazdag, Szabolcs Iván and Gergely Kovásznai: Proceedings of the 16th International Conference on Automata and Formal Languages (AFL 2023), Eger, Hungary, September 5-7, 2023, Electronic Proceedings in Theoretical Computer Science 386, pp. 269–280.
Published: 3rd September 2023.

ArXived at: bibtex PDF
References in reconstructed bibtex, XML and HTML format (approximated).
Comments and questions to:
For website issues: