Year: 2025
Type: article
Abstract: Among the cost metrics characterizing a quantum circuit, the T -count stands out as one of the most crucial as its minimization is particularly important in various areas of quantum computation such as fault-tolerant quantum computing and quantum circuit simulation. In this work, we contribute to the T -count reduction problem by proposing efficient T -count optimizers with low execution times. In particular, we greatly improve the complexity of TODD, an algorithm currently providing the best T -count reduction on various quantum circuits. We also propose some modifications to the algorithm which are leading to a significantly lower number of T gates. In addition, we propose another algorithm which has an even lower complexity and that achieves a better or equal T -count than the state of the art on most quantum circuits evaluated. We also prove that the number of T gates in the circuit obtained after executing our algorithms on a Hadamard-free circuit composed of n qubits is upper bounded by n ( n + 1 ) / 2 + 1 , which improves on the worst-case T -count of existing optimization algorithms. From this we derive an upper bound of ( n + 1 ) ( n + 2 h ) / 2 + 1 for the number of T gates in a Clifford + T circuit where h is the number of internal Hadamard gates in the circuit, i.e. the number of Hadamard gates lying between the first and the last T gate of the circuit.
Source: Quantum
Author: Vivien Vandaele
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $215
Funder: Agence Nationale de la Recherche
OpenAlex ID: W4414267006