Year: 2026
Type: preprint
Abstract: In this paper, we give a mathematical proof that bounds the number of CNOT gates required to synthesize an $n$ qubit phase polynomial with $g$ terms to be at least $O(\frac{gn}{\max (\log g, 1)})$ and at most $O(gn)$. However, when targeting restricted hardware, not all CNOTs are allowed. If we were to use SWAP-based methods to route the qubits on the architecture such that the earlier synthesized gates are natively allowed, we increase the number of CNOTs by a routing overhead factor of $O(\log n) \leq α\leq O(n \log^2 n)$. However, if we only synthesize allowed gates, we do not need to route any qubits. Moreover, in that case the routing overhead factor is $1 \leq α\leq 4 \simeq O(1)$. Additionally, since phase polynomials and Hadamard gates together form a universal gate set, we get qubit routing for almost free.
Source: arXiv (Cornell University)
Author: de Griend, Arianne Meijer-van
Institution: University of Helsinki
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: Business Finland
OpenAlex ID: W7155200898