Abstract:We develop a control-theoretic framework for understanding Quantum Advantage (QA), providing a systematic route to characterize when and how QA can arise. The bilinear controlled Schrödinger equation is the common thread: the target quantum computation is recast as an operator controllability problem on the special unitary group $SU(N)$, and QA is identified with a polynomial-in-$n$ upper bound on the associated minimal-time function.
We illustrate the framework on two paradigmatic problems: a) the Quantum Fourier Transform (QFT) on superconducting digital quantum processors (such as IBM's ibm_brisbane), for which we prove operator controllability by a Lie-algebraic argument and derive an $O(n^2)$ upper bound on the minimal time via a gate-concatenation lemma combined with the standard QFT circuit decomposition; b) the Maximum Independent Set (MIS) problem on neutral-atom analog quantum processors (such as Pasqal's hardware), for which we analyze the Rydberg-blockade Hamiltonian as a bilinear control system and reformulate the Quantum Approximate Optimization Algorithm (QAOA) as a continuous-time optimal control problem. By a controllability result, we show how the problem can be solved on Pasqal Quantum Computers and we introduce a control-based definition of Quantum Advantage for MIS.
We conclude by outlining several open problems that chart directions for future research at the intersection of Control Theory and Quantum Computing.
From: Dario Pighin [view email]
[v1]
Thu, 11 Jun 2026 15:31:26 UTC (66 KB)
[v2]
Sat, 13 Jun 2026 21:29:45 UTC (64 KB)
[v3]
Thu, 18 Jun 2026 16:12:48 UTC (65 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。