An error rate of just Θ(n⁻²) previously left open questions regarding quantum optimisation’s limits over ellipsoids. Now, a new analysis demonstrates that achieving such high accuracy necessitates at least Ω(n/(log nlog log n)) membership queries, resolving ambiguities raised by Chakrabarti et al and van Apeldoorn et al. This tightly characterises query complexity alongside existing upper bounds, clarifying potential speedups from quantum methods.
Researchers Bound Quantum Optimisation Query Complexity
An error rate of just Θ(n⁻²) previously left open questions regarding quantum optimisation’s limits over ellipsoids. Now, a new analysis demonstrates that achieving such high accuracy necessitates at least Ω(n/(log nlog log n)) membership queries, resolving ambiguities raised by Chakrabarti et al and van Apeldoorn et al. This tightly characterises query complexity alongside existing upper bounds, clarifying potential speedups from quantum methods.