Han-Hsuan Lin

Small-Bias Quantum Approximate Counting via the Multiplicative Adversary Method

We study the two-weight decision version of quantum approximate counting: given oracle access to $x\in\{0,1\}^N$, distinguish $|x|=M$ from $|x|=M+\Delta$ with success probability $1/2+\zeta$. Using the multiplicative adversary method, we prove $\Omega\left(\max\left\{\zeta\sqrt{(N-M)(M+\Delta)}/\Delta,\sqrt{\zeta N/\De...