bibkey: lidar2025dadqc authors: D. A. Lidar year: 2025 title: “Digital-Analog-Digital Quantum Supremacy” doi: 10.48550/arXiv.2512.07127 url: https://arxiv.org/abs/2512.07127v1 claim: “Let $m{H}_n$ be a family of hardware graphs as in \cref{def:QPU-R-E}. For each $n$, draw $$\begin{gathered} mG \\ sim \\ mathrmUnif[ \\ m{F}_d( \\ m{H}_n)] \end{gathered}$$ and $$\begin{gathered} theta \\ sim \\ mathrmUnif[0,2 \\ pi{)}^n \end{gathered}$$. For any fixed choice of single-qubit angles ${v}_i$ in \cref{eq:HZ’}, there exist constants $a,b>0$ (depending only on $d$) such that for every $$\begin{gathered} s \\ in \\ {0,1 \\ }^n \end{gathered}$$, $$\begin{gathered} P{r}_{ \\ mG, \\ theta} \\ bigl[P_{ \\ UIQ{P}^{( \\ theta)}}(s) \\ gea{2}^{-n} \\ bigr] \\ geb. \end{gathered}$$” strata_touched:

• D5/S3/Quantum/Measurements/IQP/LidarRestrictedAnticoncentrationRefutation license: citation-only triage: anchor

Digital-Analog-Digital Quantum Supremacy

D. A. Lidar’s paper studies QPU-restricted IQP circuits and states an anticoncentration conjecture for every fixed hardware-graph family and fixed one-qubit angles.

Verified locator

DOI: https://doi.org/10.48550/arXiv.2512.07127

Source: https://arxiv.org/abs/2512.07127v1

Definition 1 (p. 4), verbatim from the source TeX:

Let \mH_n=(\mV_{\mH},\mE_{\mH}) be a fixed simple $D$-regular hardware graph on $n$ labeled vertices, and let $3\le d\le D$ be a fixed constant ($n$-independent). The \emph{$d$-factors} of a graph \mH are \mF_d(\mH) \equiv {\mG=(\mV,\mE_{\mG}) : \mE_{\mG}\subseteq \mE_{\mH},\deg_{\mG}(v)=d\ \forall v\in\mV}. The \emph{QPU-restricted graph ensemble} is the probability space \mathrm{Unif}[\mF_d(\mH_n)] in which, for each run of \UDAD, a graph \mG\in\mF_d(\mH_n) is drawn uniformly at random.

Eqs. (17)–(20) specify the factor set, random-angle layer, circuit with its Hamiltonian, and anticoncentration event. Conjecture 2 (p. 4, labelled conj:host-anticonc) reads:

Let \{\mH_n\} be a family of hardware graphs as in \cref{def:QPU-R-E}. For each $n$, draw \mG\sim \mathrm{Unif}[\mF_d(\mH_n)] and $\theta \sim \mathrm{Unif}[0,2\pi {)}^n$. For any fixed choice of single-qubit angles $\{v_i\}$ in \cref{eq:HZ’}, there exist constants $a,b>0$ (depending only on $d$) such that for every $s\in \{0,1{\}}^n$, \Pr_{\mG,\theta} \bigl[ P_{\UIQP^{(\theta)}}(s)\ge a 2^{-n} \bigr] \ge b.

The source’s Theorem 2 assumes Conjecture 2. The Lean settlement uses the fixed choice $v_i=\pi /7$, the cyclic twin-pair hardware family with $n=6m$, and proves the negation of the conjecture’s conclusion.