arXiv subjects

Constantin Cedillo Vayson de Pradenne

Publications and source records attributed to Constantin Cedillo Vayson de Pradenne.

4 recordsLinked to original sources

arXiv2026

An analog of Quillen-Venkov for eventually negligible classes and radicality for finite irreducible Coxeter groups

Let $G$ be a finite group, $M$ a $G$-module, and $F$ a field. A continuous group homomorphism $i : Γ_L=\text{Gal}(L_{\text{sep}}/L) \rightarrow G$ yields a homomorphism $i^* : H^d(G,M) \rightarrow H^d(L,M)$ for every $d\in \mathbb{N}$. An element $u \in H^d(G,M)$ is negligible over $F$ if $u\in\ker(i^*)$ for every $i$ and every field extension $L/F$. If $M=\mathbb{F}_p$ for a prime $p$ with a trivial $G$-action, an element $u$ is eventually negligible over $F$ if $u^k$ is negligible over $F$ for some $k\geq1$. The (eventually) negligible elements over $F$ form an ideal of the cohomology ring $H^*(G,\mathbb{F}_p)$, called the (eventually) negligible ideal. We prove an analog of Quillen-Venkov for eventually negligible elements. An element $u\in H^*(G,\mathbb{F}_p)$ is eventually negligible over $F$ if and only if the restriction of $u$ to the cohomology of each elementary abelian $p$-subgroup of $G$ is eventually negligible over $F$. Paired with applications of a Gysin-type long exact sequence, we identify generators of the negligible ideal over $\mathbb{Q}$ of the mod-2 cohomology of dihedral groups, cyclic $2$-groups, and generalized quaternion groups. We prove that the negligible ideal over $\mathbb{Q}$ of the mod-2 cohomology of every finite irreducible Coxeter group is radical. The result was previously known for Weyl groups; we prove it for the remaining non-Weyl types $I_2(m)$, $H_3$, and $H_4$.

math.GR↗

arXiv2026

Proper Agnostic Learning of Matrix Product States and Tree Tensor Networks

We establish proper agnostic learning of matrix product states and tree tensor networks. Given copies of an arbitrary quantum state $ρ$, our algorithms return a state $|ψ\rangle$ of chosen bond dimension such that $\langleψ| ρ|ψ\rangle$ is within $\varepsilon$ of the optimum over the model class, without assuming that $ρ$ itself belongs to or is well approximated by that class. The main idea is to use improper learning to compress the mixed-state objective, reducing proper agnostic learning to optimization against a finite collection of explicitly specified pure states. We then introduce a comparator-dual compression procedure that reduces the bond dimension of these targets while uniformly preserving their overlaps with all bounded-bond comparators, with an error independent of system size. For matrix product states, this gives polynomial copy complexity in the system size, local dimension, bond dimension, and $1/\varepsilon$, together with polynomial runtime in the system size for fixed local dimension, bond dimension, and accuracy. The same framework yields proper agnostic learning of tree tensor networks on bounded-degree trees, with both copy complexity and runtime polynomial in the system size when the remaining parameters are fixed.

quant-ph↗

arXiv2026

Restrictions on non-Clifford fault tolerance and ruling out beyond-SQL quantum metrology

Quantum metrology promises a quadratic speedup over the standard quantum limit (SQL), but signal-aligned noise is expected to preclude this advantage in realistic settings. A potential route around known no-go results is to encode the sensors in a quantum code where the physical signal acts transversally as a logical gate. Understanding restrictions on transversal non-Clifford gates is therefore central to both quantum metrology and fault-tolerant quantum computation. Here, we prove such restrictions and apply them to transversal sensing. For any stabilizer code of distance $d\ge 3$ supporting a transversal logical action in level $D$ of the Clifford hierarchy, every stabilizer generating set must contain a check of weight at least $2^D$. Moreover, any $r$-level concatenated realization satisfies $r\leq \lfloor \log_2 n/D\rfloor$, forcing $r=1$ and ruling out concatenation when applied to beyond-SQL metrology. We then show that transversal single-qubit rotations by a small angle $θ$ can only induce a nontrivial logical action on an $n$-qubit code if its checks include irreducible stabilizers of weight $Ω(1/(n|θ|^2))$. Here, many single-qubit errors commute with every stabilizer or logical Pauli below this weight and are only detected by a high-weight check, so their syndromes cannot be fault-tolerantly reconstructed from low-weight normalizer measurements. Since beyond-SQL transversal sensing requires $|θ| = o(n^{-1/2})$, the weight of checks required for syndrome extraction diverges with $n$. Finally, we prove a broader metrological no-go theorem that avoids the assumptions of the quantum Cramér-Rao bound: constant-strength signal-aligned noise rules out any asymptotic advantage over the SQL in AC or DC sensing, even with biased estimators, nonstabilizer or approximate encodings, quantum memory, intermediate measurements, or adaptive control.

quant-ph↗

arXiv2026

Learning Hamiltonians at Long Times

We study the problem of learning an unknown $n$-qubit Hamiltonian $H$ from $U = e^{-iHt}$ for a single time $t$, where $t$ may be arbitrarily large. For broad families of local Hamiltonians, we prove that, with high probability over $H$ and $t$, any sum of local observables $A$ that is normalized and orthogonal to $H$ satisfies $\tfrac{1}{2^n}\|[U(t),A]\|_F^2 \geq 1/\text{poly}(n)$. The Hamiltonian is therefore the unique approximately conserved local observable, and we can efficiently recover $H$, up to scale, as the approximate null vector of a data matrix built from random product-state inputs and classical shadows. As a corollary, we obtain a weak equilibration statement: the infinite-temperature autocorrelation of every sum of local observables orthogonal to $H$ decays by at least an inverse-polynomial amount.

quant-ph↗