arXiv subjects

Ayoub Hafid

Publications and source records attributed to Ayoub Hafid.

3 recordsLinked to original sources

arXiv2026

Noncommutative coarse metric geometry

Motivated by coarse geometry and the classical role of Roe algebras as large-scale invariants of proper metric spaces, we show that proper quantum metric spaces as introduced by Latr\'emoli\`ere are noncommutative coarse spaces. This further allows us to develop a bridge between Latr\'emoli\`ere's framework and the W*-metric approach to quantum metric spaces. Furthermore, we construct Roe algebras for locally compact quantum metric spaces and verify that they recover the classical Roe algebras in the commutative case. We furthermore apply this framework to some examples of locally compact quantum metric spaces and show that it leads to the natural conclusion. Finally we use this framework to introduce notions of higher index theory for locally compact quantum metric spaces.

math.OA↗

arXiv2025

Hardness of classically sampling quantum chemistry circuits

Significant advances have been made in the study of quantum advantage both in theory and experiment, although these have mostly been limited to artificial setups. In this work, we extend the scope to address quantum advantage in tasks relevant to chemistry and physics. Specifically, we consider the unitary cluster Jastrow (UCJ) ansatz-a variant of the unitary coupled cluster ansatz, which is widely used to solve the electronic structure problem on quantum computers-to show that sampling from the output distributions of quantum circuits implementing the UCJ ansatz is likely to be classically hard. More specifically, we show that there exist UCJ circuits for which classical simulation of sampling cannot be performed in polynomial time, under a reasonable complexity-theoretical assumption that the polynomial hierarchy does not collapse. Our main contribution is to show that a class of UCJ circuits can be used to perform arbitrary instantaneous quantum polynomial-time (IQP) computations, which are already known to be classically hard to simulate under the same complexity assumption. As a side result, we also show that UCJ equipped with post-selection can generate the class post-BQP. Our demonstration, worst-case nonsimulatability of UCJ, would potentially imply quantum advantage in quantum algorithms for chemistry and physics using unitary coupled cluster type ansatzes, such as the variational quantum eigensolver and quantum-selected configuration interaction.

quant-ph↗

arXiv2024

Spectral Truncation Kernels: Noncommutativity in $C^*$-algebraic Kernel Machines

A central question in vector- and function-valued learning is how to design kernels that capture both local and non-local interactions while remaining computationally tractable. Existing operator-valued kernels offer only partial answers: separable kernels are efficient but fail to model interactions across the function domain, while commutative kernels capture only pointwise structure. To address this, we propose spectral truncation kernels, a new class of positive definite kernels for vector- and function-valued learning based on spectral truncation and $C^*$-algebra. By allowing noncommutative products in the kernel construction, the proposed kernels induce interactions across the data function domain and fill the gap between existing separable and commutative kernels. In addition, by using the $C^*$-algebraic framework, we reduce the computational cost compared to the existing vector-valued RKHS framework with operator-valued kernels.

stat.ML↗