Pablo Rodríguez Grasa

A PAC-Bayesian approach to generalization for quantum models. We take steps towards non-uniform and data-dependent bounds for generalization of quantum machine learning models. scirate.com/arxiv/2603.22964 In detail, #generalization is a central concept in machine learning theory, yet for quantum models, it is predominantly analyzed through uniform bounds that depend on a model's overall capacity rather than the specific function learned. These capacity-based uniform bounds are often too loose and entirely insensitive to the actual training and learning process. Previous theoretical guarantees have failed to provide #nonuniform, data-dependent bounds that reflect the specific properties of the learned solution rather than the worst-case behavior of the entire hypothesis class. To address this limitation, we derive the first #PACBayesian generalization bounds for a broad class of quantum models by analyzing layered circuits composed of general quantum channels, which include dissipative operations such as mid-circuit measurements and feedforward. Through a channel perturbation analysis, we establish non-uniform bounds that depend on the norms of learned parameter matrices; we extend these results to symmetry-constrained equivariant quantum models; and we validate our theoretical framework with numerical experiments. This work provides actionable model design insights and establishes a foundational tool for a more nuanced understanding of generalization in #quantummachinelearning. Warm thanks to the team of @pablones8, Matthias C. Caro, @EliesMiquel, @FJSchreiber, and @charl_bp for this great collaboration.

Continuing our tradition of preparing future generations for careers in #AI & #quantum (AQ), today, we proudly announced 13 inaugural @SandboxAQ Scholars! 10 PhD applicants from around the world each received $10k Research Excellence #Scholarships for their bold vision of the future and 3 received a $5k Global Travel Award to present their research at international conferences. Click here to read more about the Scholars and their research sandboxaq.com/company/schola… Watch this space for a deeper dive into these future superstars who are leveraging #AQ to tackle some of the world’s toughest challenges. #SandboxAQ #scholarships #PhD #research #education

Today our paper “Quantum approximated cloning-assisted density matrix exponentiation” has been published in @PhysRevResearch doi.org/10.1103/PhysRevResea… Congrats to @pablones8 @raist272 @Conzavin @QuantumYue and Patrick Rebentrost. @upvehu @Ikerbasque @BCAMBilbao @tecnalia

New paper in @quantumjournal on Efficient quantum amplitude encoding of polynomials quantum-journal.org/papers/q… We improve previous results introducing a controllable error. Congrats to @Conzavin and @pablones8 and our collab T. W. Watts! @ehuscientia @OpenSuperQPlus @BCAMBilbao

The @NquireC delegation at the #APSMarch is already in Minneapolis. Very interest talks on a variety of topics. See you there! @raist272 @pgaraz9 @pablones8

🚨 New preprint today on the training of embedding quantum kernels with data re-uploading quantum neural networks for classification (arxiv.org/abs/2401.04642) Congrats to @pablones8 for this great work and to @QuantumYue. We use a QNN with scalable training to build an EQK.

New preprint today on cloning-assisted density matrix exponentiation for #QML and #QuantumAlgorithms with @pablones8 @raist272 @Conzavin @QuantumYue and Patrick Rebentrost arxiv.org/abs/2311.11751 @NquireC @ehuscientia @Ikerbasque @BCAMBilbao @OpenSuperQPlus @tecnalia

🚨New preprint with several methods encoding polynomials in quantum amplitudes arxiv.org/pdf/2307.10917… Many thanks to @Conzavin @pablones8 and Thomas W. Watts from @Cornell for this collab. @OpenSuperQPlus @NquireC @ehuscientia @BCAMBilbao @tecnalia