arXiv subjects

Julián Ferreiro-Vélez

Publications and source records attributed to Julián Ferreiro-Vélez.

4 recordsLinked to original sources

arXiv2026

Shortcuts for Adiabatic and Variational Algorithms in Molecular Simulation

Quantum algorithms offer a promising route toward computational advantage, but current implementations remain constrained by limited coherence and gate errors, making circuit complexity and noise sensitivity critical considerations. Here, we develop a shortcuts-to-adiabaticity strategy for molecular ground-state preparation and apply it to both digitized adiabatic quantum computing and the variational quantum eigensolver. In the adiabatic framework, we construct an approximate counterdiabatic (CD) Hamiltonian using a nested-commutator expansion. For the molecular systems considered, the CD correction accelerates state preparation and improves energy convergence in the fast-evolution regime, enabling a target accuracy to be reached with a lower implemented-operator count. In the variational setting, we introduce the adiabatic gauge ansatz ($\mbox{AGA}$), obtained by promoting the Pauli-string components generated by the approximate adiabatic gauge potential (AGP) to independent variational generators. We further propose a reduced variant, $\mbox{AGAR}$, that retains only Pauli generators with weight not larger than two, substantially reducing the ansatz size while maintaining competitive accuracy over the regimes considered. Benchmarks on $\mathrm{LiH}$ and $\mathrm{BeH}_2$ show that the proposed ansätze achieve accuracies competitive with established approaches such as UCCSD. Experiments on the \texttt{IBM\_basquecountry} superconducting quantum processor, together with simulations under depolarizing noise, show that the reduced CD-inspired ansatz yields smaller energy discrepancies than UCCSD under the noise conditions considered. Overall, our results demonstrate how AGP-inspired operator structures can be used to balance accuracy and implementation cost in molecular simulations on current noise-limited quantum hardware.

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arXiv2026

Inertial Counterdiabatic Driving

We introduce an inertial counterdiabatic (CD) protocol that reformulates shortcut-to-adiabaticity design as a moving-frame diagonalization problem. The method employs the Magnus expansion to construct a variational propagator generated by an accessible CD ansatz. In the new rotating frame, the controls are optimized to suppress the off-diagonal Hamiltonian terms, and the CD terms are defined to counteract the corresponding inertial contribution. The propagator generated with the Magnus expansion naturally exploits additional control directions generated through its nested commutator, while the sequential design of the propagator introduces temporal nonlocality into the optimization. We benchmark the method on a two-qubit system and on the one-dimensional quantum Ising chain, where it consistently outperforms variational CD protocols based on action minimization. The largest improvements are observed near gap-closing regions, demonstrating the advantage of combining temporal and algebraic nonlocality for suppressing diabatic excitations.

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arXiv2026

Regularized Counterdiabatic Driving for the Quantum Rabi Model

Counter-diabatic (CD) driving provides a powerful route to fast and robust state preparation by suppressing diabatic excitations during finite-time evolution. Yet, deriving analytical CD protocols for complex systems remains challenging, motivating the development of variational approaches. These methods typically rely on minimizing trace-based functionals to construct approximate control Hamiltonians. However, in unbounded systems, such functionals can become ill-defined because of the unbounded bosonic Hilbert space, leading to divergent cost functions and unphysical variational coefficients. Here, we introduce a variational optimization framework equipped with physically motivated renormalization schemes that regularize the trace-based metric by restricting it to relevant displaced and low-energy subspaces. As a paradigmatic example, we apply our method to the quantum Rabi model beyond the dispersive approximation and identify two distinct CD contributions that couple the atomic degree of freedom to the position and momentum quadratures of the field. These terms suppress diabatic excitations across coupling regimes ranging from strong to deep-strong light--matter interaction. We further formulate a fidelity-based quantum optimal-control strategy that bypasses the limitations of trace-based variational methods. Finally, we show that the resulting CD terms can be implemented via Floquet engineering through parametric modulation of the native Hamiltonian. Our results demonstrate that CD driving can be consistently extended to continuous-variable systems with unbounded Hilbert spaces, providing a controlled and scalable framework for quantum control in strongly interacting light-matter platforms.

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arXiv2025

On the Transfer of Knowledge in Quantum Algorithms

Quantum computing is poised to transform computational paradigms across science and industry. As the field evolves, it can benefit from established classical methodologies, including promising paradigms such as Transfer of Knowledge (ToK). This work serves as a brief, self-contained reference for ToK, unifying its core principles under a single formal framework. We introduce a joint notation that consolidates and extends prior work in Transfer Learning and Transfer Optimization, bridging traditionally separate research lines and enabling a common language for knowledge reuse. Building on this foundation, we classify existing ToK strategies and principles into a structured taxonomy that helps researchers position their methods within a broader conceptual map. We then extend key transfer protocols to quantum computing, introducing two novel use cases--reverse annealing and multitasking Quantum Approximate Optimization Algorithm (QAOA)--alongside a sequential Variational Quantum Eigensolver (VQE) approach that supports and validates prior findings. These examples highlight ToK's potential to improve performance and generalization in quantum algorithms. Finally, we outline challenges and opportunities for integrating ToK into quantum computing, emphasizing its role in reducing resource demands and accelerating problem-solving. This work lays the groundwork for future synergies between classical and quantum computing through a shared, transferable knowledge framework.

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