Alatz Alvarez-Ahedo | Searcharxiv

arXiv2026

Phase-Programmable Free Electron Quantum States in Synthetic Momentum Space

Light-electron interactions generate synthetic momentum-space dynamics that can be used to engineer free electron quantum states. Here we develop coherent control protocols in which the optical phase acts as the controllable hopping phase of a Floquet-Bloch momentum lattice. Pontryagin optimization designs phase-only waveforms that prepare selected momentum populations and coherent few-sideband superpositions with programmable relative phases. In a complementary Bragg regime protocol, dynamical phase matching selectively couples neighboring sidebands and enables deterministic sequential state synthesis. Full wave-packet simulations based on the minimal-coupling Hamiltonian identify the tolerance window set by phase noise, detuning, and finite momentum spread. The two protocols expose a speed-selectivity tradeoff between ultrafast multilevel interference control and slower resonant engineering, establishing programmable free electron sidebands as a platform for ultrafast quantum state synthesis.

quant-ph↗

arXiv2026

Digital-Analog Quantum Computing with Qudits

Digital-analog quantum computing with two-level systems is a computational paradigm that combines an analog Hamiltonian with single-qubit gates to achieve universality. We extend this framework to $d$-level systems by conjugating an analog Hamiltonian block with single-qudit gates drawn from the Weyl-Heisenberg basis, which provides a natural set of operations for qudit architectures. More specifically, we propose a protocol to simulate arbitrary two-body Hamiltonians with at most $O(d^4 n^2)$ analog blocks. The power of this approach is illustrated by the simulation of many-body qudit spin Hamiltonians including magnetic quadrupolar terms.

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