Roberto Bondesan

Dissipative quantum algorithms for state preparation in many-body systems are increasingly recognised as promising candidates for achieving large quantum advantages in application-relevant tasks. Recent advances in algorithmic, detailed-balance Lindbladians enable the efficient simulation of open-system dynamics converging towards desired target states. However, the overall complexity of such schemes is governed by system-size dependent mixing times. In this work, we analyse algorithmic Lindbladians for Gibbs state preparation and prove that they exhibit rapid mixing, i.e., convergence in time poly-logarithmic in the system size. We first establish this for non-interacting spin systems, free fermions, and free bosons, and then show that these rapid mixing results are stable under perturbations, covering weakly interacting qudits and perturbed non-hopping fermions. Further, we adapt the techniques from separable qudits to the fermionic setting and prove rapid mixing of the strongly-interacting regime of the Fermi-Hubbard model. Our results constitute the first efficient mixing bounds for non-commuting qudit models and bosonic systems at arbitrary temperatures. Compared to prior spectral-gap-based results for fermions, we achieve exponentially faster mixing, further featuring explicit constants on the maximal allowed interaction strength. This not only improves the overall polynomial runtime for quantum Gibbs state preparation, but also enhances robustness against noise. Our analysis relies on oscillator norm techniques from mathematical physics, where we introduce tailored variants adapted to specific Lindbladians - an innovation that we expect to significantly broaden the scope of these methods.

Federated learning (FL) trains a shared model across many data holders without pooling raw data, but the parameter exchange itself is vulnerable to gradient-inversion attacks. Among privacy-preserving remedies, fully homomorphic encryption (FHE) is the strongest cryptographic option that lets an honest-but-curious server aggregate updates without ever seeing them in the clear. Extending FHE to quantum machine learning, where the model parameters are continuous rotation angles of a variational quantum circuit, has so far required either thousands of interactive client--server rounds per training step or compiling every rotation into long sequences of a discrete gate alphabet, an overhead that destroys any quantum-side advantage. The central technical observation of this work is that single-qubit rotation composition under the quaternion representation of $\mathrm{SU}(2)$ reduces to a degree-2 polynomial on $\mathbb{R}^4$, which the CKKS scheme evaluates within a single multiplicative depth without bootstrapping. The consequence is a practical construction that enables non-interactive encrypted federated training of hybrid quantum--classical neural networks: information-theoretic security at the quantum-state level is composed with RLWE-based computational security for the classical aggregation. A small-scale feasibility study ($\leq\!3$ clients, $\leq\!5$ FL rounds) on the California Housing regression benchmark shows that the encrypted model matches or slightly improves over the plaintext quantum baseline in every run ($\mathrm{MSE}=0.612$ versus $0.727$) and approaches the classical CKKS-FedAvg baseline ($0.591$), an effect that is consistent with, and which we hypothesise is driven by, mild stochastic regularisation from CKKS approximation noise. Homomorphic FedAvg matches plaintext FedAvg to within $4{\times}10^{-8}$ rad of rotation-angle error in our runs. A protocol-accounting cost model predicts a $10\times$--$30\times$ reduction in per-rotation compute relative to the discrete-gate baseline as target precision tightens, and round-trip state fidelity of $0.992$ is measured on the 156-qubit \texttt{ibm\_fez} processor. The accompanying open-source release is, to the best of our knowledge, the first publicly available implementation of continuous-rotation quantum homomorphic encryption, and is intended to lower the barrier to further work on privacy-preserving quantum machine learning.

Discovering QKD eavesdropping strategies under asymmetric and time-varying noise entails joint optimisation over discrete attack structure and continuous parameters under a strict evaluation budget. A minimal two-loop search framework, EvoluCMAES, is employed, in which the topology-mutation operator is the only domain-specific component. In BB84, compact eavesdropping circuits of 4--6 gates are consistently identified from an arbitrary-depth search space, approaching the analytical Pauli-channel cloning-machine bound under bit-flip noise. When reformulated as a sequential decision problem, the resulting policy class with feasibility masking and matched hyperparameters recovers the greedy-Oracle strategy for both BB84 and E91/DIQKD. Under soft feasibility, a regime is observed in which a small increase in detection probability yields a statistically significant improvement over the greedy oracle, indicating that budget-limited search exposes nontrivial attack strategies in the presence of noise asymmetry and temporal variation.