Sergi Ramos-Calderer

Quantum computational advantage is generally attributed to coherent interference and other non-classical resources, yet their respective roles remain difficult to disentangle in experimental platforms where multipartite entanglement is inherently present. High-dimensional quantum systems provide an attractive route for investigating these resources while simultaneously reducing hardware overhead for quantum information processing. Here we realize a programmable four-dimensional optical qudit encoded in a single trapped $^{138}\mathrm{Ba}^{+}$ ion and demonstrate universal coherent control through phase-programmable optical rotations. Using this platform, we implement an entanglement-free realization of Grover's quantum search algorithm, achieving target-state identification probabilities of up to $94.5\pm2.0\%$. Within the same processor, we further demonstrate state-dependent quantum contextuality through a Clauser--Horne--Shimony--Holt (CHSH)-type noncontextuality inequality, obtaining a maximum violation of $S = 2.816 \pm 0.082$, in close agreement with the Tsirelson bound. By integrating programmable quantum computation and contextuality measurements within a single multilevel trapped-ion platform, our work establishes a versatile architecture for investigating the relationship between coherent interference and contextuality in quantum information processing and provides a scalable route toward high-dimensional quantum technologies.

We present an exact $n$-qubit computational-basis amplitude encoder of real- or complex-valued data vectors of $d=\binom{n}{k}$ components into a subspace of fixed Hamming weight $k$. This represents a polynomial space compression of degree $k$. The circuit is optimal in that it expresses an arbitrary data vector using only $d-1$ (controlled) Reconfigurable Beam Splitter (RBS) gates and is constructed by an efficient classical algorithm that sequentially generates all bitstrings of weight $k$ and identifies the gates that superpose the corresponding states with the correct amplitudes. An explicit compilation into CNOTs and single-qubit gates is presented, with the total CNOT-gate count of $\mathcal{O}(k\, d)$ provided in analytical form. In addition, we show how to load data in the binary basis by sequentially stacking encoders of different Hamming weights using $\mathcal{O}(d\,\log(d))$ CNOT gates. Moreover, using generalized RBS gates that mix states of different Hamming weights, we extend the construction to efficiently encode arbitrary sparse vectors. Experimentally, we perform a proof-of-principle demonstration of our scheme on a commercial trapped-ion quantum computer. We successfully upload a $q$-Gaussian probability distribution in the non-log-concave regime with $n = 6$ and $k = 2$. We also showcase how the effect of hardware noise can be alleviated by quantum error mitigation. Numerically, we show how our encoder can improve the performance of variational quantum algorithms for problems that include particle-preserving symmetries. Our results constitute a versatile framework for quantum data compression with various potential applications in fields such as quantum chemistry, quantum machine learning, and constrained combinatorial optimizations.