arXiv subjects

David Amaro-Alcalá

Publications and source records attributed to David Amaro-Alcalá.

8 recordsLinked to original sources

arXiv2026

GroupFunctions.jl: computing individual entries of the irreducible representations of the unitary group U(d)

GroupFunctions.jl is a Julia library for computing individual matrix elements of irreducible representations of U(d). These matrix elements, called group functions, can be evaluated symbolically or numerically. For SU(2), they reduce to the Wigner D-functions. The library computes these matrix elements in a carrier-space basis enumerated by Gelfand-Tsetlin patterns. It can also compute entire representation operators, construct input unitaries from parameterisations common in quantum optics, translate Gelfand-Tsetlin patterns into occupation-number kets, and compute the associated Schur functions. Results can be exported in a form compatible with Mathematica.

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arXiv2026

Integrable, Mixed, and Chaotic Dynamics in a Single All-to-All Ising Spin Model

We demonstrate that the Ising all-to-all (ATA) model exhibits a range of dynamics, from integrable to chaotic, including mixed behaviour across symmetry blocks within a single system. While other works have explored the dynamics of all-to-all systems by varying parameters, we analyse a fixed set of parameters and examine the dynamics within different blocks. In addition to investigating the dynamical properties, we show that the system remains resilient to noise when the norm of the Hamiltonian representing the noise is close to 1. Our results are presented by mapping each symmetry sector of the system to a kicked top (KT) and observing that KT parameters for each sector depend on its dimension. This system, similar to the Bunimovich billiard for classical chaos, provides a new platform for studying dynamics determined by the symmetry sector, advancing quantum chaos research.

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arXiv2026

Kostant relation in filtered randomized benchmarking for passive bosonic devices

We aim to reduce the cost of the current bosonic randomized benchmarking proposal. To do this, we introduce two filter functions: one uses immanants, the other uses characters of the special unitary group. These filters avoid computing Clebsch-Gordan coefficients and yield simple variance expressions. The character filter is not only efficient to compute, but also has a constant, low variance. Our filters rely on the same data as the original proposal. We also discuss an example with photon loss and gain. Our numerical evidence shows that a scheme using weak coherent states and intensity measurements can yield estimates close to those obtained without loss or gain. Our work could support simpler platform characterization and streamline data analysis.

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arXiv2026

Characterisation of individual gates using twirling circuits

We present a method to characterise qubit gates. Utilising the supermap formalism, we create a scheme for deterministic single-qubit gate analysis. Our approach introduces a new twirling process that is applied directly through fixed circuits. This method removes the requirement to average over random gates. The results enhance randomised benchmarking techniques and are suitable for experimental setups with multi-qubit control, focusing on the precise characterisation of single-qubit gates.

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arXiv2024

Qudit non-Clifford interleaved benchmarking

We introduce a scheme to characterise a qudit T gate that has different noise than a set of Clifford gates. We developed our scheme through representation theory and ring theory to generalise non-Clifford interleaved benchmarking to qudit systems. By restricting to the qubit case, we recover the dihedral benchmarking scheme. Our characterisation scheme provides experimental physicists a practical method for characterising universal qudit gate sets and advances randomised benchmarking research by providing the characterisation of a complete qudit library.

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arXiv2024

Randomised benchmarking for universal qudit gates

We aim to establish a scalable scheme for characterising diagonal non-Clifford gates for single- and multi-qudit systems; $d$ is a prime-power integer. By employing cyclic operators and a qudit T gate, we generalise the dihedral benchmarking scheme for single- and multi-qudit circuits. Our results establish a path for experimentally benchmarking qudit systems and are of theoretical and experimental interest because our scheme is optimal insofar as it does not require preparation of the full qudit Clifford gate set to characterise a non-Clifford gate. Moreover, combined with Clifford randomised benchmarking, our scheme is useful to characterise the generators of a universal gate set.

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arXiv2024

Benchmarking of universal qutrit gates

We introduce a characterisation scheme for a universal qutrit gate set. Motivated by the rising interest in qutrit systems, we apply our criteria to establish that our hyperdihedral group underpins a scheme to characterise the performance of a qutrit T gate. Our resulting qutrit scheme is feasible, as it requires resources and data analysis techniques similar to resources employed for qutrit Clifford randomised benchmarking. Combining our T gate benchmarking procedure for qutrits with known qutrit Clifford-gate benchmarking enables complete characterisation of a universal qutrit gate set.

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arXiv2020

Log-Convex set of Lindblad semigroups acting on $N$-level system

We analyze the set ${\cal A}_N^Q$ of mixed unitary channels represented in the Weyl basis and accessible by a Lindblad semigroup acting on an $N$-level quantum system. General necessary and sufficient conditions for a mixed Weyl quantum channel of an arbitrary dimension to be accessible by a semigroup are established. The set ${\cal A}_N^Q$ is shown to be log--convex and star-shaped with respect to the completely depolarizing channel. A decoherence supermap acting in the space of Lindblad operators transforms them into the space of Kolmogorov generators of classical semigroups. We show that for mixed Weyl channels the hyper-decoherence commutes with the dynamics, so that decohering a quantum accessible channel we obtain a bistochastic matrix form the set ${\cal A}_N^C$ of classical maps accessible by a semigroup. Focusing on $3$-level systems we investigate the geometry of the sets of quantum accessible maps, its classical counterpart and the support of their spectra. We demonstrate that the set ${\cal A}_3^Q$ is not included in the set ${\cal U}^Q_3$ of quantum unistochastic channels, although an analogous relation holds for $N=2$. The set of transition matrices obtained by hyper-decoherence of unistochastic channels of order $N\ge 3$ is shown to be larger than the set of unistochastic matrices of this order, and yields a motivation to introduce the larger sets of $k$-unistochastic matrices.

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