Qudit Implementation of the Rodeo Algorithm for Quantum Spectral Filtering

Quantum Physics [Submitted on 17 Mar 2026] Qudit Implementation of the Rodeo Algorithm for Quantum Spectral Filtering Julio Cesar Siqueira Rocha, Rodrigo Alves Dias Qudits, the multi-level generalization of qubits, provide a natural extension of the binary paradigm in quantum computation and offer new opportunities to enhance algorithmic performance. Beyond their direct applicability to the simulation of multi-level quantum systems, higher-dimensional ancillae can improve sampling efficiency in quantum algorithms by enabling the simultaneous implementation of multiple control operations, thereby reducing circuit complexity. In this work, we pursue three main objectives. First, we present a formulation of the Rodeo algorithm employing a general d-level ancilla qudit. Second, we introduce the concept of the \emph{Rodeo kernel}, defined as a two-frequency interferometer, which acts as a spectral filter in the energy domain. Finally, we propose a microcanonical protocol for the Rodeo algorithm. This protocol enables the estimation of entropic quantities through a single energy sweep and admits a natural interpretation as a Gaussian convolution of the density of states. To support the theoretical analysis, we perform numerical evaluations of the corresponding quantum circuit using ancilla qudits of dimensions three, four, and five. The simulations are performed for the one-dimensional Ising model, considering both spin-\frac{1}{2} and spin-1 particles. The ancilla qutrit implementation exhibits an 18\% reduction in fluctuations compared to the qubit implementation. Our results show that the qudits provide a framework for spectral analysis and thermodynamic characterization of multi-level quantum systems. Comments: 19 pages, 6 figures Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Computational Physics (physics.comp-ph) Cite as: arXiv:2603.16049 [quant-ph]   (or arXiv:2603.16049v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.16049 Focus to learn more Submission history From: Julio Cesar Siqueira Rocha [view email] [v1] Tue, 17 Mar 2026 01:24:44 UTC (338 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: cond-mat cond-mat.stat-mech physics physics.comp-ph References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)