Denis Jankovic

@article{Hartmann2025,

title = {Nonlinearity of the Fidelity in Open Qudit Systems: Gate and Noise Dependence in High-dimensional Quantum Computing},

author = {Jean-Gabriel Hartmann and Denis Janković and Rémi Pasquier and Mario Ruben and Paul-Antoine Hervieux},

editor = {Jens Siewert},

url = {https://quantum-journal.org/papers/q-2025-04-07-1690/},

doi = {10.22331/q-2025-04-07-1690},

year  = {2025},

date = {2025-04-07},

urldate = {2025-04-07},

journal = {Quantum},

volume = {9},

pages = {1690},

abstract = {High-dimensional quantum computing has generated significant interest due to its potential to address scalability and error correction challenges faced by traditional qubit-based systems. This paper investigates the Average Gate Fidelity (AGF) of single qudit systems under Markovian noise in the Lindblad formalism, extending previous work by developing a comprehensive theoretical framework for the calculation of higher-order correction terms. We derive general expressions for the perturbative expansion of the Average Gate Infidelity (AGI) in terms of the environmental coupling coefficient and validate these with extensive numerical simulations, emphasizing the transition from linear to nonlinear behaviour in the strong coupling regime. Our findings highlight the dependence of AGI on qudit dimensionality, quantum gate choice, and noise strength, providing critical insights for optimising quantum gate design and error correction protocols. Additionally, we utilise our framework to identify universal bounds for the AGI in the strong coupling regime and explore the practical implications for enhancing the performance of near-term qudit architectures. This study offers a robust foundation for future research and development in high-dimensional quantum computing, contributing to the advancement of robust, high-fidelity quantum operations.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Janković2024,

title = {Noisy qudit vs multiple qubits: conditions on gate efficiency for enhancing fidelity},

author = {Denis Janković and Jean-Gabriel Hartmann and Mario Ruben & Paul-Antoine Hervieux},

url = {https://doi.org/10.1038/s41534-024-00829-6},

doi = {10.1038/s41534-024-00829-6},

issn = {2056-6387},

year  = {2024},

date = {2024-06-10},

urldate = {2024-06-10},

journal = {npj Quantum Inf},

volume = {10},

number = {59},

issue = {1},

abstract = {As qubit-based platforms face near-term technical challenges in terms of scalability, qudits, d-level bases of quantum information, are being implemented in multiple platforms as an alternative for Quantum Information Processing (QIP). We compare the infidelity scalings of single qudit and multiqubit systems within identical Hilbert space dimensions and noisy environments in the Lindblad formalism. We find them to be gate-independent to first-order and present an analytically-derived critical curve $$({d}^{2}-1)/3{log }_{2}(d)$$that benchmarks the operational time efficiency of qudits and qubits relative to their decoherence times. This comparison reveals conditions under which qudits offer competitive gate efficiencies compared to leading qubit platforms. Our findings, supported by numerical simulations testing the applicability and limits of the linear response formalism, highlight the relevance of qudits in near-term QIP. This provides a benchmark for evaluating qudit platforms, specifically those with lower dimensionality, in terms of their operational efficiency relative to the qubit state-of-the-art.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{Chen2024,

title = {Full- and low-rank exponential Euler integrators for the Lindblad equation},

author = {Hao Chen and Alfio Borzì and Denis Janković and Jean-Gabriel Hartmann and Paul-Antoine Hervieux},

url = {https://arxiv.org/abs/2408.13601},

doi = {10.48550/arXiv.2408.13601 Focus to learn more},

issn = {2408.13601},

year  = {2024},

date = {2024-08-24},

urldate = {2024-08-24},

journal = {arXiv},

abstract = {The Lindblad equation is a widely used quantum master equation to model the dynamical evolution of open quantum systems whose states are described by density matrices. These solution matrices are characterized by semi-positiveness and trace preserving properties, which must be guaranteed in any physically meaningful numerical simulation. In this paper, novel full- and low-rank exponential Euler integrators are developed for approximating the Lindblad equation that preserve positivity and trace unconditionally. Theoretical results are presented that provide sharp error estimates for the two classes of exponential integration methods. Results of numerical experiments are discussed that illustrate the effectiveness of the proposed schemes, beyond present state-of-the-art capabilities.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}