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This research extends the HHL algorithm from qubits to qutrits, demonstrating that higher-dimensional systems can solve linear systems with fewer physical resources while maintaining comparable gate counts. By applying this approach to quantum chemistry simulations of hydrogen molecules, the study provides a practical pathway for optimizing near-term quantum hardware efficiency. The work establishes a concrete advantage for qudit-based architectures in specific computational domains like molecular energy calculations.
The Harrow-Hassidim-Lloyd algorithm with qutrits
arXiv:2511.17960v3 Announce Type: replace Abstract: We extend the Harrow-Hassidim-Lloyd (HHL) algorithm, which is well-studied in the qubit framework, to its qutrit counterpart (which we call qutrit HHL, as opposed to qubit HHL, which is HHL using qubits), and develop a program for its implementation. We design Weyl-Heisenberg gadgets, the qutrit equivalents of Pauli gadgets, and come up with a practical implementation scheme for qutrit HHL. We test HHL with qutrits for simple matrices and verify the results against the expected outcomes. We apply the algorithm to quantum chemistry, and in particular, to the potential energy curve calculations of the model problem of the Hydrogen molecule in the split valence basis. We do so for two cases: 1-qutrit and 2-qutrit input states, where the latter makes use of our gadgets. We compare the number of qudits and the number of gates required between qubit and qutrit HHL implementations. In general, we find that for a fixed precision, the qutrit HHL circuit requires fewer number of qudits and comparable number of two-qudit gates than its qubit counterpart.
Abstract:We extend the Harrow-Hassidim-Lloyd (HHL) algorithm, which is well-studied in the qubit framework, to its qutrit counterpart (which we call qutrit HHL, as opposed to qubit HHL, which is HHL using qubits), and develop a program for its implementation. We design Weyl-Heisenberg gadgets, the qutrit equivalents of Pauli gadgets, and come up with a practical implementation scheme for qutrit HHL. We test HHL with qutrits for simple matrices and verify the results against the expected outcomes. We apply the algorithm to quantum chemistry, and in particular, to the potential energy curve calculations of the model problem of the Hydrogen molecule in the split valence basis. We do so for two cases: 1-qutrit and 2-qutrit input states, where the latter makes use of our gadgets. We compare the number of qudits and the number of gates required between qubit and qutrit HHL implementations. In general, we find that for a fixed precision, the qutrit HHL circuit requires fewer number of qudits and comparable number of two-qudit gates than its qubit counterpart.
In v3, we have fixed some details related to Weyl-Heisenberg gadgets. Comments are welcome!
Quantum Physics (quant-ph); Atomic Physics (physics.atom-ph); Chemical Physics (physics.chem-ph)
arXiv:2511.17960 [quant-ph]
(or arXiv:2511.17960v3 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2511.17960 Focus to learn more arXiv-issued DOI via DataCite
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