Qudit

In quantum computing, a qudit (/ˈkjuː/dɪt/) or quantum dit is the generalized unit of quantum information described by a superposition of d states, where the number of states is an integer equal to or greater than two.

Qudit versus qubit

A qudit, characterized by d=2 states is a qubit.^[1]

Qudits with d states greater than 2 can provide a larger Hilbert space, providing more ways to store and process quantum information.^[2][3]

Qudit States

• Qubit – Qudit with d=2 states
• Qutrit – Qudit with d=3 states
• Ququart – Qudit with d=4 states

Error Correction

Quantum decoherence is the natural process where quantum information is lost due to environmental interaction and quantum error correction is a technique that actively combats decoherence.

In a paper published by Nature on May 14th, 2025 researchers at Yale first demonstrate quantum error correction past the break-even point for higher dimensional qudit systems. The team used GKP bosonic codes to encode qutrits and ququarts in superconducting cavities and optimized the protocol using reinforcement learning.^[4] These findings are regarded as a significant step in the creation of more efficient quantum computers and opens new paths for hardware-lean quantum architectures, fault tolerant computation, and compact error protected memories.^[5]

In a paper published September 2025, researchers demonstrate a new hybrid method that encodes information in both light and matter using a cat state qudit with d>2 which allows for the detection of photon loss through the parity syndrome by entangling a light pulse with ancillary qubits. This method achieves parallel Bell-pair generation by leveraging the multi-level nature of the qudit.^[6]

The first open source qudit stabilizer simulator named "Sdim" was announced November 2025 in a pre-print paper on arXiv.^[7]

Qudit Logic Gates

A qudit logic gate (or simply qudit gate) is a basic quantum circuit that acts on a qudit.

To achieve a universal qudit gate, (a gate that can be used to approximate any unitary transformation on a quantum computer to an arbitrary degree of accuracy) a set of gates must include a finite set of single qudit gates and at least one two qudit entangling gate that can create entanglement between qudits.

Qudit Control

Qudit control is the precise navigation of a qudit’s quantum state through engineered signals to perform quantum computations.

In a paper published December 16^th, 2025 a team of researchers achieved a breakthrough in qudit control by engineering five level qudits through individually addressable transitions between Zeeman sublevels (see also Zeeman Effect), achieved by combining a large linear Zeeman shift with a state-dependent light shift. Simulations predict state-preparation fidelities of F ≃ 0.99 within ∽1 μs , single-qudit gate fidelities of F ≃ 0.99 with π pulse durations of ∽ 2.5 μs, and fast destructive imaging with durations below 10 μs . These results establish a broadly applicable framework for high-fidelity control of Zeeman sublevel-encoded qudits and a promising platform for scalable qudit-based quantum technologies.^[8]

Use In Measurement

Quantum information is traditionally used in Ramsey interferometry, a technique used for precise measurement across various areas of science and technology.

Qudits with d>2 have shown to increase precision and resolution of quantum measurements. Qutrits, for example, have shown to achieve a twofold increase in resolution compared to qubits without any reduction in measurement contrast.^[9]

References

1. "What is a Qudit? Advantages & Use Cases". www.quera.com. Retrieved 2025-09-21.
2. Meth, Michael; Zhang, Jinglei; Haase, Jan F.; Edmunds, Claire; Postler, Lukas; Jena, Andrew J.; Steiner, Alex; Dellantonio, Luca; Blatt, Rainer; Zoller, Peter; Monz, Thomas; Schindler, Philipp; Muschik, Christine; Ringbauer, Martin (2025-03-25). "Simulating two-dimensional lattice gauge theories on a qudit quantum computer". Nature Physics. 21 (4): 570–576. arXiv:2310.12110. Bibcode:2025NatPh..21..570M. doi:10.1038/s41567-025-02797-w. ISSN 1745-2473. PMC 11999872. PMID 40248572.
3. Meng, Zhe; Liu, Wen-Qiang; Song, Bo-Wen; Wang, Xiao-Yun; Zhang, An-Ning; Yin, Zhang-Qi (2024-02-20). "Experimental realization of high-dimensional quantum gates with ultrahigh fidelity and efficiency". Physical Review A. 109 (2) 022612. arXiv:2311.18179. Bibcode:2024PhRvA.109b2612M. doi:10.1103/PhysRevA.109.022612.
4. Brock, Benjamin L.; Singh, Shraddha; Eickbusch, Alec; Sivak, Volodymyr V.; Ding, Andy Z.; Frunzio, Luigi; Girvin, Steven M.; Devoret, Michel H. (May 2025). "Quantum error correction of qudits beyond break-even". Nature. 641 (8063): 612–618. doi:10.1038/s41586-025-08899-y. ISSN 1476-4687.
5. Swayne, Matt (2025-05-15). "Researchers Demonstrate Error-Corrected Qudits That Beat Break-Even". The Quantum Insider. Retrieved 2025-11-29.
6. McIntyre, Z. M.; Coish, W. A. (2025-09-10), Loss-tolerant parallelized Bell-state generation with a hybrid cat qudit, arXiv:2509.08577
7. Kabir, Adeeb; Nguyen, Steven; Ghosh, Sohan; Kiran, Tijil; Kim, Isaac H.; Huang, Yipeng (2025-11-16), Sdim: A Qudit Stabilizer Simulator, arXiv, doi:10.48550/arXiv.2511.12777, arXiv:2511.12777, retrieved 2025-11-20
8. Heizenreder, Benedikt; Gerritsen, Bas; Fouka, Katya; Spreeuw, Robert J. C.; Schreck, Florian; Naini, Arghavan Safavi; Urech, Alexander (2025-12-16), Engineering Zeeman-manifold quintets using state-dependent light shifts in neutral atoms, arXiv, doi:10.48550/arXiv.2512.14611, arXiv:2512.14611, retrieved 2025-12-20
9. Ilikj, Branislav; Vitanov, Nikolay V. (2025-09-08), Ramsey Interferometry with Qudits, arXiv:2509.06290