What is a Qudit?

A qudit is a quantum system which can realize more than two possible outcomes/states upon measurement. Qudits can be harder to manipulate, use, and conceptualize, but offer mathematical advantage over traditional qubit models. 

Qudit vs Qubit

As discussed in our discussion of the qubit, the primary building block of classical computation is the bit. Physical devices such as vacuum tubes, and later transistors, have been used to vary the bits in a classical system through induced logic. The same is true of qubit-based quantum systems: where qubits (quantum-bits) can be modified by external factors to induce logic, called quantum gates. The term bit is derived from binary (meaning two): the language of 0s and 1s used by classical systems. 

Quantum states have a property called superposition, where before a measurement, a state can take a variety of possible outcomes. Once a measurement occurs, the state collapses into a singular outcome. The probabilities which dictate the state must be normalized, such that the total probability of the system sums to one. The difference between a qubit and qudit lies in the number of states. A qubit is a state with two possible outcomes. A qudit is a generalized state for any d (dimension) outcomes. Thus, a qudit with d=2, is simply a qubit!

Qudit Advantages and Disadvantages

Quantum computation will be eventually considered advantageous due to the use of quantum effects such as superposition or entanglement in quantum-based logic. Using these concepts to surpass the performance of classical computers is generalized as Quantum Supremacy (see also Quantum Advantage). Qubits are able to compactly represent Hilbert space (or the space of all possible outcomes), more easily than their classical counterparts, which possess a worst case runtime of 2n for classically simulating n qubits. The exponential runtime of classical systems is considered very disadvantageous for many types of problems. This is why, classically, full solutions to these types of problems are avoided where possible (Ex: full electronic simulation or NP-Hard problems).  

Despite these advantages, most researchers still utilize qubits due to complications in qudit control. In fact, many leading platforms (besides pure Spin-½ systems) are more naturally qudits than qubits, researchers simply isolate the two-state systems in an attempt to prevent the occupation of any other state. As an example, many superconducting systems rely on nonlinear inductance or capacitance to create unequally spaced energy levels. Thus, control pulses can be engineered to stay within the two lowest energy levels. Similarly, QuEra using the optical pumping method, isolates Rb⁸⁷ atoms into a state where they can only be excited in one direction (given a specific polarization). These examples seem to be artifacts of a lack of control over energy states in current quantum infrastructure. As companies progress to finer and finer control, with more limited error cases, the use of qudits seems to be inevitable as a means for shrinking the amount of processing required for solving problems.

For a classical analogy: consider the transistor. Early transistors functioned as strict two-state switches. Now, some modern devices exploit additional finely spaced energy levels, with the use of multiple levels enabling multi-value logic and richer circuit primitives. As an example consider many current compute memory implementations. The move from qubits to both qubits and qudits will mirror the transition in classical electronics.

Qudit Use Cases: Quantum Computing and Qudit Stabilizers 

Companies have shown proof of concept qudit systems with full Universal Gate Sets. As an example, consider the following article from Nature: Control and readout of a 13-level trapped ion qudit. It seems that the majority of these processes are quite early in the R&D stage, but there is definite interest from a variety of quantum computing companies servicing different modalities to achieve consistent qudit design, specifically for their long-term aspirations. 

A more active area of research involving qudit design are the various forms of qudit-based stabilizers being pursued and analyzed for error correction codes, with the goal of achieving logical qubits. Positive results have included: 

• One d=4 qudit can replace two qubits, and some logic gates become native operations for specific gate mappings
• Surface codes thresholds rise as we increase d (proven for smaller d for certain noise models)
• Noise tailoring: isolated states can be included in the model for modeling where system leakage can occur

Experts in error correction believe that higher dimensionality and the use of qudits will be vital for reducing the scaling rate of turning Physical Qubits into logical ones. Only this year, authors of the Nature published Quantum error correction of qudits beyond break-even (Brock 2025) concluded the following:

“Access to a higher-dimensional error-corrected manifold of quantum states may enable more hardware-efficient architectures for quantum information processing.”