Working with measurement-based computations on qudits
2026-06-29 • Data Structures and Algorithms
Data Structures and Algorithms
AI summaryⓘ
The authors study a concept called 'flow' that helps ensure measurements in a special kind of quantum computing (measurement-based quantum computing) lead to predictable results. They focus on qudits, which are like quantum bits but with more levels, and provide a simpler way to understand and find this flow compared to previous work. Their new method makes finding flow faster and matches the best speed known for the simpler qubit case. They also explore ways to change the quantum states without losing the flow property, which could help optimize computations. Finally, they suggest a way to create large quantum computations with flow for testing or machine learning purposes.
measurement-based quantum computingquditgraph statesflowadaptive correctionquantum computationpivotingalgorithm complexityquantum optimizationmachine learning
Authors
Piotr Mitosek, Miriam Backens
Abstract
Measurement-based quantum computing is a universal model of quantum computation in which successive product measurements of an entangled resource state drive the computation. The non-deterministic nature of measurements necessitates adaptivity to ensure an overall deterministic computation. Flow structures characterise cases in which such an adaptive correction procedure is possible. Recently, flow has been defined in a setting where the resource states are prime-dimensional qudit graph states rather than the usual qubit graph states. Yet, this qudit flow definition is more burdensome to work with than analogous definitions for qubits. Here, we give a simpler definition of qudit flow and consider various useful properties of this flow, drawing on results for the qubit case. In particular, we show how to focus qudit flow and argue that focused flow is canonical. We improve the previous algebraic formulation to capture focused flow and use it to obtain an $O(n^3)$ flow-finding algorithm (where $n$ is the number of qudits), matching the best known complexity for qubit flows and improving on the previous $O(n^4)$ result for qudits. Furthermore, we explore multiple flow-preserving transformations, thus opening a pathway to using flow for optimisation. These transformations include pivoting, removal and insertion of certain types of vertices, and reversibility of flow. Lastly, we propose an algorithmic approach to generating large qudit computations with flow, for testing or machine learning.