Working With Measurement-Based Computations on Qudits
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.
Versions
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BibTeX
@misc{mitosek2026working,
title = {{Working With Measurement-Based Computations on Qudits}},
author = {Piotr Mitosek and Miriam Backens},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2606.30525},
eprint = {2606.30525},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.30525},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Working With Measurement-Based Computations on Qudits
AU - Piotr Mitosek
AU - Miriam Backens
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2606.30525
UR - https://arxiv.org/abs/2606.30525
AB - 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.
ER -