In this work, we introduce a method to construct fault-tolerant measurement-based quantum computation (MBQC) architectures and numerically estimate their performance over various types of networks. A possible application of such a paradigm is distributed quantum computation, where separate computing nodes work together on a fault-tolerant computation through entanglement. We gauge error thresholds of the architectures with an efficient stabilizer simulator to investigate the resilience against both circuit-level and network noise. We show that, for both monolithic (i.e., non-distributed) and distributed implementations, an architecture based on the diamond lattice may outperform the conventional cubic lattice. Moreover, the high erasure thresholds of non-cubic lattices may be exploited further in a distributed context, as their performance may be boosted through entanglement distillation by trading in entanglement success rates against erasure errors during the error-decoding process. These results highlight the significance of lattice geometry in the design of fault-tolerant measurement-based quantum computing on a network, emphasizing the potential for constructing robust and scalable distributed quantum computers.In this work, we introduce a method to construct fault-tolerant measurement-based quantum computation (MBQC) architectures and numerically estimate their performance over various types of networks. A possible application of such a paradigm is distributed quantum computation, where separate computing nodes work together on a fault-tolerant computation through entanglement. We gauge error thresholds of the architectures with an efficient stabilizer simulator to investigate the resilience against both circuit-level and network noise. We show that, for both monolithic (i.e., non-distributed) and distributed implementations, an architecture based on the diamond lattice may outperform the conventional cubic lattice. Moreover, the high erasure thresholds of non-cubic lattices may be exploited further in a distributed context, as their performance may be boosted through entanglement distillation by trading in entanglement success rates against erasure errors during the error-decoding process. These results highlight the significance of lattice geometry in the design of fault-tolerant measurement-based quantum computing on a network, emphasizing the potential for constructing robust and scalable distributed quantum computers.

arXiv:2402.19323QuantumMay 5, 20256 citations

YZ-plane measurement-based quantum computation: Universality and Parity Architecture implementation

Jaroslav Kysela, Katharina Ludwig, Nitica Sakharwade +2 more

We define the class of register-logic graphs and prove that any uniformly deterministic measurement-based quantum computation (MBQC) where the inputs coincide with the outputs must be driven on such graphs by measurements in the $YZ$ plane of the Bloch sphere. This observation is revisited in the context that goes beyond uniform determinism, where we present a universal $YZ$ -plane-only measurement pattern and establish a connection between $YZ$ -plane-only and $XZ$ -plane-only patterns. These results conclude the line of research on universal patterns with measurements restricted to one of the principal planes of the Bloch sphere. We further demonstrate, within the framework of the Parity Architecture, that $YZ$ -plane patterns with the register-logic graph can be embedded into another graph with purely local interactions, and we extend this case to the scenario of universal quantum computation.We define the class of register-logic graphs and prove that any uniformly deterministic measurement-based quantum computation (MBQC) where the inputs coincide with the outputs must be driven on such graphs by measurements in the $YZ$ plane of the Bloch sphere. This observation is revisited in the context that goes beyond uniform determinism, where we present a universal $YZ$-plane-only measurement pattern and establish a connection between $YZ$-plane-only and $XZ$-plane-only patterns. These results conclude the line of research on universal patterns with measurements restricted to one of the principal planes of the Bloch sphere. We further demonstrate, within the framework of the Parity Architecture, that $YZ$-plane patterns with the register-logic graph can be embedded into another graph with purely local interactions, and we extend this case to the scenario of universal quantum computation.

quant-pharXiv:2603.29379Apr 1, 20260 citations

Graphix: A software framework for Measurement-Based Quantum Computation

Mateo Uldemolins, Pranav Nair, Emlyn Graham +3 more

Measurement-based quantum computing (MBQC) is a powerful model for quantum computation, but dedicated software tools that bridge its theoretical foundations with practical research workflows remain limited. We present Graphix, a software framework for MBQC written in Python that provides a unified environment for developing, integrating, and exploring measurement-based protocols and algorithms. Graphix establishes a modular, extensible, and user-friendly architecture for the compilation and simulation of quantum computations in the MBQC model with abstractions closely aligned with the theoretical formulations of MBQC. Through examples drawn from recent research on MBQC, we demonstrate Graphix's ability to reproduce and extend previous results. Graphix thus provides a software infrastructure for MBQC, supporting education and research while enabling collaborative development and accelerating the transition toward practical implementations.Measurement-based quantum computing (MBQC) is a powerful model for quantum computation, but dedicated software tools that bridge its theoretical foundations with practical research workflows remain limited. We present Graphix, a software framework for MBQC written in Python that provides a unified environment for developing, integrating, and exploring measurement-based protocols and algorithms. Graphix establishes a modular, extensible, and user-friendly architecture for the compilation and simulation of quantum computations in the MBQC model with abstractions closely aligned with the theoretical formulations of MBQC. Through examples drawn from recent research on MBQC, we demonstrate Graphix's ability to reproduce and extend previous results. Graphix thus provides a software infrastructure for MBQC, supporting education and research while enabling collaborative development and accelerating the transition toward practical implementations.

quant-pharXiv:2608.24781Aug 26, 20260 citations

Emerging applications of measurement-based quantum computing

Zheng Qin, Xiufan Li, Yang Zhou +4 more

Quantum Information ProcessingNov 28, 20242 citations

Basics and applications of measurement-based quantum computing

Tomoyuki Morimae

International Symposium on Information Theory and its ApplicationsDec 11, 20141 citation

YZ

plane of the Bloch sphere. This observation is revisited in the context that goes beyond uniform determinism, where we present a universal

YZ

-plane-only measurement pattern and establish a connection between

YZ

-plane-only and

XZ

-plane-only patterns. These results conclude the line of research on universal patterns with measurements restricted to one of the principal planes of the Bloch sphere. We further demonstrate, within the framework of the Parity Architecture, that

YZ

-plane patterns with the register-logic graph can be embedded into another graph with purely local interactions, and we extend this case to the scenario of universal quantum computation.