Non-Clifford symmetry protected topological higher-order cluster states in multi-qubit measurement-based quantum computation

• URL: http://arxiv.org/abs/2602.20612v1
• Date: Tue, 24 Feb 2026 07:06:36 GMT
• Title: Non-Clifford symmetry protected topological higher-order cluster states in multi-qubit measurement-based quantum computation
• Authors: Motohiko Ezawa,
• Abstract summary: A cluster state is a strongly entangled state, which is a source of measurement-based quantum computation.<n>We show that there emerge $22N$ fold ground states for an open chain, indicating the emergence of $N$ free spins at each edge.<n>They can be used as an $N$-qubit input and an $N$-qubit output in measurement-based quantum computation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A cluster state is a strongly entangled state, which is a source of measurement-based quantum computation. It is generated by applying controlled-Z (CZ) gates to the state $\left\vert ++\cdots +\right\rangle $. It is protected by the $\mathbb{Z}_{2}^{\text{even}}\times \mathbb{Z}_{2}^{ \text{odd}}$ symmetry. By applying general quantum gates to the state $ \left\vert ++\cdots +\right\rangle $, we systematically obtain a general short-range entangled cluster state. If we use a non-Clifford gate such as the controlled phase-shift gate, we obtain a non-Clifford cluster state. Furthermore, if we use the controlled-controlled Z (CCZ) gate instead of the CZ gate, we obtain non-Clifford cluster states with five-body entanglement. We generalize it to the C$^{N}$Z gate, where $(2N+1)$-body entangled states are generated. The $\mathbb{Z}_{2}^{\text{even}}\times \mathbb{Z}_{2}^{\text{odd}}$ symmetry is non-Clifford for $N\geq 3$. We demonstrate that there emerge $2^{2N}$ fold degenerate ground states for an open chain, indicating the emergence of $N$ free spins at each edge. They can be used as an $N$-qubit input and an $N$-qubit output in measurement-based quantum computation. We also study the non-invertible symmetry, the Kennedy-Tasaki transformation and the string-order parameter in addition to the $\mathbb{Z}_{2}^{\text{even}}\times \mathbb{Z}_{2}^{\text{odd}}$ symmetry in these models.

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