Universal measurement-based quantum computation in a one-dimensional architecture enabled by dual-unitary circuits

• URL: http://arxiv.org/abs/2209.06191v2
• Date: Thu, 16 May 2024 05:36:29 GMT
• Title: Universal measurement-based quantum computation in a one-dimensional architecture enabled by dual-unitary circuits
• Authors: David T. Stephen, Wen Wei Ho, Tzu-Chieh Wei, Robert Raussendorf, Ruben Verresen,
• Abstract summary: We show that applying a dual-unitary circuit to a many-body state followed by appropriate measurements effectively implements quantum computation in the spatial direction. Our protocol allows generic quantum circuits to be rotated' in space-time and gives new ways to exchange between resources like qubit number and coherence time in quantum computers.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A powerful tool emerging from the study of many-body quantum dynamics is that of dual-unitary circuits, which are unitary even when read `sideways', i.e., along the spatial direction. Here, we show that this provides the ideal framework to understand and expand on the notion of measurement-based quantum computation (MBQC). In particular, applying a dual-unitary circuit to a many-body state followed by appropriate measurements effectively implements quantum computation in the spatial direction. We show how the dual-unitary dynamics generated by the dynamics of the paradigmatic one-dimensional kicked Ising chain with certain parameter choices generate resource states for universal deterministic MBQC. Specifically, after $k$ time-steps, equivalent to a depth-$k$ quantum circuit, we obtain a resource state for universal MBQC on $\sim 3k/4$ encoded qubits. Our protocol allows generic quantum circuits to be `rotated' in space-time and gives new ways to exchange between resources like qubit number and coherence time in quantum computers. Beyond the practical advantages, we also interpret the dual-unitary evolution as generating an infinite sequence of new symmetry-protected topological phases with spatially modulated symmetries, which gives a vast generalization of the well-studied one-dimensional cluster state and shows that our protocol is robust to symmetry-respecting deformations.

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