Universal Measurement-Based Quantum Computation in a One-Dimensional Architecture Enabled by Dual-Unitary Circuits

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 similar to 3 k/ 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.