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

We use dual-unitary circuits, which are unitary even when read 'sideways', as the basis of a new framework for 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 study the dynamics of the 1D kicked Ising chain and find that after k time-steps, equivalent to a depth-k quantum circuit, we obtain a resource state for universal MBQC on ∼3k/4 logical qubits. This removes the usual requirement of going to 2D to achieve universality, thereby reducing the demands imposed on potential experimental platforms. We also show that our resource states belong to a new class of symmetry-protected topological phases with spatially modulated symmetries, and that our protocol is robust to symmetric deformations.