Unitary mechanical metamaterials with embedded one-qubit logic

A class of lattice metamaterials characterized by a transfer matrix that updates polarization of a static sinusoidal displacement wave along a material coordinate in accordance with a unitary transformation is conceptualized. Specific material designs are discussed where the unitary transfer matrix takes the forms of the commonly used one-qubit quantum gates, such as the Pauli-X, Hadamard and others, depending on the unit cell geometry. Also, polarization parameters of the displacement wave are shown to form a Pauli spinor, a two-component complex vector representing the qubit state. Unitary metamaterials can be realized in practice as certain planar structures, or 3D lattices in a state of deformation similar to the continuum plain strain. Their potential application in human-scale mechanical platforms for simulating the quantum computation logic is discussed.