Abstract: A method and apparatus for performing quantum error correction using an automorphism code related to the honeycomb code. The automorphism code is based on Kramers-Wannier (KW) duality. For embodiments on a hexagonal lattice using three repeated time steps, ? of the pixels are active in a given time steps. In a given time step r, a KW circuit is applied to plaquettes labeled r mod 3, transferring quantum information from the active qubits at the beginning to a new set of active qubits at the end of the time step. Each of the three plaquette types is associated with one stabilizer either given by a product of six Z operators or three X operators. The KW circuit maps the product of X operators to the product of Z operators and vice-versa. The stabilizer group of the superlattice toric code changes every round.

Abstract: A material delivery interface includes a fixed assembly that is coupled to a primary structural attachment. The fixed assembly includes a fluid inlet and a wired input, wherein the fixed assembly defines a central axis. A rotational assembly is rotationally coupled to the fixed assembly and that rotates about the central axis with respect to the fixed assembly. The rotational assembly includes an inner portion having a fluid outlet in fluid communication with the fluid inlet and an outer portion having a wired output, wherein a conduit extends from the wired input to the wired output.

Abstract: A material delivery interface includes a fixed assembly that is coupled to a primary structural attachment. The fixed assembly includes a fluid inlet and a wired input, wherein the fixed assembly defines a central axis. A rotational assembly is rotationally coupled to the fixed assembly and that rotates about the central axis with respect to the fixed assembly. The rotational assembly includes an inner portion having a fluid outlet in fluid communication with the fluid inlet and an outer portion having a wired output, wherein a conduit extends from the wired input to the wired output.

Abstract: A material delivery interface includes a fixed assembly that is coupled to a primary structural attachment. The fixed assembly includes a fluid inlet and a wired input, wherein the fixed assembly defines a central axis. A rotational assembly is rotationally coupled to the fixed assembly and that rotates about the central axis with respect to the fixed assembly. The rotational assembly includes an inner portion having a fluid outlet in fluid communication with the fluid inlet and an outer portion having a wired output, wherein a conduit extends from the wired input to the wired output.

Abstract: A material delivery interface includes a fixed assembly that is coupled to a primary structural attachment. The fixed assembly includes a fluid inlet and a wired input, wherein the fixed assembly defines a central axis. A rotational assembly is rotationally coupled to the fixed assembly and that rotates about the central axis with respect to the fixed assembly. The rotational assembly includes an inner portion having a fluid outlet in fluid communication with the fluid inlet and an outer portion having a wired output, wherein a conduit extends from the wired input to the wired output.