We have designed and constructed DNA complexes in the form of triangles. We have created hexagonal planar tilings from these triangles via self-assembly. Unlike previously reported structures self-assembled from DNA, our structures appear to involve bending of double helices. Bending helices may be a useful design option in the creation of self-assembled DNA structures. It has been suggested that DNA self-assembly may lead to novel materials and efficient computational devices.

We designed a molecular complex, the double-double crossover, consisting of four DNA double helices connected by six reciprocal exchanges. Atomic force micrographs suggest that double-double crossover complexes self-assemble into high-density, doubly connected, two-dimensional, planar structures. Such structures may be suitable as substrates for the deposition of nanomaterials in the creation of high-density electrical and quantum devices. We speculate about a modified double-double crossover complex that might self-assemble into high-density, doubly connected, three-dimensional structures.

Steganography is the process of hiding secret information by embedding it inan "innocent" message. We present protocols for hiding quantum information in a codeword of a quantum error-correcting code passing through a channel. Steganography is the science of hiding a message within a larger innocent-looking plain-text message, and communicating the resulting data over a communications channel or by a courier so that the steganographic message is readable only by the intended receiver. The word comes from the Greek words steganos which means "covered," and graphia which means "writing."

We discuss two methods to encode one qubit into six physical qubits. Each of our two examples corrects an arbitrary single-qubit error. Our first example is a degenerate six-qubit quantum errorcorrecting code. We explicitly provide the stabilizer generators, encoding circuit, codewords, logical Pauli operators, and logical CNOT operator for this code. We also show how to convert this code into a non-trivial subsystem code that saturates the subsystem Singleton bound. We then prove that a six-qubit code without entanglement assistance cannot simultaneously possess a CalderbankShor-Steane (CSS) stabilizer and correct an arbitrary single-qubit error. A corollary of this result is that the Steane seven-qubit code is the smallest single-error correcting CSS code. Our second example is the construction of a non-degenerate six-qubit CSS entanglement-assisted code. This code uses one bit of entanglement (an ebit) shared between the sender and the receiver and corrects an arbitrary single-qubit error. The code we obtain is globally equivalent to the Steane seven-qubit code and thus corrects an arbitrary error on the receiver's half of the ebit as well. We prove that this code is the smallest code with a CSS structure that uses only one ebit and corrects an arbitrary single-qubit error on the sender's side. We discuss the advantages and disadvantages for each of the two codes.