Design of Geometric Molecular Bonds

An example of a nonspecific molecular bond is the affinity of any positive charge for any negative charge (like-unlike), or of nonpolar material for itself when in aqueous solution (like-like). This contrasts specific bonds such as the affinity of the DNA base A for T, but not for C, G, or another A. Recent experimental breakthroughs in DNA nanotechnology demonstrate that a particular nonspecific like-like bond ("blunt-end DNA stacking" that occurs between the ends of any pair of DNA double-helices) can be used to create specific "macrobonds" by careful geometric arrangement of many nonspecific blunt ends, motivating the need for sets of macrobonds that are orthogonal: two macrobonds not intended to bind should have relatively low binding strength, even when misaligned. To address this need, we introduce geometric orthogonal codes that abstractly model the engineered DNA macrobonds as two-dimensional binary codewords. While motivated by completely different applications, geometric orthogonal codes share similar features to the optical orthogonal codes studied by Chung, Salehi, and Wei. The main technical difference is the importance of 2D geometry in defining codeword orthogonality.Comment: Accepted to appear in IEEE Transactions on Molecular, Biological, and Multi-Scale Communication

Parsing a sequence of qubits

We develop a theoretical framework for frame synchronization, also known as block synchronization, in the quantum domain which makes it possible to attach classical and quantum metadata to quantum information over a noisy channel even when the information source and sink are frame-wise asynchronous. This eliminates the need of frame synchronization at the hardware level and allows for parsing qubit sequences during quantum information processing. Our framework exploits binary constant-weight codes that are self-synchronizing. Possible applications may include asynchronous quantum communication such as a self-synchronizing quantum network where one can hop into the channel at any time, catch the next coming quantum information with a label indicating the sender, and reply by routing her quantum information with control qubits for quantum switches all without assuming prior frame synchronization between users.Comment: 11 pages, 2 figures, 1 table. Final accepted version for publication in the IEEE Transactions on Information Theor

Approximate quantum error correction for generalized amplitude damping errors

We present analytic estimates of the performances of various approximate quantum error correction schemes for the generalized amplitude damping (GAD) qubit channel. Specifically, we consider both stabilizer and nonadditive quantum codes. The performance of such error-correcting schemes is quantified by means of the entanglement fidelity as a function of the damping probability and the non-zero environmental temperature. The recovery scheme employed throughout our work applies, in principle, to arbitrary quantum codes and is the analogue of the perfect Knill-Laflamme recovery scheme adapted to the approximate quantum error correction framework for the GAD error model. We also analytically recover and/or clarify some previously known numerical results in the limiting case of vanishing temperature of the environment, the well-known traditional amplitude damping channel. In addition, our study suggests that degenerate stabilizer codes and self-complementary nonadditive codes are especially suitable for the error correction of the GAD noise model. Finally, comparing the properly normalized entanglement fidelities of the best performant stabilizer and nonadditive codes characterized by the same length, we show that nonadditive codes outperform stabilizer codes not only in terms of encoded dimension but also in terms of entanglement fidelity.Comment: 44 pages, 8 figures, improved v

Optical multiple access techniques for on-board routing

The purpose of this research contract was to design and analyze an optical multiple access system, based on Code Division Multiple Access (CDMA) techniques, for on board routing applications on a future communication satellite. The optical multiple access system was to effect the functions of a circuit switch under the control of an autonomous network controller and to serve eight (8) concurrent users at a point to point (port to port) data rate of 180 Mb/s. (At the start of this program, the bit error rate requirement (BER) was undefined, so it was treated as a design variable during the contract effort.) CDMA was selected over other multiple access techniques because it lends itself to bursty, asynchronous, concurrent communication and potentially can be implemented with off the shelf, reliable optical transceivers compatible with long term unattended operations. Temporal, temporal/spatial hybrids and single pulse per row (SPR, sometimes termed 'sonar matrices') matrix types of CDMA designs were considered. The design, analysis, and trade offs required by the statement of work selected a temporal/spatial CDMA scheme which has SPR properties as the preferred solution. This selected design can be implemented for feasibility demonstration with off the shelf components (which are identified in the bill of materials of the contract Final Report). The photonic network architecture of the selected design is based on M(8,4,4) matrix codes. The network requires eight multimode laser transmitters with laser pulses of 0.93 ns operating at 180 Mb/s and 9-13 dBm peak power, and 8 PIN diode receivers with sensitivity of -27 dBm for the 0.93 ns pulses. The wavelength is not critical, but 830 nm technology readily meets the requirements. The passive optical components of the photonic network are all multimode and off the shelf. Bit error rate (BER) computations, based on both electronic noise and intercode crosstalk, predict a raw BER of (10 exp -3) when all eight users are communicating concurrently. If better BER performance is required, then error correction codes (ECC) using near term electronic technology can be used. For example, the M(8,4,4) optical code together with Reed-Solomon (54,38,8) encoding provides a BER of better than (10 exp -11). The optical transceiver must then operate at 256 Mb/s with pulses of 0.65 ns because the 'bits' are now channel symbols