Self-Orthogonal Codes Constructed from Posets and Their Applications in Quantum Communication

It is an important issue to search for self-orthogonal codes for construction of quantum codes by CSS construction (Calderbank-Sho-Steane codes); in quantum error correction, CSS codes are a special type of stabilizer codes constructed from classical codes with some special properties, and the CSS construction of quantum codes is a well-known construction. First, we employ hierarchical posets with two levels for construction of binary linear codes. Second, we find some necessary and sufficient conditions for these linear codes constructed using posets to be self-orthogonal, and we use these self-orthogonal codes for obtaining binary quantum codes. Finally, we obtain four infinite families of binary quantum codes for which the minimum distances are three or four by CSS construction, which include binary quantum Hamming codes with length n≥7. We also find some (almost) “optimal” quantum codes according to the current database of Grassl. Furthermore, we explicitly determine the weight distributions of these linear codes constructed using posets, and we present two infinite families of some optimal binary linear codes with respect to the Griesmer bound and a class of binary Hamming codes.

Magic state distillation with low space overhead and optimal asymptotic input count

We present an infinite family of protocols to distill magic states for T-gates that has a low space overhead and uses an asymptotic number of input magic states to achieve a given target error that is conjectured to be optimal. The space overhead, defined as the ratio between the physical qubits to the number of output magic states, is asymptotically constant, while both the number of input magic states used per output state and the T-gate depth of the circuit scale linearly in the logarithm of the target error δ (up to log⁡log⁡1/δ). Unlike other distillation protocols, this protocol achieves this performance without concatenation and the input magic states are injected at various steps in the circuit rather than all at the start of the circuit. The protocol can be modified to distill magic states for other gates at the third level of the Clifford hierarchy, with the same asymptotic performance. The protocol relies on the construction of weakly self-dual CSS codes with many logical qubits and large distance, allowing us to implement control-SWAPs on multiple qubits. We call this code the "inner code". The control-SWAPs are then used to measure properties of the magic state and detect errors, using another code that we call the "outer code". Alternatively, we use weakly-self dual CSS codes which implement controlled Hadamards for the inner code, reducing circuit depth. We present several specific small examples of this protocol.

A Consolidated Web Browser Interface Using Multiple Browser Libraries for Testing Web Designs

<p>This study aimed to create a consolidated web browser interface usingmultiple browser libraries for testing web designs. Specifically, this research effort intended to develop an application capable to test web designs on the top four (4) most commonly used web browsers namely, Mozilla Firefox, Google Chrome, Internet Explorer, and Safari. Furthermore, this research undertaking also meant to develop an application with syntax coloring and line numbers to help web developers determine syntax pairing and differences between browser outputs, and which would allow the users to directly edit specified CSS and HTML code through the text editor. Through experimental development approach and consultation with seventeen respondents who were selected through random sampling, the researchers were able to integrate the cited web browsers into one application enabling the web developers to avoid downloading and installing web browser applications one–by–one, and giving them the opportunity to test their web designs either online or offline. Findings revealed that the consolidated web browser interface using multiple browser libraries could help test web designs. The resulting program consolidated into one application the Mozilla Firefox, Google Chrome, Internet Explorer, and Safari, through the use of GeckoFX, WebKit, and XULRunner, making the browsers stand alone tools. In addition, RegEx and Line Numbers were also used for the syntax coloring and line numbering. Further, the consolidated web browser interface using multiple browser libraries for testing web designs could lessen the problem in following a certain standard code of a browser, especially HTML and CSS codes.</p>