Low Complexity Encoding for Network Codes

In this paper we consider the per-node run-time complexity of network multicast codes. We show that the randomized algebraic network code design algorithms described extensively in the literature result in codes that on average require a number of operations that scales quadratically with the blocklength m of the codes. We then propose an alternative type of linear network code whose complexity scales linearly in m and still enjoys the attractive properties of random algebraic network codes. We also show that these codes are optimal in the sense that any rate-optimal linear network code must have at least a linear scaling in run-time complexity

Magic-State Functional Units: Mapping and Scheduling Multi-Level Distillation Circuits for Fault-Tolerant Quantum Architectures

Quantum computers have recently made great strides and are on a long-term path towards useful fault-tolerant computation. A dominant overhead in fault-tolerant quantum computation is the production of high-fidelity encoded qubits, called magic states, which enable reliable error-corrected computation. We present the first detailed designs of hardware functional units that implement space-time optimized magic-state factories for surface code error-corrected machines. Interactions among distant qubits require surface code braids (physical pathways on chip) which must be routed. Magic-state factories are circuits comprised of a complex set of braids that is more difficult to route than quantum circuits considered in previous work [1]. This paper explores the impact of scheduling techniques, such as gate reordering and qubit renaming, and we propose two novel mapping techniques: braid repulsion and dipole moment braid rotation. We combine these techniques with graph partitioning and community detection algorithms, and further introduce a stitching algorithm for mapping subgraphs onto a physical machine. Our results show a factor of 5.64 reduction in space-time volume compared to the best-known previous designs for magic-state factories.Comment: 13 pages, 10 figure

Linux kernel compaction through cold code swapping

There is a growing trend to use general-purpose operating systems like Linux in embedded systems. Previous research focused on using compaction and specialization techniques to adapt a general-purpose OS to the memory-constrained environment, presented by most, embedded systems. However, there is still room for improvement: it has been shown that even after application of the aforementioned techniques more than 50% of the kernel code remains unexecuted under normal system operation. We introduce a new technique that reduces the Linux kernel code memory footprint, through on-demand code loading of infrequently executed code, for systems that support virtual memory. In this paper, we describe our general approach, and we study code placement algorithms to minimize the performance impact of the code loading. A code, size reduction of 68% is achieved, with a 2.2% execution speedup of the system-mode execution time, for a case study based on the MediaBench II benchmark suite

Topological quantum memory

We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated with nontrivial homology cycles of the surface. We formulate protocols for error recovery, and study the efficacy of these protocols. An order-disorder phase transition occurs in this system at a nonzero critical value of the error rate; if the error rate is below the critical value (the accuracy threshold), encoded information can be protected arbitrarily well in the limit of a large code block. This phase transition can be accurately modeled by a three-dimensional Z_2 lattice gauge theory with quenched disorder. We estimate the accuracy threshold, assuming that all quantum gates are local, that qubits can be measured rapidly, and that polynomial-size classical computations can be executed instantaneously. We also devise a robust recovery procedure that does not require measurement or fast classical processing; however for this procedure the quantum gates are local only if the qubits are arranged in four or more spatial dimensions. We discuss procedures for encoding, measurement, and performing fault-tolerant universal quantum computation with surface codes, and argue that these codes provide a promising framework for quantum computing architectures.Comment: 39 pages, 21 figures, REVTe