Towards practical classical processing for the surface code: timing analysis

Topological quantum error correction codes have high thresholds and are well suited to physical implementation. The minimum weight perfect matching algorithm can be used to efficiently handle errors in such codes. We perform a timing analysis of our current implementation of the minimum weight perfect matching algorithm. Our implementation performs the classical processing associated with an nxn lattice of qubits realizing a square surface code storing a single logical qubit of information in a fault-tolerant manner. We empirically demonstrate that our implementation requires only O(n^2) average time per round of error correction for code distances ranging from 4 to 512 and a range of depolarizing error rates. We also describe tests we have performed to verify that it always obtains a true minimum weight perfect matching.Comment: 13 pages, 13 figures, version accepted for publicatio

Topological code Autotune

Many quantum systems are being investigated in the hope of building a large-scale quantum computer. All of these systems suffer from decoherence, resulting in errors during the execution of quantum gates. Quantum error correction enables reliable quantum computation given unreliable hardware. Unoptimized topological quantum error correction (TQEC), while still effective, performs very suboptimally, especially at low error rates. Hand optimizing the classical processing associated with a TQEC scheme for a specific system to achieve better error tolerance can be extremely laborious. We describe a tool Autotune capable of performing this optimization automatically, and give two highly distinct examples of its use and extreme outperformance of unoptimized TQEC. Autotune is designed to facilitate the precise study of real hardware running TQEC with every quantum gate having a realistic, physics-based error model.Comment: 13 pages, 17 figures, version accepted for publicatio

The s=1/2s=1/2 Antiferromagnetic Heisenberg Model on Fullerene-Type Symmetry Clusters

The $s_{i}={1/2}$ nearest neighbor antiferromagnetic Heisenberg model is considered for spins sitting on the vertices of clusters with the connectivity of fullerene molecules and a number of sites $n$ ranging from 24 to 32. Using the permutational and spin inversion symmetries of the Hamiltonian the low energy spectrum is calculated for all the irreducible representations of the symmetry group of each cluster. Frustration and connectivity result in non-trivial low energy properties, with the lowest excited states being singlets except for $n=28$. Same hexagon and same pentagon correlations are the most effective in the minimization of the energy, with the $n=32-D_{3h}$ symmetry cluster having an unusually strong singlet intra-pentagon correlation. The magnetization in a field shows no discontinuities unlike the icosahedral $I_h$ fullerene clusters, but only plateaux with the most pronounced for $n=28$. The spatial symmetry as well as the connectivity of the clusters appear to be important for the determination of their magnetic properties.Comment: Extended to include low energy spectra, correlation functions and magnetization data of clusters up to 32 site

The effect of low-dose pre-operative X-irradiation of implanted mouse mammary carcinomas on local recurrence and metastasis.

Pre-operative X-irradiation of s.c. implanted first-generation mammary tumours in C3H mice, using either 500 rad or two fractions of 350 rad, produced no improvement in the success of surgery in causing local control or in reduction of distant metastases. The metastasis rate was just significantly higher after the two-fraction treatment of the implanted tumour than after surgical removal alone. The results are in agreement with previously published results on carcinomas and a sarcoma but contrast with those for murine lymphomas

Lattice-Gas Simulations of Ternary Amphiphilic Fluid Flow in Porous Media

We develop our existing two-dimensional lattice-gas model to simulate the flow of single-phase, binary-immiscible and ternary-amphiphilic fluids. This involves the inclusion of fixed obstacles on the lattice, together with the inclusion of ``no-slip'' boundary conditions. Here we report on preliminary applications of this model to the flow of such fluids within model porous media. We also construct fluid invasion boundary conditions, and the effects of invading aqueous solutions of surfactant on oil-saturated rock during imbibition and drainage are described.Comment: 9 pages, 6 figures (1 and 6 are in color), RevTeX with epsf and graphic

Towards practical classical processing for the surface code

The surface code is unarguably the leading quantum error correction code for 2-D nearest neighbor architectures, featuring a high threshold error rate of approximately 1%, low overhead implementations of the entire Clifford group, and flexible, arbitrarily long-range logical gates. These highly desirable features come at the cost of significant classical processing complexity. We show how to perform the processing associated with an nxn lattice of qubits, each being manipulated in a realistic, fault-tolerant manner, in O(n^2) average time per round of error correction. We also describe how to parallelize the algorithm to achieve O(1) average processing per round, using only constant computing resources per unit area and local communication. Both of these complexities are optimal.Comment: 5 pages, 6 figures, published version with some additional tex

Hierarchical Model for the Evolution of Cloud Complexes

The structure of cloud complexes appears to be well described by a "tree structure" representation when the image is partitioned into "clouds". In this representation, the parent-child relationships are assigned according to containment. Based on this picture, a hierarchical model for the evolution of Cloud Complexes, including star formation, is constructed, that follows the mass evolution of each sub-structure by computing its mass exchange (evaporation or condensation) with its parent and children, which depends on the radiation density at the interphase. For the set of parameters used as a reference model, the system produces IMFs with a maximum at too high mass (~2 M_sun) and the characteristic times for evolution seem too long. We show that these properties can be improved by adjusting model parameters. However, the emphasis here is to illustrate some general properties of this nonlinear model for the star formation process. Notwithstanding the simplifications involved, the model reveals an essential feature that will likely remain if additional physical processes are included. That is: the detailed behavior of the system is very sensitive to variations on the initial and external conditions, suggesting that a "universal" IMF is very unlikely. When an ensemble of IMFs corresponding to a variety of initial or external conditions is examined, the slope of the IMF at high masses shows variations comparable to the range derived from observational data. (Abridged)Comment: Latex, 29 pages, 13 figures, accepted for publication in Ap