Techniques for combining fast local decoders with global decoders under circuit-level noise

Implementing algorithms on a fault-tolerant quantum computer will require fast decoding throughput and latency times to prevent an exponential increase in buffer times between the applications of gates. In this work we begin by quantifying these requirements. We then introduce the construction of local neural network (NN) decoders using three-dimensional convolutions. These local decoders are adapted to circuit-level noise and can be applied to surface code volumes of arbitrary size. Their application removes errors arising from a certain number of faults, which serves to substantially reduce the syndrome density. Remaining errors can then be corrected by a global decoder, such as Blossom or Union Find, with their implementation significantly accelerated due to the reduced syndrome density. However, in the circuit-level setting, the corrections applied by the local decoder introduce many vertical pairs of highlighted vertices. To obtain a low syndrome density in the presence of vertical pairs, we consider a strategy of performing a syndrome collapse which removes many vertical pairs and reduces the size of the decoding graph used by the global decoder. We also consider a strategy of performing a vertical cleanup, which consists of removing all local vertical pairs prior to implementing the global decoder. Lastly, we estimate the cost of implementing our local decoders on Field Programmable Gate Arrays (FPGAs).Comment: 28 pages, 24 figures. Comments welcome! V2 Contains a more detailed FPGA analysi

Safety of growth hormone replacement in survivors of cancer and intracranial and pituitary tumours: a consensus statement

Growth hormone (GH) has been used for over 35 years, and its safety and efficacy has been studied extensively. Experimental studies showing the permissive role of GH/insulin-like growth factor 1 (IGF-I) in carcinogenesis have raised concerns regarding the safety of GH replacement in children and adults who have received treatment for cancer and those with intracranial and pituitary tumours. A consensus statement was produced to guide decision-making on GH replacement in children and adult survivors of cancer, in those treated for intracranial and pituitary tumours and in patients with increased cancer risk. With the support of the European Society of Endocrinology, the Growth Hormone Research Society convened a Workshop, where 55 international key opinion leaders representing 10 professional societies were invited to participate. This consensus statement utilized: (1) a critical review paper produced before the Workshop, (2) five plenary talks, (3) evidence-based comments from four breakout groups, and (4) discussions during report-back sessions. Current evidence reviewed from the proceedings from the Workshop does not support an association between GH replacement and primary tumour or cancer recurrence. The effect of GH replacement on secondary neoplasia risk is minor compared to host- and tumour treatment-related factors. There is no evidence for an association between GH replacement and increased mortality from cancer amongst GH-deficient childhood cancer survivors. Patients with pituitary tumour or craniopharyngioma remnants receiving GH replacement do not need to be treated or monitored differently than those not receiving GH. GH replacement might be considered in GH-deficient adult cancer survivors in remission after careful individual risk/benefit analysis. In children with cancer predisposition syndromes, GH treatment is generally contraindicated but may be considered cautiously in select patients

Attitude Control of All-Electric Satellites During Low- Thrust Orbit Transfers

Attitude control of spacecraft during low-thrust orbit-raising maneuvers poses a problem for the adoption of electric primary propulsion systems in telecommunications satellites due to the potentially large slew requirements associated with the long duration of the continuous-thrust maneuver over which the spacecraft must maintain a target attitude. For the entire duration of a transfer trajectory, which may take several months for a transfer from LEO to GEO, an all-electric spacecraft must maintain its primary thrusters pointed along a speci¿ed target direction as well as keep its solar arrays oriented to the sun for power generation. In this study, a model for the attitude dynamics and control of a spacecraft using reaction wheel actuators is developed in order to investigate the attitude control system requirements to maintain pointing along an orbit-raising trajectory. Attitude control is then simulated for three orbit-raising scenarios in which maneuvers are the solutions of minimum-time low-thrust trajectory optimization for an equatorial, polar, and three-dimensional transfer to GEO. Results from these three case studies show that for an all-electric equivalent to a typical geostationary telecommunications satellite, the spacecraft is able to maintain thrust direction and orient its solar arrays normal to the sun for maximum power generation for the entire transfer duration without exceeding maximum reaction wheel control torques or requiring momentum unloading maneuvers to spin down reaction wheels. Moreover, the simulations predict the reaction wheel power consumption remains very small relative to the spacecraft power budget during the transfer. These conclusions demonstrate predicted attitude control system requirements for low-thrust missions to GEO, with the aim to incorporate rotational dynamics into complete six degree of freedom trajectory optimizations for all-electric spacecraft in future work

The DGDD Method for Reduced-Order Modeling of Conservation Laws

The discontinuous Galerkin domain decomposition (DGDD) method couples subdomains of high-fidelity polynomial approximation to regions of low-dimensional resolution for the numerical solution of systems of conservation laws. In the low-fidelity regions, the solution is approximated by empirical modes constructed by Proper Orthogonal Decomposition and a reduced-order model is used to predict the solution. The high-dimensional model instead solves the system of conservation laws only in regions where the solution is not amenable to a low-dimensional representation. The coupling between the high-dimensional and the reduced-order models is then performed in a straightforward manner through numerical fluxes at discrete cell boundaries. We show results from application of the proposed method to parametric problems governed by the quasi-1D and 2D compressible Euler equations. In particular, we investigate the prediction of unsteady flows in a converging-diverging nozzle and over a NACA0012 airfoil in presence of shocks. The results demonstrate the stability and the accuracy of the proposed method and the significant reduction of the computational cost with respect to the high-dimensional model.Accurate Roms for Industrial Application

libCEED User Manual

<p>Library Code for Efficient Extensible Discretization</p&gt