Distributed Quantum Computation Architecture Using Semiconductor Nanophotonics

In a large-scale quantum computer, the cost of communications will dominate the performance and resource requirements, place many severe demands on the technology, and constrain the architecture. Unfortunately, fault-tolerant computers based entirely on photons with probabilistic gates, though equipped with "built-in" communication, have very large resource overheads; likewise, computers with reliable probabilistic gates between photons or quantum memories may lack sufficient communication resources in the presence of realistic optical losses. Here, we consider a compromise architecture, in which semiconductor spin qubits are coupled by bright laser pulses through nanophotonic waveguides and cavities using a combination of frequent probabilistic and sparse determinstic entanglement mechanisms. The large photonic resource requirements incurred by the use of probabilistic gates for quantum communication are mitigated in part by the potential high-speed operation of the semiconductor nanophotonic hardware. The system employs topological cluster-state quantum error correction for achieving fault-tolerance. Our results suggest that such an architecture/technology combination has the potential to scale to a system capable of attacking classically intractable computational problems.Comment: 29 pages, 7 figures; v2: heavily revised figures improve architecture presentation, additional detail on physical parameters, a few new reference

Binary black hole merger in the extreme mass ratio limit

We discuss the transition from quasi-circular inspiral to plunge of a system of two nonrotating black holes of masses $m_1$ and $m_2$ in the extreme mass ratio limit $m_1m_2\ll (m_1+m_2)^2$. In the spirit of the Effective One Body (EOB) approach to the general relativistic dynamics of binary systems, the dynamics of the two black hole system is represented in terms of an effective particle of mass $\mu\equiv m_1m_2/(m_1+m_2)$ moving in a (quasi-)Schwarzschild background of mass $M\equiv m_1+m_2$ and submitted to an ${\cal O}(\mu)$ radiation reaction force defined by Pad\'e resumming high-order Post-Newtonian results. We then complete this approach by numerically computing, \`a la Regge-Wheeler-Zerilli, the gravitational radiation emitted by such a particle. Several tests of the numerical procedure are presented. We focus on gravitational waveforms and the related energy and angular momentum losses. We view this work as a contribution to the matching between analytical and numerical methods within an EOB-type framework.Comment: 14 pages, six figures. Revised version. To appear in the CQG special issue based around New Frontiers in Numerical Relativity conference, Golm (Germany), July 17-21 200

Surface code quantum computing by lattice surgery

In recent years, surface codes have become a leading method for quantum error correction in theoretical large scale computational and communications architecture designs. Their comparatively high fault-tolerant thresholds and their natural 2-dimensional nearest neighbour (2DNN) structure make them an obvious choice for large scale designs in experimentally realistic systems. While fundamentally based on the toric code of Kitaev, there are many variants, two of which are the planar- and defect- based codes. Planar codes require fewer qubits to implement (for the same strength of error correction), but are restricted to encoding a single qubit of information. Interactions between encoded qubits are achieved via transversal operations, thus destroying the inherent 2DNN nature of the code. In this paper we introduce a new technique enabling the coupling of two planar codes without transversal operations, maintaining the 2DNN of the encoded computer. Our lattice surgery technique comprises splitting and merging planar code surfaces, and enables us to perform universal quantum computation (including magic state injection) while removing the need for braided logic in a strictly 2DNN design, and hence reduces the overall qubit resources for logic operations. Those resources are further reduced by the use of a rotated lattice for the planar encoding. We show how lattice surgery allows us to distribute encoded GHZ states in a more direct (and overhead friendly) manner, and how a demonstration of an encoded CNOT between two distance 3 logical states is possible with 53 physical qubits, half of that required in any other known construction in 2D.Comment: Published version. 29 pages, 18 figure

Integration of highly probabilistic sources into optical quantum architectures: perpetual quantum computation

In this paper we introduce a design for an optical topological cluster state computer constructed exclusively from a single quantum component. Unlike previous efforts we eliminate the need for on demand, high fidelity photon sources and detectors and replace them with the same device utilised to create photon/photon entanglement. This introduces highly probabilistic elements into the optical architecture while maintaining complete specificity of the structure and operation for a large scale computer. Photons in this system are continually recycled back into the preparation network, allowing for a arbitrarily deep 3D cluster to be prepared using a comparatively small number of photonic qubits and consequently the elimination of high frequency, deterministic photon sources.Comment: 19 pages, 13 Figs (2 Appendices with additional Figs.). Comments welcom

Path Selection for Quantum Repeater Networks

Quantum networks will support long-distance quantum key distribution (QKD) and distributed quantum computation, and are an active area of both experimental and theoretical research. Here, we present an analysis of topologically complex networks of quantum repeaters composed of heterogeneous links. Quantum networks have fundamental behavioral differences from classical networks; the delicacy of quantum states makes a practical path selection algorithm imperative, but classical notions of resource utilization are not directly applicable, rendering known path selection mechanisms inadequate. To adapt Dijkstra's algorithm for quantum repeater networks that generate entangled Bell pairs, we quantify the key differences and define a link cost metric, seconds per Bell pair of a particular fidelity, where a single Bell pair is the resource consumed to perform one quantum teleportation. Simulations that include both the physical interactions and the extensive classical messaging confirm that Dijkstra's algorithm works well in a quantum context. Simulating about three hundred heterogeneous paths, comparing our path cost and the total work along the path gives a coefficient of determination of 0.88 or better.Comment: 12 pages, 8 figure

Parsing cyclothymic disorder and other specified bipolar spectrum disorders in youth

© 2018 Elsevier B.V. Objective: Most studies of pediatric bipolar disorder (BP) combine youth who have manic symptoms, but do not meet criteria for BP I/II, into one “not otherwise specified” (NOS) group. Consequently, little is known about how youth with cyclothymic disorder (CycD) differ from youth with BP NOS. The objective of this study was to determine whether youth with a research diagnosis of CycD (RDCyc) differ from youth with operationalized BP NOS. Method: Participants from the Course and Outcome of Bipolar Youth study were evaluated to determine whether they met RDCyc criteria. Characteristics of RDCyc youth and BP NOS youth were compared at baseline, and over eight-years follow-up. Results: Of 154 youth (average age 11.96 (3.3), 42% female), 29 met RDCyc criteria. RDCyc youth were younger (p =.04) at baseline. Over follow-up, RDCyc youth were more likely to have a disruptive behavior disorder (p =.01), and were more likely to experience irritability (p =.03), mood reactivity (p =.02), and rejection sensitivity (p =.03). BP NOS youth were more likely to develop hypomania (p =.02), or depression (p =.02), and tended to have mood episodes earlier in the eight-year follow-up period. Limitations: RDCyc diagnoses were made retrospectively and followed stringent criteria, which may highlight differences that, under typical clinical conditions and more vague criteria, would not be evident. Conclusion: There were few differences between RDCyc and BP NOS youth. However, the ways in which the groups diverged could have implications; chronic subsyndromal mood symptoms may portend a severe, but ultimately non-bipolar, course. Longer follow-up is necessary to determine the trajectory and outcomes of CycD symptoms

Exact boundary conditions in numerical relativity using multiple grids: scalar field tests

Cauchy-Characteristic Matching (CCM), the combination of a central 3+1 Cauchy code with an exterior characteristic code connected across a time-like interface, is a promising technique for the generation and extraction of gravitational waves. While it provides a tool for the exact specification of boundary conditions for the Cauchy evolution, it also allows to follow gravitational radiation all the way to infinity, where it is unambiguously defined. We present a new fourth order accurate finite difference CCM scheme for a first order reduction of the wave equation around a Schwarzschild black hole in axisymmetry. The matching at the interface between the Cauchy and the characteristic regions is done by transfering appropriate characteristic/null variables. Numerical experiments indicate that the algorithm is fourth order convergent. As an application we reproduce the expected late-time tail decay for the scalar field.Comment: 14 pages, 5 figures. Included changes suggested by referee

Method to estimate ISCO and ring-down frequencies in binary systems and consequences for gravitational wave data analysis

Recent advances in the description of compact binary systems have produced gravitational waveforms that include inspiral, merger and ring-down phases. Comparing results from numerical simulations with those of post-Newtonian (PN), and related, expansions has provided motivation for employing PN waveforms in near merger epochs when searching for gravitational waves and has encouraged the development of analytic fits to full numerical waveforms. The models and simulations do not yet cover the full binary coalescence parameter space. For these yet un-simulated regions, data analysts can still conduct separate inspiral, merger and ring-down searches. Improved knowledge about the end of the inspiral phase, the beginning of the merger, and the ring-down frequencies could increase the efficiency of both coherent inspiral-merger-ring-down (IMR) searches and searches over each phase separately. Insight can be gained for all three cases through a recently presented theoretical calculation, which, corroborated by the numerical results, provides an implicit formula for the final spin of the merged black holes, accurate to within 10% over a large parameter space. Knowledge of the final spin allows one to predict the end of the inspiral phase and the quasinormal mode ring-down frequencies, and in turn provides information about the bandwidth and duration of the merger. In this work we will discuss a few of the implications of this calculation for data analysis.Comment: Added references to section 3 14 pages 5 figures. Submitted to Classical and Quantum Gravit