Noise-Adaptive Compiler Mappings for Noisy Intermediate-Scale Quantum Computers

A massive gap exists between current quantum computing (QC) prototypes, and the size and scale required for many proposed QC algorithms. Current QC implementations are prone to noise and variability which affect their reliability, and yet with less than 80 quantum bits (qubits) total, they are too resource-constrained to implement error correction. The term Noisy Intermediate-Scale Quantum (NISQ) refers to these current and near-term systems of 1000 qubits or less. Given NISQ's severe resource constraints, low reliability, and high variability in physical characteristics such as coherence time or error rates, it is of pressing importance to map computations onto them in ways that use resources efficiently and maximize the likelihood of successful runs. This paper proposes and evaluates backend compiler approaches to map and optimize high-level QC programs to execute with high reliability on NISQ systems with diverse hardware characteristics. Our techniques all start from an LLVM intermediate representation of the quantum program (such as would be generated from high-level QC languages like Scaffold) and generate QC executables runnable on the IBM Q public QC machine. We then use this framework to implement and evaluate several optimal and heuristic mapping methods. These methods vary in how they account for the availability of dynamic machine calibration data, the relative importance of various noise parameters, the different possible routing strategies, and the relative importance of compile-time scalability versus runtime success. Using real-system measurements, we show that fine grained spatial and temporal variations in hardware parameters can be exploited to obtain an average $2.9$x (and up to $18$x) improvement in program success rate over the industry standard IBM Qiskit compiler.Comment: To appear in ASPLOS'1

Effect of the Milky Way on Magellanic Cloud structure

A combination of analytic models and n-body simulations implies that the structural evolution of the Large Magellanic Cloud (LMC) is dominated by its dynamical interaction with the Milky Way. Although expected at some level, the scope of the involvement has significant observational consequences. First, LMC disk orbits are torqued out of the disk plane, thickening the disk and populating a spheroid. The torque results from direct forcing by the Milky Way tide and, indirectly, from the drag between the LMC disk and its halo resulting from the induced precession of the LMC disk. The latter is a newly reported mechanism that can affect all satellite interations. However, the overall torque can not isotropize the stellar orbits and their kinematics remains disk-like. Such a kinematic signature is observed for nearly all LMC populations. The extended disk distribution is predicted to increase the microlensing toward the LMC. Second, the disk's binding energy slowly decreases during this process, puffing up and priming the outer regions for subsequent tidal stripping. Because the tidally stripped debris will be spatially extended, the distribution of stripped stars is much more extended than the HI Magellanic Stream. This is consistent with upper limits to stellar densities in the gas stream and suggests a different strategy for detecting the stripped stars. And, finally, the mass loss over several LMC orbits is predicted by n-body simulation and the debris extends to tens of kiloparsecs from the tidal boundary. Although the overall space density of the stripped stars is low, possible existence of such intervening populations have been recently reported and may be detectable using 2MASS.Comment: 15 pages, color Postscript figures, uses emulateapj.sty. Also available from http://www-astro.phast.umass.edu/~weinberg/weinberg-pubs.htm

Modeling the dynamical evolution of the M87 globular cluster system

We study the dynamical evolution of the M87 globular cluster system (GCS) with a number of numerical simulations. We explore a range of different initial conditions for the GCS mass function (GCMF), for the GCS spatial distribution and for the GCS velocity distribution. We confirm that an initial power-law GCMF like that observed in young cluster systems can be readily transformed through dynamical processes into a bell-shaped GCMF. However,only models with initial velocity distributions characterized by a strong radial anisotropy increasing with the galactocentric distance are able to reproduce the observed constancy of the GCMF at all radii.We show that such strongly radial orbital distributions are inconsistent with the observed kinematics of the M87 GCS. The evolution of models with a bell-shaped GCMF with a turnover similar to that currently observed in old GCS is also investigated. We show that models with this initial GCMF can satisfy all the observational constraints currently available on the GCS spatial distribution,the GCS velocity distribution and on the GCMF properties.In particular these models successfully reproduce both the lack of a radial gradient of the GCS mean mass recently found in an analysis of HST images of M87 at multiple locations, and the observed kinematics of the M87 GCS.Our simulations also show that evolutionary processes significantly affect the initial GCS properties by leading to the disruption of many clusters and changing the masses of those which survive.The preferential disruption of inner clusters flattens the initial GCS number density profile and it can explain the rising specific frequency with radius; we show that the inner flattening observed in the M87 GCS spatial distribution can be the result of the effects of dynamical evolution on an initially steep density profile. (abridged)Comment: 15 pages,14 figures;accepted for publication in The Astrophysical Journa

The Kara and Ust-Kara impact structures (USSR) and their relevance to the K/T boundary event

The Kara and Ust-Kara craters are twin impact structures situated at about 69 deg 10 min N; 65 deg 00 min E at the Kara Sea. For Kara a diameter of about 55 km would be a very conservative estimate, and field observations indicate a maximum current diameter of about 60 km. The diameter of Ust-Kara has to be larger than 16 km. A better estimate might be 25 km but in all likelihood it is even larger. Suevites and impactites from the Kara area have been known since the beginning of the century, but had been misidentified as glacial deposits. Only about 15 years ago the impact origin of the two structures was demonstrated, following the recognition of shock metamorphism in the area. The composition of the target rocks is mirrored by the composition of the clasts within the suevites. In the southern part of Kara, Permian shales and limestones are sometimes accompanied by diabasic dykes, similar to in the central uplift. Due to the high degree of shock metamorphism the shocked magmatic rocks are not easily identified, although most of them seem to be of diabasic or dioritic composition. The impact melts (tagamites) are grey to dark grey fine grained crystallized rocks showing very fine mineral components and are the product of shock-melting with later recrystallization. The impact glasses show a layered structure, inclusions, and vesicles, and have colors ranging from translucent white over brown and grey to black. A complete geochemical characterization of the Kara and Ust-Kara impact craters was attempted by analyzing more than 40 samples of target rocks, shocked rocks, suevites, impact melts, and impact glasses for major and trace elements

VIRGO: computational prediction of gene functions

Dramatic advances in sequencing technology and sophisticated experimental assays that interrogate the cell, combined with the public availability of the resulting data, herald the era of systems biology. However, the biological functions of more than 40% of the genes in sequenced genomes are unknown, posing a fundamental barrier to progress in systems biology. The large scale and diversity of available data requires the development of techniques that can automatically utilize these datasets to make quantified and robust predictions of gene function that can be experimentally verified. We present a service called the VIRtual Gene Ontology (VIRGO) that (i) constructs a functional linkage network (FLN) from gene expression and molecular interaction data, (ii) labels genes in the FLN with their functional annotations in the Gene Ontology and (iii) systematically propagates these labels across the FLN in order to precisely predict the functions of unlabelled genes. VIRGO assigns confidence estimates to predicted functions so that a biologist can prioritize predictions for further experimental study. For each prediction, VIRGO also provides an informative ‘propagation diagram’ that traces the flow of information in the FLN that led to the prediction. VIRGO is available at

Bifurcations, Chaos, Controlling and Synchronization of Certain Nonlinear Oscillators

In this set of lectures, we review briefly some of the recent developments in the study of the chaotic dynamics of nonlinear oscillators, particularly of damped and driven type. By taking a representative set of examples such as the Duffing, Bonhoeffer-van der Pol and MLC circuit oscillators, we briefly explain the various bifurcations and chaos phenomena associated with these systems. We use numerical and analytical as well as analogue simulation methods to study these systems. Then we point out how controlling of chaotic motions can be effected by algorithmic procedures requiring minimal perturbations. Finally we briefly discuss how synchronization of identically evolving chaotic systems can be achieved and how they can be used in secure communications.Comment: 31 pages (24 figures) LaTeX. To appear Springer Lecture Notes in Physics Please Lakshmanan for figures (e-mail: [email protected]

Dynamical Evolution of the Mass Function of Globular Star Clusters

We present a series of simple, largely analytical models to compute the effects of disruption on the mass function of star clusters. Our calculations include evaporation by two-body relaxation and gravitational shocks and mass loss by stellar evolution. We find that, for a wide variety of initial conditions, the mass function develops a turnover or peak and that, after 12 Gyr, this is remarkably close to the observed peak for globular clusters, at M_p = 2 10^5 solar masses. Below the peak, the evolution is dominated by two-body relaxation, and the mass function always develops a tail of the form psi(M) = const, reflecting that the masses of tidally limited clusters decrease linearly with time just before they are destroyed. This also agrees well with the empirical mass function of globular clusters in the Milky Way. Above the peak, the evolution is dominated by stellar evolution at early times and gravitational shocks at late times. These processes shift the mass function to lower masses while nearly preserving its shape. The radial variation of the mass function within a galaxy depends on the initial position-velocity distribution of the clusters. We find that some radial anisotropy in the initial velocity distribution, especially when this increases outward, is needed to account for the observed near-uniformity of the mass functions of globular clusters. This may be consistent with the observed near-isotropy of the present velocity distributions because clusters on elongated orbits are preferentially destroyed. These results are based on models with static, spherical galactic potentials. We point out that there would be even more radial mixing of the orbits and hence more uniformity of the mass function if the galactic potentials were time-dependent and/or non-spherical.Comment: 39 pages including 13 figures; scheduled for publication in the Astrophysical Journal (issue of 10 Nov 2001); Minor revisions to improve clarity; no changes to equations, figures, or conclusion