A Fidelity Study of the Superconducting Phase Diagram in the 2D Single-band Hubbard Model

Extensive numerical studies have demonstrated that the two-dimensional single-band Hubbard model contains much of the key physics in cuprate high-temperature superconductors. However, there is no definitive proof that the Hubbard model truly possesses a superconducting ground state or, if it does, of how it depends on model parameters. To answer these longstanding questions, we study an extension of the Hubbard model including an infinite-range d-wave pair field term, which precipitates a superconducting state in the d-wave channel. Using exact diagonalization on 16-site square clusters, we study the evolution of the ground state as a function of the strength of the pairing term. This is achieved by monitoring the fidelity metric of the ground state, as well as determining the ratio between the two largest eigenvalues of the d-wave pair/spin/charge-density matrices. The calculations show a d-wave superconducting ground state in doped clusters bracketed by a strong antiferromagnetic state at half filling controlled by the Coulomb repulsion U and a weak short-range checkerboard charge ordered state at larger hole doping controlled by the next-nearest-neighbor hopping t'. We also demonstrate that negative t' plays an important role in facilitating d-wave superconductivity.Comment: 10 pages, 13 figure

Focusing Mirror with Tunable Eccentricity

We present a new kind of varifocal mirror with independently adjustable curvatures in the major directions. For actuation we use two stacked piezo bending actuators with crossed in-plane polarization. This mirror can be used for example as an off-axis focusing device with tunable focal length and compensation for a variable angle of incidence or for coma correction. We demonstrate the prototype of such a mirror and characterize the mechanical deflection, as well as the focusing capabilities

Observation of squeezed states with strong photon number oscillations

Squeezed states of light constitute an important nonclassical resource in the field of high-precision measurements, e.g. gravitational wave detection, as well as in the field of quantum information, e.g. for teleportation, quantum cryptography, and distribution of entanglement in quantum computation networks. Strong squeezing in combination with high purity, high bandwidth and high spatial mode quality is desirable in order to achieve significantly improved performances contrasting any classical protocols. Here we report on the observation of the strongest squeezing to date of 11.5 dB, together with unprecedented high state purity corresponding to a vacuum contribution of less than 5%, and a squeezing bandwidth of about 170 MHz. The analysis of our squeezed states reveals a significant production of higher-order pairs of quantum-correlated photons, and the existence of strong photon number oscillations.Comment: 7 pages, 6 figure

Paradeisos: a perfect hashing algorithm for many-body eigenvalue problems

We describe an essentially perfect hashing algorithm for calculating the position of an element in an ordered list, appropriate for the construction and manipulation of many-body Hamiltonian, sparse matrices. Each element of the list corresponds to an integer value whose binary representation reflects the occupation of single-particle basis states for each element in the many-body Hilbert space. The algorithm replaces conventional methods, such as binary search, for locating the elements of the ordered list, eliminating the need to store the integer representation for each element, without increasing the computational complexity. Combined with the "checkerboard" decomposition of the Hamiltonian matrix for distribution over parallel computing environments, this leads to a substantial savings in aggregate memory. While the algorithm can be applied broadly to many-body, correlated problems, we demonstrate its utility in reducing total memory consumption for a series of fermionic single-band Hubbard model calculations on small clusters with progressively larger Hilbert space dimension.Comment: 10 pages, 5 figure

Ray: A Distributed Execution Engine for the Machine Learning Ecosystem

In recent years, growing data volumes and more sophisticated computational procedures have greatly increased the demand for computational power. Machine learning and artificial intelligence applications, for example, are notorious for their computational requirements. At the same time, Moores law is ending and processor speeds are stalling. As a result, distributed computing has become ubiquitous. While the cloud makes distributed hardware infrastructure widely accessible and therefore offers the potential of horizontal scale, developing these distributed algorithms and applications remains surprisingly hard. This is due to the inherent complexity of concurrent algorithms, the engineering challenges that arise when communicating between many machines, the requirements like fault tolerance and straggler mitigation that arise at large scale and the lack of a general-purpose distributed execution engine that can support a wide variety of applications.In this thesis, we study the requirements for a general-purpose distributed computation model and present a solution that is easy to use yet expressive and resilient to faults. At its core our model takes familiar concepts from serial programming, namely functions and classes, and generalizes them to the distributed world, therefore unifying stateless and stateful distributed computation. This model not only supports many machine learning workloads like training or serving, but is also a good t for cross-cutting machine learning applications like reinforcement learning and data processing applications like streaming or graph processing. We implement this computational model as an open-source system called Ray, which matches or exceeds the performance of specialized systems in many application domains, while also offering horizontally scalability and strong fault tolerance properties