37,263 research outputs found
Random Quantum Circuits and Pseudo-Random Operators: Theory and Applications
Pseudo-random operators consist of sets of operators that exhibit many of the
important statistical features of uniformly distributed random operators. Such
pseudo-random sets of operators are most useful whey they may be parameterized
and generated on a quantum processor in a way that requires exponentially fewer
resources than direct implementation of the uniformly random set. Efficient
pseudo-random operators can overcome the exponential cost of random operators
required for quantum communication tasks such as super-dense coding of quantum
states and approximately secure quantum data-hiding, and enable efficient
stochastic methods for noise estimation on prototype quantum processors. This
paper summarizes some recently published work demonstrating a random circuit
method for the implementation of pseudo-random unitary operators on a quantum
processor [Emerson et al., Science 302:2098 (Dec.~19, 2003)], and further
elaborates the theory and applications of pseudo-random states and operators.Comment: This paper is a synopsis of Emerson et al., Science 302: 2098 (Dec
19, 2003) and some related unpublished work; it is based on a talk given at
QCMC04; 4 pages, 1 figure, aipproc.st
SpECTRE: A Task-based Discontinuous Galerkin Code for Relativistic Astrophysics
We introduce a new relativistic astrophysics code, SpECTRE, that combines a
discontinuous Galerkin method with a task-based parallelism model. SpECTRE's
goal is to achieve more accurate solutions for challenging relativistic
astrophysics problems such as core-collapse supernovae and binary neutron star
mergers. The robustness of the discontinuous Galerkin method allows for the use
of high-resolution shock capturing methods in regions where (relativistic)
shocks are found, while exploiting high-order accuracy in smooth regions. A
task-based parallelism model allows efficient use of the largest supercomputers
for problems with a heterogeneous workload over disparate spatial and temporal
scales. We argue that the locality and algorithmic structure of discontinuous
Galerkin methods will exhibit good scalability within a task-based parallelism
framework. We demonstrate the code on a wide variety of challenging benchmark
problems in (non)-relativistic (magneto)-hydrodynamics. We demonstrate the
code's scalability including its strong scaling on the NCSA Blue Waters
supercomputer up to the machine's full capacity of 22,380 nodes using 671,400
threads.Comment: 41 pages, 13 figures, and 7 tables. Ancillary data contains
simulation input file
Scalable Task-Based Algorithm for Multiplication of Block-Rank-Sparse Matrices
A task-based formulation of Scalable Universal Matrix Multiplication
Algorithm (SUMMA), a popular algorithm for matrix multiplication (MM), is
applied to the multiplication of hierarchy-free, rank-structured matrices that
appear in the domain of quantum chemistry (QC). The novel features of our
formulation are: (1) concurrent scheduling of multiple SUMMA iterations, and
(2) fine-grained task-based composition. These features make it tolerant of the
load imbalance due to the irregular matrix structure and eliminate all
artifactual sources of global synchronization.Scalability of iterative
computation of square-root inverse of block-rank-sparse QC matrices is
demonstrated; for full-rank (dense) matrices the performance of our SUMMA
formulation usually exceeds that of the state-of-the-art dense MM
implementations (ScaLAPACK and Cyclops Tensor Framework).Comment: 8 pages, 6 figures, accepted to IA3 2015. arXiv admin note: text
overlap with arXiv:1504.0504
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