29,963 research outputs found
MATEX: A Distributed Framework for Transient Simulation of Power Distribution Networks
We proposed MATEX, a distributed framework for transient simulation of power
distribution networks (PDNs). MATEX utilizes matrix exponential kernel with
Krylov subspace approximations to solve differential equations of linear
circuit. First, the whole simulation task is divided into subtasks based on
decompositions of current sources, in order to reduce the computational
overheads. Then these subtasks are distributed to different computing nodes and
processed in parallel. Within each node, after the matrix factorization at the
beginning of simulation, the adaptive time stepping solver is performed without
extra matrix re-factorizations. MATEX overcomes the stiff-ness hinder of
previous matrix exponential-based circuit simulator by rational Krylov subspace
method, which leads to larger step sizes with smaller dimensions of Krylov
subspace bases and highly accelerates the whole computation. MATEX outperforms
both traditional fixed and adaptive time stepping methods, e.g., achieving
around 13X over the trapezoidal framework with fixed time step for the IBM
power grid benchmarks.Comment: ACM/IEEE DAC 2014. arXiv admin note: substantial text overlap with
arXiv:1505.0669
Direct Application of the Phase Estimation Algorithm to Find the Eigenvalues of the Hamiltonians
The eigenvalue of a Hamiltonian, , can be estimated through the
phase estimation algorithm given the matrix exponential of the Hamiltonian,
. The difficulty of this exponentiation impedes the
applications of the phase estimation algorithm particularly when
is composed of non-commuting terms. In this paper, we present a method to use
the Hamiltonian matrix directly in the phase estimation algorithm by using an
ancilla based framework: In this framework, we also show how to find the power
of the Hamiltonian matrix-which is necessary in the phase estimation
algorithm-through the successive applications. This may eliminate the necessity
of matrix exponential for the phase estimation algorithm and therefore provide
an efficient way to estimate the eigenvalues of particular Hamiltonians. The
classical and quantum algorithmic complexities of the framework are analyzed
for the Hamiltonians which can be written as a sum of simple unitary matrices
and shown that a Hamiltonian of order written as a sum of number of
simple terms can be used in the phase estimation algorithm with
number of qubits and number of quantum operations, where is the
number of iterations in the phase estimation. In addition, we use the
Hamiltonian of the hydrogen molecule as an example system and present the
simulation results for finding its ground state energy.Comment: 10 pages, 3 figure
Models to Reduce the Complexity of Simulating a Quantum Computer
Recently Quantum Computation has generated a lot of interest due to the
discovery of a quantum algorithm which can factor large numbers in polynomial
time. The usefulness of a quantum com puter is limited by the effect of errors.
Simulation is a useful tool for determining the feasibility of quantum
computers in the presence of errors. The size of a quantum computer that can be
simulat ed is small because faithfully modeling a quantum computer requires an
exponential amount of storage and number of operations. In this paper we define
simulation models to study the feasibility of quantum computers. The most
detailed of these models is based directly on a proposed imple mentation. We
also define less detailed models which are exponentially less complex but still
pro duce accurate results. Finally we show that the two different types of
errors, decoherence and inaccuracies, are uncorrelated. This decreases the
number of simulations which must be per formed.Comment: 25 page
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