trottersuzuki 1.4

Usage

Documentation is available on Read the Docs. The following code block gives a simple example of initializing a state and calculating the expectation values of the Hamiltonian and kinetic operators and the norm of the state after the evolution.

from __future__ import print_function
import numpy as np
import trottersuzuki as ts

# lattice parameters
dim = 200
delta_x = 1.
delta_y = 1.
periods = [1, 1]

# Hamiltonian parameter
particle_mass = 1
external_potential = np.zeros((dim, dim))

# initial state
p_real = np.ones((dim, dim))
p_imag = np.zeros((dim, dim))
for y in range(0, dim):
    for x in range(0, dim):
        p_real[y, x] = np.sin(2*np.pi*x / dim) * np.sin(2*np.pi*y / dim)

# evolution parameters
delta_t = 0.001
iterations = 200

# launch evolution
ts.evolve(p_real, p_imag, particle_mass, external_potential, delta_x, delta_y,
          delta_t, iterations, periods=periods)

# expectation values
Energy = ts.calculate_total_energy(p_real, p_imag, particle_mass,
                                   external_potential, delta_x, delta_y)
print(Energy)

Kinetic_Energy = ts.calculate_kinetic_energy(p_real, p_imag, particle_mass,
                                             delta_x, delta_y)
print(Kinetic_Energy)

Norm2 = ts.calculate_norm2(p_real, p_imag, delta_x, delta_y)
print(Norm2)

Installation

The code is available on PyPI, hence it can be installed by

$ sudo pip install trottersuzuki

If you want the latest git version, follow the standard procedure for installing Python modules:

$ sudo python setup.py install

Build on Mac OS X

Before installing using pip, gcc should be installed first. As of OS X 10.9, gcc is just symlink to clang. To build trottersuzuki and this extension correctly, it is recommended to install gcc using something like:

$ brew install gcc48

and set environment using:

export CC=/usr/local/bin/gcc
export CXX=/usr/local/bin/g++
export CPP=/usr/local/bin/cpp
export LD=/usr/local/bin/gcc
alias c++=/usr/local/bin/c++
alias g++=/usr/local/bin/g++
alias gcc=/usr/local/bin/gcc
alias cpp=/usr/local/bin/cpp
alias ld=/usr/local/bin/gcc
alias cc=/usr/local/bin/gcc

Then you can issue

$ sudo pip install trottersuzuki

Citations

1. Bederián, C. and Dente, A. Boosting quantum evolutions using Trotter-Suzuki algorithms on GPUs. Proceedings of HPCLatAm-11, 4th High-Performance Computing Symposium, 2011.

2. Wittek, P. and Cucchietti, F.M. (2013). A Second-Order Distributed Trotter-Suzuki Solver with a Hybrid CPU-GPU Kernel. Computer Physics Communications, 184, pp. 1165-1171. PDF

3. Wittek, P. and Calderaro, L. (2015). Extended computational kernels in a massively parallel implementation of the Trotter-Suzuki approximation. Computer Physics Communications, 197, pp. 339-340.