Skip to content

Instantly share code, notes, and snippets.

@jrjohansson
Last active December 20, 2015 15:19
Show Gist options
  • Save jrjohansson/6153688 to your computer and use it in GitHub Desktop.
Save jrjohansson/6153688 to your computer and use it in GitHub Desktop.
smesolve-oscillator-squeezing
Display the source blob
Display the rendered blob
Raw
{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Tests for QuTiP's SME solver against analytical solution for oscillator squeezing\n",
"\n",
"Denis V. Vasilyev\n",
"\n",
"1 August 2013\n",
"\n",
"Minor edits by Robert Johansson \n",
"\n",
"5 August, 6 August 2013\n",
"\n",
"We solve the stochastic master equation for an oscillator coupled to a 1D field as discussed in [1]. There is a deterministic differential equation for the variances of the oscillator quadratures $\\langle\\delta X^2\\rangle$ and $\\langle\\delta P^2\\rangle$. This allows for a direct comparison between the numerical solution and the exact solution for a single quantum trajectory.\n",
"\n",
"In this section we solve SME with a single Wiener increment: \n",
"##$\\mathrm{d}\\rho = D[s]\\rho\\mathrm{d}t + H[s]\\rho \\mathrm{d}W + \\gamma D[a]\\rho\\mathrm{d}t$\n",
"\n",
"The steady state solution for the variance $V_{\\mathrm{c}} = \\langle X^2\\rangle - \\langle X\\rangle^2$ reads\n",
"\n",
"$V_{\\mathrm{c}} = \\frac1{4\\alpha^{2}}\\left[\\alpha\\beta - \\gamma + \\sqrt{(\\gamma-\\alpha\\beta )^{2} + 4\\gamma \\alpha^2}\\right]$\n",
"\n",
"where $\\alpha$ and $\\beta$ are parametrizing the interaction between light and the oscillator such that the jump operator is given by $s = \\frac{\\alpha+\\beta}2 a + \\frac{\\alpha-\\beta}2 a^{\\dagger}$\n",
"\n",
"[1] D. V. Vasilyev, C. a. Muschik, and K. Hammerer, Physical Review A 87, 053820 (2013). <a href=\"http://arxiv.org/abs/1303.5888\">arXiv:1303.5888</a>\n",
"\n",
"# Implementation of Milstein method for homodyne detection\n",
"\n",
"It is easy to implement the Milstein method [2] for a single Wiener increment using the given QuTiP infrastructure. For a stochastic differential equation $\\mathrm{d}\\rho = a(\\rho)\\mathrm{d}t + b(\\rho) \\mathrm{d}W\\quad$ the Milstein scheme gives:\n",
"\n",
"$\\Delta \\rho = a(\\rho_n) \\Delta t + b(\\rho_n) \\Delta W_n + \\frac{1}{2} b(\\rho_n) b'(\\rho_n) \\left( (\\Delta W_n)^2 - \\Delta t \\right)$\n",
"\n",
"The derivative can be calculated explicitly which is done below for a homodyne detection stochastic term.\n",
"\n",
"[2] G. N. Milstein, Teor. Veroyatnost. i Primenen. 19, 583\u2013588 (1974)."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%pylab inline"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from qutip import *\n",
"from scipy.linalg import eig, eigh, inv\n",
"from scipy.sparse.linalg import inv as spinv\n",
"from numpy import log2, cos, sin\n",
"from scipy.integrate import odeint\n",
"from qutip.cyQ.spmatfuncs import cy_expect, spmv"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"th = 0.1 # Interaction parameter\n",
"alpha = cos(th)\n",
"beta = sin(th)\n",
"gamma = 1\n",
"\n",
"# Exact steady state solution for Vc\n",
"Vc = (alpha*beta - gamma + sqrt((gamma-alpha*beta)**2 + 4*gamma*alpha**2))/(4*alpha**2)\n",
"\n",
"#********* Model ************\n",
"NN = 200\n",
"tlist = linspace(0,5,NN)\n",
"Nsub = 10\n",
"N = 10\n",
"Id = qeye(N)\n",
"a = destroy(N)\n",
"s = 0.5*((alpha+beta)*a + (alpha-beta)*a.dag())\n",
"x = (a + a.dag())/sqrt(2)\n",
"H = Id\n",
"c_op = [sqrt(gamma)*a]\n",
"sc_op = [s]\n",
"e_op = [x, x*x]\n",
"rho0 = fock_dm(N,0) #initial vacuum state"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Solution of the differential equation for the variance Vc\n",
"y0 = 0.5\n",
"def func(y, t):\n",
" return -(gamma - alpha*beta)*y - 2*alpha*alpha*y*y + 0.5*gamma\n",
"y = odeint(func, y0, tlist)\n",
"\n",
"# Righthand side for the Milstein method for a homodyne detection scheme\n",
"def rhs_milstein(L, rho_t, t, A_ops, dt, dW, d1, d2, args):\n",
"\n",
" drho_t = spmv(L.data,\n",
" L.indices,\n",
" L.indptr, rho_t) * dt\n",
" \n",
" A = A_ops[0]\n",
" M = A[0] + A[3]\n",
" e1 = cy_expect_rho_vec(M, rho_t)\n",
" d1_vec = spmv(A[7].data, A[7].indices, A[7].indptr, rho_t)\n",
" \n",
" d2_vec = spmv(M.data, M.indices, M.indptr, rho_t)\n",
" d2_vec2 = spmv(M.data, M.indices, M.indptr, d2_vec)\n",
" e2 = cy_expect_rho_vec(M, d2_vec)\n",
" return rho_t + drho_t + d1_vec*dt + (d2_vec - e1*rho_t)*dW[0,0] + \\\n",
" 0.5 * (d2_vec2 - 2*e1*d2_vec + (-e2 + 2*e1*e1)*rho_t)*(dW[0,0]*dW[0,0] - dt)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Solution for the expectation values\n",
"sol = smesolve(H, rho0, tlist, c_op, sc_op, e_op,\n",
" nsubsteps=Nsub, method='homodyne', store_measurement=True)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Completed: 0.0%. Elapsed time: 0.00s. Est. remaining time: 00:00:00:00.\n",
"Elapsed time: 0.60s"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"sol_mil = smesolve(H, rho0, tlist, c_op, sc_op, e_op,\n",
" nsubsteps=Nsub, method='homodyne', rhs=rhs_milstein, noise=sol.noise)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Completed: 0.0%. Elapsed time: 0.00s. Est. remaining time: 00:00:00:00.\n",
"Elapsed time: 0.70s"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Variance $V_{\\mathrm{c}}$ as a function of time"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig, ax = subplots()\n",
"\n",
"ax.plot(tlist,sol.expect[1]-sol.expect[0]*sol.expect[0].conj(), label='Euler-Maruyama')\n",
"ax.plot(tlist,sol_mil.expect[1]-sol_mil.expect[0]*sol_mil.expect[0].conj(), label='Milstein')\n",
"ax.plot(tlist,Vc*ones(NN), label='exact steady state solution')\n",
"ax.plot(tlist,y, label=\"exact solution\")\n",
"ax.legend();"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAXgAAAEACAYAAAC57G0KAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nXdxShiInAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x7f05b888d8d0>"
]
}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Deviation from exact solution"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig, ax = subplots()\n",
"\n",
"ax.plot(tlist, (y.T[0] - (sol.expect[1]-sol.expect[0]*sol.expect[0].conj())), label='Euler-Maruyama')\n",
"ax.plot(tlist, y.T[0] - (sol_mil.expect[1]-sol_mil.expect[0]*sol_mil.expect[0].conj()), label='Milstein')\n",
"ax.legend();"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAYYAAAEACAYAAAC3adEgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nCCFiSGMQQggRQxqDEEKIGH8BYp3sDZE+aDIAAAAASUVORK5CYII=\n",
"text": [
"<matplotlib.figure.Figure at 0x7f05b888d350>"
]
}
],
"prompt_number": 8
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot_expectation_values([sol,sol_mil]);"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAekAAAESCAYAAADZmy1NAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text": [
"<matplotlib.figure.Figure at 0x7f05b878d650>"
]
}
],
"prompt_number": 9
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Norm of the density matrix\n",
"\n",
"Here we calculate $|\\rho|-1$ which should be zero ideally."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Solution for the density matrix\n",
"sol2 = smesolve(H, rho0, tlist, c_op, sc_op, [],\n",
" nsubsteps=Nsub, method='homodyne', noise=sol.noise)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Completed: 0.0%. Elapsed time: 0.00s. Est. remaining time: 00:00:00:00.\n",
"Elapsed time: 0.75s"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"sol2_mil = smesolve(H, rho0, tlist, c_op, sc_op, [],\n",
" nsubsteps=Nsub, method='homodyne', rhs=rhs_milstein, noise=sol.noise)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Completed: 0.0%. Elapsed time: 0.00s. Est. remaining time: 00:00:00:00.\n",
"Elapsed time: 0.84s"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig, ax = subplots()\n",
"\n",
"ax.plot(tlist,array([sol2.states[0][n].norm() - 1 for n in range(NN)]), label='Euler-Maruyama')\n",
"ax.plot(tlist,array([sol2_mil.states[0][n].norm() - 1 for n in range(NN)]), label='Milstein')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 12,
"text": [
"[<matplotlib.lines.Line2D at 0x7f05b87f1910>]"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAYYAAAEACAYAAAC3adEgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text": [
"<matplotlib.figure.Figure at 0x7f05b8719d50>"
]
}
],
"prompt_number": 12
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Milstein method with multiple Wiener increments\n",
"\n",
"In this section we solve the following SME:\n",
"##$\\mathrm{d}\\rho = D[s]\\rho\\mathrm{d}t + \\sqrt{1-\\epsilon}H[s]\\rho \\mathrm{d}W_1 + \\sqrt{\\epsilon}H[is]\\rho \\mathrm{d}W_2 + \\gamma D[a]\\rho\\mathrm{d}t$\n",
"Analytical results can be found in [1].\n",
"\n",
"We follow [3] in implementation of the Milstein scheme.\n",
"\n",
"Stochastic equation is defined as\n",
"\n",
"$dX^i = a^i(X)dt + \\sum_{j=1}^M b^{i,j}(X)dW^j$\n",
"\n",
"It is convenient to define a differential operator as follows\n",
"\n",
"$L^j = \\sum_{k=1}^N b^{k,j}\\frac{\\partial}{\\partial x^k}$\n",
"\n",
"Then the numerical scheme is\n",
"\n",
"##$Y^i_{n+1} = Y^i_n + a^i\\Delta t + \\sum_{j=1}^M b^{i,j}(X)\\Delta W^j_n + \\sum_{j_1,j_2=1}^M L^{j_1}b^{i,j_2} I_n(j_1,j_2)$\n",
"\n",
"where $I_n(j_1,j_2) = \\int_{t_n}^{t_{n+1}}\\int_{t_n}^{s_1}dW_{s_2}^{j_1}dW_{s_1}^{j_2}$\n",
"\n",
"##Commutative noise\n",
"\n",
"An impotant case is the commutative noise which means $L^{j_1}b^{k,j_2} = L^{j_2}b^{k,j_1}$. For the homodyne detection it means that the jump operators for different stochastic terms commute. In this case we have\n",
"\n",
"$I_n(j_1,j_2) = I_n(j_2,j_1) = \\frac12\\Delta W^{j_1}_n \\Delta W^{j_2}_n$\n",
"\n",
"Evaluation of the derivatives $L^j$ for homodyne scheme provides us with the numerical scheme implemented below. We also have used the assumption of the commutative noise. The smesolve routine has to be modified. It should provide all the A_ops to the rhs function.\n",
"\n",
"[1] D. V. Vasilyev, C. a. Muschik, and K. Hammerer, Physical Review A 87, 053820 (2013). <a href=\"http://arxiv.org/abs/1303.5888\">arXiv:1303.5888</a>\n",
"\n",
"[3] S. Cyganowski, L. Gruene, and P. E. Kloeden, MAPLE for Stochastic Differential Equations."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#from stochastic_vutshi import smesolve_mil,smesolve_imp #modified smesolve routine\n",
"# with the changed rhs function we can use the standard qutip smesolve function"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 13
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"th = 0.1\n",
"alpha = cos(th)\n",
"beta = sin(th)\n",
"gamma = 1\n",
"eps = 0.3\n",
"\n",
"VcEps = ((1-2*eps)*alpha*beta - gamma + \\\n",
" sqrt((gamma-alpha*beta)**2 + 4*gamma*alpha*((1-eps)*alpha + eps*beta)))/(4*(1-eps)*alpha**2)\n",
"UcEps = (-(1-2*eps)*alpha*beta - gamma + \\\n",
" sqrt((gamma-alpha*beta)**2 + 4*eps*beta*gamma*(beta-alpha)))/(4*eps*beta**2)\n",
"\n",
"NN = 200\n",
"tlist = linspace(0,3,NN)\n",
"Nsub = 20\n",
"N = 10\n",
"Id = qeye(N)\n",
"a = destroy(N)\n",
"s = 0.5*((alpha+beta)*a + (alpha-beta)*a.dag())\n",
"x = (a + a.dag())/sqrt(2)\n",
"H = Id\n",
"c_op = [sqrt(gamma)*a]\n",
"sc_op = [sqrt(1-eps)*s, sqrt(eps)*1j*s]\n",
"e_op = [x, x*x]\n",
"rho0 = fock_dm(N,0)\n",
"y0 = 0.5"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 14
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def func(y, t):\n",
" return -(gamma - (1-2*eps)*alpha*beta)*y - 2*(1-eps)*alpha*alpha*y*y + 0.5*(gamma + eps*beta*beta)\n",
"y = odeint(func, y0, tlist)\n",
"\n",
"def funcZ(z, t):\n",
" return -(gamma + (1-2*eps)*alpha*beta)*z - 2*eps*beta*beta*z*z + 0.5*(gamma + (1-eps)*alpha*alpha)\n",
"z = odeint(funcZ, y0, tlist)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 15
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def rhs_milstein(L, rho_t, t, A, dt, dW, d1, d2, args):\n",
"\n",
" drho_t = spmv(L.data,\n",
" L.indices,\n",
" L.indptr, rho_t) * dt\n",
" \n",
" A_len = len(A)\n",
" M = array([A[n][0] + A[n][3] for n in range(A_len)])\n",
" e1 = array([cy_expect_rho_vec(M[n], rho_t) for n in range(A_len)])\n",
" d1_vec = sum([spmv(A[n][7].data, A[n][7].indices, A[n][7].indptr, rho_t)\n",
" for n in range(A_len)], axis=0)\n",
" \n",
" d2_vec = array([spmv(M[n].data, M[n].indices, M[n].indptr, rho_t)\n",
" for n in range(A_len)])\n",
" d2_vec2 = array([[spmv(M[n].data, M[n].indices, M[n].indptr, d2_vec[m]) for m in range(A_len)]\n",
" for n in range(A_len)])\n",
" e2 = array([[cy_expect_rho_vec(M[n], d2_vec[m]) for m in range(A_len)] for n in range(A_len)])\n",
" \n",
" out = d1_vec * dt\n",
" out += sum([(d2_vec[n] - e1[n]*rho_t)*dW[n] for n in range(A_len)], axis=0)\n",
" out += 0.5*sum([(d2_vec2[n,n] - 2*e1[n]*d2_vec[n] + (-e2[n,n] + 2*e1[n]*e1[n])*rho_t)*(dW[n]*dW[n] - dt)\n",
" for n in range(A_len)], axis=0)\n",
" out += 0.5*sum([(d2_vec2[n,m] - e1[m]*d2_vec[n] - e1[n]*d2_vec[m] + \\\n",
" (-e2[n,m] + 2*e1[n]*e1[m])*rho_t)*(dW[n]*dW[m])\n",
" for (n,m) in ndindex(A_len,A_len) if n != m], axis=0)\n",
" \n",
" return rho_t + drho_t + out"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 16
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Solution for expectation values\n",
"sol = smesolve(H, rho0, tlist, c_op, sc_op, e_op,\n",
" nsubsteps=Nsub, method='homodyne', store_measurement=True,\n",
" options=Odeoptions(store_states=True))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Completed: 0.0%. Elapsed time: 0.00s. Est. remaining time: 00:00:00:00.\n",
"Elapsed time: 2.38s"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
}
],
"prompt_number": 17
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"sol_mil = smesolve(H, rho0, tlist, c_op, sc_op, e_op,\n",
" nsubsteps=Nsub, method='homodyne', rhs=rhs_milstein, noise=sol.noise,\n",
" options=Odeoptions(store_states=True))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Completed: 0.0%. Elapsed time: 0.00s. Est. remaining time: 00:00:00:00.\n",
"Elapsed time: 6.88s"
]
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n"
]
}
],
"prompt_number": 18
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Variance $V_{\\mathrm{c}}$ as a function of time"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig, ax = subplots()\n",
"\n",
"ax.plot(tlist,sol.expect[1]-sol.expect[0]*sol.expect[0].conj(), label='Euler-Maruyama')\n",
"ax.plot(tlist,sol_mil.expect[1]-sol_mil.expect[0]*sol_mil.expect[0].conj(), label='Milstein expl.')\n",
"ax.plot(tlist,VcEps*ones(NN), label='Exact steady state solution')\n",
"ax.plot(tlist,y, label='Exact solution')\n",
"\n",
"ax.legend();"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAX0AAAEACAYAAABfxaZOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nBEEQKcR/AOAhUXEs7KZDAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x7f05b87f8650>"
]
}
],
"prompt_number": 19
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Deviation from exact solution"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig, ax = subplots()\n",
"\n",
"ax.plot(tlist, y.T[0] - (sol.expect[1]-sol.expect[0]*sol.expect[0].conj()), label='Euler-Maruyama')\n",
"ax.plot(tlist, y.T[0] - (sol_mil.expect[1]-sol_mil.expect[0]*sol_mil.expect[0].conj()), label='Milstein expl.')\n",
"\n",
"ax.legend();"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAYsAAAEACAYAAABCl1qQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niIgoIhYLIiKK6D82Nhx0aOFVOgAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x7f05b873b050>"
]
}
],
"prompt_number": 20
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Norm of the density matrix\n",
"\n",
"Here we calculate $|\\rho|-1$ which should be zero ideally."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fig, ax = subplots()\n",
"\n",
"ax.plot(tlist,array([sol.states[0][n].norm() - 1 for n in range(NN)]), label='Euler-Maruyama')\n",
"ax.plot(tlist,array([sol_mil.states[0][n].norm() - 1 for n in range(NN)]), label='Milstein')\n",
"\n",
"ax.legend()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 21,
"text": [
"<matplotlib.legend.Legend at 0x7f05b872f110>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": "iVBORw0KGgoAAAANSUhEUgAAAZEAAAEACAYAAAByG0uxAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
"text": [
"<matplotlib.figure.Figure at 0x7f05b86952d0>"
]
}
],
"prompt_number": 21
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Software versions"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%load_ext version_information"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 22
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%version_information Cython, numpy, matplotlib, scipy, qutip"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"<table><tr><th>Software</th><th>Version</th></tr><tr><td>Python</td><td>3.3.1 (default, Apr 17 2013, 22:30:32) [GCC 4.7.3]</td></tr><tr><td>IPython</td><td>1.0.0-dev</td></tr><tr><td>OS</td><td>posix [linux]</td></tr><tr><td>Cython</td><td>0.19.1</td></tr><tr><td>numpy</td><td>1.8.0.dev-b307a8a</td></tr><tr><td>matplotlib</td><td>1.4.x</td></tr><tr><td>scipy</td><td>0.13.0.dev-7c6d92e</td></tr><tr><td>qutip</td><td>2.3.0.dev-0b4a1a7</td></tr><tr><td colspan='2'>Tue Aug 06 12:11:46 2013 JST</td></tr></table>"
],
"json": [
"{ \"Software versions\" : [{ \"module\" : \"Python\", \"version\" : \"3.3.1 (default, Apr 17 2013, 22:30:32) [GCC 4.7.3]\" }, { \"module\" : \"IPython\", \"version\" : \"1.0.0-dev\" }, { \"module\" : \"OS\", \"version\" : \"posix [linux]\" }, { \"module\" : \"Cython\", \"version\" : \"0.19.1\" }, { \"module\" : \"numpy\", \"version\" : \"1.8.0.dev-b307a8a\" }, { \"module\" : \"matplotlib\", \"version\" : \"1.4.x\" }, { \"module\" : \"scipy\", \"version\" : \"0.13.0.dev-7c6d92e\" }, { \"module\" : \"qutip\", \"version\" : \"2.3.0.dev-0b4a1a7\" } ] }"
],
"latex": [
"\\begin{table}\n",
"\\begin{tabular}{|l|l|}\\hline\n",
"{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n",
"Python & 3.3.1 (default, Apr 17 2013, 22:30:32) [GCC 4.7.3] \\\\ \\hline\n",
"IPython & 1.0.0-dev \\\\ \\hline\n",
"OS & posix [linux] \\\\ \\hline\n",
"Cython & 0.19.1 \\\\ \\hline\n",
"numpy & 1.8.0.dev-b307a8a \\\\ \\hline\n",
"matplotlib & 1.4.x \\\\ \\hline\n",
"scipy & 0.13.0.dev-7c6d92e \\\\ \\hline\n",
"qutip & 2.3.0.dev-0b4a1a7 \\\\ \\hline\n",
"\\hline \\multicolumn{2}{|l|}{Tue Aug 06 12:11:46 2013 JST} \\\\ \\hline\n",
"\\end{tabular}\n",
"\\end{table}\n"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 23,
"text": [
"Software versions\n",
"Python 3.3.1 (default, Apr 17 2013, 22:30:32) [GCC 4.7.3]\n",
"IPython 1.0.0-dev\n",
"OS posix [linux]\n",
"Cython 0.19.1\n",
"numpy 1.8.0.dev-b307a8a\n",
"matplotlib 1.4.x\n",
"scipy 0.13.0.dev-7c6d92e\n",
"qutip 2.3.0.dev-0b4a1a7\n",
"\n",
"Tue Aug 06 12:11:46 2013 JST"
]
}
],
"prompt_number": 23
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 23
}
],
"metadata": {}
}
]
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment