121 lines
41 KiB
Plaintext
121 lines
41 KiB
Plaintext
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"\n",
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"simulating... 99 % \n",
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"done.\n"
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]
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},
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{
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"data": {
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"image/png": "iVBORw0KGgoAAAANSUhEUgAAAZkAAAEWCAYAAAC0Q+rDAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAgAElEQVR4nOydd3gVRdfAfye9J4QECAm9ioCgSFEU1FcFEcGCWLCigv2zl9cGir3yIipWQEVQUUCxgSAqiNK7INIDoaT3dr4/ZoOXmITckJvcwPyeZ5+7Ozvl7N7dPVPOnBFVxWKxWCwWT+BT2wJYLBaL5ejFKhmLxWKxeAyrZCwWi8XiMaySsVgsFovHsErGYrFYLB7DKhmLxWKxeAyrZGoYEckUkZa1LMObIvJoNefZV0R2VjFtU+e++FanTKXKuFJEvq/gfJXltxhE5FoR+cXluNaf9aMNEdkqIv8p51ywiMwSkTQR+fRwz3yptB+IyFMVnFcRaV0Vma2SqSQi8qGI7BaRdBHZKCI3VCUfVQ1T1b+dPCv8Yz2Fqo5U1SdrutzyUNXtzn0p8mAZH6nqOSXHR/LSVCci0kVElopItvPbpZx4gSLyrohsE5EMEVkhIv1rWl53cH3WqxMReUJEPqzufCtRbnPnufGr6bIrySVAQ6C+qg4p/czXFlbJVJ5ngOaqGgFcADwlIifVskyWOoyIBAAzgA+BesBEYIYTXho/YAfQB4gEHgGmiUjzGhHWcsTUgHJqBmxU1UIPl+Meqmo3NzegHbAbuLSc862Bn4A0YD8w1eWcOudvAgqAfCATmOWcbwx8DuwDtgB3VCDHecA6IAPYBdzrhPcFdgIPO+VvBa50SfcB8FSpuPcAe53ruq6CMqOB94FEIAX4sjL5AAOA5UA65mP5hMu55s598XOO5wNPAr861/Y9EFOOPD8BFzv7pzr5DHCOzwJWOPvXAr84+wuceFnOvR9ahfvQwsknA5gDvA586OZzdI7zv4lL2HagXyXTryq59nLO3wisd2RcB5zohB/n3ONUYC1wgUua+cANLscH75vL83sH8LfzbL0A+FQQt7XLM/c68LUjz2KgVal78SfmnRnv/K83lHFN/TDvTIHz3610eW9mAsnAX8CNFdyXQOBF514nAW8Cwc65BxzZSp7Fm517FOTEV6fcTKCXE+d65z6nAN8BzUrdg1uBTcAWl7CRTliqc1/EOdcK+BE44Nzfj4Aol/y2Av8p45pGlbovw8v4P9oDPzj36E9cvl+4fBOc4/sw70Cic30H/0t3t1r/YNelzXn4s50bvgwIKyfeFOC/mJZiENC71EPn+uK5/rE+wFLgMSAAaIl5mc8tp5zdwGnOfj3++Yj0BQqBl50Xqg/mg9qudLkucUcD/hjFlQ3UK6fMr4GpTnn+QJ/K5OOc7+RcY2fMyz3YOdecfyuZzUBbINg5frYceUYD/3P2H3bSPedy7jVnv/QLd8hLU4X7sAjzoQoAemOU54cu51Mr2B504twFfFMq36+AeyrxLDYEcoH25ZwfglFgJwOCqdg0c67tL+deBQBnYj76Jc/GfA6vZOZhKhtNgY0l8Su6x5hn7gDQHdMq+wj4xDkX49y/i5xzd2I+lv9SMk78Jyil0DEKfzzmfeuCqaSdWU76VzAKKRoIB2YBz7i8gwucMtpgFEfXsp5TJ2yQcz+Pc2R/BFhY6h784JQV7BL2FRDl3MN9OBUL5386G/PexjqyvOqS31bKUDJl3RcOrViFYip31zlydsUosQ5lfBP6Yd7Pjk66jzkCJWO7y9xAVW/BPJSnAdOBvHKiFmBe6Maqmquqv5QTrzQnA7GqOlpV89X0Z78NXFZBOR1EJEJVU1R1Wanzj6pqnqr+hFEOl1aQz2hVLVDV2ZiaULvSkUQkDugPjHTKK3DyPmw+qjpfVVerarGqrsIo4j4V3Iv3VXWjquYA0zAfjrL4ySWf0zHdmiXHfZzzlaWy96Ep5r96zPmffsF8tA6iqlEVbM860cIwNXdX0jDPWLmIiD/mIz1RVTeUE+0G4HlV/UMNf6nqNqCnU+6zjuw/Yj54l1dUZimeU9VkVd0OvOpG2i9U9Xc13Tkf8c9/eh6wVlWnO+fGAnsqK4yINMG0Yh9w3rcVwDvA1WXEFUwvwl3ONWQAT+O8Y6pa7KS7A/OfPq+qyysofiRGQa13ZH8a6CIizVziPOOUleMS9qyqpjr3cF7JvXD+px+c93YfpqJY0XtSWc4Htqrq+6pa6FzT55jKSGkuxbx/a1Q1C6O8qoxVMm6iqkXORyUB05Qui/sxtcffRWStiFxfyeybAY1FJLVkw9Q4G5YT/2LMC7pNRH4SkV4u51KcB6SEbZguhbI4oIf242ZjPkSlaQIkq2qKu/mISA8RmSci+0QkDfNyxpSTDxz6kSlPHjAtirYi0hDzok4CmohIDKbWvKCCMiotfykaY+5DtkvYDjfKKSETiCgVFoFpWZSJiPgAkzFdI7dVkHcTTKuuNI2BHc7HtIRtQHxlBHZwvdaKnqvSlPefNnbNU0112h1Lv5L/w/W+lXdNsUAIsNTlHfvWCS8pfyvmw98c05VVEc2A11zySsa8+65ll/VslHkvRKShiHwiIrtEJB0zXlfRe1JZmgE9Sn1brgQalRH3kP8Dcy+rjFUyVccP03/6L1R1j6reqKqNgRHA+HIsmbTU8Q5Mv61rrTdcVc8rp5w/VHUQ0AD4ElPjL6GeiIS6HDfF9K8eCTuAaBGJqkLajzE1wyaqGonpB5cjlAfnQ78U08WyRlXzgYXA3cBmVd1/pGWUwW7MfQhxCWviGsEx3y1ve9iJthbo7NSuS+jshP8LJ967mErHxapaUIGMOyj7+UzEKGHXd78ppmsNTLeq63WV9RFyvdbqeK52YyptwMHrTCg/+r/em0TM/+HaAnS9Jlf2AznA8S7vWKSqHqxMiMgAoBcwFzPmVF65YO7ziFLvbLCqLjxMuvJ42onfSY2R0TCq4T1x5PyplJxhqlpWRXk3//6Pq4xVMpVARBqIyGUiEiYiviJyLqaLYG458YeISMlLkoJ5aIrLiJqEGXcp4XcgQ0QecGzefUWko4icXEYZAY4dfKTzsUkvo4xRTrzTMM3lT9257tKo6m7gG4zSrCci/iJyeiWTh2Nqm7ki0h244khkKcVPmFp9SdfY/FLHZVH63lcap9tpCfCEc397AQNLxQmrYHvaRc4i4A7HRLmkZfJjOUW/gen7H1iq66Us3gHuFZGTxNDa6cJZjKk53+/8f30d2T9x0q0ALhKREKdiNLyMvO9z/v8mGOU+9TCyHI6vgU4iMtixwLqVspVbCUlA8xJFqao7MBWLZ0QkSEQ6O3L/y8zZacG9DbwiIg0ARCTeeadxWsDvYLobrwEGikhJJW8f5h1zfW7eBB4SkeOd9JEiUlYXVGUJx7Rw00QkHjMAXx18hWnxX+X87/4icrKIHFdG3GnAtSLSwalIPX4kBVslUzkU0zW2E6M0XgT+T1VnlhP/ZGCxiGRiau93atnzBd7FjKmkisiXauaJnI/p9tmCqXW9gzFZLYurgK1Os3okpvlbwh5H1kRM//fICvrv3eEqzNjFBowV1v9VMt0twGgRycAYNkw7THx3+Anzci4o57gsngAmOve+vLGqirgSU9s9ADyF+dCWN0ZXJk6razBmDCAVY8Uz2AlHRB4WkW+c/WaYVnEXYI9Lq+jKcvL+FBiDaUFmYFq60U7eAzFja/sxg+VXuzwbr2C64pIwJtUflZH9DEzrcQVGQbzrznWXIet+zNjA85j72QGjxMu7nyWVpQMiUjIOeTmmeysR+AJ4XFXnlJP+Acxg/W/OuzOHf8beJgAzVHW2qh7AKKt3RKS+02oeA/zqPDc9VfUL4DngEyevNZh7W1VGASdixua+xoz9HjFOV+I5mLGnRMz34TmMgUHpuN9gxtp+xNyn8io9laLEbM5yFOHUTj9U1Yq6HCzViIhMBTao6hHV+rwdEVGgjar+5cEyfDAVuitVdZ6nyrHUDLYlY7FUAaeroZWI+IhIP4wp65e1LVddRUTOFZE
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"text/plain": [
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"<Figure size 432x288 with 1 Axes>"
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]
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},
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"metadata": {
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"needs_background": "light"
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},
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"output_type": "display_data"
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}
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],
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"source": [
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"%matplotlib inline\n",
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"\n",
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"from pyqcs import State, sample\n",
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"from transfer_matrix import T_time_slice\n",
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"from hamiltonian import H\n",
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"\n",
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"from scipy.linalg import expm\n",
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"\n",
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"nqbits = 3\n",
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"g = 0.20\n",
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"N = 50\n",
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"t_stop = 5\n",
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"delta_t = 0.05\n",
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"qbits = list(range(nqbits))\n",
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"\n",
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"n_sample = 400\n",
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"measure = 0b10\n",
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"\n",
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"\n",
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"results_qc = []\n",
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"results_np = []\n",
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"print()\n",
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"for t in np.arange(0, t_stop, delta_t):\n",
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" # QC simulation\n",
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" state = State.new_zero_state(nqbits)\n",
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"\n",
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" for _ in range(N):\n",
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" state = T_time_slice(qbits, t, g, N) * state\n",
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"\n",
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" #result = sample(state, measure, n_sample)\n",
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"\n",
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" #results_qc.append(result[0] / n_sample)\n",
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"\n",
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" amplitude = np.sqrt(np.sum(np.abs(state._qm_state[[False if (i & measure) else True for i in range(2**nqbits)]])**2))\n",
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" results_qc.append(amplitude)\n",
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"\n",
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" # Simulation using matrices\n",
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" np_zero_state = np.zeros(2**nqbits)\n",
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" np_zero_state[0] = 1\n",
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"\n",
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" itH = np.matrix(-1j * t * H(nqbits, g))\n",
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" T = expm(itH)\n",
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"\n",
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" np_state = T.dot(np_zero_state)\n",
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" amplitude = np.sqrt(np.sum(np.abs(np_state[[False if (i & measure) else True for i in range(2**nqbits)]])**2))\n",
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" results_np.append(amplitude)\n",
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"\n",
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" print(f\"simulating... {int(t/t_stop*100)} % \", end=\"\\r\")\n",
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"print()\n",
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"print(\"done.\")\n",
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"\n",
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"errors_trotter = np.arange(0, t_stop, delta_t)**2 / N**2\n",
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"\n",
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"\n",
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"h0 = plt.errorbar(np.arange(0, t_stop, delta_t), results_qc, yerr=errors_trotter, label=f\"Quantum computing ({n_sample} samples, {N} trotterization steps)\")\n",
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"h1, = plt.plot(np.arange(0, t_stop, delta_t), results_np, label=\"Classical simulation using explicit transfer matrix\")\n",
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"plt.xlabel(\"t\")\n",
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"plt.ylabel(r\"$|0\\rangle$ probability amplitude for second spin\")\n",
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"plt.title(f\"{nqbits} site spin chain with g={g} coupling to external field\")\n",
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"plt.legend(handles=[h0, h1])\n",
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"\n",
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"plt.show()\n",
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"\n"
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]
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.7.3"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 2
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}
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