From 4c7249d490f1f3483e2b625d6d57f33937292c79 Mon Sep 17 00:00:00 2001 From: Sam Duffield Date: Tue, 13 Sep 2022 12:21:25 +0100 Subject: [PATCH 1/3] notebook bug fix + print Arr/Func --- examples/README.md | 4 +- examples/generative_modelling.ipynb | 59 ++-- examples/heisenberg_vqe.ipynb | 54 +-- examples/maxcut_vqe.ipynb | 16 +- examples/qaoa.ipynb | 507 +++++++++++++++++++++++++++ examples/variational_inference.ipynb | 22 +- qujax/circuit_tools.py | 4 + 7 files changed, 594 insertions(+), 72 deletions(-) create mode 100644 examples/qaoa.ipynb diff --git a/examples/README.md b/examples/README.md index d54c533..ed7770b 100644 --- a/examples/README.md +++ b/examples/README.md @@ -5,7 +5,7 @@ In this directory, you can find a selection of notebooks demonstrating some simp - [`generative_modelling.ipynb`](https://github.com/CQCL/qujax/blob/main/examples/generative_modelling.ipynb) - uses a parameterised quantum circuit as a generative model for a real life dataset. Trains via stochastic gradient Langevin dynamics on the maximum mean discrepancy between statetensor and dataset. - [`heisenberg_vqe.ipynb`](https://github.com/CQCL/qujax/blob/main/examples/heisenberg_vqe.ipynb) - an implementation of the variational quantum eigensolver to find the ground state of a quantum Hamiltonian. - [`maxcut_vqe.ipynb`](https://github.com/CQCL/qujax/blob/main/examples/maxcut_vqe.ipynb) - an implementation of the variational quantum eigensolver to solve a maxcut problem. Trains with Adam via [`optax`](https://github.com/deepmind/optax) and uses more realistic stochastic parameter shift gradients. -- [`variational_inference.ipynb`](https://github.com/CQCL/qujax/blob/main/examples/variational_inference.ipynb) - uses a parameterised quantum circuit as a variational distribution to fit to a target probability mass function. Uses Adam via [`optax`](https://github.com/deepmind/optax) to minimise the KL divergence between circuit and target distributions. - +- [`qaoa.ipynb`](https://github.com/CQCL/qujax/blob/main/examples/variational_inference.ipynb) - uses a parameterised quantum circuit as a variational distribution to fit to a target probability mass function. Uses Adam via [`optax`](https://github.com/deepmind/optax) to minimise the KL divergence between circuit and target distributions. +- [`variational_inference.ipynb`](https://github.com/CQCL/qujax/blob/main/examples/variational_inference.ipynb) - uses a problem inspired QAOA ansatz to find the ground state of quantum Hamiltonian. Demonstrates how to encode more sophisticated parameters that control multiple gates. The Heisenberg notebook with a `tk_to_qujax` implementation can be found in the [`pytket`](https://github.com/CQCL/pytket) repository at [`pytket-qujax_heisenberg_vqe.ipynb`](https://github.com/CQCL/pytket/blob/main/examples/pytket-qujax_heisenberg_vqe.ipynb). diff --git a/examples/generative_modelling.ipynb b/examples/generative_modelling.ipynb index 0130863..c699e7d 100644 --- a/examples/generative_modelling.ipynb +++ b/examples/generative_modelling.ipynb @@ -37,7 +37,7 @@ "outputs": [], "source": [ "n_qubits = 8\n", - "circuit_depth = 4\n", + "circuit_depth = 3\n", "init_rad = 0.001 / jnp.pi\n", "beta = 1e3\n", "get_stepsize = lambda step: (step + 10) ** (-1/3)\n", @@ -106,7 +106,7 @@ "id": "6f32a1cf", "metadata": {}, "source": [ - "# We will use the maximum mean discreapancy (MMD) as our training metric\n", + "# We will use the maximum mean discrepancy (MMD) as our training metric\n", "\n", "We attempt to minimise\n", "$$\n", @@ -164,7 +164,7 @@ " n_params = 2 * n_qubits * (depth + 1)\n", " \n", " \n", - " gates = ['H'] * n_qubits + ['Rx'] * n_qubits + ['Rz'] * n_qubits\n", + " gates = ['H'] * n_qubits + ['Rx'] * n_qubits + ['Ry'] * n_qubits\n", " qubit_inds = [[i] for i in range(n_qubits)] * 3\n", " param_inds = [[]] * n_qubits + [[i] for i in range(n_qubits * 2)]\n", " \n", @@ -208,26 +208,26 @@ "name": "stdout", "output_type": "stream", "text": [ - "q0: -----H-----Rx[0]---Rz[8]-----◯---------------------------------------------------\n", - " | \n", - "q1: -----H-----Rx[1]---Rz[9]-----CZ------◯-------------------------------------------\n", - " | \n", - "q2: -----H-----Rx[2]---Rz[10]------------CZ------◯-----------------------------------\n", - " | \n", - "q3: -----H-----Rx[3]---Rz[11]--------------------CZ------◯---------------------------\n", - " | \n", - "q4: -----H-----Rx[4]---Rz[12]----------------------------CZ------◯-------------------\n", - " | \n", - "q5: -----H-----Rx[5]---Rz[13]------------------------------------CZ------◯-----------\n", - " | \n", - "q6: -----H-----Rx[6]---Rz[14]--------------------------------------------CZ------◯---\n", - " | \n", - "q7: -----H-----Rx[7]---Rz[15]----------------------------------------------------CZ--\n" + "q0: -----H-----Rx[0]---Ry[8]-----◯---------------------------------------------Rx[16]--Ry[24]------------◯-----------\n", + " | | \n", + "q1: -----H-----Rx[1]---Ry[9]-----CZ------◯-------------------------------------Rx[17]--Ry[25]------------CZ------◯---\n", + " | | \n", + "q2: -----H-----Rx[2]---Ry[10]------------CZ------◯-----------------------------Rx[18]--Ry[26]--------------------CZ--\n", + " | \n", + "q3: -----H-----Rx[3]---Ry[11]--------------------CZ------◯---------------------Rx[19]--Ry[27]------------------------\n", + " | \n", + "q4: -----H-----Rx[4]---Ry[12]----------------------------CZ------◯-------------Rx[20]--Ry[28]------------------------\n", + " | \n", + "q5: -----H-----Rx[5]---Ry[13]------------------------------------CZ------◯-----Rx[21]--Ry[29]------------------------\n", + " | \n", + "q6: -----H-----Rx[6]---Ry[14]--------------------------------------------CZ------◯-----Rx[22]--Ry[30]----------------\n", + " | \n", + "q7: -----H-----Rx[7]---Ry[15]----------------------------------------------------CZ----Rx[23]--Ry[31]----------------\n" ] } ], "source": [ - "qujax.print_circuit(gates, qubit_inds, param_inds, gate_ind_max=30);" + "qujax.print_circuit(gates, qubit_inds, param_inds, gate_ind_max=48);" ] }, { @@ -336,7 +336,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Iteration: 499 \tCost: 0.0117726623\r" + "Iteration: 499 \tCost: 0.0074185435\r" ] } ], @@ -367,7 +367,17 @@ "outputs": [ { "data": { - "image/png": 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\n", + "text/plain": [ + "(0.0, 0.1)" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", 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" ] @@ -381,7 +391,8 @@ "source": [ "plt.plot(cost_vals)\n", "plt.xlabel('Iteration')\n", - "plt.ylabel('MMD');" + "plt.ylabel('MMD')\n", + "plt.ylim(0, 0.1)" ] }, { @@ -400,7 +411,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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\n", 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\n", "text/plain": [ "
" ] diff --git a/examples/heisenberg_vqe.ipynb b/examples/heisenberg_vqe.ipynb index c250387..0bc1b2b 100644 --- a/examples/heisenberg_vqe.ipynb +++ b/examples/heisenberg_vqe.ipynb @@ -47,7 +47,7 @@ " n_params = 2 * n_qubits * (depth + 1)\n", " \n", " \n", - " gates = ['H'] * n_qubits + ['Rx'] * n_qubits + ['Rz'] * n_qubits\n", + " gates = ['H'] * n_qubits + ['Rx'] * n_qubits + ['Ry'] * n_qubits\n", " qubit_inds = [[i] for i in range(n_qubits)] * 3\n", " param_inds = [[]] * n_qubits + [[i] for i in range(n_qubits * 2)]\n", " \n", @@ -106,7 +106,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "['H', 'H', 'H', 'H', 'Rx', 'Rx', 'Rx', 'Rx', 'Rz', 'Rz', 'Rz', 'Rz', 'CZ', 'CZ', 'CZ', 'Rx', 'Rx', 'Rx', 'Rx', 'Ry', 'Ry', 'Ry', 'Ry', 'CZ', 'CZ', 'CZ', 'Rx', 'Rx', 'Rx', 'Rx', 'Ry', 'Ry', 'Ry', 'Ry']\n", + "['H', 'H', 'H', 'H', 'Rx', 'Rx', 'Rx', 'Rx', 'Ry', 'Ry', 'Ry', 'Ry', 'CZ', 'CZ', 'CZ', 'Rx', 'Rx', 'Rx', 'Rx', 'Ry', 'Ry', 'Ry', 'Ry', 'CZ', 'CZ', 'CZ', 'Rx', 'Rx', 'Rx', 'Rx', 'Ry', 'Ry', 'Ry', 'Ry']\n", "34\n" ] } @@ -176,13 +176,13 @@ "name": "stdout", "output_type": "stream", "text": [ - "q0: -----H-----Rx[0]---Rz[4]-----◯-------------Rx[8]---Ry[12]------------◯-------------Rx[16]--Ry[20]\n", + "q0: -----H-----Rx[0]---Ry[4]-----◯-------------Rx[8]---Ry[12]------------◯-------------Rx[16]--Ry[20]\n", " | | \n", - "q1: -----H-----Rx[1]---Rz[5]-----CZ------◯-----Rx[9]---Ry[13]------------CZ------◯-----Rx[17]--------\n", + "q1: -----H-----Rx[1]---Ry[5]-----CZ------◯-----Rx[9]---Ry[13]------------CZ------◯-----Rx[17]--------\n", " | | \n", - "q2: -----H-----Rx[2]---Rz[6]-------------CZ------◯-----Rx[10]--Ry[14]------------CZ------◯-----Rx[18]\n", + "q2: -----H-----Rx[2]---Ry[6]-------------CZ------◯-----Rx[10]--Ry[14]------------CZ------◯-----Rx[18]\n", " | | \n", - "q3: -----H-----Rx[3]---Rz[7]---------------------CZ----Rx[11]--Ry[15]--------------------CZ----Rx[19]\n" + "q3: -----H-----Rx[3]---Ry[7]---------------------CZ----Rx[11]--Ry[15]--------------------CZ----Rx[19]\n" ] } ], @@ -323,7 +323,7 @@ "outputs": [ { "data": { - "image/png": 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"text/plain": [ "
" ] @@ -481,7 +481,7 @@ { "data": { "text/plain": [ - "DeviceArray(0.37890375, dtype=float32)" + "DeviceArray(1.6290706, dtype=float32)" ] }, "execution_count": 16, @@ -533,7 +533,7 @@ { "data": { "text/plain": [ - "DeviceArray(0.37890375, dtype=float32)" + "DeviceArray(1.6290706, dtype=float32)" ] }, "execution_count": 18, @@ -570,7 +570,7 @@ { "data": { "text/plain": [ - "DeviceArray(-0.03778487, dtype=float32)" + "DeviceArray(0.2565445, dtype=float32)" ] }, "execution_count": 19, @@ -636,15 +636,15 @@ { "data": { "text/plain": [ - "(DeviceArray(0.37890375, dtype=float32),\n", - " DeviceArray([-9.3626760e-08, 1.4044014e-07, -9.9478434e-08,\n", - " -7.0220068e-08, -1.4372616e-01, 3.9894512e-01,\n", - " -3.7416592e-01, -1.5358305e+00, -9.1433835e-01,\n", - " 1.1027540e+00, -1.0273510e+00, -8.1937420e-01,\n", - " 1.2983767e+00, 3.0651841e-01, 2.2440134e-01,\n", - " -2.1478393e+00, 9.2832714e-02, -1.2622638e+00,\n", - " 5.8574063e-01, 4.8522827e-01, -7.2519130e-01,\n", - " 1.0764527e+00, -7.1246302e-01, 3.6120212e-01], dtype=float32))" + "(DeviceArray(1.6290706, dtype=float32),\n", + " DeviceArray([ 9.3626761e-07, 5.6176054e-07, 6.0857394e-07,\n", + " 4.6813381e-07, 2.5579420e-01, 9.2308128e-01,\n", + " -2.2530050e+00, -2.1122539e+00, 1.7944418e+00,\n", + " 5.6182927e-01, -1.0677941e+00, -1.7813085e-01,\n", + " 5.0560904e-01, -1.4611506e+00, 5.2151042e-01,\n", + " -2.5418801e+00, 4.8420203e-01, -7.3182994e-01,\n", + " 1.4512728e-01, 1.4524205e-01, 5.1464313e-01,\n", + " -5.8293301e-01, -9.7354606e-02, 1.6564427e-01], dtype=float32))" ] }, "execution_count": 21, @@ -726,10 +726,10 @@ "name": "stdout", "output_type": "stream", "text": [ - "Iteration: 249 \tCost: -6.0999996\n", + "Iteration: 249 \tCost: -6.3272466\n", "\n", - "CPU times: user 25.3 s, sys: 296 ms, total: 25.6 s\n", - "Wall time: 25.6 s\n" + "CPU times: user 24.5 s, sys: 270 ms, total: 24.8 s\n", + "Wall time: 24.7 s\n" ] } ], @@ -761,7 +761,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -844,10 +844,10 @@ "name": "stdout", "output_type": "stream", "text": [ - "Iteration: 249 \tCost: -6.3269672\n", + "Iteration: 249 \tCost: -6.3270696\n", "\n", - "CPU times: user 2.14 s, sys: 24.5 ms, total: 2.17 s\n", - "Wall time: 1.69 s\n" + "CPU times: user 2.22 s, sys: 26.8 ms, total: 2.25 s\n", + "Wall time: 1.78 s\n" ] } ], @@ -881,7 +881,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] diff --git a/examples/maxcut_vqe.ipynb b/examples/maxcut_vqe.ipynb index 3c4300b..3a73df9 100644 --- a/examples/maxcut_vqe.ipynb +++ b/examples/maxcut_vqe.ipynb @@ -88,7 +88,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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\n", 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" ] @@ -162,7 +162,7 @@ " n_params = 2 * n_qubits * (depth + 1)\n", " \n", " \n", - " gates = ['H'] * n_qubits + ['Rx'] * n_qubits + ['Rz'] * n_qubits\n", + " gates = ['H'] * n_qubits + ['Rx'] * n_qubits + ['Ry'] * n_qubits\n", " qubit_inds = [[i] for i in range(n_qubits)] * 3\n", " param_inds = [[]] * n_qubits + [[i] for i in range(n_qubits * 2)]\n", " \n", @@ -209,15 +209,15 @@ "name": "stdout", "output_type": "stream", "text": [ - "q0: -----H-----Rx[0]---Rz[5]-----◯-------------------------------CZ----Rx[10]--Ry[15]----◯---\n", + "q0: -----H-----Rx[0]---Ry[5]-----◯-------------------------------CZ----Rx[10]--Ry[15]----◯---\n", " | | | \n", - "q1: -----H-----Rx[1]---Rz[6]-----CZ------◯-----------------------|-----Rx[11]--Ry[16]----CZ--\n", + "q1: -----H-----Rx[1]---Ry[6]-----CZ------◯-----------------------|-----Rx[11]--Ry[16]----CZ--\n", " | | \n", - "q2: -----H-----Rx[2]---Rz[7]-------------CZ------◯---------------|-----Rx[12]--Ry[17]--------\n", + "q2: -----H-----Rx[2]---Ry[7]-------------CZ------◯---------------|-----Rx[12]--Ry[17]--------\n", " | | \n", - "q3: -----H-----Rx[3]---Rz[8]---------------------CZ------◯-------|-----Rx[13]--Ry[18]--------\n", + "q3: -----H-----Rx[3]---Ry[8]---------------------CZ------◯-------|-----Rx[13]--Ry[18]--------\n", " | | \n", - "q4: -----H-----Rx[4]---Rz[9]-----------------------------CZ------◯-----Rx[14]--Ry[19]--------\n" + "q4: -----H-----Rx[4]---Ry[9]-----------------------------CZ------◯-----Rx[14]--Ry[19]--------\n" ] } ], @@ -406,7 +406,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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xymogxphmKFG9sMYAtwKXquqREGUyRSTb9x4YDfhmon8NmOi+nwi8Gt+Ig+vVoQ3fye8d1b6pyUkcKa8E6t8F2BhjmoJEtYE8CGTj3JYqFJG/A4hIDxGZ45bpCiwSkc+AJcB/VfUtd9tM4HwRWQ+c5y43K/26ZnOk3OlHkGyDYxljmqE6b2GJyN2q+qu61tWHqh4fYv124EL3/SZgSIhye4BR0X5+PKWnJFFaUQXAU5OGhSy3cfchfw1k7EMf8PD3TubCQTZLoTGm+YikBnJ+kHXfinUgLcGSX49i8bSjTT8j+3cJWdaXPHxmL/4ibnEZY0w8hKyBiMhPgOuAY0VkecCmbOCDeAfWHHVpG/lMXjWl1WMwRmOMaQrC3cL6P5znM/5I9Se9i1U19NR7hrk3f5OSGjWMuqRG2ZPLGGMSJWQCUdUDwAER+Q3wlaqWicgIYLCIPKOq+xsnxObnhK7Z9d4nNdkSiDGmeYnkr9ZLQKWIHI/zQF5vnNqJiaE0SyDGmGYmkr9aVe64VeOAv6nqLYB1F4oxq4EYY5qbSP5qVYjIBOCHwBvuupT4hdQ6Rfs0uzHGJEokf7UmA6cDd6nqZhHpC/wzvmG1LNeNOK7OMjY/iDGmuakzgajqKuCXwOciMhAoUtW74x5ZC3LrmP51llm94yCvFm5rhGiMMSY26kwgbs+r9cBDwMPAOhH5ZnzDan0+3rSXG58rZN/hchauTcjYkMYYUy+RjMb7F2C0qq4FEJETgGeBU+IZWGs1edYnFG7dz6rfX0Cb1LgNlmyMMQ0WSRtIii95AKjqOqwRvd56hpjytqbVOw4C4K2yId6NMU1bJAmkQEQeF5ER7utxoCDegbU0/7nuDJ6clF9nuTKvMxBjZaUlEGNM0xbJPZKfAD8FbnCX3wMeiVtELVTXtul0zkqLuHxFVVUcozHGmIYLN5hiDpDj9sK6130hIicBbYHYTjDeCtRn2g+v1UCMMU1cuFtYfwM6B1nfEfhrfMJp2USEa885jiG929dZduveI/72EGOMaYokxHTkiEiBqga9aS8iK1R1YFwji4P8/HwtKEh88423soqDpV5SPMKgO+aGLbtl5kWNFJUxxgQnIkuD5YNwNZBwQ8paL6wGSPYk0TEz1YYvMcY0a+H+gm0QkQtrrhSRbwGb4hdS65Ge4uHSIT0SHYYxxkQlXC+sm4D/ish3gaXuunyccbEujnNcrcYDE4bSr1s297y9tu7CxhjThISsgajqemAQ8C7Qx329Cwx2HyaMmojcIyJrRGS5iLwsIu2DlOknIoUBr4MicpO77Q4R2RawrVZNqTnp2oCpcI0xJlHCPgeiqmXAU3H43HnANFX1isjdwDTgVzU+ey2QByAiHmAb8HJAkftU9c9xiK3RdQuTQFQVsaF6jTFNUEJacVV1rjtJFcDHQK86dhkFbFTVL+IbWWK0bxO6T4INaWKMaaqaQjegKcCbdZS5EmcAx0A/c2+BPSkiHULtKCJTRaRARAp2726azz6Gm852V3FZI0ZijDGRi2Q49xsjWRekzHwRWRHkNTagzHTAC8wOc5xU4FLghYDVjwDH4dzi2oEzYnBQqvqoquaran5OTk5dYSdEWrIn5LaJTy7h7+9upKS8shEjMsaYukUyFtZEaj95PinIumpU9bxw20VkEk5vrlEa6mlGx7eAT1V1Z8Cx/e9F5DGOTrXbLKWlhM7jG3YdYuaba9h7uJxfX3hiI0ZljDHhhRsLawJwFdBXRF4L2JQN7G3Ih4rIGOBW4BxVPVJH8QnUuH0lIt1VdYe7+G1gRUPiSbTUCB4oPHCkohEiMcaYyIWrgXyIc3uoM9VvERUDyxv4uQ8CacA8t4fRx6p6rYj0AB5X1QsBRCQTOB+4psb+fxKRPECBLUG2NyvhaiA+lWEracYY0/hCJhC3x9MXOA8OxpSqHh9i/XbgwoDlw0CnIOV+EOuYEimSGkiV9cYyxjQxdbaBiEgxzjd9gFSccbAOq2rbeAbWmiRHkECsBmKMaWrqTCCq6h9UUZz7TWOB0+IZlKmt0mogxpgmpl7PgajjFeCC+IRjANpl1H6w0CogxpimJpJbWOMCFpNwBlQsjVtErdSdY09i3updvLduN1lpyRwoqd7rymogxpimJpLnQC4JeO/F6fU0NnhRE60fnN6HAyUVvLduN21Saz9YaG0gxpimJpI2kMmNEYiBJHfS9DZptS+L9cIyxjQ1kQxl8nTgcOsi0kFEnoxrVK1UsptAgo29azUQY0xTE0kj+mBV3e9bUNV9wNC4RdSKjejXxf239phd1gZijGlqIkkgSYGj3YpIRyJrOzH1dELXbFb+7gJ+eHqfWtusAmKMaWoiSQR/AT4SEd9ouN8B/hC/kFq3zLRkUpOraq331UBUlY827aFobwnfHda7scMzxhi/SBrRnxGRpcBId9U4VV0V37Bat5QgT6b72kBufXE5LywtArAEYoxJqEieA/mRqj4BrHSXPSIyQ1V/F/foWrFnpgwnKz2ZcQ9/CMDq7QcB/MnDGGMSLZI2kFEiMkdEuovISThT0GbXtZNpmG+ekMPJxxydaLG4zMuCtbsSGJExxlQXyS2sq0TkCuBz4DBwlap+EPfITC0rig4kOgRjjPGL5DmQXOBG4CWc4d1/ICJt4h2Yqe1QmTfRIRhjjF8kt7BeB36rqtcA5wDrgU/iGpUJqtgSiDGmCYmkG+9wVT0Izmi8wF9E5PX4hmWC+b/FXyY6BGOM8YukDeSgiAwEBgDpAZvWxS0qY4wxTV4kbSAzgL+5r5HAn4BL4xyXcU05s2+iQzDGmKAiaQO5HBgFfOWOzDsEaBfXqIzfby8+MdEhGGNMUJEkkBJVrQK8ItIW2AU0+BFoEblTRJaLSKGIzBWRHiHKTRSR9e5rYsD6U0TkcxHZICIPuNPttjgiQoc2tWcoBKdX1m9e+Zy9h8sbOSpjjIksgRS4w7k/BiwFPgU+isFn36Oqg1U1D3gDuL1mAXfgxhnAqcBwYEbAwI6PAD8Gct3XmBjE1CTNvfmcoOsHznibf338JffOW9vIERljTAQJRFWvU9X9qvp34HxgYiwmmfL17HJlAsHGm70AmKeqe91h5OcBY0SkO9BWVT92e4Y9A1zW0JiaqpzsNF689vSQ2ytrj71ojDFxF7IXloicHG6bqn7a0A8XkbuAHwIHODpYY6CewNaA5SJ3XU/3fc31LVZ+n46cnduZ99d/XWtbkLEXjTEm7sJ14y0AVgC+v1iBbQwKnFvXwUVkPtAtyKbpqvqqqk4HpovINOBnOLerYkpEpgJTAY455phYH75ReZKCN/MktczmH2NMExcugfwcpwdWCfAc8LKqHqrPwVX1vAiLzgbmUDuBbANGBCz3Aha663vVWL8tRAyPAo8C5OfnN+tpmTwhEoUlEGNMIoS8+aGq96vqWcD1OL2u3hGRf4tIXiw+2B1jy2cssCZIsbeB0e487B2A0cDbqroDOCgip7m9r34IvBqLuJqyUDWQcmsEMcYkQCRPom8SkVeBDOAHwAlAYQw+e6aI9AOqcAZpvBZARPKBa1X1alXdKyJ3cnTsrd+r6l73/XXALDeuN91Xi5bsCZ5AyiosgRhjGl+4RvRjgStxagdbcW5j/UFVS2Lxwao6PsT6AuDqgOUngSdDlBsYi1iai1C3qrxVlkCMMY0vXA1kA7Ac59bQQeAY4Ce+5/VU9d64R2eqSQ5xC6vCbmEZYxIgXAL5PUefzchqhFhMHY6UVwZdX+5t1n0DjDHNVMgEoqp3NGIcJgKffrk/6Pr5q3eyfmcxuV1tpmFjTOOxR9CakYzU0JfrqscXN2IkxhhjCaRZSU/2JDoEY4zxswTSjIR6DgSga9u0RozEGGMieA7EfS7jbKAHzlPpK3AGONwX59hMDd6qo43lg3u1Y3nRAf9yVloksxMbY0zshKyBiMhkEfkUmIbzsN5anLlAzgLmi8jTItK8B5dqZqoCEkhlVfWeVxkpdnvLGNO4wn1tbQOcGerBQXdIk1zgyzjEZYKoVCdpzBw3iFkfbqm2Ld0SiDGmkYXrxvtQuB1VtTDm0ZiwvJVOAjn9uE7kZKfxo6cL/NssgRhjGlu4oUweCLejqt4Q+3BMOFVuDSQ1OYlRJ3atts3G4zXGNLZwvbCWuq904GRgvfvKA1LjHpmpxdfuEWxYd9/trVXbD7LnUFmjxmWMaZ3C3cJ6GkBEfgKcpaped/nvwPuNE54J5EsgSTW683bOSvP30Lrwgffp3TGD92+tc74vY4xpkEieA+kAtA1YznLXmUb2p8sHc2L3trTPSKm2vmNmCpWVirq1kK17YzJgsjHGhBXJwwMzgWUisgDnVvs3gTviGZQJbtSJXWu1fQB4kpLwVimHQwy2aIwx8RDJhFJPicibwKnuql+p6lfxDcvUR3KSUKXKT/61NNGhGGNakTpvYblTxp4HDFHVV4FUERke98hMnZZMH8Wy356PJ0moqKzi/fVf+7cdLK1IYGTGmNYgkjaQh4HTgQnucjEQ9hkR0zi6ZKfTITOV5CRh7VfF1bYNvmNugqIyxrQWkbSBnKqqJ4vIMgBV3Sci1o23CTlSXsmuYuu6a4xpXJHUQCpExIM7O6GI5AA2h2oTcqjMm+gQjDGtUCQJ5AHgZaCLiNwFLAL+ENeoTL0ke+w5dGNM44ukF9ZsEVkKjMLpxnuZqq5uyIeKyJ3AWJyazC5gkqpur1EmD3gE5xmUSuAuVX3e3TYLOAfwjWc+qTWPzWXpwxiTCOHGwuoYsLgLeDZwm6rubcDn3qOqv3WPdQNwO3BtjTJHgB+q6noR6QEsFZG3VXW/u/0WVX2xATG0GDVGdjfGmEYRrgayFKfdI9gXXAWOjfZDVfVgwGKme7yaZdYFvN8uIruAHGB/tJ/bUvkGWTTGmMYUbiysvvH8YLc95Yc4t6FG1lF2OM4AjhsDVt8lIrcD7wC3qWrQbkgiMhWYCnDMMS1z/qukgMEV+3fLZk2NLr3GGBMPEc2JLiLjROReEfmLiFwW4T7zRWRFkNdYAFWdrqq9gdnAz8IcpzvwT2Cyqvp6f00D+gPDgI7Ar0Ltr6qPqmq+qubn5OREEnqzEzhXeknF0eFMxj64iC/2HE5ESMaYViCSJ9Efxmmf+BxnPvRrRaTOBwlV9TxVHRjk9WqNorOB8SE+uy3wX2C6qn4ccOwd6igDngJa9ZPxyQEJpLj0aJfez4oO8NQHWxIQkTGmNYjkQcJzgRPVHepVRJ4GVjbkQ0UkV1XXu4tjgTVByqTidB9+pmZjuYh0V9Ud7jArl+EktlbLUy2BVB/CJCc7rbHDMca0EpEkkA3AMcAX7nJvd11DzBSRfjjdeL/A7YElIvnAtap6NfBdnJF/O4nIJHc/X3fd2e4DjQIUUrsHV6sSWAOpqKzeoJ6ZalPdGmPiI5IEkg2sFpEl7vIwoEBEXgNQ1Uvr+6GqGvSWlaoWAFe77/8F/CtEOZstKYCvBvLYD/P58TMF1bbd8foqivaV8JuLByQiNGNMCxZJArk97lGYBkn2OE1Z2enBL+fjizZbAjHGxFwkT6K/C/4G7eSA9Q15kNDE0HE5WSzZvJfM1Ei+DxhjTGzU+RfHfY7i90ApTpuF0MAHCU1szbhkACP75TCoV7tEh2KMaUUi+cp6CzBQVb+us6RJiPQUD6NP6lZnOW9lFe+t3825/WtPi2uMMfUVyYOEG3HGpTLN3MMLNzJlVgEL1u5KdCjGmBYgkhrINOBDEVkM+IcLUdUb4haViYuifc73gF0HSxMciTGmJYgkgfwD+B/Ok+g2kVQz5uvu67Xhe40xMRBJAklR1Z/HPRITVwdKKvwJpNISiDEmBiJpA3lTRKaKSHcR6eh7xT0yE1NTZn2CRyyBGGNiJ5IEMgG3HQRnjpClQEHYPUzCPT1lOJ2zjo6DtfSLfXiSnMttCcQYEwuRPEgY13lBTHycc0IOmWkevj50dN0LS7cClkCMMbER0aPLIjIQGACk+9ap6jPxCspELzU5iXKv09chcKIpODrUuzWiG2NiIZIn0WcAI3ASyBzgW8AiwBJIE7ToVyM5cMQZ0j3YXMQAVZZAjDExEEkbyOXAKOArVZ0MDAFszIwmqkt2OrldswHwVUBGD6j+5HmlzaFujImBSBJIiTuVrNcdUHEXzpwgponzddttU2NOEGsDMcbEQiRtIAUi0h54DKcH1iHgo3gGZWLD1waSUWOU3sKt+ynzVpKWbJNNGWOiV2cNRFWvU9X9qvp34HxgonsryzRxnbJSgaO3snzeX/81d7y2KgERGWNakpAJRES+ISLtApZHAjcD57nzlZsmLreL0xZSUl5Za9v763c3djjGmBYmXA3k30AmgIjkAS8AX+I0oj8c98hMg/3ygn78dORxjM3rUWtb0b4SvJU2tJkxJnrhEkiGqm53338feFJV/wJMBobHPTLTYFlpydxyQX9SPMEvc5nXEogxJnrhEkjgnfNzgXcA3B5ZDSYid4rIchEpFJG5IlL7a7JTrtItUygirwWs7ysii0Vkg4g8b7fVQqsK0W233BKIMaYBwiWQ/4nIv0Xkr0AHnCHdEZHuQHkMPvseVR2sqnnAG8DtIcqVqGqe+7o0YP3dwH2qejywD/hRDGJqkUJ127UaiDGmIcIlkJuA/wBbgLNUtcJd3w2Y3tAPVtWDAYuZOPOsR0REBKdW9KK76mngsobG1FL165YddH2Zt3bjujHGRCpsN15VfU5V71PVbQHrlqnq2+D/Qx41EblLRLYC3yN0DSRdRApE5GMRucxd1wnYr6ped7kI6BniM6a6+xfs3t06ex51b5fBlpkX1Vrvq4EcKfdyuMxba7sxxoQTLoEsEJHrReSYwJUikioi54rI08DEcAcXkfkisiLIayyAqk5X1d7AbOBnIQ7zDVXNB64C7heR4yI+O+czHlXVfFXNz8nJqc+uLV5ZhZNABtz+NifNeJu3VnyV4IiMMc1JuCfRxwBTgGdFpC+wH2c0Xg8wF7hfVZeFO7iqnhdhHLNxBmqcEeQY29x/N4nIQmAo8BLQXkSS3VpIL2BbzX1NeB9v2kOP9v4BlnlowQbGDOyWwIiMMc1JyASiqqU4z3s8LCIpQGecBu39sfhgEclV1fXu4lhgTZAyHYAjqlomIp2BM4E/qaqKyAKcgR6fw6kJvRqLuFqTu+as5q45q/3LNsy7MaY+IhlMEVWtUNUdsUoerpnu7azlwGjgRgARyReRx90yJ+KMxfUZsACYqaq+MTh+BfxcRDbgtIk8EcPYWqXkpAY1aRljWpmIJpSKB1UdH2J9AXC1+/5DYFCIcpuwBxrr5dz+Xfjfml0ht3ssgRhj6iGiGohpGZ6cNCxobyyfwq37yZ0+h+LSipBljDHGxxKIqaaiUhl0x9xEh2GMaQYsgRhjjIlKwtpATOLMvvpUiksr+HdBEcflZPLY+5sTHZIxphmyBNIKnXl8ZwDGDOzO7MVfJDgaY0xzZbewWjmb1tYYEy1LIK1cWrL9ChhjomN/PVq59JTgNZA+t/2XDbsONXI0xpjmxBJIK9e3cyYQ/CHCKbM+YekXe6myIU6MMUFYAmnlju+SxaJfjeRHZ/Wtte3LvUcY/8hHPL5oUwIiM8Y0dZZADL06tAk5ayHA59sOhtxmjGm9LIEYIPS0twBdstMaMRJjTHNhCcQAUFEZen70TlmpjRiJMaa5sARigPA1kE827+XZJV82YjTGmObAEogB4GfnHs+gnu2CbluwdjfT/vN5I0dkjGnqLIEYwGlIf/36szimY5uQZTbsKuav89ejat16jTGWQEwN5d7QbSETHlvMffPX0XfaHA6Xee1BQ2NaOUsgppryMI3pR8q8/veX//0jzrv3XVbvsC6+xrRWlkBMNeHGxgq8ceVLHIVb98c3IGNMk2UJxFQz++pTmfat/kG3eYP01PKGqbEYY1q2hCQQEblTRJaLSKGIzBWRHkHKjHS3+16lInKZu22WiGwO2JbX2OfQUh2bk8U15xwXdFuw9pHySuVQmZeXlhbFOzRjTBOTqBrIPao6WFXzgDeA22sWUNUFqprnljkXOAIETtZ9i2+7qhY2Qsyt0l+vzOOcE3JCbi/3VnHbS8v5xQufsWLbgUaMzBiTaAlJIKoa2PKaSfXb68FcDrypqkfiF5UJNGF4b07omsXYvJ6M7Bc6gSxYs4stew4D4R9GNMa0PAmb0lZE7gJ+CBwARtZR/Erg3hrr7hKR24F3gNtUtSzE50wFpgIcc8wxDYq5NfnjuMH+9yk1Gta7ZKexq9j5cS/Zste/fuPuQ/Ron0GOjZ1lTKsQtxqIiMwXkRVBXmMBVHW6qvYGZgM/C3Oc7sAg4O2A1dOA/sAwoCPwq1D7q+qjqpqvqvk5OaG/SZvQalYsRp3YNWi5n//7M777j4/Yc6iM5z+xoU+MaeniVgNR1fMiLDobmAPMCLH9u8DLqloRcOwd7tsyEXkK+GXUgZo6HQ54/qNb23RuPi835NhYm78+zA+eWMKqHQcZ3rcTvTtkkOyxzn7GtESJ6oWVG7A4FlgTpvgE4Nka+3d3/xXgMmBFjEM0AXwJpHfHDObceDYdM1PJ7ZIVsvwq9xmRkX9eyORZnzRKjMaYxpeor4Yz3dtZy4HRwI0AIpIvIo/7ColIH6A38G6N/WeLyOfA50Bn4P81StSt1CE3gUw8vQ8dM1NJ9iQx7+fnRLTv++u/jmdoxpgESlQvrPGqOtDtynuJqm5z1xeo6tUB5baoak9Vraqx/7mqOsg9xvdV1QZliqOLBzuP6Zzbv0vQ7Ut/E/5u5Ycbv2bjbrtExrQ0CeuFZZqPU77RgS0zLwq5vVNW+F5XVz22GICxeT245YJ+9OoQesRfY0zzYQnExERmqofD5ZVhy7xauJ1XC7cDcM03j2XahSfyxzmr2X6glAeuzMNp0jLGNBeWQEzUXrj2dDJTnV+hpKT6/fH/x3ubqKhUnvxgMwCvf7ad0QO6ctHg7owZ2I3nlmzle6ceYz24jGnC7H+nidqwPh0Z0KMtAFcO6w3AtwZ2i3h/X/LwmbtqJzc+V8jj729mxmsreXFpEf/+ZCv5/28+B0srQhzFmOo27Cpmk7W5NQppTbPL5efna0FBQaLDaJGqqpSSiko8ScKbK3Ywb9VO5nz+FeC0oSz9Yl+9jzm8b0eWbHaedD/92E48PjGfzLSjlWZVpWhfCekpHrLSkvnL3LX89/Md/HJ0P8af0is2J9bCqCpPfbCF8Sf3ol2blESHExd9bvsvAFtmXoS3sgpPkjS526Obvz7M3sNlnPKNjv51Zd5KZry6khvPy6V7u4wERlebiCxV1fya660GYmIiKUnITEsmPcXDt4f24t7v5tG3cyYAbVI9UR3TlzwAPtq0h9P++A43PLuMP85ZzZ/fXstJM97m7D8tYNhd85n6zwIeX7SZHQdK+cULn/Hf5TsoLq2g3FtFaUXwtplw24rdGs9989bx0tIiVJXi0gr++OZqXi3c5i+35quDnHX3/9hVXFpt//U7i5m9+Av/8oZdxbz22faofg7BHCn3MvWZgnp/0/5kyz5+/8YqZrwW+tGpw2Ve/v7uRipqDNW/Ydch/vnxFyH2crxQsJW/vbOed1bv5OkPt/CrF5czf9VOwOmNV/PnBHD3W2t4vY6fzawPNvP4+5uCblN1RoRWVW57abl//Q+eWMzx09/kr++sD3nc1z/bzqUPLqKqnuO4vbN6p797e02L1n9d7Xc3mJF/Xsj4Rz6qvu6ehTz3yVb+3xur6xWLz2PvbeLHzzhfkEvKK2tdv3iwNhATF+kpHt6+6ZuUeSu5+mnnl/qvV+ax/0gFM15bCcBTk4bx21dXcLjMS7d2GXXOblhc6g35R7jm8yY//b9P/e87Z6Xy4rVnsHnPYTwifNMdXfiqxz6m4It9/HL0CZydm0NGqoe+nTN5Zdk2bnlxOf+57gz/H5+DpRX87vVV/mOOzesJwD/e3UTRvhLeWb2LCcOPjrV2xaMfs/dwOZcM6UHb9BQu/tsiSiuquOCkrqQl1z+heiuruH/+etq3SWHb/hLOOK4zc1ftxFulPDlpWNh9D5RUkOIR2qQmc7DESYw7DwYdOg6AhxZs4OGFG+mSnca4k3tRWlFJSXklVz32MbuKy7h0cI+QtZdbXlxea93zBVtZc+cYrnpsMSd0zWLODWez70gFOdlpVFYpjyzcCMAlQ2rN6uB3h/uzv/rsY2tte/S9TfzxzTXM//k3ee6Trf71vt+Jv7+7kZvOOyHoca9/dhkAO4tL6d4ugw82fE2HNqn+W7PBbNx9iB89XcBleT24/8qhtbZ//wmn12G4nos+FZVVpLjtfNsPOMm1LMy00sHsLi7jgw1fc9ccJ/F4K6s48fa3GNW/C0/U8bvRUK3qFlZ232w9ZcYpiQ6j1SnzVrH3cDnd26UDTiLwJEmtmsm+I+Ws/aoYgA5tUtl3pByArPRk2mekUrQvNoMxZ7ifW1JHrzFPkoQcYdh/jIpKUEjxJJHsOXqbxHfs9BQPIrWX66vcW1UtltTkJP/8LBl11PBKyisREdJTkqis0jr3q3lOZRVVVAX8nQh3DqF+pukpHn9tz/dzzUgJ+BnWcR6+4wYr49uW6kkKOSVzyHN1901L8ZAUYSxVVc7tprriieh8Ujwg1dfVtW+oY/n3TfEEPY9jO2eRnR5dneHdye8GvYVlNRATd2nJSf7kAYT8Je7QJpXhfTtS5q0iPdlDmbeSdPePjCpUqdIm1cPu4jKSk4RKhb6dMzlc5uVQmZee7TM4VOZlz6EykpKEQ2VeOrZJpdRbRbm3iv1HyslOTyHV/UPvEfHfhvD98clMS6bMW0VVldI+I4XD5ZWUVlTSITOVgyUVZKenoKoku73O2qR42FdSQdsa55SW7OFwmZdM9z9wqieJkvJK/3J9tUnxsO9IBZlpyZRWVJKdlsz+qgraZaRQZz5SEBEyUpxvunXtV/OcPCJUVCoZqdXPKRhPklBZqf75GUorKmmT6iEjxUNllZKZluxvL/N9gagC0jxJpHhCn0mSCKr4zyFQeorHvTbJHHS/nHiShJKKSpJEyE5LJlQnwfRkD8VlXrJ8sSikeCTs1M4A3qqqkD9Dwfl5p4c5RnJSEhWVVdW+RCWJcLjMS8fM1LqvaY1zOFBaQVaq87vbJtVDlTpfMlIDfqb17CgZkVaVQPp16sfCSQsTHYYxxjQrMjl49rFGdGOMMVGxBGKMMSYqlkCMMcZExRKIMcaYqFgCMcYYExVLIMYYY6JiCcQYY0xULIEYY4yJSqsaykREdgPhR4MLrTPQ2ib4tnNuHeycW4eGnPM3VDWn5spWlUAaQkQKgo0F05LZObcOds6tQzzO2W5hGWOMiYolEGOMMVGxBBK5RxMdQALYObcOds6tQ8zP2dpAjDHGRMVqIMYYY6JiCcQYY0xULIFEQETGiMhaEdkgIrclOp5YEJHeIrJARFaJyEoRudFd31FE5onIevffDu56EZEH3J/BchE5ObFnED0R8YjIMhF5w13uKyKL3XN7XkRS3fVp7vIGd3ufhAYeJRFpLyIvisgaEVktIqe39OssIje7v9crRORZEUlvaddZRJ4UkV0isiJgXb2vq4hMdMuvF5GJ9YnBEkgdRMQDPAR8CxgATBCRAYmNKia8wC9UdQBwGvBT97xuA95R1VzgHXcZnPPPdV9TgUcaP+SYuRFYHbB8N3Cfqh4P7AN+5K7/EbDPXX+fW645+ivwlqr2B4bgnHuLvc4i0hO4AchX1YGAB7iSlnedZwFjaqyr13UVkY7ADOBUYDgww5d0IqKq9grzAk4H3g5YngZMS3RccTjPV4HzgbVAd3ddd2Ct+/4fwISA8v5yzekF9HL/Y50LvIEzhfXXQHLN6w28DZzuvk92y0miz6Ge59sO2Fwz7pZ8nYGewFago3vd3gAuaInXGegDrIj2ugITgH8ErK9Wrq6X1UDq5vtl9Cly17UYbpV9KLAY6KqqO9xNXwFd3fct5edwP3ArUOUudwL2q6rXXQ48L/85u9sPuOWbk77AbuAp97bd4yKSSQu+zqq6Dfgz8CWwA+e6LaVlX2ef+l7XBl1vSyCtnIhkAS8BN6nqwcBt6nwlaTH9vEXkYmCXqi5NdCyNKBk4GXhEVYcChzl6WwNokde5AzAWJ3n2ADKpfaunxWuM62oJpG7bgN4By73cdc2eiKTgJI/Zqvofd/VOEenubu8O7HLXt4Sfw5nApSKyBXgO5zbWX4H2IpLslgk8L/85u9vbAXsaM+AYKAKKVHWxu/wiTkJpydf5PGCzqu5W1QrgPzjXviVfZ5/6XtcGXW9LIHX7BMh1e3Ck4jTGvZbgmBpMRAR4AlitqvcGbHoN8PXEmIjTNuJb/0O3N8dpwIGAqnKzoKrTVLWXqvbBuY7/U9XvAQuAy91iNc/Z97O43C3frL6pq+pXwFYR6eeuGgWsogVfZ5xbV6eJSBv399x3zi32Ogeo73V9GxgtIh3cmttod11kEt0I1BxewIXAOmAjMD3R8cTonM7Cqd4uBwrd14U4937fAdYD84GObnnB6Y22Efgcp4dLws+jAec/AnjDfX8ssATYALwApLnr093lDe72YxMdd5TnmgcUuNf6FaBDS7/OwO+ANcAK4J9AWku7zsCzOG08FTg1zR9Fc12BKe65bwAm1ycGG8rEGGNMVOwWljHGmKhYAjHGGBMVSyDGGGOiYgnEGGNMVCyBGGOMiYolEGOiICKH3H/7iMhVMT72r2ssfxjL4xsTK5ZAjGmYPkC9EkjA09ChVEsgqnpGPWMyplFYAjGmYWYCZ4tIoTsHhUdE7hGRT9x5F64BEJERIvK+iLyG81Q0IvKKiCx1562Y6q6bCWS4x5vtrvPVdsQ99goR+VxErgg49kI5OufHbPcJbGPiqq5vQsaY8G4DfqmqFwO4ieCAqg4TkTTgAxGZ65Y9GRioqpvd5SmquldEMoBPROQlVb1NRH6mqnlBPmsczlPlQ4DO7j7vuduGAicB24EPcMZ+WhTrkzUmkNVAjImt0ThjDhXiDI/fCWcSH4AlAckD4AYR+Qz4GGdAu1zCOwt4VlUrVXUn8C4wLODYRapahTMsTZ8YnIsxYVkNxJjYEuB6Va02IJ2IjMAZSj1w+TyciYyOiMhCnDGZolUW8L4S+79tGoHVQIxpmGIgO2D5beAn7lD5iMgJ7gRONbXDmUb1iIj0x5lW2KfCt38N7wNXuO0sOcA3cQb/MyYh7FuKMQ2zHKh0b0XNwplfpA/wqduQvRu4LMh+bwHXishqnOlFPw7Y9iiwXEQ+VWe4eZ+XcaZi/QxnJOVbVfUrNwEZ0+hsNF5jjDFRsVtYxhhjomIJxBhjTFQsgRhjjImKJRBjjDFRsQRijDEmKpZAjDHGRMUSiDHGmKj8f7axMUzGoXpAAAAAAElFTkSuQmCC\n", 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" ] diff --git a/examples/qaoa.ipynb b/examples/qaoa.ipynb new file mode 100644 index 0000000..5976dd4 --- /dev/null +++ b/examples/qaoa.ipynb @@ -0,0 +1,507 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "a52b609d", + "metadata": {}, + "source": [ + "# QAOA with `qujax`\n", + "\n", + "In this notebook, we will consider QAOA on an Ising Hamiltonian. In particular, we will demonstrate how to encode a circuit with parameters that control multiple gates." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "2678d061", + "metadata": {}, + "outputs": [], + "source": [ + "from jax import numpy as jnp, random, value_and_grad, jit\n", + "import matplotlib.pyplot as plt\n", + "\n", + "import qujax" + ] + }, + { + "cell_type": "markdown", + "id": "57aaa7eb", + "metadata": {}, + "source": [ + "# QAOA\n", + "\n", + "The Quantum Approximate Optimization Algorithm (QAOA), first introduced by [Farhi et al.](https://arxiv.org/pdf/1411.4028.pdf), is a quantum variational algorithm used to solve optimization problems. It consists of a unitary $U(\\beta, \\gamma)$ formed by alternate repetitions of $U(\\beta)=e^{-i\\beta H_B}$ and $U(\\gamma)=e^{-i\\gamma H_P}$, where $H_B$ is the mixing Hamiltonian and $H_P$ the problem Hamiltonian. The goal is to find the optimal parameters that minimize $H_P$.\n", + "\n", + "Given a depth $d$, the expression of the final unitary is $U(\\beta, \\gamma) = U(\\beta_d)U(\\gamma_d)\\cdots U(\\beta_1)U(\\gamma_1)$. Notice that for each repetition the parameters are different.\n", + "\n", + "\n", + "## Problem Hamiltonian\n", + "QAOA uses a problem dependent ansatz. Therefore, we first need to know the problem that we want to solve. In this case we will consider an Ising Hamiltonian with only $Z$ interactions. Given a set of pairs (or qubit indices) $E$, the problem Hamiltonian will be:\n", + "$$H_P = \\sum_{(i, j) \\in E}\\alpha_{ij}Z_iZ_j,$$ \n", + "where $\\alpha_{ij}$ are the coefficients.\n", + "\n", + "Let's build our problem Hamiltonian with random coefficients and a set of pairs for a given number of qubits:" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "6602f4ad", + "metadata": {}, + "outputs": [], + "source": [ + "n_qubits = 4\n", + "hamiltonian_qubit_inds = [(0, 1), (1, 2), (0, 2), (1, 3)]\n", + "hamiltonian_gates = [['Z', 'Z']] * (len(hamiltonian_qubit_inds))\n", + "\n", + "\n", + "# Notice that in order to use the random package from jax we first need to define a seeded key\n", + "seed = 13\n", + "key = random.PRNGKey(seed)\n", + "coefficients = random.uniform(key, shape=(len(hamiltonian_qubit_inds), ))" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "e80df4ff", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Gates:\t [['Z', 'Z'], ['Z', 'Z'], ['Z', 'Z'], ['Z', 'Z']]\n", + "Qubits:\t [(0, 1), (1, 2), (0, 2), (1, 3)]\n", + "Coefficients:\t [0.6794174 0.2963785 0.2863201 0.31746793]\n" + ] + } + ], + "source": [ + "print('Gates:\\t', hamiltonian_gates)\n", + "print('Qubits:\\t', hamiltonian_qubit_inds)\n", + "print('Coefficients:\\t', coefficients)" + ] + }, + { + "cell_type": "markdown", + "id": "b03a1f9d", + "metadata": {}, + "source": [ + "## Variational Circuit\n", + "\n", + "Before constructing the circuit, we still need to select the mixing Hamiltonian. In our case, we will be using $X$ gates in each qubit, so $H_B = \\sum_{i=1}^{n}X_i$, where $n$ is the number of qubits. Notice that the unitary $U(\\beta)$, given this mixing Hamiltonian, is an $X$ rotation in each qubit with angle $\\beta$.\n", + "\n", + "As for the unitary corresponding to the problem Hamiltonian, $U(\\gamma)$, it has the following form:\n", + "$$U(\\gamma)=\\prod_{(i, j) \\in E}e^{-i\\gamma\\alpha_{ij}Z_iZ_j}$$ \n", + "\n", + "The operation $e^{-i\\gamma\\alpha_{ij}Z_iZ_j}$ can be performed using two CNOT gates with qubit $i$ as control and qubit $j$ as target and a $Z$ rotation in qubit $j$ in between them, with angle $\\gamma\\alpha_{ij}$.\n", + "\n", + "Finally, the initial state used, in general, with the QAOA is an equal superposition of all the basis states. This can be achieved adding a first layer of Hadamard gates in each qubit at the beginning of the circuit." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "008e895f", + "metadata": {}, + "outputs": [], + "source": [ + "depth = 3" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "cf0fbfaa", + "metadata": {}, + "outputs": [], + "source": [ + "circuit_gates = []\n", + "circuit_qubit_inds = []\n", + "circuit_param_inds =[]\n", + "\n", + "param_ind = 0\n", + "\n", + "# Initial State\n", + "for i in range(n_qubits):\n", + " circuit_gates.append('H')\n", + " circuit_qubit_inds.append([i])\n", + " circuit_param_inds.append([])\n", + " \n", + "for d in range(depth):\n", + " \n", + " # Mixing Unitary\n", + " for i in range(n_qubits):\n", + " circuit_gates.append('Rx')\n", + " circuit_qubit_inds.append([i])\n", + " circuit_param_inds.append([param_ind])\n", + " param_ind += 1\n", + "\n", + " # Hamiltonian\n", + " for index in range(len(hamiltonian_qubit_inds)):\n", + " pair = hamiltonian_qubit_inds[index]\n", + " coef = coefficients[index]\n", + " \n", + " circuit_gates.append('CX')\n", + " circuit_qubit_inds.append([pair[0], pair[1]])\n", + " circuit_param_inds.append([])\n", + " \n", + " circuit_gates.append(lambda p: qujax.gates.Rz(p * coef))\n", + " circuit_qubit_inds.append([pair[1]])\n", + " circuit_param_inds.append([param_ind])\n", + " \n", + " circuit_gates.append('CX')\n", + " circuit_qubit_inds.append([pair[0], pair[1]])\n", + " circuit_param_inds.append([])\n", + " param_ind += 1" + ] + }, + { + "cell_type": "markdown", + "id": "24ce1e3c", + "metadata": {}, + "source": [ + "Let's check the circuit:" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "c3fb239c", + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "q0: -----H-----Rx[0]-----◯---------------◯-------------------------------◯---------------◯---------------------Rx[2]-\n", + " | | | | \n", + "q1: -----H-----Rx[0]-----CX---Func[1]----CX------◯---------------◯-------|---------------|-------◯---------------◯---\n", + " | | | | | | \n", + "q2: -----H-----Rx[0]-----------------------------CX---Func[1]----CX------CX---Func[1]----CX------|---------------|---\n", + " | | \n", + "q3: -----H-----Rx[0]-----------------------------------------------------------------------------CX---Func[1]----CX--\n" + ] + } + ], + "source": [ + "qujax.print_circuit(circuit_gates, circuit_qubit_inds, circuit_param_inds,\n", + " gate_ind_max=20);" + ] + }, + { + "cell_type": "markdown", + "id": "8c421d1d", + "metadata": {}, + "source": [ + "Then, we invoke the `qujax.get_params_to_statetensor_func`" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "1af80d12", + "metadata": {}, + "outputs": [], + "source": [ + "param_to_st = qujax.get_params_to_statetensor_func(circuit_gates, circuit_qubit_inds, circuit_param_inds)" + ] + }, + { + "cell_type": "markdown", + "id": "689e7811", + "metadata": {}, + "source": [ + "And we also construct the expectation map using the problem Hamiltonian via qujax: " + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "0857d4bb", + "metadata": {}, + "outputs": [], + "source": [ + "st_to_expectation = qujax.get_statetensor_to_expectation_func(hamiltonian_gates,\n", + " hamiltonian_qubit_inds,\n", + " coefficients)\n", + "\n", + "param_to_expectation = lambda param: st_to_expectation(param_to_st(param))" + ] + }, + { + "cell_type": "markdown", + "id": "6144236c", + "metadata": {}, + "source": [ + "# Training process\n", + "We construct a function that, given a parameter vector, returns the value of the cost function and the gradient (we also `jit` to avoid recompilation):" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "069331d5", + "metadata": {}, + "outputs": [], + "source": [ + "cost_and_grad = jit(value_and_grad(param_to_expectation))" + ] + }, + { + "cell_type": "markdown", + "id": "8f8e0741", + "metadata": {}, + "source": [ + "For the training process we'll use vanilla gradient descent with a constant stepsize:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "b28018e2", + "metadata": {}, + "outputs": [], + "source": [ + "seed = 123\n", + "key = random.PRNGKey(seed)\n", + "init_param = random.uniform(key, shape=(param_ind, ))\n", + "\n", + "n_steps = 150\n", + "stepsize = 0.01" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "c0f53be5", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Iteration: 1 \tCost: -0.09861969\r", + "Iteration: 2 \tCost: -0.30488127\r", + "Iteration: 3 \tCost: -0.43221825\r", + "Iteration: 4 \tCost: -0.49104044\r", + "Iteration: 5 \tCost: -0.51378363\r", + "Iteration: 6 \tCost: -0.5220106\r", + "Iteration: 7 \tCost: -0.52507806\r", + "Iteration: 8 \tCost: -0.5263982\r", + "Iteration: 9 \tCost: -0.52713084\r", + "Iteration: 10 \tCost: -0.5276594\r", + "Iteration: 11 \tCost: -0.5281093\r", + "Iteration: 12 \tCost: -0.5285234\r", + "Iteration: 13 \tCost: -0.5289158\r", + "Iteration: 14 \tCost: -0.5292916\r", + "Iteration: 15 \tCost: -0.5296537\r", + "Iteration: 16 \tCost: -0.53000385\r", + "Iteration: 17 \tCost: -0.5303429\r", + "Iteration: 18 \tCost: -0.5306716\r", + "Iteration: 19 \tCost: -0.5309909\r", + "Iteration: 20 \tCost: -0.5313021\r", + "Iteration: 21 \tCost: -0.53160506\r", + "Iteration: 22 \tCost: -0.53190106\r", + "Iteration: 23 \tCost: -0.53219026\r", + "Iteration: 24 \tCost: -0.5324728\r", + "Iteration: 25 \tCost: -0.53274995\r", + "Iteration: 26 \tCost: -0.533021\r", + "Iteration: 27 \tCost: -0.5332869\r", + "Iteration: 28 \tCost: -0.53354824\r", + "Iteration: 29 \tCost: -0.5338048\r", + "Iteration: 30 \tCost: -0.53405714\r", + "Iteration: 31 \tCost: -0.5343054\r", + "Iteration: 32 \tCost: -0.53454924\r", + "Iteration: 33 \tCost: -0.5347898\r", + "Iteration: 34 \tCost: -0.53502667\r", + "Iteration: 35 \tCost: -0.5352601\r", + "Iteration: 36 \tCost: -0.53549004\r", + "Iteration: 37 \tCost: -0.53571683\r", + "Iteration: 38 \tCost: -0.5359408\r", + "Iteration: 39 \tCost: -0.5361613\r", + "Iteration: 40 \tCost: -0.5363793\r", + "Iteration: 41 \tCost: -0.53659475\r", + "Iteration: 42 \tCost: -0.5368071\r", + "Iteration: 43 \tCost: -0.53701735\r", + "Iteration: 44 \tCost: -0.5372245\r", + "Iteration: 45 \tCost: -0.5374299\r", + "Iteration: 46 \tCost: -0.5376322\r", + "Iteration: 47 \tCost: -0.53783244\r", + "Iteration: 48 \tCost: -0.5380306\r", + "Iteration: 49 \tCost: -0.53822607\r", + "Iteration: 50 \tCost: -0.53841996\r", + "Iteration: 51 \tCost: -0.53861094\r", + "Iteration: 52 \tCost: -0.53880095\r", + "Iteration: 53 \tCost: -0.53898793\r", + "Iteration: 54 \tCost: -0.5391733\r", + "Iteration: 55 \tCost: -0.5393568\r", + "Iteration: 56 \tCost: -0.5395382\r", + "Iteration: 57 \tCost: -0.53971833\r", + "Iteration: 58 \tCost: -0.53989595\r", + "Iteration: 59 \tCost: -0.54007185\r", + "Iteration: 60 \tCost: -0.5402465\r", + "Iteration: 61 \tCost: -0.54041874\r", + "Iteration: 62 \tCost: -0.5405901\r", + "Iteration: 63 \tCost: -0.5407588\r", + "Iteration: 64 \tCost: -0.5409268\r", + "Iteration: 65 \tCost: -0.54109275\r", + "Iteration: 66 \tCost: -0.5412577\r", + "Iteration: 67 \tCost: -0.54141986\r", + "Iteration: 68 \tCost: -0.5415817\r", + "Iteration: 69 \tCost: -0.5417414\r", + "Iteration: 70 \tCost: -0.5419003\r", + "Iteration: 71 \tCost: -0.5420571\r", + "Iteration: 72 \tCost: -0.5422127\r", + "Iteration: 73 \tCost: -0.5423671\r", + "Iteration: 74 \tCost: -0.5425201\r", + "Iteration: 75 \tCost: -0.5426715\r", + "Iteration: 76 \tCost: -0.54282165\r", + "Iteration: 77 \tCost: -0.54297113\r", + "Iteration: 78 \tCost: -0.5431187\r", + "Iteration: 79 \tCost: -0.543265\r", + "Iteration: 80 \tCost: -0.5434102\r", + "Iteration: 81 \tCost: -0.54355454\r", + "Iteration: 82 \tCost: -0.54369736\r", + "Iteration: 83 \tCost: -0.5438389\r", + "Iteration: 84 \tCost: -0.5439794\r", + "Iteration: 85 \tCost: -0.54411876\r", + "Iteration: 86 \tCost: -0.54425716\r", + "Iteration: 87 \tCost: -0.5443945\r", + "Iteration: 88 \tCost: -0.5445305\r", + "Iteration: 89 \tCost: -0.5446654\r", + "Iteration: 90 \tCost: -0.5447996\r", + "Iteration: 91 \tCost: -0.5449326\r", + "Iteration: 92 \tCost: -0.54506487\r", + "Iteration: 93 \tCost: -0.54519576\r", + "Iteration: 94 \tCost: -0.5453257\r", + "Iteration: 95 \tCost: -0.5454546\r", + "Iteration: 96 \tCost: -0.545583\r", + "Iteration: 97 \tCost: -0.5457101\r", + "Iteration: 98 \tCost: -0.54583657\r", + "Iteration: 99 \tCost: -0.5459618\r", + "Iteration: 100 \tCost: -0.54608655\r", + "Iteration: 101 \tCost: -0.54621017\r", + "Iteration: 102 \tCost: -0.54633296\r", + "Iteration: 103 \tCost: -0.54645467\r", + "Iteration: 104 \tCost: -0.54657626\r", + "Iteration: 105 \tCost: -0.54669654\r", + "Iteration: 106 \tCost: -0.54681575\r", + "Iteration: 107 \tCost: -0.5469348\r", + "Iteration: 108 \tCost: -0.5470527\r", + "Iteration: 109 \tCost: -0.54716986\r", + "Iteration: 110 \tCost: -0.54728657\r", + "Iteration: 111 \tCost: -0.5474022\r", + "Iteration: 112 \tCost: -0.5475172\r", + "Iteration: 113 \tCost: -0.5476318\r", + "Iteration: 114 \tCost: -0.5477449\r", + "Iteration: 115 \tCost: -0.5478576\r", + "Iteration: 116 \tCost: -0.54797024\r", + "Iteration: 117 \tCost: -0.5480816\r", + "Iteration: 118 \tCost: -0.548192\r", + "Iteration: 119 \tCost: -0.54830235\r", + "Iteration: 120 \tCost: -0.5484118\r", + "Iteration: 121 \tCost: -0.54852045\r", + "Iteration: 122 \tCost: -0.548629\r", + "Iteration: 123 \tCost: -0.5487364\r", + "Iteration: 124 \tCost: -0.5488433\r", + "Iteration: 125 \tCost: -0.5489498\r", + "Iteration: 126 \tCost: -0.54905534\r", + "Iteration: 127 \tCost: -0.5491607\r", + "Iteration: 128 \tCost: -0.5492652\r", + "Iteration: 129 \tCost: -0.54936945\r", + "Iteration: 130 \tCost: -0.54947305\r", + "Iteration: 131 \tCost: -0.54957575\r", + "Iteration: 132 \tCost: -0.5496777\r", + "Iteration: 133 \tCost: -0.5497798\r", + "Iteration: 134 \tCost: -0.5498811\r", + "Iteration: 135 \tCost: -0.5499818\r", + "Iteration: 136 \tCost: -0.5500822\r", + "Iteration: 137 \tCost: -0.5501819\r", + "Iteration: 138 \tCost: -0.550281\r", + "Iteration: 139 \tCost: -0.55037963\r", + "Iteration: 140 \tCost: -0.55047804\r", + "Iteration: 141 \tCost: -0.5505761\r", + "Iteration: 142 \tCost: -0.55067325\r", + "Iteration: 143 \tCost: -0.5507698\r", + "Iteration: 144 \tCost: -0.55086654\r", + "Iteration: 145 \tCost: -0.5509624\r", + "Iteration: 146 \tCost: -0.5510575\r", + "Iteration: 147 \tCost: -0.55115235\r", + "Iteration: 148 \tCost: -0.55124706\r", + "Iteration: 149 \tCost: -0.5513411\r" + ] + } + ], + "source": [ + "param = init_param\n", + "\n", + "cost_vals = jnp.zeros(n_steps)\n", + "cost_vals = cost_vals.at[0].set(param_to_expectation(init_param))\n", + "\n", + "for step in range(1, n_steps):\n", + " cost_val, cost_grad = cost_and_grad(param)\n", + " cost_vals = cost_vals.at[step].set(cost_val)\n", + " param = param - stepsize * cost_grad\n", + " print('Iteration:', step, '\\tCost:', cost_val, end='\\r')" + ] + }, + { + "cell_type": "markdown", + "id": "b9305afc", + "metadata": {}, + "source": [ + "Let's visualise the gradient descent" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "114ed37d", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(cost_vals)\n", + "plt.xlabel('Iteration')\n", + "plt.ylabel('Cost');" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.10" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/examples/variational_inference.ipynb b/examples/variational_inference.ipynb index b0f325d..88a5375 100644 --- a/examples/variational_inference.ipynb +++ b/examples/variational_inference.ipynb @@ -128,7 +128,7 @@ " n_params = 2 * n_qubits * (depth + 1)\n", " \n", " \n", - " gates = ['H'] * n_qubits + ['Rx'] * n_qubits + ['Rz'] * n_qubits\n", + " gates = ['H'] * n_qubits + ['Rx'] * n_qubits + ['Ry'] * n_qubits\n", " qubit_inds = [[i] for i in range(n_qubits)] * 3\n", " param_inds = [[]] * n_qubits + [[i] for i in range(n_qubits * 2)]\n", " \n", @@ -172,21 +172,21 @@ "name": "stdout", "output_type": "stream", "text": [ - "q0: -----H-----Rx[0]---Rz[8]-----◯---------------------------------------------------\n", + "q0: -----H-----Rx[0]---Ry[8]-----◯---------------------------------------------------\n", " | \n", - "q1: -----H-----Rx[1]---Rz[9]-----CZ------◯-------------------------------------------\n", + "q1: -----H-----Rx[1]---Ry[9]-----CZ------◯-------------------------------------------\n", " | \n", - "q2: -----H-----Rx[2]---Rz[10]------------CZ------◯-----------------------------------\n", + "q2: -----H-----Rx[2]---Ry[10]------------CZ------◯-----------------------------------\n", " | \n", - "q3: -----H-----Rx[3]---Rz[11]--------------------CZ------◯---------------------------\n", + "q3: -----H-----Rx[3]---Ry[11]--------------------CZ------◯---------------------------\n", " | \n", - "q4: -----H-----Rx[4]---Rz[12]----------------------------CZ------◯-------------------\n", + "q4: -----H-----Rx[4]---Ry[12]----------------------------CZ------◯-------------------\n", " | \n", - "q5: -----H-----Rx[5]---Rz[13]------------------------------------CZ------◯-----------\n", + "q5: -----H-----Rx[5]---Ry[13]------------------------------------CZ------◯-----------\n", " | \n", - "q6: -----H-----Rx[6]---Rz[14]--------------------------------------------CZ------◯---\n", + "q6: -----H-----Rx[6]---Ry[14]--------------------------------------------CZ------◯---\n", " | \n", - "q7: -----H-----Rx[7]---Rz[15]----------------------------------------------------CZ--\n" + "q7: -----H-----Rx[7]---Ry[15]----------------------------------------------------CZ--\n" ] } ], @@ -320,7 +320,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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nRqpdFRGRyCWi2rC7T5nZLcD9QBz4srsfNLPPAJ3uvhf4EvA1M+sC+gnCBQAzOwzkgJSZvQd4m7s/Cfwh8FWgDvhueKu6jrasgkNEakJkwQHg7vcB980pu61oeRz4wAKv7VigvBN4VflqWR7b2urZu/8Y7s4qOLVERCQya3ZwvNI6WusZGp9iYHSy2lUREYmUgqNMLm2vB1B3lYiseQqOMtnW1gAoOERk7VNwlMmWljriMeOwgkNE1jgFR5kk4zEuXqcjq0Rk7VNwlFFHa5ZDCg4RWeMUHGV0WXsDh3rPMK1ZckVkDVNwlNErNjYyMTXDi31qdYjI2qXgKKPLNzYC8EzPcJVrIiISHQVHGe1Y34gZPK3gEJE1TMFRRnWpOB2t9WpxiMiapuAos1duaOSZEwoOEVm7FBxl9sqNjRzuG2EsP13tqoiIRELBUWaXb2zEHbpOnql2VUREIqHgKLNXhkdWPdUzVOWaiIhEQ8FRZpe01tOQTvBE92C1qyIiEgkFR5nFY8arNzex/8jpaldFRCQSCo4IvHZrM08dH2J8UgPkIrL2KDgicNXWZiannaeOa5xDRNYeBUcErtraDKDuKhFZkxQcEdjYlGFjLsMBBYeIrEEKjoi8dqsGyEVkbVJwROR1l7RwuG+UE0Pj1a6KiEhZKTgict1lbQD8/PlTVa6JiEh5KTgisnNTjuZskge6+qpdFRGRslJwRCQWM667rJWfd53CXZeSFZG1Q8ERoesua+PY4DgvnNKlZEVk7VBwROhXtwfjHA90aZxDRNYOBUeEOlqzbGur53sHe6pdFRGRslFwRMjMuPE1m/jF8330Dk9UuzoiImWh4IjYu157ETMO333ieLWrIiJSFgqOiL1iQyOv2NDAdw4oOERkbYg0OMzsBjN7xsy6zOzWeZ5Pm9nd4fMPmVlH0XN/HpY/Y2ZvLyo/bGaPm9l+M+uMsv7l8u7XXsTDh/t1OVkRWRMiCw4ziwNfAN4B7AQ+bGY756z2CWDA3bcDnwNuD1+7E9gDXAncAPyfcHsF/9Hdr3L3XVHVv5z2XHsx6USMO376fLWrIiKyYlG2OK4Futz9kLvngbuA3XPW2Q3cGS7fA1xvZhaW3+XuE+7+AtAVbu+C1NaQ5oO7tnLvL7vpGdTcVSJyYYsyODYDR4oeHw3L5l3H3aeAQaB1idc68H0ze8TMbl7ozc3sZjPrNLPO3t7eFX2Qcrj5zZcy4/D5Hz5X7aqIiKxIotoVOA9vdPduM1sP/MDMnnb3n85dyd3vAO4A2LVrV9Xn/Ni6LsvHr+vgSz97gd949abZkwOX6+TwOI8cHuDJ40McOz3O0PgkcTPW59Jc2lbPro517NyUIxaziD6BiEggyuDoBrYWPd4Sls23zlEzSwBNQN9ir3X3wv1JM7uXoAvrZcGxGv3p217Jj54+yZ/d8xj/9AfXsbEps+j63afH+Pb+br5z4DhPhpehjceMDY1pcnVJpmecB54/xfD4FACbmjK8+7UXsfuqzVyxqZGg109EpLwsqgn4wiB4Frie4I/+PuAj7n6waJ0/Al7t7r9vZnuA97r7B83sSuAbBKFwEfBvwA4gA8TcfdjM6oEfAJ9x9+8tVpddu3Z5Z+fqOADrsaOn+cgXH6KlPslXPn4t29c3nPP86dE89z3ew7f2d/PwC/1AcG2P669Yz69c2soVm3JkkvFzXnPs9Bi/eL6P+x4/zk+e7WVqxrliU46PXLuV3VdvJpdJVuzzicjaYWaPzHcQUmTBEb7pO4H/DcSBL7v7X5rZZ4BOd99rZhnga8DVQD+wx90Pha/9FPA7wBTwJ+7+XTO7FLg33HwC+Ia7/+VS9VhNwQFw4MhpbvrKwwyPT3HjazbxqouaGJ+c5sDR0/zk2V4mp53L2uv5zas3s/uqzWxdl132tgdG8nzn8ePcve8lnugeIpOMceNrLmLP67fyukta1AoRkWWrSnCsFqstOABODo3zdz85xD2PHGEo7Grauq6Ot+/cyHuu3syVF+VW/Ef+8aODfHPfS3z7l92M5KfZ1JTh7Vdu5G07N3DVxc1kUxfiEJeIVIqCY5UFR7HB0UmSCYvsD/nIxBT3H+zhe0/08JNne5mYmiFmwVntr9nSxNaWLJua69iYy1CfjpNJFm4x0ok4qUSMZNxIxmIafBepIQsFh/7lXAWastGOQdSnE7z3mi2895otjOanePBQH/uPDHLgyGl++PRJTp3JL3tbiZiFQRLcGtJxcnVJcpkkubpEeJ8kl0mQq0vSVJekOZuiJZukuS5Fc32SxnRCXWYiFzAFR43JphK85fINvOXyDbNl45PT9AyO0zM0zlh+mvHJacanphmfnGF8cpqpaSc/PUN+aobJ6eCWn5ohPz3DyMQ0Q+OTDI1N0jM0ztDYJMPjU4xNTi9Yh3jMaK5L0pRN0pJN0RyGS3M2SUs2SVNx0GSTYXmKbCquwBFZBRQcQiYZp6Otno62+rJtMz81w9D4JKdHJzk9muf06CQDo3kGx4L7oHyS02N5jg+O89TxIU6PTTKaXzhwUvEYTdkkzXVJWupTbMxl2NiUOXsfLq9vTJOIa/5OkagoOCQSqUSMtoY0bQ3pkl43MTXN4OgkA2HgDIxOMjiWDx+fDaH+kTz7j5ym5+A4+amZc7YRs2Cal01NGba0ZNmyro4tLVm2ttSxdV2Wzc11LzukWUSWT8Ehq0o6EWd9Ls763OInRxa4OwOjk2FX2xg9gxP0DI7RMzQ+25L5wZMnyE+fGy4bcmm2tmTZEobJxeuybF/fwPb1DTTqvBeRRSk45IJmZqyrT7GuPsXOi3LzrjMz45wcnuDIwChH+kc50j/GkYFRjg6Msu/wAHsPHGOm6ODCDbk0O9Y3zgbJ9vUN7FjfQGuJrSeRtUrBIWteLGazYyCv71j3sucnp2c4OjBG18kzdJ08w3Mnh3n+5Bn+sfMII0VjLuvqU1yxqZErL2riyotyXHlRE9va6onrEGWpMQoOqXnJeIxtbfVsa6vnrTvPHm3m7hwfHA/D5AzPnRjm4LEhvvrA4dmur7pk/GVh8oqNDaQTGkORtUsnAIqUaHJ6hq6TZ3iie5CDx4Z48tgQTx4f4sxEMANAImZsX9/AFZtyXL6xMbjf1Eh7Q1qHE8sFRScAipRJMh7jik05rtiU4wNh2cyM81L/KAePDXHwWBAov3i+j3t/eXZC6Nb61GyYXB7eX9Ka1WC8XHAUHCJlEIvZ7Lkwv/GaTbPlAyN5nuoZ4unjwzzdM8TTPcN87cEXmSg6hLi1PsXFrVk6Wuu5eF2WS1qzbMhl2JBL096YIZfRmfayuig4RCLUUp/iusvauO6ysxfump5xDveN8GzPMC/2j/Ji3wiHT43y8Av9fGt/N3N7j9OJGBvCExvX59K0N6RZV5+mtSFFa3hEWWtDinX1aZrrkppPTCKn4BCpsHjMuKy9gcvaG1723PjkNN2nxzgxNE7v8AQnhyY4MTTOyeEJTg6P83TPMP8+fPbiXfNtuyWbnD1EubUhfTZc6lMvC5zmbEpHhUnJFBwiq0gmGV8wVIrlp2YYGM1z6swE/SN5+kfy9J0J70cmZpefOjZE30gw1ct8YgbN2bktlxStYcDMBlD4uEVBIyg4RC5IqbD7asMyz7CfnJ5hYCRPXyFkRvL0haHTN5KnPwyap3uG6R8JpnWZjxk01yUXaM0UlRVCJ5vSvGFrkIJDpAYk4zHW5zLLnsplanqGgXBOsL4zE+cETn/YoukbyfPcyTP0j+QZGM2/bGymoDnsOiuEy7r6NG3ztGZa61O01KdIKmhWPQWHiLxMIh6jvTFNe2MaaFxy/ekZZ2B04S6zwuNDvSN0Hh5gYDR/zjQvxXKZxLmtmYaFA2ddfYpUQkFTaQoOEVmxeMzOzoa8Yen1p2ecwbFJ+kcmOHUmP6fLbIJT4fKLfaM8+tJpBkbzTC+QNI2ZxMKtmfBos1wmQWMmOXufScZ0iPMKKDhEpOLisbOTU25fv/T6M2HQFLrM+kcmwnGac7vQjg6McuDoaQZG8kwt1KQBknGjIR1cpbIxk6AxHd5ngvuGdIJsOk42GSebTpBNxalPBffZVPhcYTkVr7nuNQWHiKx6sZjREo6BLIe7MzQ2Rd9IcADA0HhwZcqh8SmGw+Wz98HyS/2j4TrBBcUWauHMJxk30ok4mWSMdCJOOrwPHsfOeW6p+3T4mlQiRioeD+4TMVLx4D5d9DhZuI9bRVtQCg4RWXPMjKZscHniS9tLf727MzE1w1h+mpH8FKP56eA2ESzPLRubnGZiKrjU8nz3p0fzCz5fQj4t8nmDAyDSYbgUh80///Eby37hMgWHiMgcZkYmGSeTjC+7lXM+3J2pGT8nSMYnZ8hPzZCfDu+nZshPT5OfmmFiap7nih5PhMuTRWWJCM67UXCIiFSJmZGMG8l4bBnHrq0etTWiIyIiK6bgEBGRkig4RESkJAoOEREpiYJDRERKouAQEZGSKDhERKQkCg4RESmJ+UKT6K8hZtYLvHieL28DTpWxOuWiepVutdZN9SrNaq0XrN66nW+9LnH3l03aUhPBsRJm1unuu6pdj7lUr9Kt1rqpXqVZrfWC1Vu3ctdLXVUiIlISBYeIiJREwbG0O6pdgQWoXqVbrXVTvUqzWusFq7duZa2XxjhERKQkanGIiEhJFBwiIlISBccCzOwGM3vGzLrM7NYq12Wrmf3IzJ40s4Nm9l/C8r8ws24z2x/e3lmFuh02s8fD9+8My9aZ2Q/M7LnwvqXCdXpl0T7Zb2ZDZvYn1dpfZvZlMztpZk8Ulc27jyzw+fB795iZXVPhev0PM3s6fO97zaw5LO8ws7Giffd3Fa7Xgj87M/vzcH89Y2Zvr3C97i6q02Ez2x+WV3J/LfT3IbrvmLvrNucGxIHngUuBFHAA2FnF+mwCrgmXG4FngZ3AXwB/WuV9dRhom1P234Fbw+Vbgdur/LPsAS6p1v4C3gxcAzyx1D4C3gl8FzDgDcBDFa7X24BEuHx7Ub06iterwv6a92cX/h4cANLAtvD3Nl6pes15/n8Ct1Vhfy309yGy75haHPO7Fuhy90PungfuAnZXqzLuftzdHw2Xh4GngM3Vqs8y7AbuDJfvBN5TvapwPfC8u5/vzAEr5u4/BfrnFC+0j3YDf++BB4FmM9tUqXq5+/fdfSp8+CCwJYr3LrVei9gN3OXuE+7+AtBF8Ptb0XqZmQEfBL4ZxXsvZpG/D5F9xxQc89sMHCl6fJRV8ofazDqAq4GHwqJbwubmlyvdJRRy4Ptm9oiZ3RyWbXD34+FyD7ChCvUq2MO5v8zV3l8FC+2j1fTd+x2C/0wLtpnZL83sJ2b2pirUZ76f3WrZX28CTrj7c0VlFd9fc/4+RPYdU3BcQMysAfgn4E/cfQj4W+Ay4CrgOEFTudLe6O7XAO8A/sjM3lz8pAdt46oc821mKeDdwD+GRathf71MNffRQszsU8AU8PWw6DhwsbtfDXwS+IaZ5SpYpVX5syvyYc79B6Xi+2uevw+zyv0dU3DMrxvYWvR4S1hWNWaWJPhSfN3d/x+Au59w92l3nwG+SERN9MW4e3d4fxK4N6zDiULTN7w/Wel6hd4BPOruJ8I6Vn1/FVloH1X9u2dmHwduBD4a/sEh7ArqC5cfIRhLeEWl6rTIz2417K8E8F7g7kJZpffXfH8fiPA7puCY3z5gh5ltC/9r3QPsrVZlwv7TLwFPufv/Kiov7pf8TeCJua+NuF71ZtZYWCYYWH2CYF/dFK52E/DtStaryDn/BVZ7f82x0D7aC3wsPPLlDcBgUXdD5MzsBuDPgHe7+2hRebuZxcPlS4EdwKEK1muhn91eYI+Zpc1sW1ivhytVr9CvA0+7+9FCQSX310J/H4jyO1aJUf8L8UZw5MGzBP8pfKrKdXkjQTPzMWB/eHsn8DXg8bB8L7CpwvW6lOCIlgPAwcJ+AlqBfwOeA/4VWFeFfVYP9AFNRWVV2V8E4XUcmCToT/7EQvuI4EiXL4Tfu8eBXRWuVxdB/3fhe/Z34brvC3/G+4FHgXdVuF4L/uyAT4X76xngHZWsV1j+VeD356xbyf210N+HyL5jmnJERERKoq4qEREpiYJDRERKouAQEZGSKDhERKQkCg4RESmJgkOkBGZ2JrzvMLOPlHnb/23O45+Xc/si5aLgEDk/HUBJwRGeYbyYc4LD3a8rsU4iFaHgEDk/fwW8KbzWwn81s7gF17LYF07E93sAZvZrZvbvZrYXeDIs+1Y4KeTBwsSQZvZXQF24va+HZYXWjYXbfsKCa598qGjbPzazeyy4hsbXw7OIRSK11H9AIjK/WwmuD3EjQBgAg+7+ejNLAw+Y2ffDda8BXuXBtN8Av+Pu/WZWB+wzs39y91vN7BZ3v2qe93ovweR+rwXawtf8NHzuauBK4BjwAPCrwM/K/WFFiqnFIVIebyOY/2c/wZTWrQTzEwE8XBQaAP/ZzA4QXO9ia9F6C3kj8E0PJvk7AfwEeH3Rto96MPnffoIuNJFIqcUhUh4G/LG7339OodmvASNzHv868CvuPmpmPwYyK3jfiaLlafQ7LRWgFofI+RkmuExnwf3AH4TTW2NmrwhnDJ6rCRgIQ+Nygkt3FkwWXj/HvwMfCsdR2gkuYVrpGWBFZum/E5Hz8xgwHXY5fRX4a4JuokfDAepe5r9k7veA3zezpwhmc32w6Lk7gMfM7FF3/2hR+b3ArxDMQuzAn7l7Txg8IhWn2XFFRKQk6qoSEZGSKDhERKQkCg4RESmJgkNEREqi4BARkZIoOEREpCQKDhERKcn/B4tju3IQ0IUnAAAAAElFTkSuQmCC\n", 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" ] @@ -345,7 +345,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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lACt2MLeU4spaLgoohI+uB2dPuP7rNq3+2ZhKAIpii7b9Fw79DFe8BiNuaXoblQCs2taUAkBy8c4HwNEF5v7U5tU/G1OdwIpii47sAJ+w05/8QSUAK7c1NZ/BvlU4Fx6C8Q+0+8kfVAJQFNtUlHH2E4arj0oAVkpKybbUAqYG52kLQqINiUMlAEWxRUUZ4Bd+5m1cvdUoICt1+HgZeWU1jPI4oi3oPMCQOFQCUBRbY66F0iPalIFnopqArNaWFG0CmJ7mFPDrDm6+hsShEoCi2JqSbJCWZt4BqARgjbak5NPFxw2PwgPQZZBhcTQrAQghJgshkoQQyUKIR5pY7yqEWK6v3yqEiGiw7lF9eZIQYlKD5WlCiN1CiEQhRHyrHI2i2IOiDO2rSgA2SUrJ1tQCLg0HkZ8MXQYbFstZh4EKIRyBd4GJQBYQJ4RYKaXc12Czm4FCKWUvIcRM4CXgWiFEFDATGAB0BdYJIfpIKc36fhdJKfNa8XgUpeNrSQIwV4OpGpxc2z4upVlS88oJKdvH45lvgoMT9L7UsFiacwcQCyRLKVOklDXAMmB6o22mAx/p338JXCKEEPryZVLKaillKpCsv56iKOeqKBMQ4BN65u1cvbWvqh6QVTmc8AufuvwLJ1cPuPVXCB1uWCzNSQChQGaDn7P0ZU1uI6U0AcVAwFn2lcAaIUSCEOK20725EOI2IUS8ECL++PHjzQhXUTq4onStXLCTy5m3q08AaiSQ1Uj8nIu33ESx8MFp7o8QYlzzDxj7JPA4KWW2ECIYWCuEOCCl3Nh4IynlImARQExMjGzvIBXFqqz/F+xaDn0m1y8ymS3EpRWyJSWfgzml5JZWY7ZILpbHuAfYuCeF6BFh+Lo7Gxe3AlIif32OA6IHH/Z4nVfP1oTXDpqTALKBhuPNwvRlTW2TJYRwAnyB/DPtK6Ws+5orhPgGrWnolASgKIpux1L47UUY9Fe44lVKq2r5dEsGi/9M5XhpNQ4CIgI96eLjhqODIKdYO+G/s3oHiWtqmDKgM/eOCyayW5jBB2Knju1GlGSxpPY2onu3/1O/TWlOAogDegshItFO3jOB2Y22WQnMATYDVwO/SimlEGIl8JkQ4nW0TuDewDYhhCfgIKUs1b+/DHimVY5IUToaKWHHp7DqQYgYj2X6e3y8NZM31m2luLKW8b0DeXraAMb1DsTHrcFVfrYT/BdeuCKCT/O70Wf703Q9sJ4F/b9i/tRRWglipf0krUYiWG8eym2R7VPt82zOmgCklCYhxDzgZ8ARWCyl3CuEeAaIl1KuBD4APhFCJAMFaEkCfbsVwD7ABNwtpTQLIToD32j9xDgBn0kpf2qD41MU25e+CVbOg4jxZF+6kAcWx7ElpYDxvQN58LK+RHfza3o/Vx8AevlIFtR8B2INAGl7tjD5cC2vXRPNBX2C2ukg7JypBvZ9S5p7FNIxiF7BXkZHBDSzD0BKuQpY1WjZPxt8XwVcc5p9nweeb7QsBTCm+IUtM5vgp39ATTlc9b7R0Sit7cgO2P0lXPwEOLufWJ53EIC4oS8w93/7kRJenjGYa2LC0C+imlbXCbz1fciO18pG7/uOl8Y7cv0+Z25YvI27JvTkwcv64uBwhtdRzo/ZBF/fArn7WOJ0LyN7+J/5c2tH6klgW2CqgTVPIBdNgLj/IXctp6ZCjezoMApS4Lt5sGgCbH4HMreevL5cG/02Z3kqIb5urL53PH8d0e3sJ5G6BJAdD/2mwozF4BlM58oUVs4bx+1DXBn85zx2vXEltWZL6x+Xos3R/N1dsO878sc+xUdlIxnTM9DoqOqpBGDlisurSVn0N9j0NtuP1fCVeRxCWrjp+UVc8dbvvLYmicyCCqPDVM7VgVXw/njtyj9ivLasIv+kTfYeSqZIejK8Zxe+vHMM3fw9mvfazh5aM1DEeJjxATg6aUXHcvbiZqnkkWP3MdkxjsElvzHvw9+oqjWf/TWV5pMSfrxfG7V18ZOs8p4BwNheKgEoZ1FjsrBwQzKPvfwqPXLXsMR9DqtHLKH2Eq017bYe+Xi5OvHjht/Z8cYMli56maPFlQZHrbTYz49pRd3mx8PVH2rLyk8kgE82p5GenkqVSwCLbxxxcifv2QgBd26C674GZzdtWecBcPwA/PosoigDLngYByGpSNnKvM92YDJbtCYLqUZcn7cdn0LChzDufrjgQTYl59HV142IgGYm8HagZgSzQhn5Fdz1WQJ7sktYERCHydSJGx98DRz1P/5dPbnQPZULI7cjc59GmKv5I6uUy96I5uUZg7l8UIixB6A0X1kuxNwEvmHaiRegQquO8lVCFk9+t5c1vhUEd+mGg+M5XK/5NaoYGhwFpiqtXyBmLoyZBxtf4YH+RVy5N4eXP1vFo1l3IobdAJOeb/o1lebJ3QcuXnDJP7FYJJtT8rm0f2eraf8HlQCsS1UJ23PN3LwkDrNF8r+ZfYn9YQsMmX3i5A8QNgJ2LYODqxF9LgdzNSOPJ9PD1Ys7l27nulHh/HPqAFyc1A2eVauthNryExOAOzqBeyeoyGdLSj7/+GoX43oF0quiEgevPq3znuGjtLlnh8+BS5/WniYO6seQkvXEBfyCd3IqQtTCgR9VAjhflYXg7g9CsO9IMUUVtYztFWB0VCdRZwhrEf8h8qXuLPrve/i4O/P9bdFcmvoamCphUKMBVv2maL9Y096GWZ9DaAzOpVl8cctwbrugB59uyeD2T+JVm661q2vr92hwUvAIpLwwhzs/TaB7gAcLrxuGQ1kueAW3znsG9IRHs2Dyv06Ukug2Ao4fINCxgvigq9hp6UF5dW3rvJ89qygAdz8A/kzW7uqsqQMYVAKwDru+QP5wH0Ja+Kvrn3xx+yi6r7sDdn4OY+ZrV20NRU2Hf6TCsBu0dl7/HiAtuJRm8diU/rxw1SA2HDzOTR/GUVZtMuaYlLNrIgGY3f05mJqGBD6YMwIfRxPUlIJnK47Xd2j0Zx81HUKiETd+T+wd/+GwVwzO5UfZl1XYeu9pjyoL6+/u/jycT69gLzr7uBkc1MlUAjDagR+R39zODocB/OgwgQliO8H7P4GU9XD5y3DZc9pJ/kz8e2hfC1IAmN1HsiXsHarTt3HrR/HUmNQQP6tUnwC0q0IpJXuLnPGoLWLh7GFEBHpqfQQAXp3bLo5el8LtG8G/By5ODlw6JgYXYeaJT3+htErdCZyzygJw70SNyUJcagFje1pX8w+oBGCslA3IL24kxbk3t9Q8QNTkW3GorYDVD0H3sTDilua9TsMEUJAC/7uUzsc38cKALDan5PPIV7uQalSH9Sk/+Q7gy4Qs9hY5E+ZawZi6oYL6MwCt1gTUDD7BkQCIkkz++d3ednvfDkfvA9iRUUhlrfnEZ2pFVAIw0oaXKHMJ4i8l93Pf1OFEDp8EXYfB0Otg9opTb9VPxzMQXLwhZQMsmQoWrdmnn1cV90/sw9c7snlj3aG2Ow7l3DRoAkrOLeOf3+3F3S8YD3PxiWGYZTna19ZsAjobX61Y3C2DnPlmRzbf7Mhqv/fuKCwWPQF04s/D+TgIGNVD3QEoDVSX5PJ7eTdG9O/BdSPDtZE+t62H6e+CawtqhQgB/pFwcLU2smTOSggZAiXZzL+4F9cMD+OtXw6xdl9Omx2Lcg4q8kE4YHLx4f4Vibg5O3DJ8CiExQRVRdo29U1A7XcHUJcALgurZUREJ578di9HkxNPDFNVzq66RJu32cOfTcl5DAr1tcpy3CoBGMRskZQX51Pl6MVLMwaf/9jgzgO1poQ532uTTPuGQXE2Qgieu2ogg0J9eWBFonpq2JpU5IF7J97/PY1dWcU8d+UgvP276OsKtBNu8joQDu17B+DmA26+OJZk89aUYP7NK4R8eiEycWn7xWDrKgsAqHbyITGzyCqbf0AlAMN8ti0DD0sZ0b26t05Z3iteg/kJ0GWg9rNPKJRo0za4Ojny7uxhSGDeZ9tVp7C1qMin2qUTb/5yiKmDQ7hicEh9hzD5h2HZbDjwA1z0WPvP6evbDQ7+RMinE5jguBuTdODAnu3tG4Mtq9RGUB0occZkkYy1suGfdVQCMEBheQ1v/7wbN1FLj25dW+dFXTy0h4jq+IZqt6FVxQCEB3jwytXR7Mwq5rW1Sa3znsp5sZTnc6jMFV93Z56ZrifuuofCPrsGDv8CV7wOFzzU/sH5dYfiTOg2Aoe7t3DcKYT0lCRVbqS5KrQEEHdM4ubsQExEp7PsYAyVAAzw6pqk+nlahZtv27xJ3YThxScmb5s8sAszR3TjvxtTSEhvYoz3obXw5hBYOb9tYlJOUpx3lKxqDxZMG4C/p/5QlmeDK8UbVsKIm40J7tIFMPsLuO5rHAIi8QuJpAt5alRQc+l3AL9lmRndIwA3Z0eDA2qaSgDtLOlYKZ9ty+CGofqJ382vbd5I78ijJBtqq7S5ZN8byxMXdiLE150Hv9hJZY3+pHDpMfjiJlh6NRSmQu7+tolJqZdTUoW5LA9XnyCuaFi7yScMRt0Ft/wCEWONCzCoD/S5rP4ZFPfACHq5FrF2Xw7rD+QaF5et0PsA9hY6MqFvO3bgt5BKAO3szV8O4unixJyh+i2h/qh4q6u7A8jZAx9P0+aSzdmDV+ZGXrl6MKl55bz88wGtHPE7sVrtl4seh96ToLqsbWJS6j37/V78KGVov14nDwBwcNDKNITFGBdcU/y64VmTR59AFxZ8v1eVGTkb/Q6gGE8utOJZ11QCaEf7jpSwavcx5o6NwFvqo3HaqgnIW7+qXLdAm2nq6sXa3UbGJsb0CuT6Ud1h63vIZbMhoIdWNvjCh7U26JrytolJAeCPfRlE738VJ2HBL6yf0eE0j28YAslzlwSQnl/Bkl93w64vtPHuyqkqCqgQnoQFeGtPdFspVQ20Hb35y0G83Zy4eVwPOLxbW9hWCcDRCToP0p4MvuFb6Bar/cFmbIHKQp60LMTFaSmbXEYTe8OXOLnpzx24eGm1Z5Q2URu3hOE/Psw4p2rMMbfiGD3L6JCaR29SjO1UwbX93ZizaSKIGq24XOgwg4OzPuaSI+RZvJhgxVf/oBJAu9mTXczPe3P4+6W98fVwrh+d02YJAOCWteDgrCUD0IrKHVwN747CpTyX5D63ct2uC3ki/jhzx9UlAE91B9BW9n+P049/Z6s5Ct/LHmXQuKlnr/NkLXz1eQXSN/N80ec4iRrt5zLVH3CSkqOw+mEcD3xPomU0F/a17gSgmoDayXsbDuPt5sRNY7U6K/VPerZlAnB2P3HyB+g+RvsqLXDLL/Sc9Qrj+3TmtTVJ5JRUaetcvMBco81DrLSqqh0ryJGdWNbrNQaN/z/bOfkD+OjDldc/h1NFHuv6PQtAUkqqgUFZESkh7n/wbiwcWsOvoXfwiOVuqyz/0JBKAO0gs6CC1XuOMjs2/MTj4FXF4OgCTu1YHjY0Bib9C+b+BKHDEELw7PSB1JolL/10QNumrgRFjeoIbm3p2Uc5Jv15aOpgo0NpOWd3rV/JIxBu/IHx0+YA8MfO/ZgtqtAgGZvhxweg61C4azMvlE5heI9gPFysu5FFJYB28NGmNIQQzBkTcWJhVbHWKdueV4EODjD6Lq3dVhce4MHccZF8vT2bxMwirQkIVDNQK9uTXUxlaQHenQLpHmC9nYJnNOtzuP03CBmMq7sPZkc3zGV5fJWgisWRpxdbnP4OWaILybllVj36p45KAG2srNrE8rhMpgwKoauf+4kVVcVt2/zTAvMu7kWglyvPfL8X6aLuAFqblJJnf9iHn0Ml4V27GB3Oues69MTzJULg4BVIb69KXl2TREWNnReKKzkCCPAOYeNBbfYvlQAUVsRlUlpt4uZxkSevsKIE4OXqxMOT+rI9o4gtWXpfgLoDaDU/781ha2oBnV2qcfawzpIA50J4BjEswExuaTWLNqYYHY6xSrK1SXscndmQlEuonzu9gltQ0dcgKgG0IYtFsmRTGsO7d2JIN7+TV1pRAgC4engYA0N9+ChBr1FfrYaCtoYak4UXV++nd7AXbuYyq/rMz5tHIL6WYq4YFMJ/fksht24ggT0qyQbfUKpNZv5MzuOCPkHnX+G3HagE0Ib+SM4jo6CCG0Z3P3VlZZFVnQwcHAT/nDqAzDL9V0LdAbSK5XEZpOVX8MSkHghztVZquaPwDILyPB6e3BeTxcLraw8aHZFxSo6AT1e2pBRQXmNmYpT1ln9oSCWANrQsLoNOHs5MGtCo3ddUo9UKsaIEABAb6U9MH228d3FJkbHBdAAVNSbe+jWZ2Ah/LgjXR39Z2Wd+XjwDoCKP7v4eXD8qghXxmSTn2mnfUXE2+ISybl8O7s6OjLHS8s+NqQTQRvLKqlm7L4e/DAs7uRJg7n54b7RWK6TrUOMCPI2bLx4EwG+71fju87VkUxrHS6t5eHJfRJVW/bXNiv8ZwSMQTFVQU8bdF/XE3dmR1+2x1HhVCdSUIn1CWbc/h/G9A622+mdjKgG0ka8Ssqg1S2bF6k9QSgm7VsAHl2nF1v72JQyfY2yQTQgP0W5d96UdIS1PNQOdq+KKWt7fcJhL+gUTE+HfPk9+t7e6WcrK8wjwcuXpQcdx2vsVu7OKjY2rvZUcASDL3ImjxVVcGtXZ4ICaTyWANiClZHlcJjHdO9Er2FtbuPld+PpWCOwNt6yD3hONDfJ0nNyRCHwcqnnNntt0z9P7Gw9TWm3iwUl9tQUdMgHozRxFGfDFjVy9dx7/dlnIm6t3GBtXeyvRnoPYfNwVIeCSfrbR/g8qAbSJbakFpOSVMys2/MTCvV9D12Fw81rw62ZccGfj4IBw8SQ21IXvdx6xv6u5VpBbUsWHf6YyLbor/UP0Tt/2KP3R3uoSwMfTYN930G8qDkgKUnaw+XC+sbG1p6JMAFZlODI8vFPrTPHaTlQCaAPf7MjG08WRywc1mOA7ezv0mQQONtA26OLF4GAnOnk4a3MGKC3y9q/JmMyS+yf2ObGwI94B1M05AdrsYZP/BcAojyO8/PMBpOzgJSKyE+D312DdU5g9u/BHjpNNNf9AMxOAEGKyECJJCJEshHikifWuQojl+vqtQoiIBuse1ZcnCSEmNdrPUQixQwjxw3kfiZWoKsgidfcfTBrY5UQdkJQNgISeFxsZWvO5eOJiruDui3rx+6E8/jiUZ3RENiM9v5zPt2UwM7bbySUfOmIC8O4Ct/0Gj2ZB70u1iqFuvlzVtZAdGUX8sidLm49i23+NjrT1JX4O/5sIvzwDnSL4ZugHmHBiYkdLAEIIR+Bd4HIgCpglhIhqtNnNQKGUshfwBvCSvm8UMBMYAEwGFuqvV+deoOPMP7jlPZzfGcZS+Th/7aMfpsUCe77S/vC72kjddFcvqCnn+tHdCfVz56WfDmBRBb+a5Y21B3FyFNxzce+TV1SXtH/xv/bQdQi46v1cQkDnQfSypDG50xFCv50Bf7wB656GWn0yeYsZDv4M5TZ8UVFZCCvnadV1HzoMt29kRbIjfTt70zPI+p/+bag5dwCxQLKUMkVKWQMsA6Y32mY68JH+/ZfAJUJ7DG46sExKWS2lTAWS9ddDCBEGXAH87/wPw2AWC/z5Jvz0CEmuA3ASFkYU/wRJP2nz7B74AUbccnJpZmvm4gXVZbg6OfLIBYHMynmNTRtWGR2V1dt/tITvdh7hxjGRBPs0OtHXPfltA0+HnpcugxBHd/Be5UMEmY6S3PMGbYKhpFVwcA28NxY++ytsW2R0pOcuZy9YTDD27+AZSG5JFXHpBSeafG1Ic85IoUBmg5+zgJGn20ZKaRJCFAMB+vItjfatazj8N/Aw4H2mNxdC3AbcBhAeHn6mTY1hNsGnV0HqRmp7X8GMfbNZ3elVIja+AuZq8AiAyS/CyDuMjrT5XLygLAfyDzN1yyyEUxY/bnKg9sLLcXZU3UYnOboTMrZC7K28+nMS3q5O3Hlhz1O3s7LSH22m6xDt5NhvKrcfu4G8Iw5s8F6H+G4+1JZDp0jtLqiyyOhIz13OXu1r5wEA/Lz3GFLCFYNCDAzq3Bjy1yyEmArkSikTzratlHKRlDJGShkTFGSF1fWKMyB1I4y7ny97vUClWeAwYq528h91FzxwEEbdaVtXfi6e2i/5R9MQpirKvHvQtSaNL1XZ3xPKcmHlfPjPhbD6IfYkbuWXA7ncfmFPbca3xuwlAQy6Bq7/FvHXj5l3+VDSC2vY0WWGNp/A5Jfg7m3aRVGtDT9jkrNHOwZv7Yp/1e5j9Ar2onfnM17LWqXmJIBsoOG4xTB9WZPbCCGcAF8g/wz7jgWmCSHS0JqULhZCfHoO8Ruvbkq8iLF8t/MoPYI86XbB9XDPDpj0gu00+zRkMYGlVisJff03ePa/lH6O2by59gBVtWajozNewkfw1jBI/Az6TAZg5cZtBHq5ctPYiFO3N5ugNMc+EoCDI/S8CBwcmdAniNhIf25LnUDF35Ng1B3g5ALOHrZdaypnr3b1LwR5ZdVsTc1nykDba/6B5iWAOKC3ECJSCOGC1qm7stE2K4G6x1qvBn6V2hiwlcBMfZRQJNAb2CalfFRKGSaljNBf71cp5XWtcDztT08ABcKPbakFTB3cVasC6N/Dtq76G4q8QBvRcfNaCBmMCI7CXVbiVHaEjzenaU8yJ/2kdejZm9oq+PF+6BwFd22BKa8AUJqbxr2X9Dp1BqiSI/D+WMjZbZWlP9qSEIJ/TO5LXlk1H/6ZdmKFiyfUVBgW13mxmCFnH3QeCGjNPxYJUwbbXvMPNKMPQG/Tnwf8DDgCi6WUe4UQzwDxUsqVwAfAJ0KIZKAA7aSOvt0KYB9gAu6WUnass0a5lgDWZ6H9IthgR9ApYm/V/tXR2zr/ElZC4vovsWx+H4fKArjqPxA906AgDZKXpN0hjboTAntjMdUicaCvewnXjmjUR5WzD768CYqz4K8fQ7//MyZmAw3v7s8l/YJ5/7fD/G1kOH4eLnoCsNE7gMPrwVRZ/zfxw86j9Aj0pK8NNv9AM/sApJSrpJR9pJQ9pZTP68v+qZ/8kVJWSSmvkVL2klLGSilTGuz7vL5fXynl6iZee4OUcmprHVC7KzsOCL49WG3TvwhnFNQPgJs9N/Gq5TXyRIA2+cWBBo9v7FoB396lNXd0ZPUdgNoV4I97j5Mj/bgopAYXpwZ/Tkk/aVf+pcdg9nKImq5NyWmHHpzUl7JqE+//pp8WXDxtsw9g0zuwdIb2u9/zYo4WV7IlNZ9pQ7raRO3/ptjnb2RrKsvB4u7PptRipgwKsdlfhDNy8wHfbvimrabUJYgZZQ9S2XMKJP8Cm96GxZO1OkeJSyH/kNHRtq2cvdooFv8e1Jq1GvhFTsGEOxae2EZK+O0lbcTLPTsgYpxx8VqB/iE+TI/uypJNqeSUVNlmH8D+72Htk9D//2D+dvDpysrEI0gJVw4JPfv+VkolgPNVfpwSx06YLdImxwE328VPwKULqLhpA0dMPnxRHg21FbDmCe2Peej12nZ1V8gdVc4eCO4PDo58EZ9Fal45/l0jESUNxkVkboMj22H0XeDhb1ysVuS+iX0wmSVv/XJIG2ZsS30A6xbA8uu0Zp8r39celEQr+TI03I+IQM8z72/FVAI4X2W5ZNd60z3Ag6iQDjTbU2PRM2HcfUR2DeKa4WG8tD+QqtDRcNHjcPtGuOI1EI7afAcdWc5eCB5AZY2ZN385yLBwPzqH9dSmBJQSsuLhq5vBvRNEzzI6WqvRPcCTWbHhLI/LpMTsrI0wsxU7l2tlXG5eV3/yP3CshAPHSm366h9UAjhv5rJckis8uHxgB23+acK9l/amVjjxuO9LcOHD2mgnJ1cI6AW5+4wOr+2k/QHlx6HzAJZsSiOnpJpHLu+P8O2mTYxy8Cf4aJr2/3Hd11pbt1Jv/sW9cHIUbM2u1u4ebYG5FkqPQmgMOJ94uvvbHUdwdBBMtdHRP3VUAjhPsjSH49KHSQNsqwjU+QjxdWfO6O58syOLQzkNJo/vHHUiAZiqIf5DrUywrSvLhR8fgI+nQ6dISnpM5b0NyVzcL5jYSH/w1a8CP58J3p214bOhNlL3qR0F+7hx09hIdubUgrlGO7lau9KjgATfsPpFFotkZWI2F/YJsqnSz01RCeB8VJfhZK6k0sWf6DA/o6NpV3dO0Ma8v7qmwRSAwQOgMA2+mwev9YMf/g7f3m1UiK3j6E74zwXaw19Dr4fbf+Pd7eWUVpt4eLI+2UunSO2rswfM+b7+CVHlVHdc0BOLs4f2gy10BBfrfTu+J5p6/kjO40hxFVcNte3mH1AJ4LzUluQAENwlHAcH+2j+qePv6cKt43vw894cdmToI2A660Vid38BvS4FnzBtBJEtW/0PrW3/tg3wf//maLULS/5M46ohofTroh9bl4Fww0p48NBJV4rKqXw9nBnRR/s/SkxpXFDAChXr5U98TxQ0WBaXQScPZy7rAHf9KgGch4MHdgPQs0cPgyMxxs3jIwnwdOGVn/W7gF4TYdK/tHovM/4LfSefKANsi8y1cGQHDJyhneSBN9cdQkptVMtJelxY30GonNnY/t0B+N8ve6x/0hh9use6yW+Ol1azZm8OM4aF4epkA5M7nYVKAOdCSkj8jJ4b7qJIetJ/mH2O8/ZydeLui3qx6XC+NmmMk4s29LGT9geOs7ttJ4Dc/Vrnrt6en5xbxor4TP42Kpxu/h4GB2e7XNy1hyXTjuayavcxg6M5i+JsrYaTnty/2p6FySKZGWvF07q2gEoALVVZCEuvgW/v5KAM55nQ/+Dp39XoqAzzt1HhhPq5Nz0FoJO79ti8tV/lnc6R7dpXPQG8tiYJd2dH5l3Uy8CgOgAXLXn2C3DkxZ/2U22y4uowxVn1zT9SSpbHZRIb4U+v4I7xxL9KAC21Yg6kbOD4+OeYXvE4QwcNMjoiQ7k6OfL3S3uzK6uYn/Y0upqrGzZnqm7/wFpD9nZtPH+nSHZkFLJ6zzFuvaCHzY/8MJyLdjU9Z3gQmQWVfLwp3eCAzqAkq775Z0tKAal55R3m6h9UAmi540kQfS3fOE9B4sDF/W2/I+h8/WVYGL2CvXh1TRIms+XEirrRHrYy5ruhkiOQ9jt0HYoEnvtxP4Fertwy3j77e1qV/nsxKNiJCX2DeOvXQxSU1xgcVBOk1JqA9I79jzal4efhzBQbnPjldFQCaKmacnD1Yd3+XPqH+BDq5250RIZzdBA8NKkvh4+X83lcg8nj6ua/NVUZE9i5kFKbxPytoVCYDtGz+HH3URLSC3loUh+8XG1wfgdrU/eAXE05j03pT3m1SSsRYU1qK+HbO6GyALoMJCO/gp/3HWN2bDhuzrbf+VtHJYCWkBJqyqgSriSkF3JJv2CjI7Ial0V1ZmSkP6+vSaK4Un/Ax1lPjrbSEZy7HxZNgFUPagXc5idQ1X8GL64+QP8QH64e3nFu/Q1VnwAq6NPZm1mx4Xy6JZ3kXCspD1GUAYsnwc7PYcJjMOxGPtyUiqMQ3DA6wujoWpVKAC1hqgIkh4vAbJFc0l8lgDpCCJ6cGkVRZS1v113N2VICMNfCl3O1Tr8r34PZX4B/JIv/TCWrsJInr+iPo50969Fm6hOAdsK/b2IfPFwceWqlFQwLzd6uTfNZkAqzlsOEf1BSY2ZFXCb/F92VLr5uZ38NG6ISQEvoTy7uyzcT6OVid0//ns3AUF+uGR7GR5vTSM0r10YBgfU3AVks8MvTWhmLaW/DkNng4MDx0moWrj/Mpf07M6ZXoNFRdhxOboCo7xsK9HLlocn9+DM5n+93HTU2tvjF2oQ/t67XnmMBVsRlUl5j5uZxkcbG1gZUAmgJ/Ypl93ETF/QJsrunf5vjwcv64uLowAur9je4A7DiTuCyXG2Sj01va6Ue+k2pX/X62iSqas08NqWfgQF2QELoJaH1UhDFWfytegWxoS48+8M+SqoMrBFUVaSN+gnUhvpWm8ws/iOV2Eh/BoZ2vDmdVQJoCb2GeV61Exf2CTI4GOsU7OPGXRf1Yu2+HHbl6MM/a630DuDwenhvLKRvgqlvaFf/up2ZRSyLy+SG0RH0CFJP+LY6F31SmKSfYOEYHNY/x2tRKeSVVfP6moPGxVVVrD34pVsRl8mR4irmX9wxn/1QCaAl9CuWCtwYq5oETuvmcZGEdXLnnd/1x+it8Q4gZx98cpU2Ycut6yFmrnZlita/88S3ewjycuW+ib0NDrSDcvaA7R/BslngHwmuPnSr2M91I7vz8eY09mQXGxNXVUl9/aqqWjPvrE8mpnsnxnXQv3eVAFpCbwIKDvAnUD0MdFpuzo4s+L8BJBXoT3haYx/A8QOAhKsXnyhip/t0Szq7s4t5cmoU3m7OxsTX0ZXqDw32mQw3rdKets5O4MFJffH3dOGfX+/AVHq8/eOqLgFXLQEs25ZBTkk190/s02Hn+lAJoAUqK7Ta91ERHedBkLZyaVRnRvXRSmTkFxl0NXcmlXoFU/eTp2zMLani1Z+TGN870OYn+7BqV7wKl78C1y7VRgWFDoecvfg6mVg0JIWFeTci3xgE1aVnf63WpN8BVNWaWbjhMLGR/ozuGdC+MbQjlQBaIDlLK/88uIft1wFvD/dNGQLAz4mpxg/va6yqSPvq7nfS4ud+3E+12cIz0wd22Ks+qzD0Ohh5Gzjop6DQ4SDN8MN9DIt/GHcncLZUknI46cyv05SClHOrPyVlfR/Af35LIbe0mgc68NU/qATQIqlHtAQwQN0BNEsX/04AZOUWWF/Vx8pCbZiq84knuf84lMfKnUe488KeRNrwRN82KXS49nXn59B/GuKq/wDwwerN1DYsL3Impcfgq1u0p7h3fNLyGExVYKml2OLOwg3JXDEohJE9Ou7VP6gE0CKZOXkAuLrb+CQn7cXJFYkgzFvw9Pd7jR3e11hloVboTVdWbeIfX+0iMtCTOyf0NDAwO+XdBa76jzaxzl8/xidEG3VTlZ91Yr6J07FY4M+34M0hsPcbcPGGA6tOrJcSqpvxlHFVCQCrDpUjBDx2Rf9zPBjboRJAM2XkV1BdrrdHqsm+m0cIhLM7l/byJq+smme+t6IJ4yuLTmr+eWHVfo4WV/LqNdEdqtaLTYmeqU2sI0T9tJqTuksWbUxh3b6c0++37ilY+yT0ukSbjCj6WkjdCKYaSPlNG+r7UoRW4O9MqrS+qs3ZJu6e0Msu6nypBNBMvycfx0NUYXF0Awd1gmg2JzeC3SV3TejFlwlZrD3TH3J7qiyqvwPYePA4n23N4NbxPRjevdOZ91Pah4snuPpycaiFAV19eOCLnWQWnGY4cfomCB8D134KAT216Uhry+GnR+DTGVB6BCy1kHfm5wvKSwsAcPPuxK0X2EfVV5UAmmnjweMEu5oQrurqv0WcPaC2knsu6U1UiA+Pfr2L/DIrmB9AbwIqLK/hH1/tolew16nTPCrG8u6CU/kxFv5tGBaL5LZPEiirNp26XUk2+Peof46DiPHg4AzxH0D4KLjuK2156Zn7oT5evwuAuZcMsZu7QJUAmsFktrApOZ8IHxDOKgG0iLMb1Fbi4uTAG9cOoaRSa2s3fFRQZSHSzY8Hv9hJflkN/77Wfv7obYZPCJQcpXuAJ2/PHsrBnFLuXrr95E5hU412YvdtMDLP1Uu7G7j+G5jzPQTppTzO0AT07Y5sdh/WSpn3624/o/xUAmiGnVlFlFabCHE3q/b/lnJyr38QrG8Xbx6b0o91+3NZtDHF2LgqC9ldIPjlQC6PTunXIeu82DzvkPqr9gl9g3nuyoH8dvA4T37boGpo6VFA1s/aVa/vZOh5sV53SGtO0rY91cGcUp74dg+D6wb8uNnPIA+VAJphU3I+QkCgS61KAC3l7H5SKYg5YyK4YlAIL/+cRFxagTEx1VaBqZK1qTVMjOrMjWMijIlDOTPvLlB2TBvlA8yKcuORMV4si8vksW/2YLFIrfkH6mftOi2fkCbvAHJLqpi7JA53F0dmDfHTFrrZz8WASgDNsOlwPv27+OBsrlIJoKWc3U4qBieE4MUZg+jWyZ27l27naHH7zxVwNFe7qpRunXjl6sEd+kEfm+YdopVmTvwU1j4Fbw7h9owHuXNCTz7flsH9KxIxF+oz0J0tATS4m6iTV1bN3/63lYLyGv53Qwy+ohKEQ/2cxfZAJYCzqKo1k5BRqD0OXlOuEkBLObmfUgzO282Z968fTkWNmblL4pvu2Gsj5dUmFiz/A4DrLorGz8Ol3d5baSF9KCgr58Ofb4KrNyLvIP+4sDMPXtaHbxOPsOyXLdo2jZuATnmtkJOagNLzy7nm/c1kFFTwwZwRRHfz054DcPU+0ZlsB5qVAIQQk4UQSUKIZCHEI02sdxVCLNfXbxVCRDRY96i+PEkIMUlf5iaE2CaE2CmE2CuEeLrVjqiVbc8opMZkYUzPAK0YnEoALePs3mQxuH5dfHj3b8M4mFPKvM+2nzyZfBupMVmY//kOivK0oahdOndp8/dUzkPXodronksXwOPH4Mp3teXHdjPv4t68/tdoKMmmBE/WJJedeWCBj3YHIM0mfth1hKlv/0FhRQ2f3TryRK2fqmKtr8COnDUBCCEcgXeBy4EoYJYQIqrRZjcDhVLKXsAbwEv6vlHATGAAMBlYqL9eNXCxlDIaGAJMFkKMapUjamVbDufjIGBEpL92JasSQMs4u592PoAL+wTx7PSBbEg6zgNf7DyRBCxmKGndmaFMZgv3LtvBrwdyuWuUXtrXXY35t2p+4XDPDhh3n9aU2CVaW35UG675l2FhXBkpyXcM4rZPErj+g238cShP6xtoRHqHgDQz/4M1zPtsB5N9M1g3uYjh3RsUA6wusav2fwCnZmwTCyRLKVMAhBDLgOlAw8c6pwML9O+/BN4RWsPqdGCZlLIaSBVCJAOxUsrNQN2z2c76PyurFqbZdDifQWF++Lg5a01Aahhoyzif2gSElPW32bNHhlNYUcMrPyfhZirmhUHHcdz2PhzZAfMTtFrx56nWbOHBL3ayes8xnpwaxYWem2A7KgHYGq8grann6E7t56oSPEtT6R7ZhycjonhvQzLXfbCVIG9XYiP8CfN3x0EIjhZV4nY4jxeByUfe4x+hZrrl/wmrBPSK0e4yKougKNOuRgBB8xJAKJDZ4OcsYOTptpFSmoQQxUCAvnxLo31Dof7OIgHoBbwrpdza1JsLIW4DbgMIDw9vRritp6LGRGJmEbeM76GNRFB9AC1XNwzUbILEpfDrs9rkKxc9Vr/J3Rf1omf+ekbtfgrH5HKkiydCmuHYrvNOACVVtdy9dDu/H8rj4cl9uXmAA/ys14lx8zuv11YM0GUwpP4GS6ZC5jYwV+MwfA43j4nkbyPDWbMvh7X7ctiZWcTafTlIJIFerkwN6gZHYCobQfSBkXdC3H9h80II7gfrntbuAMbMN/oI21VzEkCbkFKagSFCCD/gGyHEQCnlnia2WwQsAoiJiWnXu4S4tEJMFguXBuTD768CUiWAlnJ20/pO3h4GRekgHOHQmpMSAJWFTN7/OHk+PZmR/1fw6ctXNbPg+PlNDZiRX8GtH8dz+HgZ/7vIzKVH/wm/rQYEDLnO7m73O4Sw4XBwtdZZG3srDPwLdB0GaBMRTYvuyrRobR6Kuj4BIYTWDPnjJm0Cmqhp2mtV5GlJACDyApj4jNbvYEeakwCygW4Nfg7TlzW1TZYQwgnwBfKbs6+UskgIsR6tj+CUBGCk5N1bWOnyTwav0h9airwA+v+fsUHZmrqE6eQGMz+HzC3aVZepGpz0WdX2fgPmagJnLeSesjDmf7adbIIwJe0g/ALZ4mGaUkqWbs3ghVX7cXQQfDq7N6O+Gas9ITrufu0OxNd+nvbsUEbdDREXQNiIE3MJnMZJvzfObnDlwpM3mPCoNuxz4AzofZldjf6p05wEEAf0FkJEop28ZwKzG22zEpgDbAauBn6VUkohxErgMyHE60BXoDewTQgRBNTqJ393YCJ6x7E16ZO0iF6Ox+DyV7UrB79uZ99JOdmwG8GvO/SfBk4uYK7RCnPl7NWmAQTYuUx7XD9kCBcKwcp548hZFI5r1h5mLtrCY1P6a8P0zkJKyeaUfP697hDbUgsY1yuQl64eTGj+ZjBXw9UroMeEtjxapa25eEB44xbocxTQE/6yqHVey0adNQHobfrzgJ8BR2CxlHKvEOIZIF5KuRL4APhE7+QtQEsS6NutQOswNgF3SynNQogQ4CO9H8ABWCGl/KEtDvBclVTV4lSVR4FfHzxibzU6HNvlGQCDrj7xc91J/8h2rTP4h79rbf0Tn62/AosI9KT70JGY4xaTdLSYGe/+xk3ByVzQJ4ie464hxNet/upOSklWYSW/H8rjy4RMtmcUEeTtyvNXDWR2bLi23e5E7T1DotvvuBXFBjSrD0BKuQpY1WjZPxt8XwVcc5p9nweeb7RsF2DVjW3bUgoIpxh33wFGh9Kx+HYDjwDY9l8oTAPPYG1u2Ji5J20mgvvhZKliy+Qsaja+iU9JBuVxrgz4wx8fN2cCvV1BwvHSakr1B8kiAz15dvoAronpdnJht6OJ0ClCjfpRlEYM6wS2dpsO5zNUlOIbqKZ/bFVCQPhoOPAD9J0C097R7hIaC+oLgNtPD+Dm3xPZfRqe+1fy/JRIDhRICipqEECApws9g72IjfCj77EfEHvfhs73aBOL1DmSaHede4rSHCoBnMbWw7k8Icpw8A42OpSO58qFUP3ymTtiuw6D2NsgZAgMuhqx9xvYv5K/DXDT2m4bqq2C7+6GPV8CAmorTySAykJt9FHMTW11NIpis1QCaEJxRS3Hco7i4GoBj0Cjw+l43HzPPgTTyQWmvHLiZy89EZflnJwADq+Hr2+F8uNwyVPaHca6BbD9YziepI0ZB+hmlQ+aK4qhVAJoQnx6AZ3QJojGUyUAq+DVWfta1mhKyW2LtGcL5vwAkeOhNAd+fU4rIObkprX9z/gAuo9u95AVxdqpBNCEbWkFdHbUJ4BXCcA61CeA3JOX5+6D7mO0kz+Ad2e49GkwVcLo+dr4b0VRmqQSQBO2pRYwLsAMxagmIGvh7q9d6Te8A6gp10YSDbnu5G3HzGvX0BTFVqn5ABqpqDGxO6uYQZ1qtQXqDsA6ODho/QANE0DuAe1rcH9jYlIUG6cSQCM7MoowWSS9vaq1BR5NDFFUjOEVfHITUK5ekFYlAEU5JyoBNLI1tQAHAaEuZVq1SEdno0NS6nh1bnQHsF+rNtopwrCQFMWWqQTQSFxqAVFdfXCpKlDNP9bGs8EdQHEWpKzXSvk6OJ55P0VRmqQSQAM1JgvbMwqJjQiAinzwDDI6JKWhuiagDS/B2zFQkAIj7zA6KkWxWSoBNLA7M48LLVuZU/QOZG7VpqRTrIdXZ5Bm2PAC9JkEd2+D6JlGR6UoNksNA61TcoTwr65kkUsSMtUJBl6tTRChWI/eEyFjk1YiImKc0dEois1TCaDOzmUElSXxnPuDPPHAwycmK1GsR0BP+OvHRkehKB2GSgA6S/5hCqQvFX2uVCd/RVHsguoD0FUeO0Sq7ExshL/RoSiKorQLlQB0oiCFNEsXYiNVAlAUxT6oBABQU45HzXEK3cLo6ududDSKoijtQiUAQOYfBsC1c2+DI1EURWk/KgEAx9L2AxASGWVwJIqiKO1HJQAgJ3UvAL37DzE2EEVRlHZk38NA8w/D6n8wOHkdxwggomtnoyNSFEVpN/aZAKrL4Is5kPwLuHrzsdPVpIZcwdNCGB2ZoihKu7HPJqBDayB5HYyZR96cP1hQdhXd+kQbHZWiKEq7ss8EkLIBXH3gkgXE5bsAMKx7J2NjUhRFaWf2mQBSf9OKiTk6EZ9eiKuTAwO7+hodlaIoSruyvwRQmK5NJN5jAgAJ6YVEh/nh4mR//xWKotg3+znrWSyw/WP4aCogoOfFVNWa2XukWDX/KIpilzr+KCCLBQ6uht9ehqOJEBoDU16FwN7sTMmn1iyJUQlAURQ71PETQG05fHsnuHeCK9/XZpDSh3smZBQCqgNYURT71PETgKs33LgKgvqB48mHm5BWSI8gT/w9XQwKTlEUxTj20QfQZeApJ3+LRZKQUaiafxRFsVv2kQCakJJXTlFFLTHdVf1/RVHsU7MSgBBishAiSQiRLIR4pIn1rkKI5fr6rUKIiAbrHtWXJwkhJunLugkh1gsh9gkh9goh7m21I2qmhPQCQLX/K4piv86aAIQQjsC7wOVAFDBLCNG4bvLNQKGUshfwBvCSvm8UMBMYAEwGFuqvZwIekFJGAaOAu5t4zTaVkF6In4czPYM82/NtFUVRrEZz7gBigWQpZYqUsgZYBkxvtM104CP9+y+BS4QQQl++TEpZLaVMBZKBWCnlUSnldgApZSmwHwg9/8Npvvj0QoaHd0KoAnCKotip5iSAUCCzwc9ZnHqyrt9GSmkCioGA5uyrNxcNBbY29eZCiNuEEPFCiPjjx483I9yzKyivIeV4OcMjVPOPoij2y9BOYCGEF/AV8HcpZUlT20gpF0kpY6SUMUFBQa3yvtvTtfH/qgNYURR71pwEkA10a/BzmL6syW2EEE6AL5B/pn2FEM5oJ/+lUsqvzyX4cxWfXoizo2BwmCoApyiK/WpOAogDegshIoUQLmiduisbbbMSmKN/fzXwq5RS6stn6qOEIoHewDa9f+ADYL+U8vXWOJCWSEgvYEBXX9ycHdv7rRVFUazGWROA3qY/D/gZrbN2hZRyrxDiGSHENH2zD4AAIUQycD/wiL7vXmAFsA/4CbhbSmkGxgLXAxcLIRL1f1Na+diaVGOysDOrWD0ApiiK3WtWKQgp5SpgVaNl/2zwfRVwzWn2fR54vtGyPwBDht/sOVJMjcnCcJUAFEWxc3b3JHBCmtYBrEYAKYpi7+wvAaQXEu7vQbC3m9GhKIqiGMquEoCUUnsATDX/KIqi2FcCyCioIK+sWiUARVEU7CwBJNQ9AKba/xVFUewrAcSnF+Lt6kTvYG+jQ1EURTGcXSWAhLRChnbvhKODKgCnKIpiNwmguLKWg7ml6gEwRVEUnd0kgB0ZhUiJ6gBWFEXR2U0C2J5eiKODYEg3P6NDURRFsQp2kwDi0wvpH+KNp2uzql8oiqJ0eHaRAExmC4mZRQwPV80/iqIodewiARw4VkpFjZnhEWoCGEVRlDp2kQDi0woA1AggRVGUBuwjAaQXEuLrRlc/d6NDURRFsRp2kQC2qwJwiqIop+jwQ2KqTWbG9ApkfO9Ao0NRFEWxKh0+Abg6OfLqNdFGh6EoimJ17KIJSFEURTmVSgCKoih2SiUARVEUO6USgKIoip1SCUBRFMVOqQSgKIpip1QCUBRFsVMqASiKotgpIaU0OoZmE0IcB9LPcfdAIK8Vw7Fm9nSsoI63o7On422LY+0upQxqaoVNJYDzIYSIl1LGGB1He7CnYwV1vB2dPR1vex+ragJSFEWxUyoBKIqi2Cl7SgCLjA6gHdnTsYI63o7Ono63XY/VbvoAFEVRlJPZ0x2AoiiK0oBKAIqiKHaqwycAIcRkIUSSECJZCPGI0fG0BSFEmhBitxAiUQgRry/zF0KsFUIc0r/a7JyYQojFQohcIcSeBsuaPD6heUv/vHcJIYYZF3nLneZYFwghsvXPN1EIMaXBukf1Y00SQkwyJupzJ4ToJoRYL4TYJ4TYK4S4V1/e4T7fMxyrcZ+vlLLD/gMcgcNAD8AF2AlEGR1XGxxnGhDYaNnLwCP6948ALxkd53kc3wXAMGDP2Y4PmAKsBgQwCthqdPytcKwLgAeb2DZK/512BSL133VHo4+hhccbAgzTv/cGDurH1eE+3zMcq2Gfb0e/A4gFkqWUKVLKGmAZMN3gmNrLdOAj/fuPgCuNC+X8SCk3AgWNFp/u+KYDH0vNFsBPCBHSLoG2gtMc6+lMB5ZJKaullKlAMtrvvM2QUh6VUm7Xvy8F9gOhdMDP9wzHejpt/vl29AQQCmQ2+DmLM/+H2yoJrBFCJAghbtOXdZZSHtW/PwZ0Nia0NnO64+uon/k8vcljcYPmvA51rEKICGAosJUO/vk2OlYw6PPt6AnAXoyTUg4DLgfuFkJc0HCl1O4nO+x4345+fMB7QE9gCHAUeM3QaNqAEMIL+Ar4u5SypOG6jvb5NnGshn2+HT0BZAPdGvwcpi/rUKSU2frXXOAbtNvEnLpbY/1rrnERtonTHV+H+8yllDlSSrOU0gL8lxPNAB3iWIUQzmgnxKVSyq/1xR3y823qWI38fDt6AogDegshIoUQLsBMYKXBMbUqIYSnEMK77nvgMmAP2nHO0TebA3xnTIRt5nTHtxK4QR8tMgoobtCUYJMatXFfhfb5gnasM4UQrkKISKA3sK294zsfQggBfADsl1K+3mBVh/t8T3eshn6+RveMt/U/tFEDB9F60B83Op42OL4eaCMFdgJ7644RCAB+AQ4B6wB/o2M9j2P8HO3WuBatHfTm0x0f2uiQd/XPezcQY3T8rXCsn+jHsks/KYQ02P5x/ViTgMuNjv8cjnccWvPOLiBR/zelI36+ZzhWwz5fVQpCURTFTnX0JiBFURTlNFQCUBRFsVMqASiKotgplQAURVHslEoAiqIodkolAEVRFDulEoCiKIqd+n+QMgwaFCtF6gAAAABJRU5ErkJggg==\n", 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" ] diff --git a/qujax/circuit_tools.py b/qujax/circuit_tools.py index c1f5454..21b3481 100644 --- a/qujax/circuit_tools.py +++ b/qujax/circuit_tools.py @@ -66,6 +66,10 @@ def _get_gate_str(gate_obj: Union[str, """ if isinstance(gate_obj, str): gate_str = gate_obj + elif hasattr(gate_obj, '__array__'): + gate_str = 'Arr' + elif callable(gate_obj): + gate_str = 'Func' else: if hasattr(gate_obj, '__name__'): gate_str = gate_obj.__name__ From 90f586bb8d782b3f922cb01467a639d3715b4996 Mon Sep 17 00:00:00 2001 From: Sam Duffield Date: Tue, 13 Sep 2022 12:26:25 +0100 Subject: [PATCH 2/3] clean examples readme --- examples/README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/examples/README.md b/examples/README.md index ed7770b..4a5f6c1 100644 --- a/examples/README.md +++ b/examples/README.md @@ -5,7 +5,7 @@ In this directory, you can find a selection of notebooks demonstrating some simp - [`generative_modelling.ipynb`](https://github.com/CQCL/qujax/blob/main/examples/generative_modelling.ipynb) - uses a parameterised quantum circuit as a generative model for a real life dataset. Trains via stochastic gradient Langevin dynamics on the maximum mean discrepancy between statetensor and dataset. - [`heisenberg_vqe.ipynb`](https://github.com/CQCL/qujax/blob/main/examples/heisenberg_vqe.ipynb) - an implementation of the variational quantum eigensolver to find the ground state of a quantum Hamiltonian. - [`maxcut_vqe.ipynb`](https://github.com/CQCL/qujax/blob/main/examples/maxcut_vqe.ipynb) - an implementation of the variational quantum eigensolver to solve a maxcut problem. Trains with Adam via [`optax`](https://github.com/deepmind/optax) and uses more realistic stochastic parameter shift gradients. -- [`qaoa.ipynb`](https://github.com/CQCL/qujax/blob/main/examples/variational_inference.ipynb) - uses a parameterised quantum circuit as a variational distribution to fit to a target probability mass function. Uses Adam via [`optax`](https://github.com/deepmind/optax) to minimise the KL divergence between circuit and target distributions. -- [`variational_inference.ipynb`](https://github.com/CQCL/qujax/blob/main/examples/variational_inference.ipynb) - uses a problem inspired QAOA ansatz to find the ground state of quantum Hamiltonian. Demonstrates how to encode more sophisticated parameters that control multiple gates. +- [`qaoa.ipynb`](https://github.com/CQCL/qujax/blob/main/examples/qaoa.ipynb) - uses a problem inspired QAOA ansatz to find the ground state of a quantum Hamiltonian. Demonstrates how to encode more sophisticated parameters that control multiple gates. +- [`variational_inference.ipynb`](https://github.com/CQCL/qujax/blob/main/examples/variational_inference.ipynb) - uses a parameterised quantum circuit as a variational distribution to fit to a target probability mass function. Uses Adam via [`optax`](https://github.com/deepmind/optax) to minimise the KL divergence between circuit and target distributions. The Heisenberg notebook with a `tk_to_qujax` implementation can be found in the [`pytket`](https://github.com/CQCL/pytket) repository at [`pytket-qujax_heisenberg_vqe.ipynb`](https://github.com/CQCL/pytket/blob/main/examples/pytket-qujax_heisenberg_vqe.ipynb). From dc0f0079767e5d2c7de1bbd5cd3ee9f2bf8c2191 Mon Sep 17 00:00:00 2001 From: Sam Duffield Date: Tue, 13 Sep 2022 14:01:38 +0100 Subject: [PATCH 3/3] version bump --- qujax/version.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/qujax/version.py b/qujax/version.py index 44b1806..407b8a2 100644 --- a/qujax/version.py +++ b/qujax/version.py @@ -1 +1 @@ -__version__ = '0.2.6' +__version__ = '0.2.7'