docs/source/whitepaper/6-3-vmap.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "43778e92",
   "metadata": {},
   "source": [
    "# Utilizing vmap in quantum circuit simulations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6326b34d",
   "metadata": {},
   "source": [
    "## Overview\n",
    "\n",
    "We introduce vmap, the advanced feature of modern machine learning library, to quantum circuit simulations.\n",
    "By vmapping different ingredients of quantum circuit simulaion, we can implement variational quantum algorithms with high efficiency.\n",
    "\n",
    "It is worth noting that in the following use cases, vmap is supported together with jit and AD which renders highly efficient differentiable simulation.\n",
    "\n",
    "The ingredients support vmap paradigm are show in the following figure.\n",
    "![vmap ingredients](../statics/vmap_ingredients.png)\n",
    "\n",
    "We have two different types of APIs for vmap, the first one is ``vmap`` while the second one is ``vectorized_value_and_grad``, aka, ``vvag``. The latter one can also return the gradient information over a batch of different circuit."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a14001c5",
   "metadata": {},
   "source": [
    "## Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "5398ff95",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0.220402\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import tensorcircuit as tc\n",
    "\n",
    "tc.set_backend(\"tensorflow\")\n",
    "print(tc.__version__)\n",
    "\n",
    "nwires = 5\n",
    "nlayers = 2\n",
    "batch = 6"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65d543db",
   "metadata": {},
   "source": [
    "## vmap the input states\n",
    "\n",
    "Use case: batch processing of input states in quantum machine learning task.\n",
    "\n",
    "For applications of batched input state processing, please see [MNIST QML tutorial](../tutorials/mnist_qml.ipynb)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ae562cb",
   "metadata": {},
   "source": [
    "### Minimal example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ba8de9bd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<tf.Tensor: shape=(6,), dtype=float32, numpy=\n",
       " array([10.88678, 10.88678, 10.88678, 10.88678, 10.88678, 10.88678],\n",
       "       dtype=float32)>,\n",
       " <tf.Tensor: shape=(4, 5), dtype=complex64, numpy=\n",
       " array([[ 0.0000000e+00+1.3064140e+02j, -1.1444092e-05+1.3064142e+02j,\n",
       "          0.0000000e+00+1.3064140e+02j,  0.0000000e+00+1.3064139e+02j,\n",
       "          0.0000000e+00+0.0000000e+00j],\n",
       "        [-1.9073486e-06-5.1765751e-06j, -5.1105431e+01-5.7347143e-07j,\n",
       "         -8.1339760e+01-6.6063179e+01j, -5.1105446e+01+3.3477118e-06j,\n",
       "         -7.6293945e-06+1.5500746e-07j],\n",
       "        [ 0.0000000e+00+8.4607742e+01j, -1.3292285e+02+1.1209973e+02j,\n",
       "         -1.3292284e+02+1.1209971e+02j,  1.5258789e-05+8.4607750e+01j,\n",
       "          0.0000000e+00+0.0000000e+00j],\n",
       "        [ 1.9073486e-06+5.9908474e+01j, -1.5258789e-05-1.9285599e+01j,\n",
       "         -8.1339752e+01+3.8049275e-06j,  3.8146973e-06-1.9285591e+01j,\n",
       "         -9.5367432e-06+5.9908482e+01j]], dtype=complex64)>)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def f(inputs, weights):\n",
    "    c = tc.Circuit(nwires, inputs=inputs)\n",
    "    c = tc.templates.blocks.example_block(c, weights, nlayers=nlayers)\n",
    "    loss = c.expectation([tc.gates.z(), [2]])\n",
    "    loss = tc.backend.real(loss)\n",
    "    return loss\n",
    "\n",
    "\n",
    "f_vg = tc.backend.jit(tc.backend.vvag(f, argnums=1, vectorized_argnums=0))\n",
    "f_vg(tc.backend.ones([batch, 2**nwires]), tc.backend.ones([2 * nlayers, nwires]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53f11707",
   "metadata": {},
   "source": [
    "## vmap the circuit weights\n",
    "\n",
    "Use case: batched VQE, where different random initialization parameters are optimized simutaneously.\n",
    "\n",
    "For application on batched VQE, please refer [TFIM VQE tutorial](../tutorials/tfim_vqe.ipynb)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "09f90b5e",
   "metadata": {},
   "source": [
    "### Minimal example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8c1dc0f8",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<tf.Tensor: shape=(6,), dtype=float32, numpy=\n",
       " array([-2.9802322e-08, -2.9802322e-08, -2.9802322e-08, -2.9802322e-08,\n",
       "        -2.9802322e-08, -2.9802322e-08], dtype=float32)>,\n",
       " <tf.Tensor: shape=(6, 4, 5), dtype=complex64, numpy=\n",
       " array([[[ 1.1614500e-08+2.1480869e-08j, -9.2439478e-10-1.8808342e-08j,\n",
       "           2.6397275e-08-8.0511313e-09j,  2.7981415e-08-1.6564460e-08j,\n",
       "           0.0000000e+00+0.0000000e+00j],\n",
       "         [ 4.1470027e-09-1.9918247e-08j, -7.7494953e-09+9.5806874e-09j,\n",
       "           0.0000000e+00-1.3076999e-08j,  1.2109957e-09+3.2571617e-08j,\n",
       "          -1.0110498e-08+1.6951747e-08j],\n",
       "         [ 1.1614500e-08-1.0295013e-08j, -1.6102263e-08+2.5077789e-08j,\n",
       "          -3.2204525e-08+5.0155577e-08j,  1.8346144e-08-3.5633683e-09j,\n",
       "           0.0000000e+00+0.0000000e+00j],\n",
       "         [-7.1439974e-09-3.3070933e-09j,  0.0000000e+00+6.8412485e-09j,\n",
       "           1.4287995e-08-9.5050003e-09j, -7.1439974e-09-6.5384995e-09j,\n",
       "          -2.3792996e-08-7.8779987e-09j]],\n",
       " \n",
       "        [[ 1.1614500e-08+2.1480869e-08j, -9.2439478e-10-1.8808342e-08j,\n",
       "           2.6397275e-08-8.0511313e-09j,  2.7981415e-08-1.6564460e-08j,\n",
       "           0.0000000e+00+0.0000000e+00j],\n",
       "         [ 4.1470027e-09-1.9918247e-08j, -7.7494953e-09+9.5806874e-09j,\n",
       "           0.0000000e+00-1.3076999e-08j,  1.2109957e-09+3.2571617e-08j,\n",
       "          -1.0110498e-08+1.6951747e-08j],\n",
       "         [ 1.1614500e-08-1.0295013e-08j, -1.6102263e-08+2.5077789e-08j,\n",
       "          -3.2204525e-08+5.0155577e-08j,  1.8346144e-08-3.5633683e-09j,\n",
       "           0.0000000e+00+0.0000000e+00j],\n",
       "         [-7.1439974e-09-3.3070933e-09j,  0.0000000e+00+6.8412485e-09j,\n",
       "           1.4287995e-08-9.5050003e-09j, -7.1439974e-09-6.5384995e-09j,\n",
       "          -2.3792996e-08-7.8779987e-09j]],\n",
       " \n",
       "        [[ 1.1614500e-08+2.1480869e-08j, -9.2439478e-10-1.8808342e-08j,\n",
       "           2.6397275e-08-8.0511313e-09j,  2.7981415e-08-1.6564460e-08j,\n",
       "           0.0000000e+00+0.0000000e+00j],\n",
       "         [ 4.1470027e-09-1.9918247e-08j, -7.7494953e-09+9.5806874e-09j,\n",
       "           0.0000000e+00-1.3076999e-08j,  1.2109957e-09+3.2571617e-08j,\n",
       "          -1.0110498e-08+1.6951747e-08j],\n",
       "         [ 1.1614500e-08-1.0295013e-08j, -1.6102263e-08+2.5077789e-08j,\n",
       "          -3.2204525e-08+5.0155577e-08j,  1.8346144e-08-3.5633683e-09j,\n",
       "           0.0000000e+00+0.0000000e+00j],\n",
       "         [-7.1439974e-09-3.3070933e-09j,  0.0000000e+00+6.8412485e-09j,\n",
       "           1.4287995e-08-9.5050003e-09j, -7.1439974e-09-6.5384995e-09j,\n",
       "          -2.3792996e-08-7.8779987e-09j]],\n",
       " \n",
       "        [[ 1.1614500e-08+2.1480869e-08j, -9.2439478e-10-1.8808342e-08j,\n",
       "           2.6397275e-08-8.0511313e-09j,  2.7981415e-08-1.6564460e-08j,\n",
       "           0.0000000e+00+0.0000000e+00j],\n",
       "         [ 4.1470027e-09-1.9918247e-08j, -7.7494953e-09+9.5806874e-09j,\n",
       "           0.0000000e+00-1.3076999e-08j,  1.2109957e-09+3.2571617e-08j,\n",
       "          -1.0110498e-08+1.6951747e-08j],\n",
       "         [ 1.1614500e-08-1.0295013e-08j, -1.6102263e-08+2.5077789e-08j,\n",
       "          -3.2204525e-08+5.0155577e-08j,  1.8346144e-08-3.5633683e-09j,\n",
       "           0.0000000e+00+0.0000000e+00j],\n",
       "         [-7.1439974e-09-3.3070933e-09j,  0.0000000e+00+6.8412485e-09j,\n",
       "           1.4287995e-08-9.5050003e-09j, -7.1439974e-09-6.5384995e-09j,\n",
       "          -2.3792996e-08-7.8779987e-09j]],\n",
       " \n",
       "        [[ 1.1614500e-08+2.1480869e-08j, -9.2439478e-10-1.8808342e-08j,\n",
       "           2.6397275e-08-8.0511313e-09j,  2.7981415e-08-1.6564460e-08j,\n",
       "           0.0000000e+00+0.0000000e+00j],\n",
       "         [ 4.1470027e-09-1.9918247e-08j, -7.7494953e-09+9.5806874e-09j,\n",
       "           0.0000000e+00-1.3076999e-08j,  1.2109957e-09+3.2571617e-08j,\n",
       "          -1.0110498e-08+1.6951747e-08j],\n",
       "         [ 1.1614500e-08-1.0295013e-08j, -1.6102263e-08+2.5077789e-08j,\n",
       "          -3.2204525e-08+5.0155577e-08j,  1.8346144e-08-3.5633683e-09j,\n",
       "           0.0000000e+00+0.0000000e+00j],\n",
       "         [-7.1439974e-09-3.3070933e-09j,  0.0000000e+00+6.8412485e-09j,\n",
       "           1.4287995e-08-9.5050003e-09j, -7.1439974e-09-6.5384995e-09j,\n",
       "          -2.3792996e-08-7.8779987e-09j]],\n",
       " \n",
       "        [[ 1.1614500e-08+2.1480869e-08j, -9.2439478e-10-1.8808342e-08j,\n",
       "           2.6397275e-08-8.0511313e-09j,  2.7981415e-08-1.6564460e-08j,\n",
       "           0.0000000e+00+0.0000000e+00j],\n",
       "         [ 4.1470027e-09-1.9918247e-08j, -7.7494953e-09+9.5806874e-09j,\n",
       "           0.0000000e+00-1.3076999e-08j,  1.2109957e-09+3.2571617e-08j,\n",
       "          -1.0110498e-08+1.6951747e-08j],\n",
       "         [ 1.1614500e-08-1.0295013e-08j, -1.6102263e-08+2.5077789e-08j,\n",
       "          -3.2204525e-08+5.0155577e-08j,  1.8346144e-08-3.5633683e-09j,\n",
       "           0.0000000e+00+0.0000000e+00j],\n",
       "         [-7.1439974e-09-3.3070933e-09j,  0.0000000e+00+6.8412485e-09j,\n",
       "           1.4287995e-08-9.5050003e-09j, -7.1439974e-09-6.5384995e-09j,\n",
       "          -2.3792996e-08-7.8779987e-09j]]], dtype=complex64)>)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def f(weights):\n",
    "    c = tc.Circuit(nwires)\n",
    "    c = tc.templates.blocks.example_block(c, weights, nlayers=nlayers)\n",
    "    loss = c.expectation([tc.gates.z(), [2]])\n",
    "    loss = tc.backend.real(loss)\n",
    "    return loss\n",
    "\n",
    "\n",
    "f_vg = tc.backend.jit(tc.backend.vvag(f, argnums=0, vectorized_argnums=0))\n",
    "f_vg(tc.backend.ones([batch, 2 * nlayers, nwires]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc964c68",
   "metadata": {},
   "source": [
    "## vmap the quantum noise\n",
    "\n",
    "Use case: parallel Monte Carlo noise simulation.\n",
    "\n",
    "For applications that combines vmapped Monte Carlo noise simulation and quantum machine learning task, please see [noisy QML script](../../../examples/noisy_qml.py)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d4640f6",
   "metadata": {},
   "source": [
    "### Minimal example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c375d869",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<tf.Tensor: shape=(6,), dtype=float32, numpy=\n",
       " array([ 0.34873545, -0.34873542,  0.34873548, -0.34873542, -0.34873542,\n",
       "         0.34873545], dtype=float32)>,\n",
       " <tf.Tensor: shape=(4, 5), dtype=complex64, numpy=\n",
       " array([[ 4.1566270e-08-2.7387195e-09j, -2.2305253e-08+5.6167501e-08j,\n",
       "          3.8269725e-09-2.9772337e-08j,  1.2039662e-08+2.3984430e-08j,\n",
       "          0.0000000e+00+0.0000000e+00j],\n",
       "        [-1.2210242e-08-2.1714307e-08j,  6.1271228e-09-7.0552990e-09j,\n",
       "          0.0000000e+00+0.0000000e+00j,  4.6692023e-08-2.2532541e-08j,\n",
       "          3.2784932e-08-6.2270239e-08j],\n",
       "        [-4.8202367e-09-4.7757482e-08j,  0.0000000e+00+0.0000000e+00j,\n",
       "          6.4294035e-08+7.3475164e-08j, -4.8914863e-08+4.0707999e-08j,\n",
       "          0.0000000e+00+0.0000000e+00j],\n",
       "        [-1.4287995e-08+7.7190005e-09j,  0.0000000e+00+0.0000000e+00j,\n",
       "          2.6153998e-08+7.1439974e-09j, -1.3076999e-08+1.8434998e-08j,\n",
       "         -1.2109957e-09+2.3747528e-08j]], dtype=complex64)>)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def f(weights, status):\n",
    "    c = tc.Circuit(nwires)\n",
    "    c = tc.templates.blocks.example_block(c, weights, nlayers=nlayers)\n",
    "    for i in range(nwires):\n",
    "        c.depolarizing(i, px=0.2, py=0.2, pz=0.2, status=status[i])\n",
    "    loss = c.expectation([tc.gates.x(), [2]])\n",
    "    loss = tc.backend.real(loss)\n",
    "    return loss\n",
    "\n",
    "\n",
    "f_vg = tc.backend.jit(tc.backend.vvag(f, argnums=0, vectorized_argnums=1))\n",
    "\n",
    "\n",
    "def g(weights):\n",
    "    status = tc.backend.implicit_randu(shape=[batch, nwires])\n",
    "    return f_vg(weights, status)\n",
    "\n",
    "\n",
    "g(tc.backend.ones([2 * nlayers, nwires]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f2f659f9",
   "metadata": {},
   "source": [
    "## vmap the circuit structure\n",
    "\n",
    "Use case: differentiable quantum architecture search (DQAS). \n",
    "\n",
    "For more detail on DQAS application, see [DQAS tutorial](../tutorials/dqas.ipynb)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "445e5538",
   "metadata": {},
   "source": [
    "### Minimal example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3d821d37",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<tf.Tensor: shape=(6,), dtype=float32, numpy=\n",
       " array([2.4917054e+08, 2.4917054e+08, 2.4917054e+08, 2.4917054e+08,\n",
       "        2.4917054e+08, 2.4917054e+08], dtype=float32)>,\n",
       " <tf.Tensor: shape=(5, 2, 3), dtype=complex64, numpy=\n",
       " array([[[-4.8252989e+08+2.3603376e+07j, -6.4132224e+08+1.1064736e+08j,\n",
       "          -4.5701562e+08-7.4987272e+07j],\n",
       "         [-5.4175347e+08+5.2096408e+07j, -5.5254317e+08-4.6495180e+07j,\n",
       "          -4.5219101e+08-5.6013205e+06j]],\n",
       " \n",
       "        [[-7.1430163e+08-1.2090212e+08j, -6.2410163e+08-4.1363908e+07j,\n",
       "          -3.9189485e+08+4.0016840e+06j],\n",
       "         [-5.8365677e+08+9.4236816e+07j, -5.7693280e+08-9.7727496e+07j,\n",
       "          -3.9540646e+08+3.4906362e+06j]],\n",
       " \n",
       "        [[-5.9637555e+08+8.9477632e+07j, -7.6615610e+08+1.1949610e+08j,\n",
       "          -3.8039136e+08-4.7556400e+07j],\n",
       "         [-1.1637092e+09-4.0144461e+08j, -1.1735478e+09+4.5104198e+08j,\n",
       "          -1.5947418e+08+1.5322706e+07j]],\n",
       " \n",
       "        [[-7.1430170e+08-1.2090210e+08j, -6.2410170e+08-4.1363864e+07j,\n",
       "          -3.9189485e+08+4.0016840e+06j],\n",
       "         [-5.8365658e+08+9.4236840e+07j, -5.7693261e+08-9.7727496e+07j,\n",
       "          -3.9540637e+08+3.4906552e+06j]],\n",
       " \n",
       "        [[-4.8253002e+08+2.3603400e+07j, -6.4132237e+08+1.1064734e+08j,\n",
       "          -4.5701565e+08-7.4987248e+07j],\n",
       "         [-5.4175334e+08+5.2096460e+07j, -5.5254304e+08-4.6495116e+07j,\n",
       "          -4.5219091e+08-5.6013120e+06j]]], dtype=complex64)>)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "eye = tc.gates.i().tensor\n",
    "x = tc.gates.x().tensor\n",
    "y = tc.gates.y().tensor\n",
    "z = tc.gates.z().tensor\n",
    "\n",
    "\n",
    "def f(params, structures):\n",
    "    c = tc.Circuit(nwires)\n",
    "    for i in range(nwires):\n",
    "        c.H(i)\n",
    "    for j in range(nlayers):\n",
    "        for i in range(nwires - 1):\n",
    "            c.cz(i, i + 1)\n",
    "        for i in range(nwires):\n",
    "            c.unitary(\n",
    "                i,\n",
    "                unitary=structures[i, j, 0]\n",
    "                * (\n",
    "                    tc.backend.cos(params[i, j, 0]) * eye\n",
    "                    + tc.backend.sin(params[i, j, 0]) * x\n",
    "                )\n",
    "                + structures[i, j, 1]\n",
    "                * (\n",
    "                    tc.backend.cos(params[i, j, 1]) * eye\n",
    "                    + tc.backend.sin(params[i, j, 1]) * y\n",
    "                )\n",
    "                + structures[i, j, 2]\n",
    "                * (\n",
    "                    tc.backend.cos(params[i, j, 2]) * eye\n",
    "                    + tc.backend.sin(params[i, j, 2]) * z\n",
    "                ),\n",
    "            )\n",
    "    loss = c.expectation([tc.gates.z(), (2,)])\n",
    "    return tc.backend.real(loss)\n",
    "\n",
    "\n",
    "structures = tc.backend.ones([batch, nwires, nlayers, 3])\n",
    "params = tc.backend.ones([nwires, nlayers, 3])\n",
    "f_vg = tc.backend.jit(tc.backend.vvag(f, argnums=0, vectorized_argnums=1))\n",
    "f_vg(params, structures)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "313d65f4",
   "metadata": {},
   "source": [
    "## vmap the circuit measurements\n",
    "\n",
    "Use case: accelerating evaluation of Pauli string sum by parallel the parameterized measurment.\n",
    "\n",
    "For applications on evaluation of parameterized measurements via vmap on large-scale systems, see [large-scale vqe example script](../../../examples/vqe_extra.py)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b307196",
   "metadata": {},
   "source": [
    "### Minimal example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c43c8aa1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(<tf.Tensor: shape=(5,), dtype=float32, numpy=\n",
       " array([-0.3118263 ,  0.00371493,  0.3487355 ,  0.00371514, -0.31182614],\n",
       "       dtype=float32)>,\n",
       " <tf.Tensor: shape=(4, 5), dtype=complex64, numpy=\n",
       " array([[ 1.6707865e+00-0.40178323j, -1.1992662e+00-0.23834792j,\n",
       "         -1.1992660e+00-0.2383478j ,  1.6707866e+00-0.40178335j,\n",
       "          0.0000000e+00+0.j        ],\n",
       "        [-1.8267021e-01-0.6483071j ,  7.7729575e-02+0.58401704j,\n",
       "         -1.0082662e-01-0.52953976j,  7.7729806e-02+0.58401704j,\n",
       "         -1.8267024e-01-0.6483072j ],\n",
       "        [ 1.6707866e+00+0.19420199j, -1.1992658e+00+0.50487465j,\n",
       "         -1.1992657e+00+0.504875j  ,  1.6707867e+00+0.19420168j,\n",
       "          0.0000000e+00+0.j        ],\n",
       "        [ 7.4505806e-09+0.99540246j,  1.4901161e-08+0.7925009j ,\n",
       "         -7.4505806e-09+0.71156096j, -7.4505806e-09+0.7925008j ,\n",
       "          2.2351742e-08+0.9954027j ]], dtype=complex64)>)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def f(params, structures):\n",
    "    c = tc.Circuit(nwires)\n",
    "    c = tc.templates.blocks.example_block(c, params, nlayers=nlayers)\n",
    "    loss = tc.templates.measurements.parameterized_measurements(\n",
    "        c, structures, onehot=True\n",
    "    )\n",
    "    return loss\n",
    "\n",
    "\n",
    "# measure X0 to X3\n",
    "structures = tc.backend.eye(nwires)\n",
    "f_vvag = tc.backend.jit(tc.backend.vvag(f, vectorized_argnums=1, argnums=0))\n",
    "f_vvag(tc.backend.ones([2 * nlayers, nwires]), structures)"
   ]
  }
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