{ "cells": [ { "cell_type": "markdown", "id": "b351908d-c15d-4799-9de9-84ca0c761033", "metadata": {}, "source": [ "Extended VQE\n", "=============\n", "\n", "In [Tutorial 1](https://docs.quantinuum.com/inquanto/tutorials/InQ_tut_vqe_1.html), we considered a canonical VQE calculation at a single geometry with no resource optimization. However, in general, this will only be the first step in an analysis of the quantum algorithm. We may wish to expand on this analysis by considering more molecular geometries or systems -- for example, looking at the energetics of bond dissociation. We also may wish to compare optimization methods in order to assess their effectiveness at reducing the overall cost with regards to quantum computational resources.\n", "\n", "In this tutorial, we will look at how to achieve these goals using InQuanto. We start by examining bond dissociation in molecular hydrogen using a canonical VQE approach. Then, we will look at a slightly larger system -- the bending and stretching of water. As this is a larger system, we will have to introduce optimizations to enable the simulations to run on a standard laptop. Specifically, we introduce how to reduce the active space (and thus the number of qubits in the quantum computation) by freezing orbitals using the [inquanto-pyscf](https://docs.quantinuum.com/inquanto/extensions/inquanto-pyscf.html) driver. Finally, we look at one optimization strategy in InQuanto - Ansatz parameter reduction by point group symmetry. " ] }, { "cell_type": "code", "execution_count": null, "id": "1c5a4ee1-a589-41ef-9191-861402c35d18", "metadata": {}, "outputs": [], "source": [ "from pytket.extensions.qiskit import AerStateBackend\n", "from inquanto.express import run_vqe\n", "from inquanto.minimizers import MinimizerScipy\n", "from inquanto.ansatzes import FermionSpaceAnsatzUCCSD\n", "from inquanto.mappings import QubitMappingJordanWigner\n", "from inquanto.extensions.pyscf import ChemistryDriverPySCFMolecularRHF\n", "import datetime\n", "import matplotlib.pyplot as plt\n", "import numpy as np" ] }, { "attachments": {}, "cell_type": "markdown", "id": "04c3d306-a971-4e17-b336-dc2b2a6d203e", "metadata": {}, "source": [ "H2 Bond Stretching\n", "------------------\n", "\n", " After imports, we start by examining bond dissociation in molecular hydrogen in order to present a general workflow." ] }, { "cell_type": "code", "execution_count": null, "id": "75506747-d937-46d4-bbd7-60dcdaee4e2b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "# TIMER BLOCK-0 BEGINS AT 2025-06-12 15:14:32.611265\n", "# TIMER BLOCK-0 ENDS - DURATION (s): 0.0935207 [0:00:00.093521]\n", "(-1.137274405529437, np.float64(-1.1167061372361053))\n" ] } ], "source": [ "def hydrogen_vqe_energy(bond_length):\n", " basis = 'STO-3G'\n", " geometry = [[\"H\", [0, 0, 0]], [\"H\", [0, 0, bond_length]]]\n", " charge = 0\n", " \n", " driver = ChemistryDriverPySCFMolecularRHF(basis=basis, geometry=geometry, charge=charge)\n", " fermionic_hamiltonian, fock_space, fock_state = driver.get_system()\n", " jw = QubitMappingJordanWigner\n", " qubit_hamiltonian = jw.operator_map(fermionic_hamiltonian)\n", " ansatz = FermionSpaceAnsatzUCCSD(fock_space, fock_state, jw)\n", " backend = AerStateBackend()\n", " minimizer = MinimizerScipy(method=\"L-BFGS-B\", disp=False)\n", " vqe = run_vqe(ansatz, qubit_hamiltonian, backend=backend, with_gradient=True, minimizer=minimizer)\n", "\n", " ground_state_energy = vqe.generate_report()[\"final_value\"]\n", " hartree_fock_energy = driver.mf_energy\n", " return ground_state_energy, hartree_fock_energy\n", "\n", "print(hydrogen_vqe_energy(0.741))" ] }, { "cell_type": "markdown", "id": "f4681779-b178-4340-be67-f5951cf6253a", "metadata": {}, "source": [ "The code here does all that is necessary to generate a ground state energy using canonical VQE for the hydrogen molecule, as in [Tutorial 1](https://docs.quantinuum.com/inquanto/tutorials/InQ_tut_vqe_1.html). Here, we have wrapped it in a function to allow us to easily view the change with bond length:" ] }, { "cell_type": "code", "execution_count": null, "id": "70a3fe54-b905-4032-b65e-628a1f670118", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "# TIMER BLOCK-1 BEGINS AT 2025-06-12 15:14:32.729111\n", "# TIMER BLOCK-1 ENDS - DURATION (s): 0.1384337 [0:00:00.138434]\n", "# TIMER BLOCK-2 BEGINS AT 2025-06-12 15:14:32.885048\n", "# TIMER BLOCK-2 ENDS - DURATION (s): 0.0897306 [0:00:00.089731]\n", "# TIMER BLOCK-3 BEGINS AT 2025-06-12 15:14:32.992863\n", "# TIMER BLOCK-3 ENDS - DURATION (s): 0.0905248 [0:00:00.090525]\n", "# TIMER BLOCK-4 BEGINS AT 2025-06-12 15:14:33.101135\n", "# TIMER BLOCK-4 ENDS - DURATION (s): 0.0902723 [0:00:00.090272]\n", "# TIMER BLOCK-5 BEGINS AT 2025-06-12 15:14:33.208650\n", "# TIMER BLOCK-5 ENDS - DURATION (s): 0.0883024 [0:00:00.088302]\n", "# TIMER BLOCK-6 BEGINS AT 2025-06-12 15:14:33.314443\n", "# TIMER BLOCK-6 ENDS - DURATION (s): 0.0873017 [0:00:00.087302]\n", "# TIMER BLOCK-7 BEGINS AT 2025-06-12 15:14:33.419324\n", "# TIMER BLOCK-7 ENDS - DURATION (s): 0.0874910 [0:00:00.087491]\n", "# TIMER BLOCK-8 BEGINS AT 2025-06-12 15:14:33.524386\n", "# TIMER BLOCK-8 ENDS - DURATION (s): 0.0893634 [0:00:00.089363]\n", "# TIMER BLOCK-9 BEGINS AT 2025-06-12 15:14:33.631203\n", "# TIMER BLOCK-9 ENDS - DURATION (s): 0.0867588 [0:00:00.086759]\n", "# TIMER BLOCK-10 BEGINS AT 2025-06-12 15:14:33.735360\n", "# TIMER BLOCK-10 ENDS - DURATION (s): 0.0868349 [0:00:00.086835]\n", "# TIMER BLOCK-11 BEGINS AT 2025-06-12 15:14:33.839784\n", "# TIMER BLOCK-11 ENDS - DURATION (s): 0.0908607 [0:00:00.090861]\n", "# TIMER BLOCK-12 BEGINS AT 2025-06-12 15:14:33.947699\n", "# TIMER BLOCK-12 ENDS - DURATION (s): 0.0883470 [0:00:00.088347]\n", "# TIMER BLOCK-13 BEGINS AT 2025-06-12 15:14:34.053480\n", "# TIMER BLOCK-13 ENDS - DURATION (s): 0.0875535 [0:00:00.087553]\n", "# TIMER BLOCK-14 BEGINS AT 2025-06-12 15:14:34.158521\n", "# TIMER BLOCK-14 ENDS - DURATION (s): 0.0860777 [0:00:00.086078]\n", "# TIMER BLOCK-15 BEGINS AT 2025-06-12 15:14:34.261786\n", "# TIMER BLOCK-15 ENDS - DURATION (s): 0.0871267 [0:00:00.087127]\n", "# TIMER BLOCK-16 BEGINS AT 2025-06-12 15:14:34.366618\n", "# TIMER BLOCK-16 ENDS - DURATION (s): 0.0868856 [0:00:00.086886]\n", "# TIMER BLOCK-17 BEGINS AT 2025-06-12 15:14:34.470820\n", "# TIMER BLOCK-17 ENDS - DURATION (s): 0.0852530 [0:00:00.085253]\n", "# TIMER BLOCK-18 BEGINS AT 2025-06-12 15:14:34.573670\n", "# TIMER BLOCK-18 ENDS - DURATION (s): 0.0852002 [0:00:00.085200]\n", "# TIMER BLOCK-19 BEGINS AT 2025-06-12 15:14:34.677044\n", "# TIMER BLOCK-19 ENDS - DURATION (s): 0.0854226 [0:00:00.085423]\n", "# TIMER BLOCK-20 BEGINS AT 2025-06-12 15:14:34.780018\n", "# TIMER BLOCK-20 ENDS - DURATION (s): 0.1520678 [0:00:00.152068]\n", "[(-0.9141497046270839, np.float64(-0.9043613941635402)), (-1.03964419336842, np.float64(-1.0278952240485921)), (-1.1027234512173365, np.float64(-1.0885821110334761)), (-1.1303984654811365, np.float64(-1.1133931546411708)), (-1.1373027360323482, np.float64(-1.1169158055488677)), (-1.1320031440770353, np.float64(-1.1076586023375483)), (-1.1196476526566386, np.float64(-1.0906923776851996)), (-1.1033573201316114, np.float64(-1.069043221449619)), (-1.0850885605499434, np.float64(-1.0445649211858916)), (-1.0661536707290793, np.float64(-1.0184750668009022)), (-1.047492324194346, np.float64(-0.9916426659510074)), (-1.0297900705318137, np.float64(-0.9647203151980037)), (-1.0135255910407293, np.float64(-0.9382014307919533)), (-0.9989959202496173, np.float64(-0.9124510069368064)), (-0.9863403143934907, np.float64(-0.8877296363816175)), (-0.9755678355211708, np.float64(-0.8642149983652554)), (-0.9665878877681982, np.float64(-0.8420201240601861)), (-0.9592413973101772, np.float64(-0.8212077601664914)), (-0.9533300339756425, np.float64(-0.8018012103709649)), (-0.9486411121756371, np.float64(-0.7837926542773532))]\n" ] } ], "source": [ "h2_bond_lengths = np.linspace(0.4,2.0,20)\n", "h2_results = [hydrogen_vqe_energy(x) for x in h2_bond_lengths]\n", "print(h2_results)" ] }, { "attachments": {}, "cell_type": "markdown", "id": "a03b0cb5-b554-40a7-8298-549df551f904", "metadata": {}, "source": [ "We have successfully generated a potential energy curve for the dissociation of the H2 molecule using VQE and, as a reference, Hartree-Fock. We can now separate the VQE and HF results and plot them:" ] }, { "cell_type": "code", "execution_count": null, "id": "0d2f6d02-3833-46d8-a21b-5af58a251d15", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": null, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "h2_vqe_results,h2_hf_results = zip(*h2_results)\n", "plt.plot(h2_bond_lengths,h2_vqe_results,label='VQE')\n", "plt.plot(h2_bond_lengths,h2_hf_results,label='HF')\n", "plt.xlabel('H-H Bond Length/Å')\n", "plt.ylabel('Ground state energy/Ha')\n", "plt.legend()" ] }, { "attachments": {}, "cell_type": "markdown", "id": "40c81434-ef36-45f7-a924-32a5f0d8ea53", "metadata": {}, "source": [ "Here we can see the improvement obtained by using UCCSD VQE -- indeed, this system is sufficiently low in number of spin-orbitals that UCCSD is exact (i.e. FCI-level). On the other hand, we can also observe the increasing inaccuracy of (restricted) Hartree-Fock at higher bond lengths." ] }, { "attachments": {}, "cell_type": "markdown", "id": "2f882bce-922b-4817-8967-40a2ecb3d37c", "metadata": {}, "source": [ "H2O Bending - active space reduction\n", "-------------------------------------\n", "\n", "H2O in an STO-3G basis is a 14 spin-orbital (and thus 14 qubit for conventional qubit mappings) system. This is within the capacity of a classical computer to simulate, but such a simulation may perhaps require more resources than is practical for this tutorial. We can reduce the active spin-orbital space by freezing orbitals. While our purpose here is to demonstrate, in a real experiment it may be necessary to freeze orbitals in order to reduce the (exponentially growing) resources to a level that is actually implementable. In InQuanto, orbital freezing is performed by passing the `frozen` parameter to the driver:\n" ] }, { "cell_type": "code", "execution_count": null, "id": "8f8d04c7-7a92-4de6-ac64-11d9ed1fed68", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "# TIMER BLOCK-21 BEGINS AT 2025-06-12 15:14:35.203567\n", "# TIMER BLOCK-21 ENDS - DURATION (s): 16.1498821 [0:00:16.149882]\n", "(-75.01966834467413, np.float64(-74.96466253913087))\n" ] } ], "source": [ "def water_bending_vqe_energy(bond_angle):\n", " \n", " x_h2 = np.sin(bond_angle / 360 * np.pi)\n", " x_h1 = -x_h2\n", " y_h1 = np.cos(bond_angle / 360 * np.pi)\n", " y_h2 = y_h1\n", " \n", " geometry = [['H', [x_h1, y_h1, 0.]], ['O', [0., 0., 0.]], ['H', [x_h2, y_h2, 0.]]]\n", " basis = 'STO-3G'\n", " charge = 0\n", " frozen = [0]\n", " \n", " driver = ChemistryDriverPySCFMolecularRHF(basis=basis, geometry=geometry, charge=charge, frozen=frozen)\n", " fermionic_hamiltonian, fock_space, fock_state = driver.get_system()\n", " jw = QubitMappingJordanWigner\n", " qubit_hamiltonian = jw.operator_map(fermionic_hamiltonian)\n", " ansatz = FermionSpaceAnsatzUCCSD(fock_space, fock_state, jw)\n", " backend = AerStateBackend()\n", " minimizer = MinimizerScipy(method=\"L-BFGS-B\", disp=False)\n", " vqe = run_vqe(ansatz, qubit_hamiltonian, backend=backend, with_gradient=True, minimizer=minimizer)\n", "\n", " ground_state_energy = vqe.generate_report()[\"final_value\"]\n", " hartree_fock_energy = driver.mf_energy\n", " return ground_state_energy, hartree_fock_energy\n", "\n", "print(water_bending_vqe_energy(104.5))" ] }, { "attachments": {}, "cell_type": "markdown", "id": "f2a2522d-1e9f-4a1e-83b8-6c04c3c6fa77", "metadata": {}, "source": [ "This block may take up to a minute to run, as the system is a bit bigger than molecular hydrogen. Here, we have asked the driver to freeze the lowest energy spatial orbital (i.e. the core electrons). Note that frozen orbitals are specified as a list of indices of spatial orbitals, not spin-orbitals - so every orbital frozen in this way will save two qubits. Note that for consistency, we have here specified the geometry in Cartesian co-ordinates by explicitly calculating the position of each atom. It is also possible in InQuanto to specify geometries in z-matrix format.\n", "\n", "As before, we have successfully calculated the VQE and HF energy at (roughly) the equilibrium geometry. We can again calculate the effect of changing the bond angle and plot the results (this may take a few minutes to run - reducing the amount of data points generated will speed it up if needed):\n" ] }, { "cell_type": "code", "execution_count": null, "id": "d48351cd-ebf0-4e15-93bb-1394881c30c5", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "# TIMER BLOCK-22 BEGINS AT 2025-06-12 15:14:51.593978\n", "# TIMER BLOCK-22 ENDS - DURATION (s): 16.3598469 [0:00:16.359847]\n", "# TIMER BLOCK-23 BEGINS AT 2025-06-12 15:15:08.144957\n", "# TIMER BLOCK-23 ENDS - DURATION (s): 15.8236252 [0:00:15.823625]\n", "# TIMER BLOCK-24 BEGINS AT 2025-06-12 15:15:24.152356\n", "# TIMER BLOCK-24 ENDS - DURATION (s): 15.5590248 [0:00:15.559025]\n", "# TIMER BLOCK-25 BEGINS AT 2025-06-12 15:15:39.892634\n", "# TIMER BLOCK-25 ENDS - DURATION (s): 15.5031348 [0:00:15.503135]\n", "# TIMER BLOCK-26 BEGINS AT 2025-06-12 15:15:55.577054\n", "# TIMER BLOCK-26 ENDS - DURATION (s): 15.4873130 [0:00:15.487313]\n", "# TIMER BLOCK-27 BEGINS AT 2025-06-12 15:16:11.254418\n", "# TIMER BLOCK-27 ENDS - DURATION (s): 17.3344193 [0:00:17.334419]\n", "# TIMER BLOCK-28 BEGINS AT 2025-06-12 15:16:28.775288\n", "# TIMER BLOCK-28 ENDS - DURATION (s): 17.0493604 [0:00:17.049360]\n", "# TIMER BLOCK-29 BEGINS AT 2025-06-12 15:16:46.007682\n", "# TIMER BLOCK-29 ENDS - DURATION (s): 18.8701448 [0:00:18.870145]\n", "# TIMER BLOCK-30 BEGINS AT 2025-06-12 15:17:05.061662\n", "# TIMER BLOCK-30 ENDS - DURATION (s): 20.2502192 [0:00:20.250219]\n", "# TIMER BLOCK-31 BEGINS AT 2025-06-12 15:17:25.491678\n", "# TIMER BLOCK-31 ENDS - DURATION (s): 12.6648190 [0:00:12.664819]\n" ] } ], "source": [ "h2o_bond_angles = np.linspace(45.,180.,10)\n", "h2o_bending_results = [water_bending_vqe_energy(x) for x in h2o_bond_angles]" ] }, { "cell_type": "code", "execution_count": null, "id": "f4fb8229-4579-4e3e-9fcb-d92f76de4cc1", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": null, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "h2o_angle_vqe_results,h2o_angle_hf_results = zip(*h2o_bending_results)\n", "plt.plot(h2o_bond_angles,h2o_angle_vqe_results,label='VQE')\n", "plt.plot(h2o_bond_angles,h2o_angle_hf_results,label='HF')\n", "plt.xlabel('HOH bond angle /°')\n", "plt.ylabel('Ground state energy/Ha')\n", "plt.legend()" ] }, { "attachments": {}, "cell_type": "markdown", "id": "acfa9464-78ac-4dd2-b5cc-8a3a0f5abb27", "metadata": {}, "source": [ "H2O Stretching - symmetry-allowed excitations\n", "---------------------------------------------\n", "\n", "In larger systems, we may be interested in benchmarking the cost of VQE with various optimization schemes. Choosing optimization schemes is a question of balancing the need for accuracy and resource constraints. Several resource constraints occur when performing quantum algorithms -- for instance, the number of qubits and the circuit length. Similar to space and time in classical computing, certain optimization schemes may reduce cost in one metric while having a detrimental effect on others. Such tradeoff in resources applies to VQE itself; VQE as an algorithm is designed to replace the (extremely) long quantum circuits of the phase estimation algorithm with significantly more but much shorter circuits.\n", "\n", "Many such optimization schemes are available in InQuanto and examples of their use can be found in the examples directory. In this tutorial, we will look at the use of point group symmetry to exclude unphysical symmetry-violating excitations. This is a technique commonly used in quantum chemistry codes on classical computers, and can substantially reduce the number of Ansatz parameters. In turn, the quantum circuit length can be reduced, as is the difficulty of classical optimization (and consequentially the number of individual VQE shots required, and thus the overall runtime). As this technique is simply removing excitations that are unphysical, it is essentially \"free\" with regards to other computational resources.\n", "\n", "First, we modify our VQE routine to incorporate point group symmetry -- this time, in the context of symmetric bond stretching:" ] }, { "cell_type": "code", "execution_count": null, "id": "b137e66c-b72e-46af-a4b7-95f007aadf28", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "# TIMER BLOCK-32 BEGINS AT 2025-06-12 15:17:38.375798\n", "# TIMER BLOCK-32 ENDS - DURATION (s): 9.5187483 [0:00:09.518748]\n", "(-75.01969733754343, np.float64(-74.96468314023912))\n" ] } ], "source": [ "def water_stretching_vqe_energy(bond_length):\n", " \n", " x_h2 = bond_length * np.sin(104.45 / 360 * np.pi)\n", " x_h1 = -x_h2\n", " y_h1 = bond_length * np.cos(104.45 / 360 * np.pi)\n", " y_h2 = y_h1\n", " \n", " geometry = [['H', [x_h1, y_h1, 0.]], ['O', [0., 0., 0.]], ['H', [x_h2, y_h2, 0.]]]\n", " basis = 'STO-3G'\n", " charge = 0\n", " frozen = [0]\n", " \n", " driver = ChemistryDriverPySCFMolecularRHF(basis=basis, geometry=geometry, charge=charge, frozen=frozen,point_group_symmetry=True)\n", " fermionic_hamiltonian, fock_space, fock_state = driver.get_system()\n", " jw = QubitMappingJordanWigner\n", " qubit_hamiltonian = jw.operator_map(fermionic_hamiltonian)\n", " ansatz = FermionSpaceAnsatzUCCSD(fock_space, fock_state, jw)\n", " backend = AerStateBackend()\n", " minimizer = MinimizerScipy(method=\"L-BFGS-B\", disp=False)\n", " vqe = run_vqe(ansatz, qubit_hamiltonian, backend=backend, with_gradient=True, minimizer=minimizer)\n", "\n", " ground_state_energy = vqe.generate_report()[\"final_value\"]\n", " hartree_fock_energy = driver.mf_energy\n", " return ground_state_energy, hartree_fock_energy\n", "print(water_stretching_vqe_energy(1.))" ] }, { "attachments": {}, "cell_type": "markdown", "id": "f60c8bda-f8e2-4d26-8090-486c23659547", "metadata": {}, "source": [ "Here, incorporating point group symmetry is as simple as passing `point_group_symmetry=True` to the driver. Note that the ability to use point group symmetry is reliant on the capacity of the underlying classical quantum chemistry package (in this case, [PySCF](https://pyscf.org/)). We then generate a plot of the change in the ground state energy as the bonds stretch:" ] }, { "cell_type": "code", "execution_count": null, "id": "57f042c7-de9e-4266-a833-9e51668f8484", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "# TIMER BLOCK-33 BEGINS AT 2025-06-12 15:17:48.024091\n", "# TIMER BLOCK-33 ENDS - DURATION (s): 8.2633004 [0:00:08.263300]\n", "# TIMER BLOCK-34 BEGINS AT 2025-06-12 15:17:56.400945\n", "# TIMER BLOCK-34 ENDS - DURATION (s): 8.2046726 [0:00:08.204673]\n", "# TIMER BLOCK-35 BEGINS AT 2025-06-12 15:18:04.717991\n", "# TIMER BLOCK-35 ENDS - DURATION (s): 8.8756690 [0:00:08.875669]\n", "# TIMER BLOCK-36 BEGINS AT 2025-06-12 15:18:13.705589\n", "# TIMER BLOCK-36 ENDS - DURATION (s): 9.1500813 [0:00:09.150081]\n", "# TIMER BLOCK-37 BEGINS AT 2025-06-12 15:18:22.969054\n", "# TIMER BLOCK-37 ENDS - DURATION (s): 9.8433982 [0:00:09.843398]\n", "# TIMER BLOCK-38 BEGINS AT 2025-06-12 15:18:32.925705\n", "# TIMER BLOCK-38 ENDS - DURATION (s): 12.4455665 [0:00:12.445566]\n", "# TIMER BLOCK-39 BEGINS AT 2025-06-12 15:18:45.486134\n", "# TIMER BLOCK-39 ENDS - DURATION (s): 11.1354904 [0:00:11.135490]\n", "# TIMER BLOCK-40 BEGINS AT 2025-06-12 15:18:56.734705\n", "# TIMER BLOCK-40 ENDS - DURATION (s): 13.7937376 [0:00:13.793738]\n", "# TIMER BLOCK-41 BEGINS AT 2025-06-12 15:19:10.642642\n", "# TIMER BLOCK-41 ENDS - DURATION (s): 17.6474461 [0:00:17.647446]\n", "# TIMER BLOCK-42 BEGINS AT 2025-06-12 15:19:28.413094\n", "# TIMER BLOCK-42 ENDS - DURATION (s): 19.9391872 [0:00:19.939187]\n" ] } ], "source": [ "h2o_bond_lengths = np.linspace(0.6,2.,10)\n", "h2o_stretching_results = [water_stretching_vqe_energy(x) for x in h2o_bond_lengths]" ] }, { "cell_type": "code", "execution_count": null, "id": "79528ca8-dc36-4795-afd5-95a0f310c622", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": null, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "h2o_lengths_vqe_results,h2o_lengths_hf_results = zip(*h2o_stretching_results)\n", "plt.plot(h2o_bond_lengths,h2o_lengths_vqe_results,label='VQE')\n", "plt.plot(h2o_bond_lengths,h2o_lengths_hf_results,label='HF')\n", "plt.xlabel('OH bond length /Å')\n", "plt.ylabel('Ground state energy/Ha')\n", "plt.legend()" ] }, { "attachments": {}, "cell_type": "markdown", "id": "5ee2c69f-c37a-4ad5-8faa-40d269747b32", "metadata": {}, "source": [ "We have successfully demonstrated that the point group symmetry reductions yield the correct ground state energy. However, we have not yet looked at the resource reductions obtained. We can adapt our VQE wrapper functions to return this, but for simplicity here we just look at one configuration:" ] }, { "cell_type": "code", "execution_count": null, "id": "54a84479-91fa-426f-a4ff-f5327b2d156e", "metadata": {}, "outputs": [], "source": [ "x_h2 = np.sin(104.45 / 360 * np.pi)\n", "x_h1 = -x_h2\n", "y_h1 = np.cos(104.45 / 360 * np.pi)\n", "y_h2 = y_h1\n", "\n", "geometry = [['H', [x_h1, y_h1, 0.]], ['O', [0., 0., 0.]], ['H', [x_h2, y_h2, 0.]]]\n", "basis = 'STO-3G'\n", "charge = 0\n", "frozen = [0]\n", " \n", "driver_with_symmetry = ChemistryDriverPySCFMolecularRHF(basis=basis, geometry=geometry, charge=charge, frozen=frozen,point_group_symmetry=True)\n", "driver_without_symmetry = ChemistryDriverPySCFMolecularRHF(basis=basis, geometry=geometry, charge=charge, frozen=frozen,point_group_symmetry=False)\n", "fermionic_hamiltonian_with_symmetry, fock_space_with_symmetry, fock_state_with_symmetry = driver_with_symmetry.get_system()\n", "fermionic_hamiltonian_without_symmetry, fock_space_without_symmetry, fock_state_without_symmetry = driver_without_symmetry.get_system()\n", "jw = QubitMappingJordanWigner()\n", "\n", "ansatz_with_symmetry = FermionSpaceAnsatzUCCSD(fock_space_with_symmetry, fock_state_with_symmetry, jw)\n", "ansatz_without_symmetry = FermionSpaceAnsatzUCCSD(fock_space_without_symmetry, fock_state_without_symmetry, jw)" ] }, { "attachments": {}, "cell_type": "markdown", "id": "87d8788f-d3b0-448a-82d9-97a9c3249428", "metadata": {}, "source": [ "For simplicity, we restrict ourselves to looking at the impact on the resources required for generating the Ansatz state. Note that many quantum resources can be estimated without actually running VQE in this manner; this dramatically decreases the resources necessary to perform an experiment.\n", "\n", "We can get an idea of the ansatz resources via the `circuit_resources()` method.\n" ] }, { "cell_type": "code", "execution_count": null, "id": "4aed69b7-efc3-4404-add9-8af2617eb9c6", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "### ANSATZ RESOURCES WITH SYMMETRY REDUCTION ###\n", "{'depth': 1629, 'gates': 3684, 'qubits': 12, 'gates_2q': 1888, 'gates_1q': 1796}\n", "\n", "### ANSATZ RESOURCES WITHOUT SYMMETRY REDUCTION ###\n", "{'depth': 5553, 'gates': 12616, 'qubits': 12, 'gates_2q': 6976, 'gates_1q': 5640}\n" ] } ], "source": [ "print('### ANSATZ RESOURCES WITH SYMMETRY REDUCTION ###')\n", "print(ansatz_with_symmetry.circuit_resources())\n", "print('\\n### ANSATZ RESOURCES WITHOUT SYMMETRY REDUCTION ###')\n", "print(ansatz_without_symmetry.circuit_resources())" ] } ], "metadata": {}, "nbformat": 4, "nbformat_minor": 5 }