{ "cells": [ { "cell_type": "markdown", "id": "ea3f4d79", "metadata": {}, "source": [ "# Quantum Computing Quantum Monte Carlo: ground state energy of H$_2$\n", "\n", "In this notebook, we demonstrate how to augment classical QMC calculations using quantum computers (QC) using auxiliary-field QMC (AFQMC) [1]. Compared to the variational quantum eigensolver (VQE) [2], a popular quantum algorithm for solving the electronic structure problem, QC‑AFQMC does not require an expensive optimization loop. The circuit depth of both methods is similar. This notebook presents an example AFQMC calculation to find the ground state of H$_2$ molecule. The code can be run on both classical simulators and quantum computers. For more details about the algorithm, see this [example notebook](https://github.com/aws/amazon-braket-examples/blob/feature/quantum-monte-carlo/examples/hybrid_quantum_algorithms/Quantum_Monte_Carlo_Chemistry/Quantum_Monte_Carlo_Chemistry.ipynb) in Amazon Braket Examples.\n", "\n", "\n", "[1] Motta, Mario, and Shiwei Zhang. \"Ab initio computations of molecular systems by the auxiliary‐field quantum Monte Carlo method.\" [Wiley Interdisciplinary Reviews: Computational Molecular Science 8.5 (2018): e1364](https://doi.org/10.1002/wcms.1364).\n", "\n", "[2] Peruzzo, Alberto, et al. \"A variational eigenvalue solver on a photonic quantum processor.\" [Nature Communications 5.1 (2014): 1-7](https://www.nature.com/articles/ncomms5213?ref=https://githubhelp.com).\n", "\n", "