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qce23-qpde-tutorial

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Solving PDEs with quantum algorithms: A tutorial at IEEE QCE 2023

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# TUT27 — Solving Partial Differential Equations (PDEs) with Quantum Computers

[Zhixin Song, Georgia Institute of Technology, USA](https://www.linkedin.com/in/kaminotesf524/) \
[Spencer Bryngelson, Georgia Institute of Technology, USA](https://cse.gatech.edu/people/spencer-bryngelson)

**Date:** Fri, Sep 22, 2023 \
 **Time:** Between 10:00-14:30 Pacific Time (PDT) — UTC-7 \
 **Duration:** 3 hours (2 x 1.5 hours)

Many important systems in nature are described by the space-time evolution of physical quantities using partial differential equations (PDEs), which can range from the microscale, such as the Schrödinger equation in quantum systems, to the macroscale, such as the Navier–Stokes equations of fluid dynamics. Thus, efficient PDE solvers are critical to understanding and solving many science and engineering problems. Quantum algorithms have been proposed to solve PDEs and verified on small-scale simulators. For long-term PDE solvers, the Harrow-Hassidim-Lloyd (HHL) algorithm could bring an exponential speedup over classical methods. For the near-term quantum hardware, variational quantum algorithms such as the Variational Quantum Linear Solver (VQLS) are applied to solve PDEs. In this tutorial, we will introduce users to QPDE-Benchmark, a new programming toolkit, powered by a set of quantum PDE solvers, that enable a user to more seamlessly test and improve quantum solvers for various PDEs. More specifically, we will show users how to solve the Schrödinger, Wave, and Poisson equation on near-term quantum computers using Hamiltonian simulation, VQLS and Variational Quantum Eigensolver (VQE).

**Note:** Session 1 notebook is based on IBM Open Science Prize 2021. Please check this [repo](https://github.com/qiskit-community/open-science-prize-2021) for more details and advanced technique to enhance fidelity of Hamiltonian simulation on IBMQ's hardware.

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