Differentiable quantum computational chemistry with PennyLane

TL;DR

This paper introduces PennyLane's differentiable quantum chemistry capabilities, enabling gradient-based optimization of molecular properties and quantum algorithms within a unified framework, advancing quantum computational chemistry research.

Contribution

It presents the first implementation of differentiable quantum chemistry in PennyLane, including a differentiable Hartree-Fock solver and specialized quantum operations for chemistry.

Findings

Efficient simulation of molecular Hamiltonians using sparse matrix techniques.

Ability to compute gradients of molecular energies with respect to nuclear and basis parameters.

Implementation of variational quantum algorithms for ground and excited states.

Abstract

This work describes the theoretical foundation for all quantum chemistry functionality in PennyLane, a quantum computing software library specializing in quantum differentiable programming. We provide an overview of fundamental concepts in quantum chemistry, including the basic principles of the Hartree-Fock method. A flagship feature in PennyLane is the differentiable Hartree-Fock solver, allowing users to compute exact gradients of molecular Hamiltonians with respect to nuclear coordinates and basis set parameters. PennyLane provides specialized operations for quantum chemistry, including excitation gates as Givens rotations and templates for quantum chemistry circuits. Moreover, built-in simulators exploit sparse matrix techniques for representing molecular Hamiltonians that lead to fast simulation for quantum chemistry applications. In combination with PennyLane's existing methods for constructing, optimizing, and executing circuits, these methods allow users to implement a wide range of quantum algorithms for quantum chemistry. We discuss how PennyLane can be used to implement variational algorithms for calculating ground-state energies, excited-state energies, and energy derivatives, all of which can be differentiated with respect to both circuit and Hamiltonian parameters. We provide an example workflow describing how to jointly optimize circuit parameters, nuclear coordinates, and basis set parameters for quantum chemistry algorithms. We discuss a functionality for reducing the number of qubits by using symmetries and explain how PennyLane can be used to estimate quantum resources needed to implement several quantum algorithms. By combining insights from quantum computing, computational chemistry, and machine learning, PennyLane is the first library for differentiable quantum computational chemistry.