  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.
