Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz

By Jonathan Romero, Ryan Babbush, Jarrod R. McClean, Cornelius Hempel, Peter J. Love, A. Aspuru‐Guzik. Quantum Science and Technology, 2017

768 citations recorded by the source corpus.

The variational quantum eigensolver (VQE) algorithm combines the ability of quantum computers to efficiently compute expectation values with a classical optimization routine in order to approximate ground state energies of quantum systems. In this paper, we study the application of VQE to the simulation of molecular energies using the unitary coupled cluster (UCC) ansatz. We introduce new strategies to reduce the circuit depth for the implementation of UCC and improve the optimization of the wavefunction based on efficient classical approximations of the cluster amplitudes. Additionally, we propose an analytical method to compute the energy gradient that reduces the sampling cost for gradient estimation by several orders of magnitude compared to numerical gradients. We illustrate our methodology with numerical simulations for a system of four hydrogen atoms that exhibit strong correlation and show that the circuit depth of VQE using a UCC ansatz can be reduced without introducing significant loss of accuracy in the final wavefunctions and energies.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/0bcd7c44dd81ce617189df877030870da9310589

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Citations in the corpus

Variational Quantum Computation of Excited States (2018, methodology): “For ground state VQE problems, second order Møller-Plesset perturbation theory (MP2) has previously been proposed as a UCC ansatz initialisation method [32].”
Potential of quantum computing for drug discovery (2018, background): “There are also improvements to these quantum algorithms, which are motivated by insights from quantum chemistry [102–104].”
Variational quantum algorithms for nonlinear problems (2019, background): “[29] J.”
VQE method: a short survey and recent developments (2021, methodology): “To address this problem, a variational hybrid quantum method VQE was proposed [11, 12, 13].”
Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator (2018, methodology): “A vast majority of the other amplitudes are typically extremely small [57], such that one may choose a threshold value for the ~ θ0 provided by the classical coupled cluster method to further reduce the number of relevant eθγ(Tγ−T † γ ) terms.”
t|ket⟩: a retargetable compiler for NISQ devices (2020, methodology): “They correspond to VQE circuits for estimating the ground state energy of small molecules by the Unitary Coupled Cluster approach [83], using some choice of qubit encoding (Jordan–Wigner, parity mapping, or Bravyi–Kitaev [84]).”
qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansatze on a quantum processor (2019, background): “(A product of four fermionic operators gives 16 terms in total, but each symmetric term is cancelled by its Hermitian conjugate [34].)”
Variational quantum algorithms (2020, methodology): “Gradient-based [109, 110], derivative-free [32, 111] as well as reinforcement learning [112] methods were investigated, and this still remains an active field to guarantee a good performance for the QAOA.”
An adaptive variational algorithm for exact molecular simulations on a quantum computer (2018, methodology): “The re-optimization subroutine in step 8 can be implemented on either a classical or quantum processor using any of the gradient- or non-gradient-based optimization routines that have been proposed or demonstrated for VQE [12, 15, 16, 18].”
Classification with Quantum Neural Networks on Near Term Processors (2018, background): “There is an alternative strategy for computing each component of the gradient [14] which works when the individual unitaries are all of the form (8).”
Barren plateaus in quantum neural network training landscapes (2018, background): “Circuits of this form are a natural choice due to a straightforward evaluation of the gradient with respect to most objective functions and have been introduced in a number of contexts already [26, 41].”