Benchmarking Adaptive Variational Quantum Eigensolvers

Abstract

By design, the variational quantum eigensolver (VQE) strives to recover the lowest-energy eigenvalue of a given Hamiltonian by preparing quantum states guided by the variational principle. In practice, the prepared quantum state is indirectly assessed by the value of the associated energy. Novel adaptive derivative-assembled pseudo-trotter (ADAPT) ansatz approaches and recent formal advances now establish a clear connection between the theory of quantum chemistry and the quantum state ansatz used to solve the electronic structure problem. Here we benchmark the accuracy of VQE and ADAPT-VQE to calculate the electronic ground states and potential energy curves for a few selected diatomic molecules, namely H2, NaH, and KH. Using numerical simulation, we find both methods provide good estimates of the energy and ground state, but only ADAPT-VQE proves to be robust to particularities in optimization methods. Another relevant finding is that gradient-based optimization is overall more economical and delivers superior performance than analogous simulations carried out with gradient-free optimizers. The results also identify small errors in the prepared state fidelity which show an increasing trend with molecular size.

Benchmarking Quantum Chemistry Computations with Variational, Imaginary Time Evolution, and Krylov Space Solver Algorithms

“…Several implementations that followed focused on the utility of unitary coupled cluster methods and variations thereof. [7,[20][21][22][23] Other implementations demonstrated that the trial Ansatz need not be in UCC form to obtain chemical accuracy. [3] Eventually, variational methods were modified to be able to compute excited states as well.…”

Numerical Simulations of Noisy Quantum Circuits for Computational Chemistry

“…We defer the description of constructing these linear combinations to prior work [30]. Various details on both ansatz operators have been reported previously [10,26]. An alternative to the fixed-depth ansatz operators above is an adaptive ansatz that changes the generating operator based on iterative evaluations of the energy estimate.…”

“…Previously, Claudino et al investigated the fidelity of several variational methods in approximating the ground state of few-electron molecular models [26]. Those results show that VQE methods with sophisticated ansatz circuits could approximate the ground electronic state with very high fidelity in the absence of circuit noise, depending on the ansatz and method of parameter selection.…”

Solving nonlinear differential equations with differentiable quantum circuits

“…The paradigmatic hybrid algorithm corresponds to the variational quantum eigensolver (VQE) [42,43], where a quantum computer is used to prepare parametrized quantum states and measure their energy, while classical optimization is used for finding the best variational parameters. This strategy enables quantum calculations with relatively noisy devices, and allows for numerous advances from the experimental [44][45][46][47][48][49][50][51][52] and theoretical [53][54][55][56][57][58][59][60][61][62][63][64][65][66] perspectives.…”