Through numerical examples, we show that the driven imaginary-time evolution can converge to the desired ground state exponentially faster than the standard imaginary-time evolution for some difficult physical systems involving small energy gaps, such as diatomic molecules HF with a large intra-molecular distance and spin models with long-range couplings. To make the method accessible in the noisy intermediate-scale quantum era, we further propose a variational form of the algorithm that could work with shallow quantum circuits. Different from the typical setting of performing optimal control in the realtime domain, we extend the Lyapunov control method to the imaginary-time domain for the groundstate preparation. In this work, we first propose a Lyapunov control-inspired strategy to accelerate the well-established imaginary-time method for the ground-state preparation. Quantum computers have been widely speculated to offer significant advantages in obtaining the ground state of difficult Hamiltonians in chemistry and physics. To quantify the performance of our scheme, we implement numerical simulations, and show that we can prepare ground states of the two-dimensional Heisenberg model with a high fidelity. As long as the rotating wave approximation is valid, the inductive coupling between the superconducting flux qubits produces the desired Hamiltonian in the rotating frame, and we can use such an interaction for the quantum annealing while the microwave fields driving play a role of the transverse fields.
The key idea is to use a recently proposed spin-lock quantum annealing where the qubits are driven by microwave fields. In this work, we propose a quantum annealing for the XXZ model, which contains both Ising interaction and energy-exchange interaction, by using inductively coupled superconducting flux qubits. Although quantum annealing provides a way to prepare a ground state of a Hamiltonian, we can only use the Hamiltonian with Ising interaction by using currently available commercial quantum annealing devices. The interaction Hamiltonians typically contain not only diagonal but also off-diagonal elements. Preparing ground states of Hamiltonians is important in the condensed matter physics and the quantum chemistry. We identify those that are most physically meaningful by comparing with our results that avoid such a choice through the use of mass-weighted coordinates. Finally, we collect the various choices for the phonon mass that have been introduced in the literature. We calculate the influence of isotope substitution and strain on the quantum paraelectric behavior, and find that, while complete replacement of oxygen-16 by oxygen-18 has a surprisingly small effect, experimentally accessible strains can induce large changes. Using BaTiO$_3$, SrTiO$_3$ and KTaO$_3$ as model systems, we show that the approach can straightforwardly distinguish between ferroelectric, paraelectric and quantum paraelectric materials, based on simple quantities extracted from standard density functional and density functional perturbation theories. We present an inexpensive first-principles approach for describing quantum paraelectricity that combines density functional theory (DFT) treatment of the electronic subsystem with quantum mechanical treatment of the ions through solution of the single-particle Schrödinger equation with the DFT-calculated potential.