We propose a general-purpose, self-adaptive approach to construct a variational wave-function ansatz for highly accurate quantum dynamics simulations based on McLachlan’s variational principle. The key idea is to dynamically expand the variational ansatz along the time-evolution path such that the “McLachlan distance”, which is a measure of the simulation accuracy, remains below a set threshold. We apply this adaptive variational quantum dynamics simulation (AVQDS) approach to the integrable Lieb-Schultz-Mattis spin chain and the nonintegrable mixed-field Ising model, where it captures both finite-rate and sudden post-quench dynamics with high fidelity. The AVQDS quantum circuits that prepare the time-evolved state are much shallower than those obtained from first-order Trotterization and contain up to 2 orders of magnitude fewer cnot gate operations. We envision that a wide range of dynamical simulations of quantum many-body systems on near-term quantum-computing devices will be made possible through the AVQDS framework.

An adaptive variational quantum imaginary time evolution (AVQITE) approach is introduced that yields efficient representations of ground states for interacting Hamiltonians on near‐term quantum computers. It is based on McLachlan's variational principle applied to imaginary time evolution of variational wave functions. The variational parameters evolve deterministically according to equations of motions that minimize the difference to the exact imaginary time evolution, which is quantified by the McLachlan distance. Rather than working with a fixed variational ansatz, where the McLachlan distance is constrained by the quality of the ansatz, the AVQITE method iteratively expands the ansatz along the dynamical path to keep the McLachlan distance below a chosen threshold. This ensures the state is able to follow the quantum imaginary time evolution path in the system Hilbert space rather than in a restricted variational manifold set by a predefined fixed ansatz. AVQITE is used to prepare ground states of H ₄ , H ₂ O, and BeH ₂ molecules, where it yields compact variational ansätze and ground state energies within chemical accuracy. Polynomial scaling of circuit depth with system size is shown through a set of AVQITE calculations of quantum spin models. Finally, quantum Lanczos calculations are demonstrated alongside AVQITE without additional quantum resource costs.

We develop a new implementation of the Gutzwiller approximation in combination with the local density approximation, which enables us to study complex $4f$ and $5f$ systems beyond the reach of previous approaches. We calculate from first principles the zero-temperature phase diagram and electronic structure of Pr and Pu, finding good agreement with the experiments. Our study of Pr indicates that its pressure-induced volume-collapse transition would not occur without change of lattice structure—contrarily to Ce. Our study of Pu shows that the most important effect originating the differentiation between the equilibrium densities of its allotropes is the competition between the Peierls effect and the Madelung interaction and not the dependence of the electron correlations on the lattice structure.

A grand challenge underlies the entire field of topology-enabled quantum logic and information science: how to establish topological control principles driven by quantum coherence and understand the time dependence of such periodic driving. Here we demonstrate a few-cycle THz-pulse-induced phase transition in a Dirac semimetal ${\mathrm{ZrTe}}_5$ that is periodically driven by vibrational coherence due to excitation of the lowest Raman active mode. Above a critical THz-pump field threshold, there emerges a long-lived metastable phase, approximately 100 ps, with unique Raman phonon-assisted topological switching dynamics absent for optical pumping. The switching also manifests itself by distinct features: nonthermal spectral shape, relaxation slowing near the Lifshitz transition where the critical Dirac point occurs, and diminishing signals at the same temperature that the Berry-curvature-induced anomalous Hall effect magnetoresistance vanishes. These results, together with first-principles modeling, identify a mode-selective Raman coupling that drives the system from strong to weak topological insulators with a Dirac semimetal phase established at a critical atomic displacement controlled by the phonon coherent pumping. Harnessing of vibrational coherence can be extended to steer symmetry-breaking transitions, i.e., Dirac to Weyl ones, with implications for THz topological quantum gate and error correction applications.