Dynamic Quantum Variational Ansatz

Philipp O. J. Scherer

Manuel Kreibich, Jörg Main, Günter Wunner

We investigate the stability properties and the dynamics of Bose–Einstein condensates with axial symmetry, especially with dipolar long-range interaction, using both simulations on grids and variational calculations. We present an extended variational ansatz which is applicable for axial symmetry and show that this ansatz can reproduce the lowest eigenfrequencies of the Bogoliubov spectrum, and also the corresponding eigenfunctions. Our variational ansatz is capable of describing the roton instability of pancake-shaped dipolar condensates for arbitrary angular momenta. After investigating the linear regime we apply the ansatz to determine the dynamics and show how the angular collapse is correctly described within the variational framework.

Béla Gazdy

Yong-Xin Yao, Niladri Gomes, Feng Zhang +4 more

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 timeevolved 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.

Yongxin Yao, Niladri Gomes, Feng Zhang +4 more

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.

Stephen L. Adler