Abstract
We propose a general-purpose, self-adaptive approach to construct variational wavefunction ans\"atze 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 two 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.
Highlights
One of the primary scientific quantum-computing focuses has been to simulate the ground-state, excitedstate, and dynamical properties of spin and fermion systems [1,2,3,4,5,6,7,8,9,10,11,12,13]
This highlights the need for flexible variational circuits that can adapt to the changes of the wave function during time evolution, while still keeping the circuit sufficiently shallow to be run on noisy intermediate-scale quantum (NISQ) quantum-processing units (QPUs)
In the adaptive variational quantum dynamics simulation (AVQDS) simulations reported below, we focus on the dynamics simulation part, where we dynamically construct the variational ansatz and update the parameters according to Eq (11)
Summary
One of the primary scientific quantum-computing focuses has been to simulate the ground-state, excitedstate, and dynamical properties of spin and fermion systems [1,2,3,4,5,6,7,8,9,10,11,12,13]. Attempts to construct ansatzes of fixed variational circuits for VQDS have been reported [32], but the simulation accuracy quickly deteriorates as the system grows from two sites to a few sites This highlights the need for flexible variational circuits that can adapt to the changes of the wave function during time evolution, while still keeping the circuit sufficiently shallow to be run on NISQ quantum-processing units (QPUs). We apply AVQDS to study linear-ramp quantum dynamics of the integrable Lieb-Schultz-Mattis (LSM) spin model [35,36], and sudden quench dynamics of the nonintegrable mixed-field Ising model (MFIM) In both cases, we find that dynamical quantities of interest (such as local observables, total energy, and the Loschmidt echo) are described accurately with the adaptively generated variational ansatz.
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