Wen Wei Ho

State preparation protocols ideally require as minimal operations as possible, in order to be implemented in near-term, potentially noisy quantum devices. Motivated by long range interactions (LRIs) intrinsic to many present-day experimental platforms (trapped ions, Rydberg atom arrays, etc.), we investigate the efficacy of variationally simulating non-trivial quantum states using the Variational Quantum-Classical Simulation (VQCS) protocol explored recently in [SciPost Phys. 6, 029 (2019)], in the presence of LRIs. We show that this approach leads to extremely efficient state preparation: for example, Greene-Horne-Zeilinger (GHZ) states can be prepared with O(1) iterations of the protocol, and a quantum critical point of the long range transverse field Ising model (TFIM) can be prepared with > 99% fidelity on a 100 qubit system with only one iteration. Furthermore, we show that VQCS with LRIs is a promising route for exploring generic points in the phase diagram of the long-range TFIM. Our approach thus provides concrete, ultrafast protocols for quantum simulators equipped with long range interactions.

Long-range interacting systems such as nitrogen vacancy centers in diamond and trapped ions serve as useful experimental setups to probe a range of nonequilibrium many-body phenomena. In particular, via driving, various effective Hamiltonians with physics potentially quite distinct from short-range systems can be realized. In this Letter, we derive general bounds on the linear response energy absorption rates of periodically driven systems of spins or fermions with long-range interactions that are sign changing and fall off as $1/r^α$ with $α> d/2$. We show that the disordered averaged energy absorption rate at high temperature decays exponentially with the driving frequency. This strongly suggests the presence of a prethermal plateau in which dynamics is governed by an effective, static Hamiltonian for long times, and we provide numerical evidence to support such a statement. Our results are relevant for understanding timescales of both heating and hence new dynamical regimes described by effective Hamiltonians in such long-range systems.