Jian-Xin Zhu

Quantum computers are an ideal platform to study the ground state properties of strongly correlated systems due to the limitation of classical computing techniques particularly for systems exhibiting quantum phase transitions. While the error rates of Noisy Intermediate-Scale Quantum (NISQ) computers are still high, simulating strongly correlated systems on such devices and extracting information of possible phases may be within reach. The frustrated transverse-field Ising model (TFIM) is such a system with multiple ordered magnetic phases. In this study, we simulate a two-dimensional frustrated TFIM with next-nearest-neighbor spin-exchange interactions at zero temperature. The competition between the nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic coupling gives rise to frustration in the system. Moreover, the presence of quantum fluctuations makes the ground-state phase profile even richer. We use the Variational Quantum Eigensolver (VQE) to compute the phases on a square lattice with periodic boundary conditions for a system of 16 sites (qubits). The trained VQE circuits are compared to exact diagonalization, allowing us to extract error measures of VQE. We focus on the ground-state phase transitions of this model, where VQE succeeds in finding the dominant magnetic phases. The optimized VQE circuits are then executed on the Quantinuum H1-1 trapped-ion quantum computer without using any error mitigation techniques. Our experiments show near perfect recovery of the magnetic phases of the frustrated model through ground-state energy, the energy derivative, and the spin correlation functions. Thus, we show that the trapped-ion quantum processor is able to achieve reliable simulations of a strongly correlated system within the limitations of the VQE approach.

Periodically driven quantum systems exhibit a diverse set of phenomena but are more challenging to simulate than their equilibrium counterparts. Here, we introduce the Quantum High-Frequency Floquet Simulation (QHiFFS) algorithm as a method to simulate fast-driven quantum systems on quantum hardware. Central to QHiFFS is the concept of a kick operator which transforms the system into a basis where the dynamics is governed by a time-independent effective Hamiltonian. This allows prior methods for time-independent simulation to be lifted to simulate Floquet systems. We use the periodically driven biaxial next-nearest neighbor Ising (BNNNI) model, a natural test bed for quantum frustrated magnetism and criticality, as a case study to illustrate our algorithm. We implemented a 20-qubit simulation of the driven two-dimensional BNNNI model on Quantinuum's trapped ion quantum computer. Our error analysis shows that QHiFFS exhibits not only a cubic advantage in driving frequency $ω$ but also a linear advantage in simulation time $t$ compared to~Trotterization.