Variational Simulation Of Long-range Interacting Systems

Quantum technologies will revolutionize almost every aspect of our lives,from communication to computation and sensing.Quantum simulation is one of the pillars of quantum technologies.Simulating the behavior of a quantum system on a classical computer becomes quickly intractable due to the exponential growth of the Hilbert space.The true simulation of a quantum system is only possible on another quantum system,namely quantum simulator,which is usually simpler and more controllable.Thanks to recent advancements in fabrication of quantum devices,quantum simulators are now emerging in various physical setups,including cold atoms and ions,superconducting devices and optical systems.However,current Noisy Intermediate Scale Quantum(NISQ)devices are far from being perfect and suffer from multiple limitations such as short coherence time,noisy operations,faulty readout and restricted qubit connectivity.An important open problem is whether such imperfect quantum systems can provide any advantage over their classical counterparts.Variational quantum algorithms are the most promising approach in near-term quantum simulation to achieve quantum advantage over classical computers.In these algorithms,the complexity is divided between a quantum simulator and a classical optimizer which allows a shallow quantum circuit to solve complex problems.Here,we explore variational quantum algorithms,with different levels of qubit connectivity,for digital simulation of the ground state of long-range interacting systems.Specifically,we focus on Variational Quantum Eigensolver(VQE)as one of the most widely used algorithms in quantum simulation.We find that as the interaction becomes more long-ranged,the VQE algorithm become less efficient,achieving lower fidelity and demanding more optimization iterations.In particular,when the system is near its criticality the efficiency is even lower.Increasing the connectivity between distant qubits improves the results,even with less quantum and classical resources.Our results show that by mixing circuit layers with different levels of connectivity one can sensibly improve the results.Interestingly,the order of layers becomes very important and grouping the layers with long-distance connectivity at the beginning of the circuit outperforms other permutations.The same design of circuits can also be used to variationally produce spin squeezed states,as a resource for quantum metrology.The quantum variational method indeed outperforms the ground state and quench dynamics approach for creating spin squeezing.