Variational quantum simulation of long-range interacting systems

TL;DR

This paper investigates the efficiency of variational quantum algorithms for simulating long-range interacting systems and generating spin squeezed states, highlighting the importance of connectivity and circuit design in near-term quantum devices.

Contribution

It demonstrates how qubit connectivity and circuit layering impact the performance of variational algorithms in simulating complex quantum states.

Findings

Long-range interactions reduce algorithm efficiency.

Enhanced connectivity improves fidelity and reduces resource demands.

Layer ordering significantly affects simulation performance.

Abstract

Current quantum simulators suffer from multiple limitations such as short coherence time, noisy operations, faulty readout and restricted qubit connectivity in some platforms. Variational quantum algorithms are the most promising approach in near-term quantum simulation to achieve practical quantum advantage over classical computers. Here, we explore variational quantum algorithms, with different levels of qubit connectivity, for digital simulation of the ground state of long-range interacting systems as well as generation of spin squeezed states. We find that as the interaction becomes more long-ranged, the variational algorithms 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 performance. 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.