Enhancing quantum utility: simulating large-scale quantum spin chains on superconducting quantum computers

TL;DR

This paper demonstrates large-scale quantum spin chain simulations on superconducting quantum computers, showcasing the potential for quantum advantage in many-body physics before fault-tolerant quantum computing is achieved.

Contribution

First implementation of Hamiltonian with next-nearest neighbor interactions on superconducting qubits and development of second-order Trotterization for large-scale quantum simulations.

Findings

Successful simulation of 100-qubit spin chains

Constant circuit depth per Trotter step regardless of qubit number

Accurate measurement of expectation values in large quantum systems

Abstract

We present the quantum simulation of the frustrated quantum spin-$\frac{1}{2}$ antiferromagnetic Heisenberg spin chain with competing nearest-neighbor $(J_1)$ and next-nearest-neighbor $(J_2)$ exchange interactions in the real superconducting quantum computer with qubits ranging up to 100. In particular, we implement, for the first time, the Hamiltonian with the next-nearest neighbor exchange interaction in conjunction with the nearest neighbor interaction on IBM's superconducting quantum computer and carry out the time evolution of the spin chain by employing first-order Trotterization. Furthermore, our novel implementation of second-order Trotterization for the isotropic Heisenberg spin chain, involving only nearest-neighbor exchange interaction, enables precise measurement of the expectation values of staggered magnetization observable across a range of up to 100 qubits. Notably, in both cases, our approach results in a constant circuit depth in each Trotter step, independent of the initial number of qubits. Our demonstration of the accurate measurement of expectation values for the large-scale quantum system using superconducting quantum computers designates the quantum utility of these devices for investigating various properties of many-body quantum systems. This will be a stepping stone to achieving the quantum advantage over classical ones in simulating quantum systems before the fault tolerance quantum era.