Finite-size criticality in fully connected spin models on superconducting quantum hardware

TL;DR

This paper demonstrates how superconducting quantum hardware can be used to detect quantum criticality in fully connected spin models, providing a pathway for studying phase transitions in finite quantum systems.

Contribution

It introduces a variational quantum algorithm approach to identify quantum critical behavior in fully connected spin-1/2 models on superconducting qubits, highlighting scalability prospects.

Findings

Successful detection of energy gap, magnetization, and correlations at finite sizes.

Feasibility analysis for scaling to larger quantum systems.

Potential for studying quantum phase transitions with quantum hardware.

Abstract

The emergence of a collective behavior in a many-body system is responsible of the quantum criticality separating different phases of matter. Interacting spin systems in a magnetic field offer a tantalizing opportunity to test different approaches to study quantum phase transitions. In this work, we exploit the new resources offered by quantum algorithms to detect the quantum critical behaviour of fully connected spin$-1/2$ models. We define a suitable Hamiltonian depending on an internal anisotropy parameter $\gamma,$ that allows us to examine three paradigmatic examples of spin models, whose lattice is a fully connected graph. We propose a method based on variational algorithms run on superconducting transmon qubits to detect the critical behavior for systems of finite size. We evaluate the energy gap between the first excited state and the ground state, the magnetization along the easy-axis of the system, and the spin-spin correlations. We finally report a discussion about the feasibility of scaling such approach on a real quantum device for a system having a dimension such that classical simulations start requiring significant resources.