Simulating the Quantum Magnet

TL;DR

This paper demonstrates the experimental simulation of quantum spin systems using trapped ions, achieving high fidelity in quantum phase transition states and establishing a foundation for scalable quantum simulations of complex magnetic phenomena.

Contribution

It provides a practical implementation of a quantum simulator with trapped ions, simulating quantum phase transitions with high fidelity and showing potential for scaling to larger systems.

Findings

Achieved 98% magnetization in simulating quantum phase transition.

Produced entangled states with up to 88% fidelity.

Demonstrated control over Hamiltonian parameters independently.

Abstract

To gain deeper insight into the dynamics of complex quantum systems we need a quantum leap in computer simulations. We can not translate quantum behaviour arising with superposition states or entanglement efficiently into the classical language of conventional computers. The final solution to this problem is a universal quantum computer [1], suggested in 1982 and envisioned to become functional within the next decade(s); a shortcut was proposed via simulating the quantum behaviour of interest in a different quantum system, where all parameters and interactions can be controlled and the outcome detected sufficiently well. Here we study the feasibility of a quantum simulator based on trapped ions [2]. We experimentally simulate the adiabatic evolution of the smallest non-trivial spin system from the paramagnetic into the (anti-)ferromagnetic order with a quantum magnetisation for two spins of 98%, controlling and manipulating all relevant parameters of the Hamiltonian independently via electromagnetic fields. We prove that the observed transition is not driven by thermal fluctuations, but of quantum mechanical origin, the source of quantum fluctuations in quantum phase transitions [3]. We observe a final superposition state of the two degenerate spin configurations for the ferromagnetic and the antiferromagnetic order, respectively. These correspond to deterministically entangled states achieved with a fidelity up to 88%. Our work demonstrates a building block for simulating quantum spin-Hamiltonians with trapped ions. The method has potential for scaling to a higher number of coupled spins [2].