Simulating a quantum magnet with trapped ions

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 anti-ferromagnetic (|↑↓ + |↓↑ ) 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].

Motional averaging in a superconducting qubit

“…Finally, the recent progress in the field of nanomechanical oscillators makes possible the study of frequency jumps in nanomechanical resonators 16 , which is predicted to be accompanied by squeezing 31 . Our work paves the way for further simulations of quantum coherence phenomena using superconducting quantum circuits 32,33 .…”

Nonlocality in many-body quantum systems detected with two-body correlators

“…The pioneering experiments were reported in Refs. [86,87]. While in the early theory studies [85,[88][89][90] spin interactions decaying with the third power of the distance were considered, it was experimentally demonstrated that management of phonon dispersion allows to achieve powers between 0.1 and 3 in the 2D arrays of traps [91].…”

The “arch” of simulating quantum spin systems with trapped ions

“…The implementation of the experimental protocol for our feasibility study in the case of two spins is realized in the following way and is further described in [3] and illustrated in Fig. 6.…”

“…5 of the final state after the phase-gate operation. Figure 7 depicts the probability to detect both spins in the same state after steps (1,2,3,4,5) of the protocol for the QS described above. Since the initialized state |→→ can be rewritten in our measurement basis (omitting normalization factors) as (|↓ + |↑ )(|↓ + |↑ ) = (|↓↓ + |↓↑ + |↑↓ + |↑↑ ), we expect already a 50% probability P ↓↓ + P ↑↑ to project this state in either |↓↓ or |↑↑ .…”

“…The task of providing the feasibility test for QS involving several simulation ions/spins in an one-dimensional ion trap was achieved in our group recently [3]. In the following section, we try to introduce and briefly discuss the building blocks for generic quantum spin Hamiltonians.…”