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. 2020 Mar 6;6(10):eaaw9268.
doi: 10.1126/sciadv.aaw9268. eCollection 2020 Mar.

Initialization of Quantum Simulators by Sympathetic Cooling

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Free PMC article

Initialization of Quantum Simulators by Sympathetic Cooling

Meghana Raghunandan et al. Sci Adv. .
Free PMC article

Abstract

Simulating computationally intractable many-body problems on a quantum simulator holds great potential to deliver insights into physical, chemical, and biological systems. While the implementation of Hamiltonian dynamics within a quantum simulator has already been demonstrated in many experiments, the problem of initialization of quantum simulators to a suitable quantum state has hitherto remained mostly unsolved. Here, we show that already a single dissipatively driven auxiliary particle can efficiently prepare the quantum simulator in a low-energy state of largely arbitrary Hamiltonians. We demonstrate the scalability of our approach and show that it is robust against unwanted sources of decoherence. While our initialization protocol is largely independent of the physical realization of the simulation device, we provide an implementation example for a trapped ion quantum simulator.

Figures

Fig. 1
Fig. 1. Sympathetic cooling of a quantum simulator.
(A) A system of N spins performing the quantum simulation is interacting with an additional bath spin that is dissipatively driven. (B) Sketch of the energy level structure showing resonant energy transport between the system and the bath, after which the bath spin is dissipatively pumped into its ground state. (C) Level scheme for the implementation with trapped 40Ca+ ions.
Fig. 2
Fig. 2. Sympathetic cooling of the transverse field Ising model in the ferromagnetic phase (J/g = 5, N = 5, fx, y, z = {1,1.1,0.9}).
The speed of the cooling dynamics and the final energy of the system depend on the system-bath coupling gsb for γ/g = 1.9 (A) and the dissipation rate γ for gsb/g = 1.15 (B). The ground-state energy is indicated by the dashed line. The insets show that the ground state can be prepared with greater than 90% fidelity.
Fig. 3
Fig. 3. Sympathetic cooling of the antiferromagnetic Heisenberg model (N = 4, gsb/J = 0.2, γ/J = 0.6, fx,y,z = {0.4,2.3,0.3}).
(A) The efficiency of the cooling procedure depends on the choice of the bath spin splitting Δ. (B) The optimal cooling leading to the lowest system energy 〈Hsys〉 corresponds to setting Δ to the many-body gap ΔE (vertical dashed line). The same minimum is observed when measuring the energy Edis that is being dissipated during the cooling process. The ground-state energy is indicated by the horizontal dashed line.
Fig. 4
Fig. 4. Scalability of the cooling protocol.
The preparation time tp to reach a final dimensionless energy of ε = 0.2 grows linearly on a log-log scale, i.e., tpNα. The solid line is a fit to the data according to α = 3.1 ± 0.1.
Fig. 5
Fig. 5. Cooling performance in the presence of decoherence in the quantum simulator for the transverse field Ising chain (J/g = 5, N = 4).
The inset shows the dimensionless energy ε as a function of the product κtp, where tp was taken from the dynamics without decoherence corresponding to a ground-state preparation fidelity of f = 0.9 (dashed line).
Fig. 6
Fig. 6. Cooling performance of an Ising-like chain of 5 + 1 ions of tp = 80ℏ/g = 24s.
The blue line shows the dynamics in the decoherence-free case resulting in a fidelity of f = 0.92, while the orange line indicates the dynamics under a collective decoherence mechanism with rate κc = 3.3Hz, resulting in f = 0.89. The dashed line indicates the ground-state energy of the system.

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