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Dissipative preparation of W states in trapped ion systems

Daniel C. Cole, Jenny J. Wu, Stephen D. Erickson, Pan‐Yu Hou, A. C. Wilson, Dietrich G. Leibfried, Florentin Reiter

Published Jul 1, 2021• 31 citations
Publisher

Abstract

We present protocols for dissipative entanglement of three trapped-ion qubits and discuss a scheme that uses sympathetic cooling as the dissipation mechanism. This scheme relies on tailored destructive interference to generate any one of six entangled W states in a three-ion qubit space. Using a beryllium–magnesium ion crystal as an example system, we theoretically investigate the protocol's performance and the effects of likely error sources, including thermal secular motion of the ion crystal, calibration imperfections, and spontaneous photon scattering. We estimate that a fidelity of ~98% may be achieved in typical trapped ion experiments with ~1 ms interaction time. These protocols avoid timescale hierarchies for faster preparation of entangled states.

DOI
10.3929/ethz-b-000495572

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We present protocols for dissipative entanglement of three trapped-ion qubits and discuss a scheme that uses sympathetic cooling as the dissipation mechanism. This scheme relies on tailored destructive interference to generate any one of six entangled W states in a three-ion qubit space. Using a beryllium–magnesium ion crystal as an example system, we theoretically investigate the protocol's performance and the effects of likely error sources, including thermal secular motion of the ion crystal, calibration imperfections, and spontaneous photon scattering. We estimate that a fidelity of ~98% may be achieved in typical trapped ion experiments with ~1 ms interaction time. These protocols avoid timescale hierarchies for faster preparation of entangled states.
Abstract We present protocols for dissipative entanglement of three trapped-ion qubits and discuss a scheme that uses sympathetic cooling as the dissipation mechanism. This scheme relies on tailored destructive interference to generate any one of six entangled W states in a three-ion qubit space. Using a beryllium–magnesium ion crystal as an example system, we theoretically investigate the protocol’s performance and the effects of likely error sources, including thermal secular motion of the ion crystal, calibration imperfections, and spontaneous photon scattering. We estimate that a fidelity of ∼98% may be achieved in typical trapped ion experiments with ∼1 ms interaction time. These protocols avoid timescale hierarchies for faster preparation of entangled states.
We propose a series of dissipation-assisted entanglement generation protocols that can be implemented on a trapped-ion quantum simulator. Our approach builds on the single-site molecular electron transfer (ET) model recently realized in the experiment [So et al. Sci. Adv. 10, eads8011 (2024)]. This model leverages spin-dependent boson displacement and dissipation controlled by sympathetic cooling. We show that, when coupled to external degrees of freedom, the ET model can be used as a dissipative quantum control mechanism, enabling the precise tailoring of both spin and phonon steady state of a target sub-system. We derive simplified analytical formalisms that offer intuitive insights into the dissipative dynamics. Using realistic interactions in a trapped-ion system, we develop a protocol for generating NNN-qubit and NNN-boson WWW states. Additionally, we generalize this protocol to realize generic NNN-qubit Dicke states with tunable excitation numbers. Finally, we outline a realistic experimental setup to implement our schemes in the presence of noise sources.
Driven dissipative steady state entanglement schemes take advantage of coupling to the environment to robustly prepare highly entangled states. We present a scheme for two trapped ions to generate a maximally entangled steady state with fidelity above 0.99, appropriate for use in quantum protocols. Furthermore, we extend the scheme by introducing detection of our dissipation process, significantly enhancing the fidelity. Our scheme is robust to anomalous heating and requires no sympathetic cooling.
We introduce a scheme to perform dissipation-assisted quantum information processing in ion traps considering realistic decoherence rates, for example, due to motional heating. By means of continuous sympathetic cooling, we overcome the trap heating by showing that the damped vibrational excitations can still be exploited to mediate coherent interactions as well as collective dissipative effects. We describe how to control their relative strength experimentally, allowing for protocols of coherent or dissipative generation of entanglement. This scheme can be scaled to larger ion registers for coherent or dissipative many-body quantum simulations.
Entangled states are a key resource in fundamental quantum physics, quantum cryptography, and quantum computation. In this thesis, we focus on the demonstrations of two novel methods to generate entanglement. First, we implement dissipative production of a maximally entangled steady state on two trapped ions. Dissipative and coherent processes are combined and implemented in a continuous time-independent fashion, analogous to optical pumping of atomic states, continuously driving the system towards the steady entangled state. With this method, we obtain a Bell state fidelity up to 0.89(2). Second, we propose and demonstrate a novel coherent process to confine quantum evolution in a subspace between an initial separable state and the target entangled state. We demonstrate this scheme on two and three ions obtaining a Bell state fidelity up to 0.992(2). Both of these methods are robust against certain types of experimental noise and decoherence. Additionally, we demonstrate sympathetic cooling of ion chains to near the ground\nstate of motion with an electromagnetically-induced-transparency (EIT) method. This results in roughly an order of magnitude faster cooling time while using significantly lower laser power compared to the conventional resolved sideband cooling method. These techniques may be helpful for scaled-up quantum computing.