In trapped-ion chains, multipartite GHZ states can be prepared natively with the help of a single bichromatic laser pulse. However, higher-order terms in the expansion in the Lamb-Dicke parameter η limit the GHZ state preparation infidelity for rectangular and bell-like pulses to the order of η4. For tens of ions, the infidelity caused by out-of-Lamb-Dicke effects can reach several percents. We propose an amplitude and phase-modulated pulse shape, an "echoed lemniscate pulse", which cancels this contribution into error in the leading order. For the proposed pulse, the infidelity scales as η6. The improved scaling is achieved because of a special phase trajectory of a collective motional mode following the figure-eight curve (lemniscate). We demonstrate that the lemniscate pulse allows achieving lower infidelity than bell-like pulses, which can be as low as 10−4 for 20-ion chains.
Multiqubit GHZ state preparation with 171Yb+ ions for frequency standards
Multiqubit Greenberger-Horne-Zeilinger (GHZ) state preparation is demonstrated on two to eight qubits in the chain of ten 171Yb+ ions in the linear Paul trap with a sequence of single-qubit and two-qubit operations and pulsed dynamical decupling. Fidelity of the 8-qubit GHZ state is estimated to be 58.9±0.6%. The expected enhanced sensitivity of the parity oscillations phase to the analyzing pulse phase is observed. This result is a step towards a multi-ion optical clock with ytterbium ions with frequency averaging following 1/N scaling law in contrast to the slower 1/N scaling for an ensemble of independent particles in case when the decoherence is dominated by the spontaneous decay.
Abstract We propose a protocol for the preparation of generalized Greenberger–Horne–Zeilinger (GHZ) states of N atoms each with d = 3 or 4 internal levels. We generalize the celebrated one-axis twisting (OAT) Hamiltonian for N qubits to qudits by including OAT interactions of equal strengths between every pair of qudit levels, a protocol we call as balanced OAT (BOAT). Analogous to OAT for qubits, we find that starting from a product state of an arbitrary number of atoms N, dynamics under BOAT leads to the formation of GHZ states for qutrits (d = 3) and ququarts (d = 4). While BOAT could potentially be realized on several platforms where all-to-all coupling is possible, here we propose specific implementations using trapped ion systems. We show that preparing these states with fidelity above a threshold value rules out lower dimensional entanglement than that of the generalized GHZ states. For qutrits, we also propose a protocol to bound the fidelity that requires only global addressing of the ion crystal and single-shot readout of one of the levels. Our results open a path for the scalable generation and certification of high-dimensional multipartite entanglement on current atom-based quantum hardware.