Scalable Creation of Long-Lived Multipartite Entanglement

We demonstrate the deterministic generation of multipartite entanglement based on scalable methods. Four qubits are encoded in ${}^{40}{\mathrm{Ca}}^{+}$, stored in a microstructured segmented Paul trap. These qubits are sequentially entangled by laser-driven pairwise gate operations. Between these, the qubit register is dynamically reconfigured via ion shuttling operations, where ion crystals are separated and merged, and ions are moved in and out of a fixed laser interaction zone. A sequence consisting of three pairwise entangling gates yields a four-ion Greenberger-Horne-Zeilinger state $|\psi ⟩=(1/\sqrt{2})(|0000⟩+|1111⟩)$, and full quantum state tomography reveals a state fidelity of 94.4(3)%. We analyze the decoherence of this state and employ dynamic decoupling on the spatially distributed constituents to maintain 69(5)% coherence at a storage time of 1.1 sec.

Figure 1

Shuttling sequence for the creation, storage, and analysis of a four-ion GHZ state. State creation takes place above the dashed line. Entangling gates $\widehat{G}$ and single-qubit rotations $\widehat{R}$ are carried out in the LIZ. After the GHZ state is created, it can be stored for hundreds of milliseconds by employing DD. The ions are not stored in the LIZ to prevent depolarization from residual light near the cycling transition.

Figure 2

(a) Quantum circuit for the creation, storage, and analysis of a four-ion GHZ state. The state is generated by three subsequent entangling gates. Evenly spaced DD $\pi$ pulses are employed to achieve long coherence times, followed by state tomography on the individual ions. The green (b) and blue (c) dashed boxes show how the respective entangling gates are realized in the experiment—they correspond to the unitary operators ${\widehat{U}}_1$ and ${\widehat{U}}_2$, from Eq. (1). The upper numbers in the boxes indicating the single-qubit operations represent the laser pulse areas, whereas the lower numbers indicate the phase of the respective pulse. Red boxes represent an additional phase which arises from the shuttling operations; see the text.

Figure 3

Reconstructed density matrix of a maximally entangled four-ion GHZ state with correction for readout errors. Linear reconstruction with correction for SPAM errors yields a state fidelity of $\mathcal{F}=94.38\%$. We determine the GHZ phase [see Eq. (3)] to $\theta =-2\pi \times 0.217(2)$.

Figure 4

Preservation of the parity contrast of a four-ion GHZ state by DD. Green triangles for short times correspond to a measurement without the execution of the rephasing block. Blue circles represent a measurement with $N_{\pi }=15$ rephasing pulses on each qubit, while red squares correspond to $N_{\pi }=3$. The dotted black line represents a Gaussian decay, whereas the gray dashed line represents an exponential decay. The data shown are not corrected for SPAM errors.