Generation of genuine all-way entanglement in defect-nuclear spin systems through dynamical decoupling sequences

Evangelia Takou, Edwin Barnes, and Sophia E. Economou

Department of Physics, Virginia Polytechnic Institute and State University, 24061 Blacksburg, VA, USA
Virginia Tech Center for Quantum Information Science and Engineering, Blacksburg, VA 24061, USA

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Multipartite entangled states are an essential resource for sensing, quantum error correction, and cryptography. Color centers in solids are one of the leading platforms for quantum networking due to the availability of a nuclear spin memory that can be entangled with the optically active electronic spin through dynamical decoupling sequences. Creating electron-nuclear entangled states in these systems is a difficult task as the always-on hyperfine interactions prohibit complete isolation of the target dynamics from the unwanted spin bath. While this emergent cross-talk can be alleviated by prolonging the entanglement generation, the gate durations quickly exceed coherence times. Here we show how to prepare high-quality GHZ$_M$-like states with minimal cross-talk. We introduce the $M$-tangling power of an evolution operator, which allows us to verify genuine all-way correlations. Using experimentally measured hyperfine parameters of an NV center spin in diamond coupled to carbon-13 lattice spins, we show how to use sequential or single-shot entangling operations to prepare GHZ$_M$-like states of up to $M=10$ qubits within time constraints that saturate bounds on $M$-way correlations. We study the entanglement of mixed electron-nuclear states and develop a non-unitary $M$-tangling power which additionally captures correlations arising from all unwanted nuclear spins. We further derive a non-unitary $M$-tangling power which incorporates the impact of electronic dephasing errors on the $M$-way correlations. Finally, we inspect the performance of our protocols in the presence of experimentally reported pulse errors, finding that XY decoupling sequences can lead to high-fidelity GHZ state preparation.

Solid-state defect spins are appealing candidates for quantum networks and quantum sensing. They possess an optically-active electronic spin qubit that enables communication with other nodes and fast information processing, as well as long-lived nuclear spins that can store quantum information. Nuclear memories are often controlled indirectly through the electron and contribute to several quantum protocols. Electron-nuclear entangled states act as an enhanced sensor or provide robust information encoding that protects against computational errors.

Utilizing defect platforms for quantum technologies requires precise control over the electron-nuclear entanglement. Generating entanglement in these systems is challenging since the electron couples to multiple nuclei at once. One way to control these always-on interactions is by applying periodic pulses on the electron. This approach entangles the electron with a subset of spins from the nuclear register and “weakens'' the remaining interactions. The isolation of the electron from some nuclei is often imperfect or demands extremely long pulses that lead to slow and faulty entanglement generation.

We provide a detailed analysis of the multipartite electron-nuclear entanglement structure in an arbitrarily large register and develop methods for its precise manipulation. This is done by designing entangling gates that maximize the so-called “all-way correlations” within a subsystem from the register and simultaneously suppress unintended interactions arising from the remaining spins. We inspect how residual correlations, control errors, or decoherence mechanisms modify the multipartite entanglement structure. Our analysis provides a complete understanding of the entanglement dynamics and paves the way for higher precision control techniques in nuclear-spin-based platforms.

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Cited by

[1] Regina Finsterhoelzl, Wolf-Rüdiger Hannes, and Guido Burkard, "High-Fidelity Entangling Gates for Electron and Nuclear Spin Qubits in Diamond", arXiv:2403.11553, (2024).

[2] Dominik Maile and Joachim Ankerhold, "Performance of quantum registers in diamond in the presence of spin impurities", arXiv:2211.06234, (2022).

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