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arXiv:2002.10596 · Physical Review Applied

Dynamical Decoupling of a Geometric Qubit

Yuhei Sekiguchi, Yusuke Komura, Hideo Kosaka

Published Nov 1, 2019• 19 citations

Abstract

A $g\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}m\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}c$ $q\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}b\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t$, consisting of $e.g.$ a spin-triplet electron in a nitrogen-vacancy center in diamond, is crucial as an interface to integrate quantum communication, computing, and sensing, owing to its structural similarity to a photonic polarization qubit. Implementation is held back because such a system's holonomic gate operations unexpectedly induce slow depopulation from the qubit space. This study demonstrates robust dynamical decoupling, by applying intentional detuning to the qubit's operations, to suppress the depopulation. This approach should have an impact on engineering a robust quantum gate sequence to facilitate large-scale quantum information processing.

DOI: 10.1103/physrevapplied.12.051001

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A

g\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}m\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}c

q\phantom{\rule{0}{0ex}}u\phantom{\rule{0}{0ex}}b\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t

, consisting of

e.g.

a spin-triplet electron in a nitrogen-vacancy center in diamond, is crucial as an interface to integrate quantum communication, computing, and sensing, owing to its structural similarity to a photonic polarization qubit. Implementation is held back because such a system's holonomic gate operations unexpectedly induce slow depopulation from the qubit space. This study demonstrates robust dynamical decoupling, by applying intentional detuning to the qubit's operations, to suppress the depopulation. This approach should have an impact on engineering a robust quantum gate sequence to facilitate large-scale quantum information processing.

Quantum bits or qubits naturally decohere by becoming entangled with uncontrollable environments. Dynamical decoupling is, therefore, required to disentangle qubits from an environment by periodically reversing the qubit bases, but this causes rotation error to accumulate. Whereas a conventional qubit is rotated within the SU(2) two-level system, a geometric qubit defined in the degenerate subspace of a V-shaped SU(3) three-level system is geometrically rotated via the third ancillary level to acquire a geometric phase. We demonstrate that simply by introducing detuning, the dynamical decoupling of the geometric qubit on a spin triplet electron in a nitrogen-vacancy center in diamond can be made to spontaneously suppress error accumulation. The geometric dynamical decoupling extends the coherence time of the geometric qubit up to 1.9 ms, limited by the relaxation time, with 128 decoupling gates at room temperature. Our technique opens a route to holonomic quantum memory for use in various quantum applications requiring sequential operations.

High-fidelity and decoherence-insensitive quantum gates are essential for achieving universal quantum computing. In quantum information processing, decoherence arising from excited states significantly contributes to the scheme's infidelity. Therefore, minimizing the average population of the excited state is crucial when designing quantum protocols. A promising approach involves utilizing capture-and-release dynamics to induce a complex phase on the ground state in a two-level system, effectively suppressing the integrated excited-state population. By applying this dynamics protocol to a $\mathrm{\ensuremath{\Lambda}}$ three-level system, we propose a scheme to construct arbitrary decoherence suppressed single-qubit and nontrivial two-qubit gates; meanwhile, by incorporating the Zeno dynamics process in the construction of two-qubit logic gates, the large detuning and excitation of virtual photons render the scheme insensitive to qubit decoherence and cavity dissipation. Applying our scheme to the nitrogen-vacancy (NV) center as an example, we prove our scheme with higher fidelity than conventional nonadiabatic non-Abelian geometric gates while significantly enhancing the robustness against decoherence and frequency shift errors. These studies provide alternative approaches for constructing robust quantum gate operations. We also emphasize that the scheme is feasible for three-level quantum systems, not limited to NV center systems.

We perform a detailed theoretical-experimental study of the dynamical decoupling (DD) of the nitrogen-vacancy (NV) center in diamond. We investigate the DD sequences applied to suppress the dephasing of the electron spin of the NV center induced by the coupling to a spin bath composed of the substitutional nitrogen atoms. The decoupling efficiency of various DD schemes is studied, including both periodic and aperiodic pulse sequences. For ideal control pulses, we find that the DD protocols with the Carr-Purcell-Meiboom-Gill (CPMG) timing of the pulses provides best performance. We show that, as the number of control pulses increases, the decoupling fidelity scaling differs qualitatively from the predictions of the Magnus expansion, and explain the origin of this difference. In particular, more advanced symmetrized or concatenated protocols do not improve the DD performance. Next, we investigate the impact of the systematic instrumental pulse errors in different periodic and aperiodic pulse sequences. The DD protocols with the single-axis control do not preserve all spin components in the presence of the pulse errors, and the two-axis control is needed. We demonstrate that the two-axis control sequence with the CPMG timing is very robust with respect to the pulse errors. The impact of the pulse errors can be diminished further by symmetrizing this protocol. For all protocols studied here, we present a detailed account of the pulse error parameters which make the strongest impact on the DD performance. In conclusion, we give specific recommendations about choosing the decoupling protocol for the system under investigation.