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Dynamical Decoupling of a Geometric Qubit

Yuhei Sekiguchi, Yusuke Komura, Hideo Kosaka, 20361199

Published Nov 1, 2019• 14 citations
OpenAlex

Abstract

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.

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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.

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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.
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.e.g.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.
Dynamical decoupling is a powerful technique for extending the coherence time ( T 2 ) of qubits. We apply this technique to the electron spin qubit of a single nitrogen-vacancy center in type-IIa diamond. In a crystal with natural abundance of 13 C nuclear spins, we extend the decoherence time up to 2.2 ms. This is close to the T 1 value of this NV center (4 ms). Since dynamical decoupling must perform well for arbitrary initial conditions, we measured the dependence on the initial state and compared the performance of different sequences with respect to initial state dependence and robustness to experimental imperfections.
Implementing precise operations on quantum systems is one of the biggest challenges for building quantum devices in a noisy environment. Dynamical decoupling attenuates the destructive effect of the environmental noise, but so far, it has been used primarily in the context of quantum memories. Here, we experimentally demonstrate a general scheme for combining dynamical decoupling with quantum logical gate operations using the example of an electron-spin qubit of a single nitrogen-vacancy center in diamond. We achieve process fidelities >98% for gate times that are 2 orders of magnitude longer than the unprotected dephasing time T2.
Hybrid systems consisting of different types of qubits are promising for building quantum computers if they combine useful properties of their constituent qubits. However, they also pose additional challenges if one type of qubits is more susceptible to environmental noise than the others. Dynamical decoupling can help to protect such systems by reducing the decoherence due to the environmental noise, but the protection must be designed such that it does not interfere with the control fields driving the logical operations. Here, we test such a protection scheme on a quantum register consisting of the electronic and nuclear spins of a nitrogen-vacancy center in diamond. The results show that processing is compatible with protection: The dephasing time was extended almost to the limit given by the longitudinal relaxation time of the electron spin.
Realistic quantum computing is subject to noise. Therefore, an important frontier in quantum computing is to implement noise-resilient quantum control over qubits. At the same time, dynamical decoupling can protect the coherence of qubits. Here we demonstrate non-trivial quantum evolution steered by dynamical decoupling control, which simultaneously suppresses noise effects. We design and implement a self-protected controlled-NOT gate on the electron spin of a nitrogen-vacancy centre and a nearby carbon-13 nuclear spin in diamond at room temperature, by employing an engineered dynamical decoupling control on the electron spin. Final state fidelity of 0.91(1) is observed in preparation of a Bell state using the gate. At the same time, the qubit coherence time is elongated at least 30 fold. The design scheme does not require the dynamical decoupling control to commute with the qubit interaction and therefore works for general qubit systems. This work marks a step towards implementing realistic quantum computing systems. Realistic quantum computers require a high degree of qubit control and must also be resilient to noise. Using dynamical decoupling control techniques, Liuet al.implement a self-protected controlled-NOT gate for electron and nuclear spins that retains a high final state fidelity.
The holonomic approach to controlling (nitrogen-vacancy) NV-center qubits provides an elegant way of theoretically devising universal quantum gates that operate on qubits via calculable microwave pulses. There is, however, a lack of simulated results from the theory of holonomic control of quantum registers with more than two qubits describing the transition between the dark states. Considering this, we have been experimenting with the IBM Quantum Experience technology to determine the capabilities of simulating holonomic control of NV-centers for three qubits describing an eight-level system that produces a non-Abelian geometric phase. The tunability of the geometric phase via the detuning frequency is demonstrated through the high fidelity (~85%) of three-qubit off-resonant holonomic gates over the on-resonant ones. The transition between the dark states shows the alignment of the gate's dark state with the qubit's initial state hence decoherence of the multi-qubit system is well-controlled through a π/3 rotation.