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arXiv:1310.4120 · Nature Communications

Noise-resilient quantum evolution steered by dynamical decoupling

Gang‐Qin Liu, Hoi Chun Po, Jiangfeng Du, Ren‐Bao Liu, Xinyu Pan

Published Aug 5, 2013• 78 citations

Abstract

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.

DOI: 10.1038/ncomms3254

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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.

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.

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.

Dephasing--phase randomization of a quantum superposition state--is a major obstacle for the realization of high fidelity quantum logic operations. Here, we implement a two-qubit controlled-NOT gate using dynamical decoupling (DD), despite the gate time being more than 1 order of magnitude longer than the intrinsic coherence time of the system. For realizing this universal conditional quantum gate, we have devised a concatenated DD sequence that ensures robustness against imperfections of DD pulses that otherwise may destroy quantum information or interfere with gate dynamics. We compare its performance with three other types of DD sequences. These experiments are carried out using a well-controlled prototype quantum system--trapped atomic ions coupled by an effective spin-spin interaction. The scheme for protecting conditional quantum gates demonstrated here is applicable to other physical systems, such as nitrogen vacancy centers, solid state nuclear magnetic resonance, and circuit quantum electrodynamics.

Selective control of qubits in a quantum register for the purposes of quantum information processing represents a critical challenge for dense spin ensembles in solid-state systems. Here we present a protocol that achieves a complete set of selective electron-nuclear gates and single nuclear rotations in such an ensemble in diamond facilitated by a nearby nitrogen-vacancy (NV) center. The protocol suppresses internuclear interactions as well as unwanted coupling between the NV center and other spins of the ensemble to achieve quantum gate fidelities well exceeding 99%. Notably, our method can be applied to weakly coupled, distant spins representing a scalable procedure that exploits the exceptional properties of nuclear spins in diamond as robust quantum memories.

Precise control of an open quantum system is critical to quantum information processing but is challenging due to inevitable interactions between the quantum system and the environment. We demonstrated experimentally a type of dynamically corrected gates using only bounded-strength pulses on the nitrogen-vacancy centers in diamond. The infidelity of quantum gates caused by a nuclear-spin bath is reduced from being the second order to the sixth order of the noise-to-control-field ratio, which offers greater efficiency in reducing infidelity. The quantum gates have been protected to the limit essentially set by the spin-lattice relaxation time T1. Our work marks an important step towards fault-tolerant quantum computation in realistic systems.

Realizing individual control on single qubits in a spin-based quantum register is an ever-increasing challenge due to the close proximity of the qubits' resonance frequencies. Current schemes typically suffer from an inherent trade-off between fidelity and qubits selectivity. Here, we report on a scheme which combines noise protection by dynamical decoupling and magnetic gradient based selectivity, to enhance both the fidelity and the selectivity. With a single nitrogen-vacancy center in diamond, we experimentally demonstrate quantum gates with fidelity $=0.9\phantom{\rule{4pt}{0ex}}\ifmmode\pm\else\textpm\fi{}\phantom{\rule{4pt}{0ex}}0.02$ and a $50\ensuremath{-}\mathrm{kHz}$ spectral bandwidth, which is almost an order of magnitude narrower than the unprotected bandwidth. Our scheme will enable selective control of an individual nitrogen-vacancy qubit in an interacting qubits array using relatively moderate gradients of about

1\phantom{\rule{4pt}{0ex}}\mathrm{mG}/\mathrm{nm}

.