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arXiv:1110.1870 · Physical Review A

Robust trapped-ion quantum logic gates by continuous dynamical decoupling

A. Bermúdez, Piet O. Schmidt, Martin Bodo Plenio, Alex Retzker

Published Apr 4, 2012• 112 citations
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Abstract

We introduce a scheme that combines phonon-mediated quantum logic gates in trapped ions with the benefits of continuous dynamical decoupling. We demonstrate theoretically that a strong driving of the qubit decouples it from external magnetic-field noise, enhancing the fidelity of two-qubit quantum gates. Moreover, the scheme does not require ground-state cooling, and is inherently robust to undesired ac Stark shifts. The underlying mechanism can be extended to a variety of other systems where a strong driving protects the quantum coherence of the qubits without compromising the two-qubit couplings.

DOI
10.1103/physreva.85.040302

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We introduce a scheme that combines phonon-mediated quantum logic gates in trapped ions with the benefits of continuous dynamical decoupling. We demonstrate theoretically that a strong driving of the qubit decouples it from external magnetic-field noise, enhancing the fidelity of two-qubit quantum gates. Moreover, the scheme does not require ground-state cooling, and is inherently robust to undesired ac Stark shifts. The underlying mechanism can be extended to a variety of other systems where a strong driving protects the quantum coherence of the qubits without compromising the two-qubit couplings.
We propose a pulsed dynamical decoupling protocol as the generator of tunable, fast, and robust quantum phase gates between two microwave-driven trapped-ion hyperfine qubits. The protocol consists of sequences of $\ensuremath{\pi}$ pulses acting on ions that are oriented along an externally applied magnetic-field gradient. In contrast to existing approaches, in our design the two vibrational modes of the ion chain cooperate under the influence of the external microwave driving to achieve significantly increased gate speeds. Our scheme is robust against the dominant noise sources, which are errors on the magnetic-field and microwave pulse intensities, as well as motional heating, predicting two-qubit gates with fidelities above 99.9% in tens of microseconds.
Entangling gates of trapped ions are typically mediated by collective motional degrees of freedom. Weak coupling between qubit and motional degrees of freedom and the resulting harmonic dynamics give access to a broad range of gate schemes, but also impose strict limitations on achievable gate times. In this paper, we devise optimally designed driving schemes for the realization of fast, high-fidelity entangling gates mediated by anharmonic dynamics. The driving can also be optimized to achieve resilience to multiple system imperfections, and the anharmonicity in the motional dynamics can be used to enhance such resilience.
A novel two-qubit entangling gate for trapped-ion quantum processors is proposed theoretically and demonstrated experimentally. During the gate, double-dressed quantum states are created by applying a phase-modulated continuous driving field. The speed of this quantum gate is an order of magnitude higher than that of previously demonstrated rf controlled two-qubit entangling gates in static magnetic field gradients. At the same time, the field driving the gate dynamically decouples the qubits from amplitude and frequency noise, increasing the qubits’ coherence time by 3 orders of magnitude. The gate requires only a single continuous rf field per qubit, making it well suited for scaling a quantum processor to large numbers of qubits. Implementing this entangling gate, we generate the Bell states | Φ + ⟩ and | Ψ + ⟩ in less than or equal to 313 μ s with fidelities up to 98 − 3 + 2 % in a static magnetic gradient of only 19.09 T / m . At higher magnetic field gradients, the entangling gate speed can be further improved to match that of laser-based counterparts.
Dynamical decoupling techniques are a versatile tool for engineering quantum states with tailored properties. In trapped ions, nested layers of continuous dynamical decoupling by means of radio-frequency field dressing can cancel dominant magnetic and electric shifts and therefore provide highly prolonged coherence times of electronic states. Exploiting this enhancement for frequency metrology, quantum simulation or quantum computation, poses the challenge to combine the decoupling with laser-ion interactions for the quantum control of electronic and motional states of trapped ions. Ultimately, this will require running quantum gates on qubits from dressed decoupled states. We provide here a compact representation of nested continuous dynamical decoupling in trapped ions, and apply it to electronic SSS and DDD states and optical quadrupole transitions. Our treatment provides all effective transition frequencies and Rabi rates, as well as the effective selection rules of these transitions. On this basis, we discuss the possibility of combining continuous dynamical decoupling and Mølmer-Sørensen gates.
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.
The loss of coherence is one of the main obstacles for the implementation of quantum information processing. The efficiency of dynamical decoupling schemes, which have been introduced to address this problem, is limited itself by the fluctuations in the driving fields which will themselves introduce noise. We address this challenge by introducing the concept of concatenated continuous dynamical decoupling, which can overcome not only external magnetic noise but also noise due to fluctuations in driving fields. We show theoretically that this approach can achieve relaxation limited coherence times, and demonstrate experimentally that already the most basic implementation of this concept yields an order of magnitude improvement to the decoherence time for the electron spin of nitrogen vacancy centers in diamond. The proposed scheme can be applied to a wide variety of other physical systems, including trapped atoms and ions and quantum dots, and may be combined with other quantum technologies challenges such as quantum sensing and quantum information processing.