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arXiv:2310.10991 · Physical Review A

Higher-order protection of quantum gates: Hamiltonian engineering coordinated with dynamical decoupling

P. Z. Zhao, Tianqi Chen, Sirui Liu, Jiangbin Gong

Published Feb 20, 2025• 2 citations
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Abstract

Dynamical decoupling represents an active approach towards the protection of quantum memories and quantum gates. Because dynamical decoupling operations can interfere with a system's own time evolution, the protection of quantum gates is more challenging than that of quantum states. In this work, we put forward a simple but general approach towards the realization of higher-order protection of quantum gates and further execute the first cloud-based demonstration of dynamical-decoupling-protected quantum gates at the first order and the second order. The central idea of our approach is to engineer (hence regain the control of) the gate Hamiltonian in coordination with higher-order dynamical decoupling sequences originally proposed for the protection of quantum memories. The physical demonstration on an IBM quantum processor indicates the effectiveness and potential of our approach on noisy intermediate scale quantum computers.

DOI
10.1103/physreva.111.022621

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Dynamical decoupling represents an active approach towards the protection of quantum memories and quantum gates. Because dynamical decoupling operations can interfere with a system's own time evolution, the protection of quantum gates is more challenging than that of quantum states. In this work, we put forward a simple but general approach towards the realization of higher-order protection of quantum gates and further execute the first cloud-based demonstration of dynamical-decoupling-protected quantum gates at the first order and the second order. The central idea of our approach is to engineer (hence regain the control of) the gate Hamiltonian in coordination with higher-order dynamical decoupling sequences originally proposed for the protection of quantum memories. The physical demonstration on an IBM quantum processor indicates the effectiveness and potential of our approach on noisy intermediate scale quantum computers.
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.
In the field of quantum information, a major challenge is to protect and shield quantum systems from environmental influences, which cause dissipation and decoherence. One approach to address this problem is called dynamical decoupling, where we act on a quantum system with a series of fast and strong local control operations. If done correctly, the system's state gets rotated in discrete steps in its state space in such a way that the effects of the environment cancel up to a certain order. In the first part of this thesis, we will introduce the basics of dynamical decoupling and present a new approach for constructing dynamical decoupling schemes based on sequences of Weyl operators on networks of qudits. This approach goes beyond merely protecting a quantum system, as it is also capable of altering existing Hamiltonian interactions in ways suitable for quantum simulation purposes. We will also investigate how imperfect controls influence the effectiveness of dynamical decoupling and focus particularly on stochastic noise. In the second part of the thesis, we study concrete scenarios for the application of dynamical decoupling. First, we consider the task of quantum state transfer on a linear chain of qubits and use decoupling to protect the transfer from detrimental influences caused by a bend in the chain. We also look at how to design the specific interaction strengths required on the chain to make the state transfer work and extend this result to chains of qudits. Another chapter deals with decoupling the atomic centre-of-mass motion of a trapped atom or ion in a cavity interacting with a radiation field. Finally, we use decoupling to execute sequences of one- and two-qubit quantum gates on a chain of coupled qubits. Particular care is taken to ensure high fidelity operations in the presence of imperfect decoupling pulses.
In addition to the traditional two-level system, the three-level system serves as another important elemental building block for the manipulation of qubits. However, the quantum information processing in the three-level system is also subject to the decoherence induced by the interaction between the quantum system and its environment or by the crosstalk between different qutrits. In this work, we construct a sequence of physically feasible dynamical decoupling operators for the three-level system to mitigate not only the transverse dephasing between the excited state and ground states but also the longitudinal relaxation among them. Combining the Hamiltonian engineering and our constructed dynamical decoupling sequence, we further realize the dynamical decoupling protection of qutrit-based quantum gates. Our scheme can effectively enhance the fidelity of three-level-based quantum gates through filtering out the environmental noises, which may provide a new horizon to improve the accuracy of three-level-based quantum manipulation.
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 main obstacles to the realization of high-fidelity quantum gates are the control errors arising from inaccurate manipulation of a quantum system and the decoherence caused by the interaction between the quantum system and its environment. Nonadiabatic holonomic quantum computation allows for high-speed implementation of whole-geometric quantum gates, making quantum computation robust against control errors. Dynamical decoupling provides an effective method to protect quantum gates against environment-induced decoherence, regardless of collective decoherence or independent decoherence. In this paper, we put forward a protocol of nonadiabatic holonomic quantum computation protected by dynamical decoupling. Due to the combination of nonadiabatic holonomic quantum computation and dynamical decoupling, our protocol not only possesses the intrinsic robustness against control errors but also protects quantum gates against environment-induced decoherence.
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.