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arXiv:2203.00852 · Physical Review A

Preserving multilevel quantum coherence by dynamical decoupling

Xinxing Yuan, Yue Li, Mengxiang Zhang, Chang Liu, Mingdong Zhu, Xi Qin, Nikolay V. Vitanov, Yiheng Lin, Jiangfeng Du

Published Aug 15, 2022• 14 citations
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Abstract

Quantum information processing with multilevel systems (qudits) provides additional features and applications than the two-level systems. However, qudits are more prone to dephasing and dynamical decoupling for qudits has never been experimentally demonstrated. Here, as a proof-of-principle demonstration, we experimentally apply dynamical decoupling to protect superpositions with three levels of a trapped $^{9}\mathrm{Be}^{+}$ ion from ambient noisy magnetic field, prolonging coherence by up to approximately an order of magnitude. Our demonstration, straightforwardly scalable to more levels, may open up a path toward long coherence quantum memory, metrology, and information processing with qudits.

DOI
10.1103/physreva.106.022412

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Quantum information processing with multilevel systems (qudits) provides additional features and applications than the two-level systems. However, qudits are more prone to dephasing and dynamical decoupling for qudits has never been experimentally demonstrated. Here, as a proof-of-principle demonstration, we experimentally apply dynamical decoupling to protect superpositions with three levels of a trapped 9Be+^{9}\mathrm{Be}^{+}9Be+ ion from ambient noisy magnetic field, prolonging coherence by up to approximately an order of magnitude. Our demonstration, straightforwardly scalable to more levels, may open up a path toward long coherence quantum memory, metrology, and information processing with qudits.
The use of multilevel quantum information carriers, also known as qudits, has attracted significant interest as a way of further scaling quantum computing devices. However, such multilevel systems usually express shorter coherence time than their two-level counterparts, which limits their computational potential. We thus propose and experimentally demonstrate two approaches for realizing the continuous dynamical decoupling of magnetic-sensitive states with mF = ±1 for qudits encoded in optical transition of trapped 171Yb+ ions. We improve the coherence time of qudit levels by an order of magnitude (more than 9 ms) without any magnetic shielding, revealing the potential advantage of the symmetry of the 171Yb+ ion energy structure for counteracting magnetic field noise. Our results are a step toward realizing qudit-based algorithms using trapped ions.
Methods that preserve coherence broadly impact all quantum information processing and metrology applications. Dynamical decoupling methods accomplish this by protecting qubits in noisy environments but are typically constrained to the limit where the qubits themselves are non-interacting. Here we consider the alternate regime wherein the inter-qubit couplings are of the same order as dephasing interactions with the environment. We propose and demonstrate a multi-pulse protocol that protects transverse spin states by suitably Hamiltonian engineering the inter-spin coupling while simultaneously suppressing dephasing noise on the qubits. We benchmark the method on 13C nuclear spin qubits in diamond, dipolar coupled to each other and embedded in a noisy electronic spin bath, and hyperpolarized via optically pumped NV centers. We observe effective state lifetimes of 13C nuclei $T_2^{\prime}\approx$2.5s at room temperature, an extension of over 4700-fold over the conventional T2∗T_2^{\ast}T2∗​ free induction decay. The spins are continuously interrogated during the applied quantum control, resulting in 13C NMR line narrowing and an $>$500-fold boost in SNR due to the lifetime extension. Together with hyperpolarization spin interrogation is accelerated by >1011>10^{11}>1011 over conventional 7T NMR. This work suggests strategies for the dynamical decoupling of coupled qubit systems with applications in a variety of experimental platforms.
Encoding quantum information in ddd-dimensional systems (qudits) with d>2d>2d>2 offers appealing new directions for resource-efficient quantum computing. However, protecting the coherence of nonclassical qudit resource states remains an open challenge. Dynamical decoupling (DD) is a well-established technique for extending coherence, but its application to qudits is hindered by the quadratic scaling of the decoupling sequence overhead with the dimension ddd. As a result, demonstrations of qudit DD have so far been limited to low-dimensional qudits. Here, we show that noise-biased qudits enable a nontrivial reduction of this overhead, for example, from quadratic to linear. We perform qudit DD on a model d=8d=8d=8 qudit, the nuclear spin of an antimony donor in silicon. We benchmark DD performance on highly nonclassical states such as uniform superpositions, cat states, and Haar random states and measure coherence improvements up to a factor 555 to 101010. For a spin-cat error correction code, continuous DD extends the coherence time of the logical superposition ∣+⟩L|+\rangle_L∣+⟩L​ to 225225225~ms, compared to 191919~ms under free evolution and 858585~ms with a Hahn echo. This improvement shows that DD sequences tailored to a system's noise bias can significantly enhance the lifetime of encoded logical qubits.
Quantum systems are affected by interactions with their environments, causing decoherence through two processes: pure dephasing and energy relaxation. For quantum information processing it is important to increase the coherence time of Josephson qubits and other artificial two-level atoms. We show theoretically that if the coupling between these qubits and a cavity field is longitudinal and in the ultrastrong-coupling regime, the system is strongly protected against relaxation. Vice versa, if the coupling is transverse and in the ultrastrong-coupling regime, the system is protected against pure dephasing. Taking advantage of the relaxation suppression, we show that it is possible to enhance their coherence time and use these qubits as quantum memories. Indeed, to preserve the coherence from pure dephasing, we prove that it is possible to apply dynamical decoupling. We also use an auxiliary atomic level to store and retrieve quantum information.
In quantum information processing, it is vital to protect the coherence of qubits in noisy environments. Dynamical decoupling (DD), which applies a sequence of flips on qubits and averages the qubit-environment coupling to zero, is a promising strategy compatible with other desired functionalities, such as quantum gates. Here, we review the recent progresses in theories of dynamical decoupling and experimental demonstrations. We give both semiclassical and quantum descriptions of the qubit decoherence due to coupling to noisy environments. Based on the quantum picture, a geometrical interpretation of DD is presented. The periodic Carr-Purcell-Meiboom-Gill DD and the concatenated DD are reviewed, followed by a detailed exploration of the recently developed Uhrig DD, which employs the least number of pulses in an unequally spaced sequence to suppress the qubit-environment coupling to a given order of the evolution time. Some new developments and perspectives are also discussed.
Multilevel qudit systems are increasingly being explored as alternatives to traditional qubit systems due to their denser information storage and processing potential. However, qudits are more susceptible to decoherence than qubits due to increased loss channels, noise sensitivity, and crosstalk. To address these challenges, we develop protocols for dynamical decoupling (DD) of qudit systems based on the Heisenberg-Weyl group. We implement and experimentally verify these DD protocols on a superconducting transmon processor that supports qudit operation based on qutrits (d=3) and ququarts (d=4). Specifically, we demonstrate single-qudit DD sequences to decouple qutrits and ququarts from system-bath-induced decoherence. We also introduce two-qudit DD sequences designed to suppress the detrimental cross-Kerr couplings between coupled qudits. This allows us to demonstrate a significant improvement in the fidelity of time-evolved qutrit Bell states. Our results highlight the utility of leveraging DD to enable scalable qudit-based quantum computing.