Introduction and overview As mentioned in Chapter 4, dynamical decoupling (DD) techniques have developed decades of tradition in the context of NMR spectroscopy, where they continue to play a pervasive role throughout all aspects of imaging and coherent control of multi-spin dynamics in the liquid and solid state. A dedicated experimental characterization and exploitation of DD as a tool for high-fidelity dynamical control and decoherence suppression in different quantum information processing (QIP) platforms has been undertaken only in more recent years, largely enabled by impressive laboratory progress in fast and ultrafast coherent control capabilities over the past decade. Without attempting to provide a comprehensive in-depth account, it is our goal in this chapter to highlight some key experimental advances to illustrate the significance of DD strategies for near-term practical quantum error control in QIP; and justify why, quoting from a recent experimental work [MTA+06], they “will likely form a quintessential element in real quantum computers.” The large majority of dynamical error-suppression implementations in QIP have aimed thus far to validate DD as a tool for enhanced quantum memory in different qubit devices in the presence of various decoherence mechanisms. Likewise, with the exception of a recent work reporting the suppression of collisional decoherence using a “continuous spin echo” close in spirit to Eulerian DD [SAD10], the majority of experiments have employed (sufficiently) “hard” pulses, such that any evolution other than that due to the control field could be taken as negligible and the bang-bang (BB) limit formalized in Chapter 4 invoked as an adequate approximation.
Introduction and overview As mentioned in Chapter 4, dynamical decoupling (DD) techniques have developed decades of tradition in the context of NMR spectroscopy, where they continue to play a pervasive role throughout all aspects of imaging and coherent control of multi-spin dynamics in the liquid and solid state. A dedicated experimental characterization and exploitation of DD as a tool for high-fidelity dynamical control and decoherence suppression in different quantum information processing (QIP) platforms has been undertaken only in more recent years, largely enabled by impressive laboratory progress in fast and ultrafast coherent control capabilities over the past decade. Without attempting to provide a comprehensive in-depth account, it is our goal in this chapter to highlight some key experimental advances to illustrate the significance of DD strategies for near-term practical quantum error control in QIP; and justify why, quoting from a recent experimental work [MTA+06], they “will likely form a quintessential element in real quantum computers.” The large majority of dynamical error-suppression implementations in QIP have aimed thus far to validate DD as a tool for enhanced quantum memory in different qubit devices in the presence of various decoherence mechanisms. Likewise, with the exception of a recent work reporting the suppression of collisional decoherence using a “continuous spin echo” close in spirit to Eulerian DD [SAD10], the majority of experiments have employed (sufficiently) “hard” pulses, such that any evolution other than that due to the control field could be taken as negligible and the bang-bang (BB) limit formalized in Chapter 4 invoked as an adequate approximation.
Motivation and overview The aim of this chapter is to illustrate the basic physical principles and mathematical framework of dynamical decoupling (DD) techniques for open quantum systems, as relevant to quantum information processing (QIP) applications. Historically, the physical origins of DD date back to the idea of coherent averaging of interactions, as pioneered in high-resolution solid-state nuclear magnetic resonance (NMR) by Haeberlen and Waugh using elegantly designed multiple-pulse sequences [HW68, WHH68, H76]. It was in the same landmark work [HW68] that average Hamiltonian theory was developed as a formalism on which the design and analysis of DD sequences has largely relied since then. In the original context of NMR spectroscopy, decoupling serves the purpose of enhancing resolution by simplifying complex spectra. This is achieved by realizing that an otherwise static spin Hamiltonian “can be made to appear time-dependent in a controlled way,” so that “as the characteristic repetition period of the pulses becomes [sufficiently] small, the spin system comes to behave over long times as though under the influence of a time-independent average Hamiltonian” [HW68]. Some basic insight may be gained by revisiting the paradigmatic example offered by the so-called Hahn echo [H50] and Carr–Purcell (CP) sequences [CP54] in the simplest setting of a two spin-1/2 system.
Dynamical decoupling (DD) is a popular technique for protecting qubits from the environment. However, unless special care is taken, experimental errors in the control pulses used in this technique can destroy the quantum information instead of preserving it. Here, we investigate techniques for making DD sequences robust against different types of experimental errors while retaining good decoupling efficiency in a fluctuating environment. We present experimental data from solid-state nuclear spin qubits and introduce a new DD sequence that is suitable for quantum computing and quantum memory.
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.
Dynamical decoupling (DD) and Decoherence free subspace (DFS) are powerful techniques in quantum computing aimed at enhancing fidelity by mitigating the detrimental effects of noise and environmental interactions. In quantum systems, noise and decoherence can degrade the coherence of quantum states, leading to errors and reduced computational accuracy. DD employs carefully designed sequences of control pulses to periodically intervene and counteract these undesired interactions, while DFS utilizes subspace encoding techniques to protect quantum information from decoherence. To evaluate and compare the fidelity achieved by DD and DFS, this paper presents a series of experiments considering the effect of time and the number of qubits. The experiments provide valuable insights into the performance of both methods under different conditions. By systematically examining the fidelity results, the impact of time and the scaling behavior with increasing qubits can be assessed. The experimental findings showcase the effectiveness of DD in reducing the impact of noise and extending the coherence time of quantum states. By strategically manipulating the quantum system, DD minimizes error accumulation and preserves the integrity of fragile quantum information. It is observed that the decrease in fidelity with increasing t is relatively small and gradual. Despite being outperformed by DD, the DFS method exhibits robustness and maintains a high degree of fidelity even in the presence of extended time durations.
Abstract Dynamical decoupling (DD) is one of the simplest error suppression methods, aiming to enhance the coherence of qubits in open quantum systems. Moreover, DD has demonstrated effectiveness in reducing coherent crosstalk, one major error source in near-term quantum hardware, which manifests from two types of interactions. Static crosstalk exists in various hardware platforms, including superconductor and semiconductor qubits, by virtue of always-on qubit-qubit coupling. Additionally, driven crosstalk may occur as an unwanted drive term due to leakage from driven gates on other qubits. Here we explore a novel staggered DD protocol tailored for multi-qubit systems that suppresses the decoherence error and both types of coherent crosstalk. We develop two experimental setups—an ‘idle–idle’ experiment in which two pairs of qubits undergo free evolution simultaneously and a ‘driven-idle’ experiment in which one pair is continuously driven during the free evolution of the other pair. These experiments are performed on an IBM Quantum superconducting processor and demonstrate the significant impact of the staggered DD protocol in suppressing both types of coherent crosstalk. When compared to the standard DD sequences from state-of-the-art methodologies with the application of X 2 sequences, our staggered DD protocol enhances circuit fidelity by 19.7% and 8.5%, respectively, in addressing these two crosstalk types.
Quantum computation (QC) relies on the ability to implement high-fidelity quantum gate operations and successfully preserve quantum state coherence. One of the most challenging obstacles for reliable QC is overcoming the inevitable interaction between a quantum system and its environment. Unwanted interactions result in decoherence processes that cause quantum states to deviate from a desired evolution, consequently leading to computational errors and loss of coherence. Dynamical decoupling (DD) is one such method, which seeks to attenuate the effects of decoherence by applying strong and expeditious control pulses solely to the system. Provided the pulses are applied over a time duration sufficiently shorter than the correlation time associated with the environment dynamics, DD effectively averages out undesirable interactions and preserves quantum states with a low probability of error, or fidelity loss. In this study various aspects of this approach are studied from sequence construction to applications of DD to protecting QC. First, a comprehensive examination of the error suppression properties of a near-optimal DD approach is given to understand the relationship between error suppression capabilities and the number of required DD control pulses in the case of ideal, instantaneous pulses. While such considerations are instructive for examining DD efficiency, i.e., performance vs the number of control pulses, high-fidelity DD in realizable systems is difficult to achieve due to intrinsic pulse imperfections which further contribute to decoherence. As a second consideration, it is shown how one can overcome this hurdle and achieve robustness and recover high-fidelity DD in the presence of faulty control pulses using Genetic Algorithm optimization and sequence symmetrization. Thirdly, to illustrate the implementation of DD in conjunction with QC, the utilization of DD and quantum error correction codes (QECCs) as a protection method for adiabatic quantum computing (AQC) is discussed. A performance comparison between two deterministic DD schemes is given, where preference towards one particular method is found due to sequence structure and procedure from which higher accuracy sequences are generated.