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Hybridizing different degrees of freedom or physical platforms potentially offers various advantages in building scalable quantum architectures. Here, we introduce a fault-tolerant hybrid quantum computation by building on the advantages of both discrete-variable (DV) and continuous-variable (CV) systems. In particular, we define a CV-DV hybrid qubit with a bosonic cat code and a single photon, which is implementable in current photonic platforms. Due to the cat code encoded in the CV part, the predominant loss errors are readily correctable without multiqubit encoding, while the logical basis is inherently orthogonal due to the DV part. We design fault-tolerant architectures by concatenating hybrid qubits and an outer DV quantum error-correction code such as a topological code, exploring their potential merit in developing scalable quantum computation. We demonstrate by numerical simulations that our scheme is at least an order of magnitude more resource efficient compared to all previous proposals in photonic platforms, allowing us to achieve a record-high loss threshold among existing CV and hybrid approaches. We discuss the realization of our approach not only in all-photonic platforms but also in other hybrid platforms including superconducting and trapped-ion systems, which allows us to find various efficient routes toward fault-tolerant quantum computing. 

Two-dimensional (2D) atomic layer materials have attracted a great deal of attention due to their superior chemical, physical, and electronic properties, and have demonstrated excellent performance in various applications such as energy storage devices, catalysts, sensors, and transistors. Nevertheless, the cost-effective and large-scale production of high-quality 2D materials is critical for practical applications and progressive development in the industry. Electrochemical exfoliation is a recently introduced technique for the facile, environmentally friendly, fast, large-scale production of 2D materials. In this review, we summarize recent advances in different types of electrochemical exfoliation methods for efficiently preparing 2D materials, along with the characteristics of each method, and then introduce their applications as electrode materials for energy storage devices. Finally, the remaining challenges and prospects for developing the electrochemical exfoliation process of 2D materials for energy storage devices are discussed. 

Metal-free carbon materials have emerged as cost-effective and high-performance catalysts for the production of hydrogen peroxide (H 2 O 2 ) through the two-electron oxygen reduction reaction (ORR). Here, we show that 3D crumpled graphene with controlled oxygen and defect configurations significantly improves the electrocatalytic production of H 2 O 2 . The crumpled graphene electrocatalyst with optimal defect structures and oxygen functional groups exhibits outstanding H 2 O 2 selectivity of 92–100% in a wide potential window of 0.05–0.7 V vs. reversible hydrogen electrode (RHE) and a high mass activity of 158 A g −1 at 0.65 V vs. RHE in alkaline media. In addition, the crumpled graphene catalyst showed an excellent H 2 O 2 production rate of 473.9 mmol gcat −1 h −1 and stability over 46 h at 0.4 V vs. RHE. Moreover, density functional theory calculations revealed the role of the functional groups and defect sites in the two-electron ORR pathway through the scaling relation between OOH and O adsorption strengths. These results establish a structure-mechanism-performance relationship of functionalized carbon catalysts for the effective production of H 2 O 2 .