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Predicting the properties of complex, large-scale quantum systems is essential for developing quantum technologies. We present an efficient method for constructing an approximate classical description of a quantum state using very few measurements of the state. This description, called a ‘classical shadow’, can be used to predict many different properties; order log ( M ) measurements suffice to accurately predict M different functions of the state with high success probability. The number of measurements is independent of the system size and saturates information-theoretic lower bounds. Moreover, target properties to predict can be selected after the measurements are completed. We support our theoretical findings with extensive numerical experiments. We apply classical shadows to predict quantum fidelities, entanglement entropies, two-point correlation functions, expectation values of local observables and the energy variance of many-body local Hamiltonians. The numerical results highlight the advantages of classical shadows relative to previously known methods. An efficient method has been proposed through which the properties of a complex, large-scale quantum system can be predicted without fully characterizing the quantum state.

Fostering students' problem-solving abilities and design thinking has been recognized as a crucial educational objective. In the conventional collaborative project-based learning approach, co-regulative learning (CRL) has been adopted to guide learners to plan and monitor the progress of their projects. However, without providing adequate supports or feedback to individual teams, the innovation and design quality of the project outcomes could be disappointing. In this study, a generative AI (artificial intelligence)-based co-regulative learning (GAI-CRL) approach is proposed to address this issue. Moreover, an experiment was conducted in a digital game development (DGD) to assess this approach. A total of 46 university students from two classes were recruited in this study. The experimental group adopted the GAI-CRL approach, while the control group adopted the conventional CRL (C-CRL) approach. The results showed that the GAI-CRL approach significantly enhanced students' project design performance, learning motivation, self-efficacy, and creative thinking compared to the C-CRL approach. This study serves as a reference not only for implementing DGD projects but also for applying CRL to other educational domains.

Solving linear systems of equations is essential for many problems in science and technology, including problems in machine learning. Existing quantum algorithms have demonstrated the potential for large speedups, but the required quantum resources are not immediately available on near-term quantum devices. In this work, we study near-term quantum algorithms for linear systems of equations, with a focus on the two-norm and Tikhonov regression settings. We investigate the use of variational algorithms and analyze their optimization landscapes. There exist types of linear systems for which variational algorithms designed to avoid barren plateaus, such as properly-initialized imaginary time evolution and adiabatic-inspired optimization, suffer from a different plateau problem. To circumvent this issue, we design near-term algorithms based on a core idea: the classical combination of variational quantum states (CQS). We exhibit several provable guarantees for these algorithms, supported by the representation of the linear system on a so-called ansatz tree. The CQS approach and the ansatz tree also admit the systematic application of heuristic approaches, including a gradient-based search. We have conducted numerical experiments solving linear systems as large as 2 300 × 2 300 by considering cases where we can simulate the quantum algorithm efficiently on a classical computer. Our methods may provide benefits for solving linear systems within the reach of near-term quantum devices.

Modern quantum machine learning (QML) methods involve variationally optimizing a parameterized quantum circuit on a training data set, and subsequently making predictions on a testing data set (i.e., generalizing). In this work, we provide a comprehensive study of generalization performance in QML after training on a limited number N of training data points. We show that the generalization error of a quantum machine learning model with T trainable gates scales at worst as T / N . When only K  ≪  T gates have undergone substantial change in the optimization process, we prove that the generalization error improves to K / N . Our results imply that the compiling of unitaries into a polynomial number of native gates, a crucial application for the quantum computing industry that typically uses exponential-size training data, can be sped up significantly. We also show that classification of quantum states across a phase transition with a quantum convolutional neural network requires only a very small training data set. Other potential applications include learning quantum error correcting codes or quantum dynamical simulation. Our work injects new hope into the field of QML, as good generalization is guaranteed from few training data. The power of quantum machine learning algorithms based on parametrised quantum circuits are still not fully understood. Here, the authors report rigorous bounds on the generalisation error in variational QML, confirming how known implementable models generalize well from an efficient amount of training data.

The use of quantum computing for machine learning is among the most exciting prospective applications of quantum technologies. However, machine learning tasks where data is provided can be considerably different than commonly studied computational tasks. In this work, we show that some problems that are classically hard to compute can be easily predicted by classical machines learning from data. Using rigorous prediction error bounds as a foundation, we develop a methodology for assessing potential quantum advantage in learning tasks. The bounds are tight asymptotically and empirically predictive for a wide range of learning models. These constructions explain numerical results showing that with the help of data, classical machine learning models can be competitive with quantum models even if they are tailored to quantum problems. We then propose a projected quantum model that provides a simple and rigorous quantum speed-up for a learning problem in the fault-tolerant regime. For near-term implementations, we demonstrate a significant prediction advantage over some classical models on engineered data sets designed to demonstrate a maximal quantum advantage in one of the largest numerical tests for gate-based quantum machine learning to date, up to 30 qubits. Expectations for quantum machine learning are high, but there is currently a lack of rigorous results on which scenarios would actually exhibit a quantum advantage. Here, the authors show how to tell, for a given dataset, whether a quantum model would give any prediction advantage over a classical one.

The recent proliferation of NISQ devices has made it imperative to understand their power. In this work, we define and study the complexity class NISQ, which encapsulates problems that can be efficiently solved by a classical computer with access to noisy quantum circuits. We establish super-polynomial separations in the complexity among classical computation, NISQ, and fault-tolerant quantum computation to solve some problems based on modifications of Simon’s problems. We then consider the power of NISQ for three well-studied problems. For unstructured search, we prove that NISQ cannot achieve a Grover-like quadratic speedup over classical computers. For the Bernstein-Vazirani problem, we show that NISQ only needs a number of queries logarithmic in what is required for classical computers. Finally, for a quantum state learning problem, we prove that NISQ is exponentially weaker than classical computers with access to noiseless constant-depth quantum circuits. Our current understanding of the computational abilities of near-intermediate scale quantum (NISQ) computing devices is limited, in part due to the absence of a precise definition for this regime. Here, the authors formally define the NISQ realm and provide rigorous evidence that its capabilities are situated between the complexity classes BPP and BQP.

The behavior of genetic circuits is often poorly predictable. A gene’s expression level is not only determined by the intended regulators, but also affected by changes in ribosome availability imparted by expression of other genes. Here we design a quasi-integral biomolecular feedback controller that enables the expression level of any gene of interest (GOI) to adapt to changes in available ribosomes. The feedback is implemented through a synthetic small RNA (sRNA) that silences the GOI’s mRNA, and uses orthogonal extracytoplasmic function (ECF) sigma factor to sense the GOI’s translation and to actuate sRNA transcription. Without the controller, the expression level of the GOI is reduced by 50% when a resource competitor is activated. With the controller, by contrast, gene expression level is practically unaffected by the competitor. This feedback controller allows adaptation of genetic modules to variable ribosome demand and thus aids modular construction of complicated circuits. Competition for shared cellular resources often renders genetic circuits poorly predictable. Here the authors design a biomolecular quasi-integral controller that allows gene expression to adapt to variable demand in translation resources.

Atopic dermatitis (AD) is a chronic, inflammatory, pruritic form of dermatosis with heterogeneous manifestations that can substantially affect patients' quality of life. AD has a complex pathogenesis, making treatment challenging for dermatologists. The Janus kinase (JAK)–signal transducer and activator of transcription (STAT) pathway plays a central role in modulating multiple immune axes involved in the immunopathogenesis of AD. In particular, Th2 cytokines, including interleukin (IL)-4, IL-5, IL-13, IL-31, and thymic stromal lymphopoietin, which contribute to the symptoms of chronic inflammation and pruritus in AD, are mediated by JAK–STAT signal transduction. Furthermore, JAK–STAT is involved in the regulation of the epidermal barrier and the modulation of peripheral nerves related to the transduction of pruritus. Targeting the JAK–STAT pathway may attenuate these signals and show clinical efficacy through the suppression of various immune pathways associated with AD. Topical and oral JAK inhibitors with variable selectivity have emerged as promising therapeutic options for AD. Notably, topical ruxolitinib, oral upadacitinib, and oral abrocitinib were approved by the U.S. Food and Drug Administration for treating patients with AD. Accordingly, the present study reviewed the role of JAK–STAT pathways in the pathogenesis of AD and explored updated applications of JAK inhibitors in treating AD.

Arsenic, a metal ubiquitously distributed in the environment, remains an important global health threat. Drinking arsenic-contaminated water is the major route of human exposure. Exposure to arsenic contributes to several malignancies, in the integumentary, respiratory, hepatobiliary, and urinary systems. Cutaneous lesions are important manifestations after long-term arsenic exposure. Arsenical skin cancers usually herald the development of other internal cancers, making the arsenic-induced skin carcinogenesis a good model to investigate the progression of chemical carcinogenesis. In fact, only a portion of arsenic-exposed humans eventually develop malignancies, likely attributed to the arsenic-impaired immunity in susceptible individuals. Currently, the exact pathophysiology of arsenic-induced carcinogenesis remains elusive, although increased reactive oxidative species, aberrant immune regulations, and chromosome abnormalities with uncontrolled cell growth might be involved. This review discusses how arsenic induces carcinogenesis, and how the dysregulated innate and adaptive immunities in systemic circulation and in the target organs contribute to arsenic carcinogenesis. These findings offer evidence for illustrating the mechanism of arsenic-related immune dysregulation in the progression of carcinogenesis, and this may help explain the nature of multiple and recurrent clinical lesions in arsenic-induced skin cancers.

Cr(VI) can be released into soil as a result of mining, electroplating, and smelting operations. Due to the high toxicity of Cr(VI), its removal is necessary in order to protect ecosystems. Vermiculite is applied in situations where there is a high degree of metal pollution, as it is helpful during the remediation process due to its high cation exchange capacity. The Cr(VI) contained in the vermiculite should be extracted in order to recover it and to reduce the impact on the environment. In this work, adsorption equilibrium data for Cr(VI) in a simulated sorbent for soil remediation (a mixture that included both humic acid (HA) and vermiculite) were a good fit with the Langmuir isotherm model. The simulated sorbent for soil remediation was a favorable sorbent for Cr(VI) when it was in the test soil. An ionic liquid, [C4mim]Cl (1-butyl-3-methylimidazolium chloride), was studied to determine its efficiency in extracting Cr(VI) from the Cr- contaminated simulated sorbent in soil remediation. At 298 K and within 30 min, approximately 33.48 ± 0.79% of Cr(VI) in the simulated sorbent in soil remediation was extracted into [C4mim]Cl. Using FTIR spectroscopy, the absorbance intensities of the bands at 1032 and 1010 cm−1, which were attributed to C-O bond stretching in the polysaccharides of HA, were used to detect the changes in HA in the Cr-contaminated simulated sorbent for soil remediation before and after extraction. The results showed that Cr(VI) that has been absorbed on HA can be extracted into [C4mim]Cl. Using 1H NMR, it was observed that the 1-methylimizadole of [C4mim] Cl played an important role in the extraction of Cr(VI), which bonded with HA on vermiculite and was able to be transformed into the [C4mim]Cl phase.