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Quantum error mitigation has been proposed as a means to combat unwanted and unavoidable errors in near-term quantum computing without the heavy resource overheads required by fault-tolerant schemes. Recently, error mitigation has been successfully applied to reduce noise in near-term applications. In this work, however, we identify strong limitations to the degree to which quantum noise can be effectively 'undone' for larger system sizes. Our framework rigorously captures large classes of error-mitigation schemes in use today. By relating error mitigation to a statistical inference problem, we show that even at shallow circuit depths comparable to those of current experiments, a superpolynomial number of samples is needed in the worst case to estimate the expectation values of noiseless observables, the principal task of error mitigation. Notably, our construction implies that scrambling due to noise can kick in at exponentially smaller depths than previously thought. Noise also impacts other near-term applications by constraining kernel estimation in quantum machine learning, causing an earlier emergence of noise-induced barren plateaus in variational quantum algorithms and ruling out exponential quantum speed-ups in estimating expectation values in the presence of noise or preparing the ground state of a Hamiltonian., Competing Interests: Competing interestsThe authors declare no competing interests., (© The Author(s) 2024.)

The advent of noisy intermediate-scale quantum computers has put the search for possible applications to the forefront of quantum information science. One area where hopes for an advantage through near-term quantum computers are high is quantum machine learning, where variational quantum learning models based on parametrized quantum circuits are discussed. In this work, we introduce the concept of a classical surrogate, a classical model which can be efficiently obtained from a trained quantum learning model and reproduces its input-output relations. As inference can be performed classically, the existence of a classical surrogate greatly enhances the applicability of a quantum learning strategy. However, the classical surrogate also challenges possible advantages of quantum schemes. As it is possible to directly optimize the Ansatz of the classical surrogate, they create a natural benchmark the quantum model has to outperform. We show that large classes of well-analyzed reuploading models have a classical surrogate. We conducted numerical experiments and found that these quantum models show no advantage in performance or trainability in the problems we analyze. This leaves only generalization capability as a possible point of quantum advantage and emphasizes the dire need for a better understanding of inductive biases of quantum learning models.

Atrial fibrillation (AF) is the most common arrhythmia affecting more than 1.6 million patients in Germany. Based on demographic developments, an the number is expected to increase. Embolic strokes in AF patients are particularly severe, and individualized new oral anticoagulant (NOAC) therapy reduces the incidence of stroke in these patients by approximately 70%. Besides vitamin K antagonists, the NOACs rivaroxaban, dabigatran, apixaban, and edoxaban have been introduced into clinical practice; however, major bleeding still occurs at a rate of 2-3% per year. Moreover, randomized studies and real-life registries suggest that >20% of patients with AF and an indication for anticoagulation cannot tolerate chronic oral anticoagulant therapy. Therefore, an alternative method for stroke prevention in AF patients has been developed, i. e., catheter-based exclusion of the left atrial appendage (LAA), a location that is prone for thrombus formation in these patients. The randomized trials of catheter-based LAA occlusion have compared this interventional therapy with vitamin K antagonists. In the future, however, LAA exclusion needs to be compared with NOAC therapy. Moreover, percutaneous LAA exclusion in clinical practice is mostly offered to patients ineligible for long-term oral anticoagulation or with high bleeding risk. However, no controlled, randomized trial data exist for this patient population. These data are needed for appropriate clinical judgment and optimal clinical management. Ongoing studies and scientific questions that are important to define the future for catheter-based LAA closure are discussed in this review.