Extracting information efficiently from quantum systems is a major component of quantum information processing tasks. Randomized measurements, or classical shadows, enable predicting many properties of arbitrary quantum states using few measurements. While random single qubit measurements are experimentally friendly and suitable for learning low-weight Pauli observables, they perform poorly for nonlocal observables. Prepending a shallow random quantum circuit before measurements maintains this experimental friendliness, but also has favorable sample complexities for observables beyond low-weight Paulis, including high-weight Paulis and global low-rank properties such as fidelity. However, in realistic scenarios, quantum noise accumulated with each additional layer of the shallow circuit biases the results. To address these challenges, we propose the robust shallow shadows protocol. Our protocol uses Bayesian inference to learn the experimentally relevant noise model and mitigate it in postprocessing. This mitigation introduces a bias-variance trade-off: correcting for noise-induced bias comes at the cost of a larger estimator variance. Despite this increased variance, as we demonstrate on a superconducting quantum processor, our protocol correctly recovers state properties such as expectation values, fidelity, and entanglement entropy, while maintaining a lower sample complexity compared to the random single qubit measurement scheme. We also theoretically analyze the effects of noise on sample complexity and show how the optimal choice of the shallow shadow depth varies with noise strength. This combined theoretical and experimental analysis positions the robust shallow shadow protocol as a scalable, robust, and sample-efficient protocol for characterizing quantum states on current quantum computing platforms.

The recent success of neural networks in natural language processing has drawn renewed attention to learning sequence-to-sequence (seq2seq) tasks. While there exists a rich literature that studies classification and regression tasks using solvable models of neural networks, seq2seq tasks have not yet been studied from this perspective. Here, we propose a simple model for a seq2seq task that has the advantage of providing explicit control over the degree of memory, or non-Markovianity, in the sequences -- the stochastic switching-Ornstein-Uhlenbeck (SSOU) model. We introduce a measure of non-Markovianity to quantify the amount of memory in the sequences. For a minimal auto-regressive (AR) learning model trained on this task, we identify two learning regimes corresponding to distinct phases in the stationary state of the SSOU process. These phases emerge from the interplay between two different time scales that govern the sequence statistics. Moreover, we observe that while increasing the integration window of the AR model always improves performance, albeit with diminishing returns, increasing the non-Markovianity of the input sequences can improve or degrade its performance. Finally, we perform experiments with recurrent and convolutional neural networks that show that our observations carry over to more complicated neural network architectures.

Quantum computers are actively competing to surpass classical supercomputers, but quantum errors remain their chief obstacle. The key to overcoming these on near-term devices has emerged through the field of quantum error mitigation, enabling improved accuracy at the cost of additional runtime. In practice, however, the success of mitigation is limited by a generally exponential overhead. Can classical machine learning address this challenge on today's quantum computers? Here, through both simulations and experiments on state-of-the-art quantum computers using up to 100 qubits, we demonstrate that machine learning for quantum error mitigation (ML-QEM) can drastically reduce overheads, maintain or even surpass the accuracy of conventional methods, and yield near noise-free results for quantum algorithms. We benchmark a variety of machine learning models -- linear regression, random forests, multi-layer perceptrons, and graph neural networks -- on diverse classes of quantum circuits, over increasingly complex device-noise profiles, under interpolation and extrapolation, and for small and large quantum circuits. These tests employ the popular digital zero-noise extrapolation method as an added reference. We further show how to scale ML-QEM to classically intractable quantum circuits by mimicking the results of traditional mitigation results, while significantly reducing overhead. Our results highlight the potential of classical machine learning for practical quantum computation.