Susanne F. Yelin

Jonathan Z. Lu, Rodrigo A. Bravo, Kaiying Hou et al.

A symmetry of a state $\vert ψ\rangle$ is a unitary operator of which $\vert ψ\rangle$ is an eigenvector. When $\vert ψ\rangle$ is an unknown state supplied by a black-box oracle, the state's symmetries provide key physical insight into the quantum system; symmetries also boost many crucial quantum learning techniques. In this paper, we develop a variational hybrid quantum-classical learning scheme to systematically probe for symmetries of $\vert ψ\rangle$ with no a priori assumptions about the state. This procedure can be used to learn various symmetries at the same time. In order to avoid re-learning already known symmetries, we introduce an interactive protocol with a classical deep neural net. The classical net thereby regularizes against repetitive findings and allows our algorithm to terminate empirically with all possible symmetries found. Our scheme can be implemented efficiently on average with non-local SWAP gates; we also give a less efficient algorithm with only local operations, which may be more appropriate for current noisy quantum devices. We simulate our algorithm on representative families of states, including cluster states and ground states of Rydberg and Ising Hamiltonians. We also find that the numerical query complexity scales well with qubit size.

Weishun Zhong, Xun Gao, Susanne F. Yelin et al.

Born machines are quantum-inspired generative models that leverage the probabilistic nature of quantum states. Here, we present a new architecture called many-body localized (MBL) hidden Born machine that utilizes both MBL dynamics and hidden units as learning resources. We show that the hidden units act as an effective thermal bath that enhances the trainability of the system, while the MBL dynamics stabilize the training trajectories. We numerically demonstrate that the MBL hidden Born machine is capable of learning a variety of tasks, including a toy version of MNIST handwritten digits, quantum data obtained from quantum many-body states, and non-local parity data. Our architecture and algorithm provide novel strategies of utilizing quantum many-body systems as learning resources, and reveal a powerful connection between disorder, interaction, and learning in quantum many-body systems.

Hong-Ye Hu, Andi Gu, Swarnadeep Majumder et al.

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 \emph{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.

Jonathan Z. Lu, Lucy Jiao, Kristina Wolinski et al.

We propose hybrid digital-analog learning algorithms on Rydberg atom arrays, combining the potentially practical utility and near-term realizability of quantum learning with the rapidly scaling architectures of neutral atoms. Our construction requires only single-qubit operations in the digital setting and global driving according to the Rydberg Hamiltonian in the analog setting. We perform a comprehensive numerical study of our algorithm on both classical and quantum data, given respectively by handwritten digit classification and unsupervised quantum phase boundary learning. We show in the two representative problems that digital-analog learning is not only feasible in the near term, but also requires shorter circuit depths and is more robust to realistic error models as compared to digital learning schemes. Our results suggest that digital-analog learning opens a promising path towards improved variational quantum learning experiments in the near term.

Hong-Ye Hu, Muzhou Ma, Weiyuan Gong et al.

Learning the unknown interactions that govern a quantum system is crucial for quantum information processing, device benchmarking, and quantum sensing. The problem, known as Hamiltonian learning, is well understood under the assumption that interactions are local, but this assumption may not hold for arbitrary Hamiltonians. Previous methods all require high-order inverse polynomial dependency with precision, unable to surpass the standard quantum limit and reach the gold standard Heisenberg-limited scaling. Whether Heisenberg-limited Hamiltonian learning is possible without prior assumptions about the interaction structures, a challenge we term \emph{ansatz-free Hamiltonian learning}, remains an open question. In this work, we present a quantum algorithm to learn arbitrary sparse Hamiltonians without any structure constraints using only black-box queries of the system's real-time evolution and minimal digital controls to attain Heisenberg-limited scaling in estimation error. Our method is also resilient to state-preparation-and-measurement errors, enhancing its practical feasibility. We numerically demonstrate our ansatz-free protocol for learning physical Hamiltonians and validating analog quantum simulations, benchmarking our performance against the state-of-the-art Heisenberg-limited learning approach. Moreover, we establish a fundamental trade-off between total evolution time and quantum control on learning arbitrary interactions, revealing the intrinsic interplay between controllability and total evolution time complexity for any learning algorithm. These results pave the way for further exploration into Heisenberg-limited Hamiltonian learning in complex quantum systems under minimal assumptions, potentially enabling new benchmarking and verification protocols.

Andi Gu, J. Pablo Bonilla Ataides, Mikhail D. Lukin et al.

Quantum error correction (QEC) is essential for scalable quantum computing. However, it requires classical decoders that are fast and accurate enough to keep pace with quantum hardware. While quantum low-density parity-check codes have recently emerged as a promising route to efficient fault tolerance, current decoding algorithms do not allow one to realize the full potential of these codes in practical settings. Here, we introduce a convolutional neural network decoder that exploits the geometric structure of QEC codes, and use it to probe a novel "waterfall" regime of error suppression, demonstrating that the logical error rates required for large-scale fault-tolerant algorithms are attainable with modest code sizes at current physical error rates, and with latencies within the real-time budgets of several leading hardware platforms. For example, for the $[144, 12, 12]$ Gross code, the decoder achieves logical error rates up to $\sim 17$x below existing decoders - reaching logical error rates $\sim 10^{-10}$ at physical error $p=0.1\%$ - with 3-5 orders of magnitude higher throughput. This decoder also produces well-calibrated confidence estimates that can significantly reduce the time overhead of repeat-until-success protocols. Taken together, these results suggest that the space-time costs associated with fault-tolerant quantum computation may be significantly lower than previously anticipated.

Hong-Ye Hu, Abigail McClain Gomez, Liyuan Chen et al.

Analog quantum simulators with global control fields have emerged as powerful platforms for exploring complex quantum phenomena. Recent breakthroughs, such as the coherent control of thousands of atoms, highlight the growing potential for quantum applications at scale. Despite these advances, a fundamental theoretical question remains unresolved: to what extent can such systems realize universal quantum dynamics under global control? Here we establish a necessary and sufficient condition for universal quantum computation using only global pulse control, proving that a broad class of analog quantum simulators is, in fact, universal. We further extend this framework to fermionic and bosonic systems, including modern platforms such as ultracold atoms in optical superlattices. Crucially, to connect the theoretical possibility with experimental reality, we introduce a new control technique into the experiment - direct quantum optimal control. This method enables the synthesis of complex effective Hamiltonians and allows us to incorporate realistic hardware constraints. To show its practical power, we experimentally engineer three-body interactions outside the blockade regime and demonstrate topological dynamics on a Rydberg atom array. Using the new control framework, we overcome key experimental challenges, including hardware limitations and atom position fluctuations in the non-blockade regime, by identifying smooth, short-duration pulses that achieve high-fidelity dynamics. Experimental measurements reveal dynamical signatures of symmetry-protected-topological edge modes, confirming both the expressivity and feasibility of our approach. Our work opens a new avenue for quantum simulation beyond native hardware Hamiltonians, enabling the engineering of effective multi-body interactions and advancing the frontier of quantum information processing with globally-controlled analog platforms.

Katherine Van Kirk, Christian Kokail, Jonathan Kunjummen et al.

Efficiently estimating large numbers of non-commuting observables is an important subroutine of many quantum science tasks. We present the derandomized shallow shadows (DSS) algorithm for efficiently learning a large set of non-commuting observables, using shallow circuits to rotate into measurement bases. Exploiting tensor network techniques to ensure polynomial scaling of classical resources, our algorithm outputs a set of shallow measurement circuits that approximately minimizes the sample complexity of estimating a given set of Pauli strings. We numerically demonstrate systematic improvement, in comparison with state-of-the-art techniques, for energy estimation of quantum chemistry benchmarks and verification of quantum many-body systems, and we observe DSS's performance consistently improves as one allows deeper measurement circuits. These results indicate that in addition to being an efficient, low-depth, stand-alone algorithm, DSS can also benefit many larger quantum algorithms requiring estimation of multiple non-commuting observables.