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We study the problem of learning the parameters for the Hamiltonian of a quantum many-body system, given limited access to the system. In this work, we build upon recent approaches to Hamiltonian learning via derivative estimation. We propose a protocol that improves the scaling dependence of prior works, particularly with respect to parameters relating to the structure of the Hamiltonian (e.g., its locality k). Furthermore, by deriving exact bounds on the performance of our protocol, we are able to provide a precise numerical prescription for theoretically optimal settings of hyperparameters in our learning protocol, such as the maximum evolution time (when learning with unitary dynamics) or minimum temperature (when learning with Gibbs states). Thanks to these improvements, our protocol has practical scaling for large problems: we demonstrate this with a numerical simulation of our protocol on an 80-qubit system.

Generalization bounds are a critical tool to assess the training data requirements of Quantum Machine Learning (QML). Recent work has established guarantees for in-distribution generalization of quantum neural networks (QNNs), where training and testing data are drawn from the same data distribution. However, there are currently no results on out-of-distribution generalization in QML, where we require a trained model to perform well even on data drawn from a different distribution to the training distribution. Here, we prove out-of-distribution generalization for the task of learning an unknown unitary. In particular, we show that one can learn the action of a unitary on entangled states having trained only product states. Since product states can be prepared using only single-qubit gates, this advances the prospects of learning quantum dynamics on near term quantum hardware, and further opens up new methods for both the classical and quantum compilation of quantum circuits. Generalization - that is, the ability to extrapolate from training data to unseen data - is fundamental in machine learning, and thus also for quantum ML. Here, the authors show that QML algorithms are able to generalise the training they had on a specific distribution and learn over different distributions.

Kernel methods in Quantum Machine Learning (QML) have recently gained significant attention as a potential candidate for achieving a quantum advantage in data analysis. Among other attractive properties, when training a kernel-based model one is guaranteed to find the optimal model’s parameters due to the convexity of the training landscape. However, this is based on the assumption that the quantum kernel can be efficiently obtained from quantum hardware. In this work we study the performance of quantum kernel models from the perspective of the resources needed to accurately estimate kernel values. We show that, under certain conditions, values of quantum kernels over different input data can be exponentially concentrated (in the number of qubits) towards some fixed value. Thus on training with a polynomial number of measurements, one ends up with a trivial model where the predictions on unseen inputs are independent of the input data. We identify four sources that can lead to concentration including expressivity of data embedding, global measurements, entanglement and noise. For each source, an associated concentration bound of quantum kernels is analytically derived. Lastly, we show that when dealing with classical data, training a parametrized data embedding with a kernel alignment method is also susceptible to exponential concentration. Our results are verified through numerical simulations for several QML tasks. Altogether, we provide guidelines indicating that certain features should be avoided to ensure the efficient evaluation of quantum kernels and so the performance of quantum kernel methods. Quantum kernel methods are usually believed to enjoy better trainability than quantum neural networks which may suffer from a well-studied barren plateau. Here, building over previous evidence, the authors show that practical implications of exponential concentration result in a trivial data-insensitive model after training, and identify commonly used features that induce the concentration.

We study the problem of learning the parameters for the Hamiltonian of a quantum many-body system, given limited access to the system. In this work, we build upon recent approaches to Hamiltonian learning via derivative estimation. We propose a protocol that improves the scaling dependence of prior works, particularly with respect to parameters relating to the structure of the Hamiltonian (e.g., its locality k ). Furthermore, by deriving exact bounds on the performance of our protocol, we are able to provide a precise numerical prescription for theoretically optimal settings of hyperparameters in our learning protocol, such as the maximum evolution time (when learning with unitary dynamics) or minimum temperature (when learning with Gibbs states). Thanks to these improvements, our protocol has practical scaling for large problems: we demonstrate this with a numerical simulation of our protocol on an 80-qubit system. Efficient characterisation of quantum many-body Hamiltonians has important applications for benchmarking NISQ devices. Here, the authors propose a method employing Chebyshev regression to learn the full Hamiltonian of a quantum system, with a sample complexity that scales efficiently with the system size.

Quantum annealers of D-Wave Systems, Inc., offer an efficient way to compute high quality solutions of NP-hard problems. This is done by mapping a problem onto the physical qubits of the quantum chip, from which a solution is obtained after quantum annealing. However, since the connectivity of the physical qubits on the chip is limited, a minor embedding of the problem structure onto the chip is required. In this process, and especially for smaller problems, many qubits will stay unused. We propose a novel method, called parallel quantum annealing, to make better use of available qubits, wherein either the same or several independent problems are solved in the same annealing cycle of a quantum annealer, assuming enough physical qubits are available to embed more than one problem. Although the individual solution quality may be slightly decreased when solving several problems in parallel (as opposed to solving each problem separately), we demonstrate that our method may give dramatic speed-ups in terms of the Time-To-Solution (TTS) metric for solving instances of the Maximum Clique problem when compared to solving each problem sequentially on the quantum annealer. Additionally, we show that solving a single Maximum Clique problem using parallel quantum annealing reduces the TTS significantly.

Kernel methods in Quantum Machine Learning (QML) have recently gained significant attention as a potential candidate for achieving a quantum advantage in data analysis. Among other attractive properties, when training a kernel-based model one is guaranteed to find the optimal model’s parameters due to the convexity of the training landscape. However, this is based on the assumption that the quantum kernel can be efficiently obtained from quantum hardware. In this work we study the performance of quantum kernel models from the perspective of the resources needed to accurately estimate kernel values. We show that, under certain conditions, values of quantum kernels over different input data can be exponentially concentrated (in the number of qubits) towards some fixed value. Thus on training with a polynomial number of measurements, one ends up with a trivial model where the predictions on unseen inputs are independent of the input data. We identify four sources that can lead to concentration including expressivity of data embedding, global measurements, entanglement and noise. For each source, an associated concentration bound of quantum kernels is analytically derived. Lastly, we show that when dealing with classical data, training a parametrized data embedding with a kernel alignment method is also susceptible to exponential concentration. Our results are verified through numerical simulations for several QML tasks. Altogether, we provide guidelines indicating that certain features should be avoided to ensure the efficient evaluation of quantum kernels and so the performance of quantum kernel methods.

A bstract We propose an adaptation of Entanglement Renormalization for quantum field theories that, through the use of discrete wavelet transforms, strongly parallels the tensor network architecture of the Multiscale Entanglement Renormalization Ansatz (a.k.a. MERA). Our approach, called wMERA, has several advantages of over previous attempts to adapt MERA to continuum systems. In particular, (i) wMERA is formulated directly in position space, hence preserving the quasi-locality and sparsity of entanglers; and (ii) it enables a built-in RG flow in the implementation of real-time evolution and in computations of correlation functions, which is key for efficient numerical implementations. As examples, we describe in detail two concrete implementations of our wMERA algorithm for free scalar and fermionic theories in (1+1) spacetime dimensions. Possible avenues for constructing wMERAs for interacting field theories are also discussed.

The rapid growth of quantum information science and technology (QIST) presents unique educational challenges as it brings together students and researchers from many disciplines. This work presents findings from in-depth interviews with leading quantum researchers who are also educators, whose perspectives provide guidance for developing a framework for interdisciplinary QIST teaching and builds on our earlier paper that focused on QIST courses and curricula. We discuss quantum educators’ reflections on three critical aspects of QIST education: (1) the development of a common interdisciplinary language, (2) determining appropriate levels of abstraction and physical detail for diverse student populations from various disciplines, and (3) why students should pursue courses, degrees, and careers in this rapidly evolving field. Our analysis reveals that the emergence of linguistic evolutions such as “qubits” and “measurement bases”, rather than a focus on measurement of physical observables and their corresponding Hermitian operators, has begun to create a unifying framework that transcends disciplinary boundaries. Nevertheless, educators face ongoing challenges in balancing the level of abstractness with physical details as well as mathematical rigor with conceptual accessibility, particularly when teaching foundational QIST courses to an interdisciplinary group of students. The experts emphasize that successful QIST education for an interdisciplinary student body not only requires a shift from traditional quantum mechanics pedagogy for physics majors, but careful consideration of students’ diverse prior conceptual and mathematical foundations overall. They encourage students to pursue QIST related courses, degrees, and careers, highlighting the unique historical opportunity to participate in creating transformative quantum technologies while developing transferable skills for an evolving technological landscape. These findings provide valuable guidance for developing a framework for interdisciplinary QIST teaching especially useful for foundational courses.

The present study examined student outcomes from a quantum information science and technology (QIST) summer outreach program for U.S. secondary students. The program focused on foundational principles and skills from classical physics, quantum physics, and quantum computing. Students’ attitudes towards QIST learning and careers were measured through a pretest/posttest research design. Exploratory factor analysis was utilized to identify latent attitudinal themes, followed by comparisons of means to measure changes in these factors and analysis of covariance to assess whether these changes were related to student demographics and prior academic coursework. Two latent themes were identified: (1) QIST career aspiration formation and self-concept, and (2) QIST interest and behavioral intentions. Results indicated that students improved their QIST career aspiration formation and self-concept with a medium to large effect size, yet their QIST interest and behavioral intentions were unchanged. These results were independent of student demographics (gender, ethnicity, grade level) and prior mathematics and computer science course enrollment; however, students who had previously taken chemistry and physics were more likely to improve QIST career aspiration formation and self-concept. Students also increased their intention to take four years of elective mathematics and science with a small effect size. These results suggest that early exposure to QIST principles, skills, and applications may increase students’ consideration of related careers and academic coursetaking plans; however, their interest in QIST may be independent of career aspiration formation. Further research is needed to measure attitudinal sub-domains that may be influenced by early QIST education and specific programmatic elements.

Periodically driven quantum systems exhibit a diverse set of phenomena but are more challenging to simulate than their equilibrium counterparts. Here, we introduce the Quantum High-Frequency Floquet Simulation (QHiFFS) algorithm as a method to simulate fast-driven quantum systems on quantum hardware. Central to QHiFFS is the concept of a kick operator which transforms the system into a basis where the dynamics is governed by a time-independent effective Hamiltonian. This allows prior methods for time-independent simulation to be lifted to simulate Floquet systems. We use the periodically driven biaxial next-nearest neighbor Ising (BNNNI) model, a natural test bed for quantum frustrated magnetism and criticality, as a case study to illustrate our algorithm. We implemented a 20-qubit simulation of the driven two-dimensional BNNNI model on Quantinuum’s trapped ion quantum computer. Our error analysis shows that QHiFFS exhibits not only a cubic advantage in driving frequency ω but also a linear advantage in simulation time t compared to Trotterization.