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Leakage errors are unwanted transfer of population outside of a defined computational subspace and they occur in almost every platform for quantum computing. While prevalent, leakage is often overlooked when measuring and reporting the performance of quantum computers with standard randomized benchmarking methods. In fact, when leakage is substantial it can cause a large overestimation of fidelity. We provide several methods for measuring fidelity with randomized benchmarking in the presence of leakage errors that are applicable in different error regimes or under differnt control assumptions. We numerically demonstrate the methods for two-qubit randomized benchmarking, which often have the largest leakage contribution. Finally, we implement the methods on previously shared data from Quantinuum systems., Comment: 20 pages, 10 figures

Ballots are the core records of elections. Electronic records of actual ballots cast (cast vote records) are available to the public in some jurisdictions. However, they have been released in a variety of formats and have not been independently evaluated. Here we introduce a database of cast vote records from the 2020 U.S. general election. We downloaded publicly available unstandardized cast vote records, standardized them into a multi-state database, and extensively compared their totals to certified election results. Our release includes vote records for President, Governor, U.S. Senate and House, and state upper and lower chambers -- covering 42.7 million voters in 20 states who voted for more than 2,204 candidates. This database serves as a uniquely granular administrative dataset for studying voting behavior and election administration. Using this data, we show that in battleground states, 1.9 percent of solid Republicans (as defined by their congressional and state legislative voting) in our database split their ticket for Joe Biden, while 1.2 percent of solid Democrats split their ticket for Donald Trump., Comment: 26 pages and appendix

We introduce a toluene-filled fiber platform for two-photon absorption measurements. By confining both the light and molecular sample inside the 5 $\mu$m hollow core of the fiber, we increase the distance over which the nonlinear light-matter interaction occurs. With only a 7.3 nL excitation volume, we measure classical two-photon absorption (C2PA) at an average laser power as low as 1.75 nW, which is a 45-fold improvement over a conventional free-space technique. We use this platform to attempt to measure entangled two-photon absorption (E2PA), a process with a limited regime where the quantum advantage is large. This regime arises due to a crossover from linear to quadratic scaling with photon flux as photon flux is increased. Recently, several teams of researchers have reported that E2PA cross-sections are much smaller than previously claimed. As a result, the linear scaling dominates at photon fluxes so low that it is extremely difficult or impossible to measure using conventional free-space techniques. In this report, we implement the first E2PA measurement using a waveguide. We see no evidence of E2PA, and we set an upper bound on the cross-section consistent with these recent reports.

In this study, we introduce a novel MRI-compatible rotary series elastic actuator module utilizing velocity-sourced ultrasonic motors for force-controlled robots operating within MRI scanners. Unlike previous MRI-compatible SEA designs, our module incorporates a transmission force sensing series elastic actuator structure, with four off-the-shelf compression springs strategically placed between the gearbox housing and the motor housing. This design features a compact size, thus expanding possibilities for a wider range of MRI robotic applications. To achieve precise torque control, we develop a controller that incorporates a disturbance observer tailored for velocity-sourced motors. This controller enhances the robustness of torque control in our actuator module, even in the presence of varying external impedance, thereby augmenting its suitability for MRI-guided medical interventions. Experimental validation demonstrates the actuator's torque control performance in both 3 Tesla MRI and non-MRI environments, achieving a 5% settling time of 0.05 seconds and a steady-state error within 2.5% of its maximum output torque. Notably, our torque controller exhibits consistent performance across low and high external impedance scenarios, in contrast to conventional controllers for velocity-sourced series elastic actuators, which struggle with steady-state performance under low external impedance conditions.

Empirical evidence for a gap between the computational powers of classical and quantum computers has been provided by experiments that sample the output distributions of two-dimensional quantum circuits. Many attempts to close this gap have utilized classical simulations based on tensor network techniques, and their limitations shed light on the improvements to quantum hardware required to frustrate classical simulability. In particular, quantum computers having in excess of $\sim 50$ qubits are primarily vulnerable to classical simulation due to restrictions on their gate fidelity and their connectivity, the latter determining how many gates are required (and therefore how much infidelity is suffered) in generating highly-entangled states. Here, we describe recent hardware upgrades to Quantinuum's H2 quantum computer enabling it to operate on up to $56$ qubits with arbitrary connectivity and $99.843(5)\%$ two-qubit gate fidelity. Utilizing the flexible connectivity of H2, we present data from random circuit sampling in highly connected geometries, doing so at unprecedented fidelities and a scale that appears to be beyond the capabilities of state-of-the-art classical algorithms. The considerable difficulty of classically simulating H2 is likely limited only by qubit number, demonstrating the promise and scalability of the QCCD architecture as continued progress is made towards building larger machines., Comment: Includes minor updates to the text and an updated author list to include researchers who made technical contributions in upgrading the machine to 56 qubits but were left off the original version by mistake

The Super-Kamiokande and T2K collaborations present a joint measurement of neutrino oscillation parameters from their atmospheric and beam neutrino data. It uses a common interaction model for events overlapping in neutrino energy and correlated detector systematic uncertainties between the two datasets, which are found to be compatible. Using 3244.4 days of atmospheric data and a beam exposure of $19.7(16.3) \times 10^{20}$ protons on target in (anti)neutrino mode, the analysis finds a 1.9$\sigma$ exclusion of CP-conservation (defined as $J_{CP}=0$) and a preference for the normal mass ordering., Comment: 12 pages, 4 figures

We implement logically encoded three-qubit circuits for the quantum Fourier transform (QFT), using the [[7,1,3]] Steane code, and benchmark the circuits on the Quantinuum H2-1 trapped-ion quantum computer. The circuits require multiple logical two-qubit gates, which are implemented transversally, as well as logical non-Clifford single-qubit rotations, which are performed by non-fault-tolerant state preparation followed by a teleportation gadget. First, we benchmark individual logical components using randomized benchmarking for the logical two-qubit gate, and a Ramsey-type experiment for the logical $T$ gate. We then implement the full QFT circuit, using two different methods for performing a logical control-$T$, and benchmark the circuits by applying it to each basis state in a set of bases that is sufficient to lower bound the process fidelity. We compare the logical QFT benchmark results to predictions based on the logical component benchmarks.

We present a general method for describing the annihilators of modules of Lie algebras under certain conditions, which hold for some tensor modules of vector field Lie algebras. As an example, we apply the method to obtain an efficient proof of previously known results on the annihilators of the bounded irreducible modules of Vec(R)., Comment: 20 pages

The QED-C suite of Application-Oriented Benchmarks provides the ability to gauge performance characteristics of quantum computers as applied to real-world applications. Its benchmark programs sweep over a range of problem sizes and inputs, capturing key performance metrics related to the quality of results, total time of execution, and quantum gate resources consumed. In this manuscript, we investigate challenges in broadening the relevance of this benchmarking methodology to applications of greater complexity. First, we introduce a method for improving landscape coverage by varying algorithm parameters systematically, exemplifying this functionality in a new scalable HHL linear equation solver benchmark. Second, we add a VQE implementation of a Hydrogen Lattice simulation to the QED-C suite, and introduce a methodology for analyzing the result quality and run-time cost trade-off. We observe a decrease in accuracy with increased number of qubits, but only a mild increase in the execution time. Third, unique characteristics of a supervised machine-learning classification application are explored as a benchmark to gauge the extensibility of the framework to new classes of application. Applying this to a binary classification problem revealed the increase in training time required for larger anzatz circuits, and the significant classical overhead. Fourth, we add methods to include optimization and error mitigation in the benchmarking workflow which allows us to: identify a favourable trade off between approximate gate synthesis and gate noise; observe the benefits of measurement error mitigation and a form of deterministic error mitigation algorithm; and to contrast the improvement with the resulting time overhead. Looking ahead, we discuss how the benchmark framework can be instrumental in facilitating the exploration of algorithmic options and their impact on performance., Comment: 21 pages, 21 figures

To extend the limited scope of autonomy used in prior missions for operation in distant and complex environments, there is a need to further develop and mature autonomy that jointly reasons over multiple subsystems, which we term system-level autonomy. System-level autonomy establishes situational awareness that resolves conflicting information across subsystems, which may necessitate the refinement and interconnection of the underlying spacecraft and environment onboard models. However, with a limited understanding of the assumptions and tradeoffs of modeling to arbitrary extents, designing onboard models to support system-level capabilities presents a significant challenge. In this paper, we provide a detailed analysis of the increasing levels of model fidelity for several key spacecraft subsystems, with the goal of informing future spacecraft functional- and system-level autonomy algorithms and the physics-based simulators on which they are validated. We do not argue for the adoption of a particular fidelity class of models but, instead, highlight the potential tradeoffs and opportunities associated with the use of models for onboard autonomy and in physics-based simulators at various fidelity levels. We ground our analysis in the context of deep space exploration of small bodies, an emerging frontier for autonomous spacecraft operation in space, where the choice of models employed onboard the spacecraft may determine mission success. We conduct our experiments in the Multi-Spacecraft Concept and Autonomy Tool (MuSCAT), a software suite for developing spacecraft autonomy algorithms., Comment: Project page: https://sites.google.com/stanford.edu/spacecraft-models. 20 pages, 8 figures. Accepted to the IEEE Conference on Aerospace (AeroConf) 2024

Regularization in modern machine learning is crucial, and it can take various forms in algorithmic design: training set, model family, error function, regularization terms, and optimizations. In particular, the learning rate, which can be interpreted as a temperature-like parameter within the statistical mechanics of learning, plays a crucial role in neural network training. Indeed, many widely adopted training strategies basically just define the decay of the learning rate over time. This process can be interpreted as decreasing a temperature, using either a global learning rate (for the entire model) or a learning rate that varies for each parameter. This paper proposes TempBalance, a straightforward yet effective layer-wise learning rate method. TempBalance is based on Heavy-Tailed Self-Regularization (HT-SR) Theory, an approach which characterizes the implicit self-regularization of different layers in trained models. We demonstrate the efficacy of using HT-SR-motivated metrics to guide the scheduling and balancing of temperature across all network layers during model training, resulting in improved performance during testing. We implement TempBalance on CIFAR10, CIFAR100, SVHN, and TinyImageNet datasets using ResNets, VGGs, and WideResNets with various depths and widths. Our results show that TempBalance significantly outperforms ordinary SGD and carefully-tuned spectral norm regularization. We also show that TempBalance outperforms a number of state-of-the-art optimizers and learning rate schedulers., Comment: NeurIPS 2023 Spotlight, first two authors contributed equally