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Functionally constrained stochastic optimization problems, where neither the objective function nor the constraint functions are analytically available, arise frequently in machine learning applications. In this work, assuming we only have access to the noisy evaluations of the objective and constraint functions, we propose and analyze stochastic zeroth-order algorithms for solving this class of stochastic optimization problem. When the domain of the functions is [Formula: see text], assuming there are m constraint functions, we establish oracle complexities of order [Formula: see text] and [Formula: see text] in the convex and nonconvex settings, respectively, where ϵ represents the accuracy of the solutions required in appropriately defined metrics. The established oracle complexities are, to our knowledge, the first such results in the literature for functionally constrained stochastic zeroth-order optimization problems. We demonstrate the applicability of our algorithms by illustrating their superior performance on the problem of hyperparameter tuning for sampling algorithms and neural network training. Funding: K. Balasubramanian was partially supported by a seed grant from the Center for Data Science and Artificial Intelligence Research, University of California–Davis, and the National Science Foundation [Grant DMS-2053918]. 

Introduction Electrical stimulation is increasingly relevant in a variety of medical treatments. In this study, the quality of referred sensations evoked using surface electrical stimulation was evaluated using the rubber hand and foot illusions. Methods The rubber hand and foot illusions were attempted under 4 conditions: (1) multi-location tapping; (2) one-location tapping; (3) electrical stimulation of sensation referred to the hand or foot; (4) asynchronous control. The strength of each illusion was quantified using a questionnaire and proprioceptive drift, where a stronger response suggested embodiment of the rubber limb. Results 45 able-bodied individuals and two individuals with amputations participated in this study. Overall, the illusion evoked by nerve stimulation was not as strong as illusions evoked by physically tapping but stronger than the control illusion. Conclusion This study has found that the rubber hand and foot illusion can be performed without touching the distal limb of the participant. Electrical stimulation that produced referred sensation in the distal extremity was realistic enough to partially incorporate the rubber limb into a person’s body image. 

Within-person research has become increasingly popular in Psychology for its unique theoretical and methodological advantages for studying dynamic psychological processes. Despite the advancements, there remain serious challenges for many organizational researchers to fully appreciate and appropriately implement within-person research—more specifically, to correctly conceptualize and compute the within-person measurement reliability, as well as navigate key within-person research design factors (e.g., number of measurement occasions, T; number of participants, N; and scale length, I) to optimize within-person reliability. By conducting a comprehensive Monte Carlo simulation with 3240 data conditions, we offer a practical guideline table showing the expected within-person reliability as a function of key design factors. In addition, we provide three easy-to-use, free R Shiny web applications for within-person researchers to conveniently (a) compute expected within-person reliability based on their customized research design, (b) compute observed validity based on the expected reliability and hypothesized within-person validity, and (c) compute observed within-person (as well as between-person) reliability from collected within-person research datasets. We hope these much-needed evidence-based guidelines and practical tools will help enhance within-person research in organizational studies. 

Abstract The leakage of quantum information out of the two computational states of a qubit into other energy states represents a major challenge for quantum error correction. During the operation of an error-corrected algorithm, leakage builds over time and spreads through multi-qubit interactions. This leads to correlated errors that degrade the exponential suppression of the logical error with scale, thus challenging the feasibility of quantum error correction as a path towards fault-tolerant quantum computation. Here, we demonstrate a distance-3 surface code and distance-21 bit-flip code on a quantum processor for which leakage is removed from all qubits in each cycle. This shortens the lifetime of leakage and curtails its ability to spread and induce correlated errors. We report a tenfold reduction in the steady-state leakage population of the data qubits encoding the logical state and an average leakage population of less than 1 × 10⁻³throughout the entire device. Our leakage removal process efficiently returns the system back to the computational basis. Adding it to a code circuit would prevent leakage from inducing correlated error across cycles. With this demonstration that leakage can be contained, we have resolved a key challenge for practical quantum error correction at scale. 

We demonstrate a high dynamic range Josephson parametric amplifier (JPA) in which the active nonlinear element is implemented using an array of rf-SQUIDs. The device is matched to the 50 Ω environment with a Klopfenstein-taper impedance transformer and achieves a bandwidth of 250–300 MHz with input saturation powers up to −95 dBm at 20 dB gain. A 54-qubit Sycamore processor was used to benchmark these devices, providing a calibration for readout power, an estimation of amplifier added noise, and a platform for comparison against standard impedance matched parametric amplifiers with a single dc-SQUID. We find that the high power rf-SQUID array design has no adverse effect on system noise, readout fidelity, or qubit dephasing, and we estimate an upper bound on amplifier added noise at 1.6 times the quantum limit. Finally, amplifiers with this design show no degradation in readout fidelity due to gain compression, which can occur in multi-tone multiplexed readout with traditional JPAs. 

Abstract Practical quantum computing will require error rates well below those achievable with physical qubits. Quantum error correction^1,2offers a path to algorithmically relevant error rates by encoding logical qubits within many physical qubits, for which increasing the number of physical qubits enhances protection against physical errors. However, introducing more qubits also increases the number of error sources, so the density of errors must be sufficiently low for logical performance to improve with increasing code size. Here we report the measurement of logical qubit performance scaling across several code sizes, and demonstrate that our system of superconducting qubits has sufficient performance to overcome the additional errors from increasing qubit number. We find that our distance-5 surface code logical qubit modestly outperforms an ensemble of distance-3 logical qubits on average, in terms of both logical error probability over 25 cycles and logical error per cycle ((2.914 ± 0.016)% compared to (3.028 ± 0.023)%). To investigate damaging, low-probability error sources, we run a distance-25 repetition code and observe a 1.7 × 10⁻⁶logical error per cycle floor set by a single high-energy event (1.6 × 10⁻⁷excluding this event). We accurately model our experiment, extracting error budgets that highlight the biggest challenges for future systems. These results mark an experimental demonstration in which quantum error correction begins to improve performance with increasing qubit number, illuminating the path to reaching the logical error rates required for computation.