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Practical implementation of many quantum algorithms known today is limited by the coherence time of the executing quantum hardware and quantum sampling noise. Here we present a machine learning algorithm, NISQRC, for qubit-based quantum systems that enables inference on temporal data over durations unconstrained by decoherence. NISQRC leverages mid-circuit measurements and deterministic reset operations to reduce circuit executions, while still maintaining an appropriate length persistent temporal memory in quantum system, confirmed through the proposed Volterra Series analysis. This enables NISQRC to overcome not only limitations imposed by finite coherence, but also information scrambling in monitored circuits and sampling noise, problems that persist even in hypothetical fault-tolerant quantum computers that have yet to be realized. To validate our approach, we consider the channel equalization task to recover test signal symbols that are subject to a distorting channel. Through simulations and experiments on a 7-qubit quantum processor we demonstrate that NISQRC can recover arbitrarily long test signals, not limited by coherence time., Comment: 15+17 pages, 4+7 figures

The expressive capacity of physical systems employed for learning is limited by the unavoidable presence of noise in their extracted outputs. Though present in physical systems across both the classical and quantum regimes, the precise impact of noise on learning remains poorly understood. Focusing on supervised learning, we present a mathematical framework for evaluating the resolvable expressive capacity (REC) of general physical systems under finite sampling noise, and provide a methodology for extracting its extrema, the eigentasks. Eigentasks are a native set of functions that a given physical system can approximate with minimal error. We show that the REC of a quantum system is limited by the fundamental theory of quantum measurement, and obtain a tight upper bound for the REC of any finitely-sampled physical system. We then provide empirical evidence that extracting low-noise eigentasks can lead to improved performance for machine learning tasks such as classification, displaying robustness to overfitting. We present analyses suggesting that correlations in the measured quantum system enhance learning capacity by reducing noise in eigentasks. The applicability of these results in practice is demonstrated with experiments on superconducting quantum processors. Our findings have broad implications for quantum machine learning and sensing applications., Comment: 37 pages, 10 figures, 1 table. Significantly expanded version of arXiv:2301.00042 [quant-ph], covering physical systems operating in the classical and quantum regimes

The expressive capacity of quantum systems for machine learning is limited by quantum sampling noise incurred during measurement. Although it is generally believed that noise limits the resolvable capacity of quantum systems, the precise impact of noise on learning is not yet fully understood. We present a mathematical framework for evaluating the available expressive capacity of general quantum systems from a finite number of measurements, and provide a methodology for extracting the extrema of this capacity, its eigentasks. Eigentasks are a native set of functions that a given quantum system can approximate with minimal error. We show that extracting low-noise eigentasks leads to improved performance for machine learning tasks such as classification, displaying robustness to overfitting. We obtain a tight bound on the expressive capacity, and present analyses suggesting that correlations in the measured quantum system enhance learning capacity by reducing noise in eigentasks. These results are supported by experiments on superconducting quantum processors. Our findings have broad implications for quantum machine learning and sensing applications., Comment: 7 + 21 pages, 4 + 12 figures, 1 table

Quantum computers can potentially achieve an exponential speedup versus classical computers on certain computational tasks, as recently demonstrated in systems of superconducting qubits. However, these qubits have large footprints due to their large capacitor electrodes needed to suppress losses by avoiding dielectric materials. This tactic hinders scaling by increasing parasitic coupling among circuit components, degrading individual qubit addressability, and limiting the spatial density of qubits. Here, we take advantage of the unique properties of the van der Waals (vdW) materials to reduce the qubit area by a factor of $>1000$ while preserving the required capacitance without increasing substantial loss. Our qubits combine conventional aluminum-based Josephson junctions with parallel-plate capacitors composed of crystalline layers of superconducting niobium diselenide (NbSe$_2$) and insulating hexagonal-boron nitride (hBN). We measure a vdW transmon $T_1$ relaxation time of 1.06 $\mu$s, which demonstrates a path to achieve high-qubit-density quantum processors with long coherence times, and illustrates the broad utility of layered heterostructures in low-loss, high-coherence quantum devices., Comment: 6 pages, 5 figures, and 1 table

High-fidelity single- and two-qubit gates are essential building blocks for a fault-tolerant quantum computer. While there has been much progress in suppressing single-qubit gate errors in superconducting qubit systems, two-qubit gates still suffer from error rates that are orders of magnitude higher. One limiting factor is the residual ZZ-interaction, which originates from a coupling between computational states and higher-energy states. While this interaction is usually viewed as a nuisance, here we experimentally demonstrate that it can be exploited to produce a universal set of fast single- and two-qubit entangling gates in a coupled transmon qubit system. To implement arbitrary single-qubit rotations, we design a new protocol called the two-axis gate that is based on a three-part composite pulse. It rotates a single qubit independently of the state of the other qubit despite the strong ZZ-coupling. We achieve single-qubit gate fidelities as high as 99.1% from randomized benchmarking measurements. We then demonstrate both a CZ gate and a CNOT gate. Because the system has a strong ZZ-interaction, a CZ gate can be achieved by letting the system freely evolve for a gate time $t_g=53.8$ ns. To design the CNOT gate, we utilize an analytical microwave pulse shape based on the SWIPHT protocol for realizing fast, low-leakage gates. We obtain fidelities of 94.6% and 97.8% for the CNOT and CZ gates respectively from quantum progress tomography.

Measurements that occur within the internal layers of a quantum circuit -- mid-circuit measurements -- are an important quantum computing primitive, most notably for quantum error correction. Mid-circuit measurements have both classical and quantum outputs, so they can be subject to error modes that do not exist for measurements that terminate quantum circuits. Here we show how to characterize mid-circuit measurements, modelled by quantum instruments, using a technique that we call quantum instrument linear gate set tomography (QILGST). We then apply this technique to characterize a dispersive measurement on a superconducting transmon qubit within a multiqubit system. By varying the delay time between the measurement pulse and subsequent gates, we explore the impact of residual cavity photon population on measurement error. QILGST can resolve different error modes and quantify the total error from a measurement; in our experiment, for delay times above 1000 ns we measured a total error rate (i.e., half diamond distance) of $\epsilon_{\diamond} = 8.1 \pm 1.4 \%$, a readout fidelity of $97.0 \pm 0.3\%$, and output quantum state fidelities of $96.7 \pm 0.6\%$ and $93.7 \pm 0.7\%$ when measuring $0$ and $1$, respectively., Comment: 13 pages, 8 figures, 3 tables

The rapidity and low power consumption of superconducting electronics makes them an ideal substrate for physical reservoir computing, which commandeers the computational power inherent to the evolution of a dynamical system for the purposes of performing machine learning tasks. We focus on a subset of superconducting circuits that exhibit soliton-like dynamics in simple transmission line geometries. With numerical simulations we demonstrate the effectiveness of these circuits in performing higher-order parity calculations and channel equalization at rates approaching 100 Gb/s. The availability of a proven superconducting logic scheme considerably simplifies the path to a fully integrated reservoir computing platform and makes superconducting reservoirs an enticing substrate for high rate signal processing applications., Comment: 7 pages, 4 figures

Demonstrating a quantum computational advantage will require high-fidelity control and readout of multi-qubit systems. As system size increases, multiplexed qubit readout becomes a practical necessity to limit the growth of resource overhead. Many contemporary qubit-state discriminators presume single-qubit operating conditions or require considerable computational effort, limiting their potential extensibility. Here, we present multi-qubit readout using neural networks as state discriminators. We compare our approach to contemporary methods employed on a quantum device with five superconducting qubits and frequency-multiplexed readout. We find that fully-connected feedforward neural networks increase the qubit-state-assignment fidelity for our system. Relative to contemporary discriminators, the assignment error rate is reduced by up to 25% due to the compensation of system-dependent nonidealities such as readout crosstalk which is reduced by up to one order of magnitude. Our work demonstrates a potentially extensible building block for high-fidelity readout relevant to both near-term devices and future fault-tolerant systems., Comment: 18 Pages, 9 figures

We demonstrate that matching the symmetry properties of a reservoir computer (RC) to the data being processed dramatically increases its processing power. We apply our method to the parity task, a challenging benchmark problem that highlights inversion and permutation symmetries, and to a chaotic system inference task that presents an inversion symmetry rule. For the parity task, our symmetry-aware RC obtains zero error using an exponentially reduced neural network and training data, greatly speeding up the time to result and outperforming hand crafted artificial neural networks. When both symmetries are respected, we find that the network size $N$ necessary to obtain zero error for 50 different RC instances scales linearly with the parity-order $n$. Moreover, some symmetry-aware RC instances perform a zero error classification with only $N=1$ for $n\leq7$. Furthermore, we show that a symmetry-aware RC only needs a training data set with size on the order of $(n+n/2)$ to obtain such performance, an exponential reduction in comparison to a regular RC which requires a training data set with size on the order of $n2^n$ to contain all $2^n$ possible $n-$bit-long sequences. For the inference task, we show that a symmetry-aware RC presents a normalized root-mean-square error three orders-of-magnitude smaller than regular RCs. For both tasks, our RC approach respects the symmetries by adjusting only the input and the output layers, and not by problem-based modifications to the neural network. We anticipate that generalizations of our procedure can be applied in information processing for problems with known symmetries., Comment: 10 pages, 7 Figures

Control electronics for superconducting quantum processors have strict requirements for accurate command of the sensitive quantum states of their qubits. Hinging on the purity of ultra-phase-stable oscillators to upconvert very-low-noise baseband pulses, conventional control systems can become prohibitively complex and expensive when scaling to larger quantum devices, especially as high sampling rates become desirable for fine-grained pulse shaping. Few-GHz radio-frequency digital-to-analog converters (RF DACs) present a more economical avenue for high-fidelity control while simultaneously providing greater command over the spectrum of the synthesized signal. Modern RF DACs with extra-wide bandwidths are able to directly synthesize tones above their sampling rates, thereby keeping the system clock rate at a level compatible with modern digital logic systems while still being able to generate high-frequency pulses with arbitrary profiles. We have incorporated custom superconducting qubit control logic into off-the-shelf hardware capable of low-noise pulse synthesis up to 7.5 GHz using an RF DAC clocked at 5 GHz. Our approach enables highly linear and stable microwave synthesis over a wide bandwidth, giving rise to high-resolution control and a reduced number of required signal sources per qubit. We characterize the performance of the hardware using a five-transmon superconducting device and demonstrate consistently reduced two-qubit gate error (as low as 1.8%) which we show results from superior control chain linearity compared to traditional configurations. The exceptional flexibility and stability further establish a foundation for scalable quantum control beyond intermediate-scale devices., Comment: 12 pages, 9 figures

One of the most challenging obstacles to realizing exascale computing is minimizing the energy consumption of L2 cache, main memory, and interconnects to that memory. For promising cryogenic computing schemes utilizing Josephson junction superconducting logic, this obstacle is exacerbated by the cryogenic system requirements that expose the technology's lack of high-density, high-speed and power-efficient memory. Here we demonstrate an array of cryogenic memory cells consisting of a non-volatile three-terminal magnetic tunnel junction element driven by the spin Hall effect, combined with a superconducting heater-cryotron bit-select element. The write energy of these memory elements is roughly 8 pJ with a bit-select element, designed to achieve a minimum overhead power consumption of about 30%. Individual magnetic memory cells measured at 4 K show reliable switching with write error rates below $10^{-6}$, and a 4x4 array can be fully addressed with bit select error rates of $10^{-6}$. This demonstration is a first step towards a full cryogenic memory architecture targeting energy and performance specifications appropriate for applications in superconducting high performance and quantum computing control systems, which require significant memory resources operating at 4 K., Comment: 10 pages, 6 figures, submitted

We propose a low noise, triply-resonant, electro-optic (EO) scheme for quantum microwave-to-optical conversion based on coupled nanophotonics resonators integrated with a superconducting qubit. Our optical system features a split resonance - a doublet - with a tunable frequency splitting that matches the microwave resonance frequency of the superconducting qubit. This is in contrast to conventional approaches where large optical resonators with free-spectral range comparable to the qubit microwave frequency are used. In our system, EO mixing between the optical pump coupled into the low frequency doublet mode and a resonance microwave photon results in an up-converted optical photon on resonance with high frequency doublet mode. Importantly, the down-conversion process, which is the source of noise, is suppressed in our scheme as the coupled-resonator system does not support modes at that frequency. Our device has at least an order of magnitude smaller footprint than the conventional devices, resulting in large overlap between optical and microwave fields and large photon conversion rate ($g/2\pi$) in the range of $\sim$5-15 kHz. Owing to large $g$ factor and doubly-resonant nature of our device, microwave-to-optical frequency conversion can be achieved with optical pump powers in the range of tens of microwatts, even with moderate values for optical $\it{Q}$ ($\sim 10^6$) and microwave $Q$ ($ \sim10^4$). The performance metrics of our device, with substantial improvement over the previous EO-based approaches, promise a scalable quantum microwave-to-optical conversion and networking of superconducting processors via optical fiber communication.