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Quantum error mitigation is a promising route to achieving quantum utility, and potentially quantum advantage in the near-term. Many state-of-the-art error mitigation schemes use knowledge of the errors in the quantum processor, which opens the question to what extent inaccuracy in the error model impacts the performance of error mitigation. In this work, we develop a methodology to efficiently compute upper bounds on the impact of error-model inaccuracy in error mitigation. Our protocols require no additional experiments, and instead rely on comparisons between the error model and the error-learning data from which the model is generated. We demonstrate the efficacy of our methodology by deploying it on an IBM Quantum superconducting qubit quantum processor, and through numerical simulation of standard error models. We show that our estimated upper bounds are typically close to the worst observed performance of error mitigation on random circuits. Our methodology can also be understood as an operationally meaningful metric to assess the quality of error models, and we further extend our methodology to allow for comparison between error models. Finally, contrary to what one might expect we show that observable error in noisy layered circuits of sufficient depth is not always maximized by a Clifford circuit, which may be of independent interest., Comment: 22 pages including references and appendices, 9 figures

Dissipation engineering is a powerful framework for quantum state preparation and autonomous error correction in few-qubit systems. In this work, we examine the scalability of this approach and give three criteria which any dissipative state stabilization protocol should satisfy to be truly scalable as the number of qubits grows. Besides the requirement that it can be constructed in a resource-efficient manner from simple-to-engineer building blocks, a scalable protocol must also exhibit favorable scaling of the stabilization time with the increase in system size. We present a family of protocols which employ fixed-depth qubit-qubit interactions alongside engineered linear dissipation to stabilize an $N$-qubit W state. We find that a modular approach to dissipation engineering, with several overlapping few-qubit dissipators rather than a single $N$-qubit dissipator, is essential for our protocol to be scalable. With this approach, as the number of qubits increases our protocol exhibits low-degree polynomial scaling of the stabilization time and linear growth of the number of control drives in the best case. While the proposed protocol is most easily accessible with current state-of-the-art circuit-QED architectures, the modular dissipation engineering approach presented here can be readily adapted to other platforms and for stabilization of other interesting quantum states., Comment: 22 pages, 9 figures, 7 appendices

Mid-circuit measurements are a key component in many quantum information computing protocols, including quantum error correction, fault-tolerant logical operations, and measurement based quantum computing. As such, techniques to quickly and efficiently characterize or benchmark their performance are of great interest. Beyond the measured qubit, it is also relevant to determine what, if any, impact mid-circuit measurement has on adjacent, unmeasured, spectator qubits. Here, we present a mid-circuit measurement benchmarking suite developed from the ubiquitous paradigm of randomized benchmarking. We show how our benchmarking suite can be used to both detect as well as quantify errors on both measured and spectator qubits, including measurement-induced errors on spectator qubits and entangling errors between measured and spectator qubits. We demonstrate the scalability of our suite by simultaneously characterizing mid-circuit measurement on multiple qubits from an IBM Quantum Falcon device, and support our experimental results with numerical simulations. Further, using a mid-circuit measurement tomography protocol we establish the nature of the errors identified by our benchmarking suite., Comment: 28 pages, 10 figures

It is well known that qubits immersed in a squeezed vacuum environment exhibit many exotic phenomena, including dissipative entanglement stabilization. Here, we show that these effects only require interference between excitation and decay processes, and can be faithfully mimicked without non-classical light using simple classical temporal modulation. We present schemes that harnesses this idea to stabilize entanglement between two remote qubits coupled via a transmission line or waveguide, where either the qubit-waveguide coupling is modulated, or the qubits are directly driven. We analyze the resilience of these approaches against various imperfections, and also characterize the trade-off between the speed and quality of entanglement stabilization. Our protocols are compatible with state of the art cavity QED systems., Comment: 16 pages, 6 figures, equivalent to the published version

Variational quantum algorithms such as the quantum approximate optimization algorithm (QAOA) are particularly attractive candidates for implementation on near-term quantum processors. As hardware realities such as error and qubit connectivity will constrain achievable circuit depth in the near future, new ways to achieve high-performance at low depth are of great interest. In this work, we present a modification to QAOA that adds additional variational parameters in the form of freedom of the rotation-axis in the $XY$-plane of the mixer Hamiltonian. Via numerical simulation, we show that this leads to a drastic performance improvement over standard QAOA at finding solutions to the MAXCUT problem on graphs of up to 7 qubits. Furthermore, we explore the Z-phase error mitigation properties of our modified ansatz, its performance under a realistic error model for a neutral atom quantum processor, and the class of problems it can solve in a single round., Comment: 8 pages, 4 figures, 3 pages and 5 figures supplementary

The nascent computational paradigm of quantum reservoir computing presents an attractive use of near-term, noisy-intermediate-scale quantum processors. To understand the potential power and use cases of quantum reservoir computing, it is necessary to define a conceptual framework to separate its constituent components and determine their impacts on performance. In this manuscript, we utilize such a framework to isolate the input encoding component of contemporary quantum reservoir computing schemes. We find that across the majority of schemes the input encoding implements a nonlinear transformation on the input data. As nonlinearity is known to be a key computational resource in reservoir computing, this calls into question the necessity and function of further, post-input, processing. Our findings will impact the design of future quantum reservoirs, as well as the interpretation of results and fair comparison between proposed designs., Comment: 9 pages, 1 figure

We present a systematic method to implement a perturbative Hamiltonian diagonalization based on the time-dependent Schrieffer-Wolff transformation. Applying our method to strong parametric interactions we show how, even in the dispersive regime, full Rabi model physics is essential to describe the dressed spectrum. Our results unveil several qualitatively new results including realization of large energy-level shifts, tunable in magnitude and sign with the frequency and amplitude of the pump mediating the parametric interaction. Crucially Bloch-Siegert shifts, typically thought to be important only in the ultra-strong or deep-strong coupling regimes, can be rendered large even for weak dispersive interactions to realize points of exact cancellation of dressed shifts (`blind spots') at specific pump frequencies. The framework developed here highlights the rich physics accessible with time-dependent interactions and serves to significantly expand the functionalities for control and readout of strongly-interacting quantum systems., Comment: 17+ pages, 5 figures

Cavity quantum electrodynamics (QED) with in-situ tunable interactions is important for developing novel systems for quantum simulation and computing. The ability to tune the dispersive shifts of a cavity QED system provides more functionality for performing either quantum measurements or logical manipulations. Here, we couple two transmon qubits to a lumped-element cavity through a shared dc-SQUID. Our design balances the mutual capacitive and inductive circuit components so that both qubits are highly decoupled from the cavity, offering protection from decoherence processes. We show that by parametrically driving the SQUID with an oscillating flux it is possible to independently tune the interactions between either of the qubits and the cavity dynamically. The strength and detuning of this cavity QED interaction can be fully controlled through the choice of the parametric pump frequency and amplitude. As a practical demonstration, we perform pulsed parametric dispersive readout of both qubits while statically decoupled from the cavity. The dispersive frequency shifts of the cavity mode follow the expected magnitude and sign based on simple theory that is supported by a more thorough theoretical investigation. This parametric approach creates a new tunable cavity QED framework for developing quantum information systems with various future applications, such as entanglement and error correction via multi-qubit parity readout, state and entanglement stabilization, and parametric logical gates., Comment: 7 pages, 4 figures

Accelerating computational tasks with quantum resources is a widely-pursued goal that is presently limited by the challenges associated with high-fidelity control of many-body quantum systems. The paradigm of reservoir computing presents an attractive alternative, especially in the noisy intermediate-scale quantum era, since control over the internal system state and knowledge of its dynamics are not required. Instead, complex, unsupervised internal trajectories through a large state space are leveraged as a computational resource. Quantum systems offer a unique venue for reservoir computing, given the presence of interactions unavailable in analogous classical systems, and the potential for a computational space that grows exponentially with physical system size. Here, we consider a reservoir comprised of a single qudit ($d$-dimensional quantum system). We demonstrate a robust performance advantage compared to an analogous classical system accompanied by a clear improvement with Hilbert space dimension for two benchmark tasks: signal processing and short-term memory capacity. Qudit reservoirs are directly realized by current-era quantum hardware, offering immediate practical implementation, and a promising outlook for increased performance in larger systems., Comment: 6 pages, 3 figures, 6 supplementary pages, 6 supplementary figures

Realizing the promise of quantum information processing remains a daunting task, given the omnipresence of noise and error. Adapting noise-resilient classical computing modalities to quantum mechanics may be a viable path towards near-term applications in the noisy intermediate-scale quantum era. Here, we propose continuous variable quantum reservoir computing in a single nonlinear oscillator. Through numerical simulation of our model we demonstrate quantum-classical performance improvement, and identify its likely source: the nonlinearity of quantum measurement. Beyond quantum reservoir computing, this result may impact the interpretation of results across quantum machine learning. We study how the performance of our quantum reservoir depends on Hilbert space dimension, how it is impacted by injected noise, and briefly comment on its experimental implementation. Our results show that quantum reservoir computing in a single nonlinear oscillator is an attractive modality for quantum computing on near-term hardware., Comment: 9 pages, 5 figures

Spin-spin interactions generated by a detuned cavity are a standard mechanism for generating highly entangled spin squeezed states. We show here how introducing a weak detuned parametric (two-photon) drive on the cavity provides a powerful means for controlling the form of the induced interactions. Without a drive, the induced interactions cannot generate Heisenberg-limited spin squeezing, but a weak optimized drive gives rise to an ideal two-axis twist interaction and Heisenberg-limited squeezing. Parametric driving is also advantageous in regimes limited by dissipation, and enables an alternate adiabatic scheme which can prepare optimally squeezed, Dicke-like states. Our scheme is compatible with a number of platforms, including solid-state systems where spin ensembles are coupled to superconducting quantum circuits or mechanical modes., Comment: 5 pages, 4 figures (+ supp. material)

Quantum key distribution (QKD) promises provably secure cryptography, even to attacks from an all-powerful adversary. However, with quantum computing development lagging behind QKD, the assumption that there exists an adversary equipped with a universal fault-tolerant quantum computer is unrealistic for at least the near future. Here, we explore the effect of restricting the eavesdropper's computational capabilities on the security of QKD, and find that improved secret key rates are possible. Specifically, we show that for a large class of discrete variable protocols higher key rates are possible if the eavesdropper is restricted to a unitary operation from the Clifford group. Further, we consider Clifford-random channels consisting of mixtures of Clifford gates. We numerically calculate a secret key rate lower bound for BB84 with this restriction, and show that in contrast to the case of a single restricted unitary attack, the mixture of Clifford based unitary attacks does not result in an improved key rate., Comment: 6 pages + 8 pages appendices, 2 figures

Quantum process tomography has become increasingly critical as the need grows for robust verification and validation of candidate quantum processors. Here, we present an approach for efficient quantum process tomography that uses a physically motivated ansatz for an unknown quantum process. Our ansatz bootstraps to an effective description for an unknown process on a multi-qubit processor from pairwise two-qubit tomographic data. Further, our approach can inherit insensitivity to system preparation and measurement error from the two-qubit tomography scheme. We benchmark our approach using numerical simulation of noisy three-qubit gates, and show that it produces highly accurate characterizations of quantum processes. Further, we demonstrate our approach experimentally, building three-qubit gate reconstructions from two-qubit tomographic data., Comment: 7 pages with 5 figures + 6 pages with 3 figures appendix

We study theoretically how loss impacts the amplification and squeezing performance of a generic quantum travelling wave parametric amplifier. Unlike previous studies, we analyze how having different levels of loss at signal and idler frequencies can dramatically alter properties compared to the case of frequency-independent loss. We find that loss asymmetries increase the amplifier's added noise in comparison to the symmetric loss case. More surprisingly, even small levels of loss asymmetry can completely destroy any quantum squeezing of symmetric collective output quadratures, while nonetheless leaving the output state strongly entangled., Comment: 11 pages, 7 figures, 3 pages appendix

A crucial limit to measurement efficiencies of superconducting circuits comes from losses involved when coupling to an external quantum amplifier. Here, we realize a device circumventing this problem by directly embedding a two-level artificial atom, comprised of a transmon qubit, within a flux-pumped Josephson parametric amplifier. Surprisingly, this configuration is able to enhance dispersive measurement without exposing the qubit to appreciable excess backaction. This is accomplished by engineering the circuit to permit high-power operation that reduces information loss to unmonitored channels associated with the amplification and squeezing of quantum noise. By mitigating the effects of off-chip losses downstream, the on-chip gain of this device produces end-to-end measurement efficiencies of up to 80 percent. Our theoretical model accurately describes the observed interplay of gain and measurement backaction, and delineates the parameter space for future improvement. The device is compatible with standard fabrication and measurement techniques, and thus provides a route for definitive investigations of fundamental quantum effects and quantum control protocols., Comment: 11 pages, 7 figures

We analyze a modified Bose-Hubbard model, where two cavities having on-site Kerr interactions are subject to two-photon driving and correlated dissipation. We derive an exact solution for the steady state of this interacting driven-dissipative system, and use it show that the system permits the preparation and stabilization of pure entangled non-Gaussian states, so-called entangled cat states. Unlike previous proposals for dissipative stabilization of such states, our approach requires only a linear coupling to a single engineered reservoir (as opposed to nonlinear couplings to two or more reservoirs). Our scheme is within the reach of state-of-the-art experiments in circuit QED., Comment: 5 pages main text, 5 pages appendices, 6 figures

We present and analyze a method where parametric (two-photon) driving of a cavity is used to exponentially enhance the light-matter coupling in a generic cavity QED setup, with time-dependent control. Our method allows one to enhance weak-coupling systems, such that they enter the strong coupling regime (where the coupling exceeds dissipative rates) and even the ultra-strong coupling regime (where the coupling is comparable to the cavity frequency). As an example, we show how the scheme allows one to use a weak-coupling system to adiabatically prepare the highly entangled ground state of the ultra-strong coupling system. The resulting state could be used for remote entanglement applications., Comment: 4 pages, 5 figures, 3 pages supplement

We introduce a simple, physically-motivated variational ground state for the quantum Rabi model, and demonstrate that it provides a high-fidelity approximation of the true ground state in all parameter regimes (including intermediate and strong coupling regimes). Our variational state is constructed using Gaussian cavity states and nonorthogonal qubit pointer states, and contains only three variational parameters. We use our state to develop a heuristic understanding of how the ground state evolves with increasing coupling, and find a previously unexplored regime where the ground state corresponds to the cavity being in a nearly pure Schr\"odinger cat state., Comment: 9 pages + 3 page appendix, 8 figures

High fidelity microwave photon counting is an important tool for various areas from background radiation analysis in astronomy to the implementation of circuit QED architectures for the realization of a scalable quantum information processor. In this work we describe a microwave photon counter coupled to a semi-infinite transmission line. We employ input-output theory to examine a continuously driven transmission line as well as traveling photon wave packets. Using analytic and numerical methods, we calculate the conditions on the system parameters necessary to optimize measurement and achieve high detection efficiency., Comment: 10 pages + 4 pages supplementary, 7 figures + 1 figure supplementary