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The dominant contribution to the energy relaxation of state-of-the-art superconducting qubits is often attributed to their coupling to an ensemble of material defects which behave as two-level systems. These defects have varying microscopic characteristics which result in a large range of observable defect properties such as resonant frequencies, coherence times and coupling rates to qubits $g$. Here, we investigate strategies to mitigate losses to the family of defects that strongly couple to qubits ($g/2\pi\ge$ 0.5 MHz). Such strongly coupled defects are particularly detrimental to the coherence of qubits and to the fidelities of operations relying on frequency excursions, such as flux-activated two-qubit gates. To assess their impact, we perform swap spectroscopy on 92 frequency-tunable qubits and quantify the spectral density of these strongly coupled modes. We show that the frequency configuration of the defects is rearranged by warming up the sample to room temperature, whereas the total number of defects on a processor tends to remain constant. We then explore methods for fabricating qubits with a reduced number of strongly coupled defect modes by systematically measuring their spectral density for decreasing Josephson junction dimensions and for various surface cleaning methods. Our results provide insights into the properties of strongly coupled defect modes and show the benefits of minimizing Josephson junction dimensions to improve qubit properties.

Quantum computers will require quantum error correction to reach the low error rates necessary for solving problems that surpass the capabilities of conventional computers. One of the dominant errors limiting the performance of quantum error correction codes across multiple technology platforms is leakage out of the computational subspace arising from the multi-level structure of qubit implementations. Here, we present a resource-efficient universal leakage reduction unit for superconducting qubits using parametric flux modulation. This operation removes leakage down to our measurement accuracy of $7\cdot 10^{-4}$ in approximately $50\, \mathrm{ns}$ with a low error of $2.5(1)\cdot 10^{-3}$ on the computational subspace, thereby reaching durations and fidelities comparable to those of single-qubit gates. We demonstrate that using the leakage reduction unit in repeated weight-two stabilizer measurements reduces the total number of detected errors in a scalable fashion to close to what can be achieved using leakage-rejection methods which do not scale. Our approach does neither require additional control electronics nor on-chip components and is applicable to both auxiliary and data qubits. These benefits make our method particularly attractive for mitigating leakage in large-scale quantum error correction circuits, a crucial requirement for the practical implementation of fault-tolerant quantum computation.

The performance of a wide range of quantum computing algorithms and protocols depends critically on the fidelity and speed of the employed qubit readout. Examples include gate sequences benefiting from mid-circuit, real-time, measurement-based feedback, such as qubit initialization, entanglement generation, teleportation, and perhaps most importantly, quantum error correction. A prominent and widely-used readout approach is based on the dispersive interaction of a superconducting qubit strongly coupled to a large-bandwidth readout resonator, frequently combined with a dedicated or shared Purcell filter protecting qubits from decay. By dynamically reducing the qubit-resonator detuning and thus increasing the dispersive shift, we demonstrate a beyond-state-of-the-art two-state-readout error of only $0.25\,\%$ in 100 ns integration time. Maintaining low readout-drive strength, we nearly quadruple the signal-to-noise ratio of the readout by doubling the readout mode linewidth, which we quantify by considering the hybridization of the readout-resonator and its dedicated Purcell-filter. We find excellent agreement between our experimental data and our theoretical model. The presented results are expected to further boost the performance of new and existing algorithms and protocols critically depending on high-fidelity, fast, mid-circuit measurements.

The emergence of blockchain technology has renewed the interest in consensus-based data management systems that are resilient to failures. To maximize the throughput of these systems, we have recently seen several prototype consensus solutions that optimize for throughput at the expense of overall implementation complexity, high costs, and reliability. Due to this, it remains unclear how these prototypes will perform in real-world environments. In this paper, we present SPOTLESS, a novel concurrent rotational consensus protocol made practical. Central to SPOTLESS is the combination of (1) a chained rotational consensus design for replicating requests with a reduced message cost and low-cost failure recovery that eliminates the traditional complex, error-prone view-change protocol; (2) the novel Rapid View Synchronization protocol that enables SPOTLESS to work in more general network assumptions, without a need for a Global Synchronization Time to synchronize view, and recover valid earlier views with the aid of non-faulty replicas without the need to rely on the primary; (3) a high-performance concurrent consensus architecture in which independent instances of the chained consensus operate concurrently to process requests with high throughput, thereby avoiding the bottlenecks seen in other rotational protocols. Due to the concurrent consensus architecture, SPOTLESS greatly outperforms traditional primary-backup consensus protocols such as PBFT (by up to 430%), NARWHAL-HS (by up to 137%), and HOTSTUFF (by up to 3803%). Due to its reduced message cost, SPOTLESS is even able to outperform RCC, a state-of-the-art high-throughput concurrent consensus protocol, by up to 23%. Furthermore, SPOTLESS is able to maintain a stable and low latency and consistently high throughput even during failures., Comment: 16 pages, 15 figures

Cryogenic semiconductor device models are essential in designing control systems for quantum devices and in benchmarking the benefits of cryogenic cooling for high-performance computing. In particular, the saturation of subthreshold swing due to band tails is an important phenomenon to include in low-temperature analytical MOSFET models as it predicts theoretical lower bounds on the leakage power and supply voltage in tailored cryogenic CMOS technologies with tuned threshold voltages. Previous physics-based modeling required to evaluate functions with no closed-form solutions, defeating the purpose of fast and efficient model evaluation. Thus far, only the empirically proposed expressions are in closed form. This article bridges this gap by deriving a physics-based and closed-form model for the full saturating trend of the subthreshold swing from room down to low temperature. The proposed model is compared against experimental data taken on some long and short devices from a commercial 28-nm bulk CMOS technology down to 4.2 K., Comment: Accepted for publication in IEEE Transactions on Nanotechnology

The ability to execute high-fidelity operations is crucial to scaling up quantum devices to large numbers of qubits. However, signal distortions originating from non-linear components in the control lines can limit the performance of single-qubit gates. In this work, we use a measurement based on error amplification to characterize and correct the small single-qubit rotation errors originating from the non-linear scaling of the qubit drive rate with the amplitude of the programmed pulse. With our hardware, and for a 15-ns pulse, the rotation angles deviate by up to several degrees from a linear model. Using purity benchmarking, we find that control errors reach $2\times 10^{-4}$, which accounts for half of the total gate error. Using cross-entropy benchmarking, we demonstrate arbitrary-angle single-qubit gates with coherence-limited errors of $2\times 10^{-4}$ and leakage below $6\times 10^{-5}$. While the exact magnitude of these errors is specific to our setup, the presented method is applicable to any source of non-linearity. Our work shows that the non-linearity of qubit drive line components imposes a limit on the fidelity of single-qubit gates, independent of improvements in coherence times, circuit design, or leakage mitigation when not corrected for.

Josephson traveling wave parametric amplifiers enable the amplification of weak microwave signals close to the quantum limit with large bandwidth, which has a broad range of applications in superconducting quantum computing and in the operation of single-photon detectors. While the large bandwidth allows for their use in frequency-multiplexed detection architectures, an increased number of readout tones per amplifier puts more stringent requirements on the dynamic range to avoid saturation. Here, we characterize the undesired mixing processes between the different frequency-multiplexed tones applied to a Josephson traveling wave parametric amplifier, a phenomenon also known as intermodulation distortion. The effect becomes particularly significant when the amplifier is operated close to its saturation power. Furthermore, we demonstrate that intermodulation distortion can lead to significant crosstalk and reduction of fidelity for multiplexed readout of superconducting qubits. We suggest using large detunings between the pump and signal frequencies to mitigate crosstalk. Our work provides insights into the limitations of current Josephson traveling wave parametric amplifiers and highlights the importance of performing further research on these devices., Comment: 11 pages, 12 figures

High-fidelity control of superconducting qubits requires the generation of microwave-frequency pulses precisely tailored on nanosecond timescales. These pulses are most commonly synthesized by up-converting and superimposing two narrow-band intermediate-frequency signals referred to as the in-phase (I) and quadrature (Q) components. While the calibration of their DC-offsets, relative amplitude and phase allows one to cancel unwanted sideband and carrier leakage, this IQ mixing approach suffers from the presence of additional spurious frequency components. Here, we experimentally study an alternative approach based on double frequency conversion, which overcomes this challenge and circumvents the need for IQ-calibration. We find a spurious-free dynamic range of more than 70$\,$dB and compare the quality of pulse generation against a state-of-the-art IQ mixing scheme by performing repeated single-qubit randomized benchmarking on a superconducting qubit.

The introduction of Bitcoin fueled the development of blockchain-based resilient data management systems that are resilient against failures, enable federated data management, and can support data provenance. The key factor determining the performance of such resilient data management systems is the consensus protocol used by the system to replicate client transactions among all participants. Unfortunately, existing high-throughput consensus protocols are costly and impose significant latencies on transaction processing, which rules out their usage in responsive high-performance data management systems. In this work, we improve on this situation by introducing the Proof-of-Execution consensus protocol (PoE), a consensus protocol designed for high-performance low-latency resilient data management. PoE introduces speculative execution, which minimizes latencies by starting execution before consensus is reached, and PoE introduces proof-of-executions to guarantee successful execution to clients. Furthermore, PoE introduces a single-round check-commit protocol to reduce the overall communication costs of consensus. Hence, we believe that PoE is a promising step towards flexible general-purpose low-latency resilient data management systems., Comment: An extended abstract of this work appeared at the 24th International Conference on Extending Database Technology (EDBT 2021), see also arXiv:1911.00838

Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited control accuracy. Here, we demonstrate quantum error correction using the surface code, which is known for its exceptionally high tolerance to errors. Using 17 physical qubits in a superconducting circuit we encode quantum information in a distance-three logical qubit building up on recent distance-two error detection experiments. In an error correction cycle taking only $1.1\,\mu$s, we demonstrate the preservation of four cardinal states of the logical qubit. Repeatedly executing the cycle, we measure and decode both bit- and phase-flip error syndromes using a minimum-weight perfect-matching algorithm in an error-model-free approach and apply corrections in postprocessing. We find a low error probability of $3\,\%$ per cycle when rejecting experimental runs in which leakage is detected. The measured characteristics of our device agree well with a numerical model. Our demonstration of repeated, fast and high-performance quantum error correction cycles, together with recent advances in ion traps, support our understanding that fault-tolerant quantum computation will be practically realizable., Comment: 28 pages, 17 figures

Quantum computing crucially relies on the ability to efficiently characterize the quantum states output by quantum hardware. Conventional methods which probe these states through direct measurements and classically computed correlations become computationally expensive when increasing the system size. Quantum neural networks tailored to recognize specific features of quantum states by combining unitary operations, measurements and feedforward promise to require fewer measurements and to tolerate errors. Here, we realize a quantum convolutional neural network (QCNN) on a 7-qubit superconducting quantum processor to identify symmetry-protected topological (SPT) phases of a spin model characterized by a non-zero string order parameter. We benchmark the performance of the QCNN based on approximate ground states of a family of cluster-Ising Hamiltonians which we prepare using a hardware-efficient, low-depth state preparation circuit. We find that, despite being composed of finite-fidelity gates itself, the QCNN recognizes the topological phase with higher fidelity than direct measurements of the string order parameter for the prepared states.

Traditional resilient systems operate on fully-replicated fault-tolerant clusters, which limits their scalability and performance. One way to make the step towards resilient high-performance systems that can deal with huge workloads, is by enabling independent fault-tolerant clusters to efficiently communicate and cooperate with each other, as this also enables the usage of high-performance techniques such as sharding and parallel processing. Recently, such inter-cluster communication was formalized as the Byzantine cluster-sending problem, and worst-case optimal protocols have been proposed that solve this problem. Unfortunately, these protocols have an all-case linear complexity in the size of the clusters involved. In this paper, we propose probabilistic cluster-sending techniques that can reliably send messages from one Byzantine fault-tolerant cluster to another with only an expected constant message complexity, this independent of the size of the clusters involved. Depending on the robustness of the clusters involved, our techniques require only two-to-four message round-trips. Furthermore, our protocols can support worst-case linear communication between clusters, which is optimal, and deal with asynchronous and unreliable communication. As such, our work provides a strong foundation for the further development of resilient high-performance systems.

To enable high-performance and scalable blockchains, we need to step away from traditional consensus-based fully-replicated designs. One direction is to explore the usage of sharding in which we partition the managed dataset over many shards that independently operate as blockchains. Sharding requires an efficient fault-tolerant primitive for the ordering and execution of multi-shard transactions, however. In this work, we seek to design such a primitive suitable for distributed ledger networks with high transaction throughput. To do so, we propose Cerberus, a set of minimalistic primitives for processing single-shard and multi-shard UTXO-like transactions. Cerberus aims at maximizing parallel processing at shards while minimizing coordination within and between shards. First, we propose Core-Cerberus, that uses strict environmental requirements to enable simple yet powerful multi-shard transaction processing. In our intended UTXO-environment, Core-Cerberus will operate perfectly with respect to all transactions proposed and approved by well-behaved clients, but does not provide any guarantees for other transactions. To also support more general-purpose environments, we propose two generalizations of Core-Cerberus: we propose Optimistic-Cerberus, a protocol that does not require any additional coordination phases in the well-behaved optimistic case, while requiring intricate coordination when recovering from attacks; and we propose Pessimistic-Cerberus, a protocol that adds sufficient coordination to the well-behaved case of Core-Cerberus, allowing it to operate in a general-purpose fault-tolerant environments without significant costs to recover from attacks. Finally, we compare the three protocols, showing their potential scalability and high transaction throughput in practical environments.

A major challenge in operating multi-qubit quantum processors is to mitigate multi-qubit coherent errors. For superconducting circuits, besides crosstalk originating from imperfect isolation of control lines, dispersive coupling between qubits is a major source of multi-qubit coherent errors. We benchmark phase errors in a controlled-phase gate due to dispersive coupling of either of the qubits involved in the gate to one or more spectator qubits. We measure the associated gate infidelity using quantum process tomography. In addition, we point out that, due to coupling of the gate qubits to a non-computational state during the gate, two-qubit conditional phase errors are enhanced. Our work is important for understanding limits to the fidelity of two-qubit gates with finite on/off ratio in multi-qubit settings., Comment: 9 pages, 5 figures

Variational quantum algorithms are believed to be promising for solving computationally hard problems and are often comprised of repeated layers of quantum gates. An example thereof is the quantum approximate optimization algorithm (QAOA), an approach to solve combinatorial optimization problems on noisy intermediate-scale quantum (NISQ) systems. Gaining computational power from QAOA critically relies on the mitigation of errors during the execution of the algorithm, which for coherence-limited operations is achievable by reducing the gate count. Here, we demonstrate an improvement of up to a factor of 3 in algorithmic performance as measured by the success probability, by implementing a continuous hardware-efficient gate set using superconducting quantum circuits. This gate set allows us to perform the phase separation step in QAOA with a single physical gate for each pair of qubits instead of decomposing it into two C$Z$-gates and single-qubit gates. With this reduced number of physical gates, which scales with the number of layers employed in the algorithm, we experimentally investigate the circuit-depth-dependent performance of QAOA applied to exact-cover problem instances mapped onto three and seven qubits, using up to a total of 399 operations and up to 9 layers. Our results demonstrate that the use of continuous gate sets may be a key component in extending the impact of near-term quantum computers.

Recent developments in blockchain technology have inspired innovative new designs in resilient distributed and database systems. At their core, these blockchain applications typically use Byzantine fault-tolerant consensus protocols to maintain a common state across all replicas, even if some replicas are faulty or malicious. Unfortunately, existing consensus protocols are not designed to deal with geo-scale deployments in which many replicas spread across a geographically large area participate in consensus. To address this, we present the Geo-Scale Byzantine FaultTolerant consensus protocol (GeoBFT). GeoBFT is designed for excellent scalability by using a topological-aware grouping of replicas in local clusters, by introducing parallelization of consensus at the local level, and by minimizing communication between clusters. To validate our vision of high-performance geo-scale resilient distributed systems, we implement GeoBFT in our efficient ResilientDB permissioned blockchain fabric. We show that GeoBFT is not only sound and provides great scalability, but also outperforms state-of-the-art consensus protocols by a factor of six in geo-scale deployments.

In the two-user Gaussian interference channel with Gaussian inputs and treating interference as noise (TIN), improper complex signals can be beneficial if time-sharing is not allowed or if only the data rates are averaged over several transmit strategies (convex hull formulation). On the other hand, proper (circularly symmetric) signals have recently been shown to be optimal if coded time-sharing is considered, i.e., if both the data rates and the transmit powers are averaged. In this paper, we show that both conclusions remain the same if single-input multiple-output (SIMO) systems with multiple antennas at the receivers are considered. The proof for the case with coded time-sharing is via a novel enhanced channel concept for the two-user SIMO interference channel, which turns out to deliver a tight outer bound to the TIN rate region with coded time-sharing. The result for the case without coded time-sharing is demonstrated by studying specific examples in which a newly proposed composite real gradient-projection method for improper signaling can outperform the globally optimal proper signaling strategy. In addition, we discuss how the achievable TIN rate region with coded time-sharing can be computed numerically., Comment: This work has been submitted to the IEEE for possible publication

It is known that circularly symmetric Gaussian signals are the optimal input signals for the partial decode-and-forward (PDF) coding scheme in the Gaussian multiple-input multiple-output (MIMO) relay channel, but there is currently no method to find the optimal covariance matrices nor to compute the optimal achievable PDF rate since the optimization is a non-convex problem in its original formulation. In this paper, we show that it is possible to find a convex reformulation of the problem by means of an approximation and a primal decomposition. We derive an explicit solution for the inner problems as well as an explicit gradient for the outer problem, so that the efficient cutting-plane method can be applied for solving the outer problem. As the accuracy of this provably convergent algorithm might be impaired by the previous approximation, we additionally propose a modified algorithm, for which we cannot give a converge guarantee, but which provides rigorous upper and lower bounds to the optimum of the original rate maximization. In numerical simulations, these bounds become tight in all considered instances of the problem, showing that the proposed method manages to find the global optimum in all these instances., Comment: This work has been submitted to the IEEE for possible publication

Multi-party data management and blockchain systems require data sharing among participants. To provide resilient and consistent data sharing, transactions engines rely on Byzantine FaultTolerant consensus (BFT), which enables operations during failures and malicious behavior. Unfortunately, existing BFT protocols are unsuitable for high-throughput applications due to their high computational costs, high communication costs, high client latencies, and/or reliance on twin-paths and non-faulty clients. In this paper, we present the Proof-of-Execution consensus protocol (PoE) that alleviates these challenges. At the core of PoE are out-of-order processing and speculative execution, which allow PoE to execute transactions before consensus is reached among the replicas. With these techniques, PoE manages to reduce the costs of BFT in normal cases, while guaranteeing reliable consensus for clients in all cases. We envision the use of PoE in high-throughput multi-party data-management and blockchain systems. To validate this vision, we implement PoE in our efficient ResilientDB fabric and extensively evaluate PoE against several state-of-the-art BFT protocols. Our evaluation showcases that PoE achieves up-to-80% higher throughputs than existing BFT protocols in the presence of failures., Comment: To appear in the proceedings of 24th International Conference on Extending Database Technology (EDBT)

Recently, we saw the emergence of consensus-based database systems that promise resilience against failures, strong data provenance, and federated data management. Typically, these fully-replicated systems are operated on top of a primary-backup consensus protocol, which limits the throughput of these systems to the capabilities of a single replica (the primary). To push throughput beyond this single-replica limit, we propose concurrent consensus. In concurrent consensus, replicas independently propose transactions, thereby reducing the influence of any single replica on performance. To put this idea in practice, we propose our RCC paradigm that can turn any primary-backup consensus protocol into a concurrent consensus protocol by running many consensus instances concurrently. RCC is designed with performance in mind and requires minimal coordination between instances. Furthermore, RCC also promises increased resilience against failures. We put the design of RCC to the test by implementing it in ResilientDB, our high-performance resilient blockchain fabric, and comparing it with state-of-the-art primary-backup consensus protocols. Our experiments show that RCC achieves up to 2.75x higher throughput than other consensus protocols and can be scaled to 91 replicas., Comment: To appear in the proceedings of 37th IEEE International Conference on Data Engineering (ICDE) 2021

While globally optimal solutions to many convex programs can be computed efficiently in polynomial time, this is, in general, not possible for nonconvex optimization problems. Therefore, locally optimal approaches or other efficient suboptimal heuristics are usually applied for practical implementations. However, there is also a strong interest in computing globally optimal solutions of nonconvex problems in offline simulations in order to benchmark the faster suboptimal algorithms. Global solutions often rely on monotonicity properties. A common approach is to reformulate problems into a canonical monotonic optimization problem where the monotonicity becomes evident, but this often comes at the cost of nested optimizations, increased numbers of variables, and/or slow convergence. The framework of mixed monotonic programming (MMP) proposed in this paper avoids such performance-deteriorating reformulations by revealing hidden monotonicity properties directly in the original problem formulation. By means of a wide range of application examples from the area of signal processing for communications (including energy efficiency for green communications, resource allocation in interference networks, scheduling for fairness and quality of service, as well as beamformer design in multiantenna systems), we demonstrate that the novel MMP approach leads to tremendous complexity reductions compared to state-of-the-art methods for global optimization. However, the framework is not limited to optimizing communication systems, and we expect that similar speed-ups can be obtained for optimization problems from other areas of research as well., Comment: submitted to IEEE Transactions on Signal Processing; Source code available at https://github.com/bmatthiesen/mixed-monotonic