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Quantum bits (qubits) are prone to several types of error as the result of uncontrolled interactions with their environment. Common strategies to correct these errors are based on architectures of qubits involving daunting hardware overheads1. One possible solution is to build qubits that are inherently protected against certain types of error, so the overhead required to correct the remaining errors is greatly reduced2–7. However, this strategy relies on one condition: any quantum manipulations of the qubit must not break the protection that has been so carefully engineered5,8. A type of qubit known as a cat qubit is encoded in the manifold of metastable states of a quantum dynamical system, and thereby acquires continuous and autonomous protection against bit-flips. Here, in a superconducting-circuit experiment, we implemented a cat qubit with bit-flip times exceeding 10 s. This is an improvement of four orders of magnitude over previously published cat-qubit implementations. We prepared and imaged quantum superposition states, and measured phase-flip times greater than 490 ns. Most importantly, we controlled the phase of these quantum superpositions without breaking the bit-flip protection. This experiment demonstrates the compatibility of quantum control and inherent bit-flip protection at an unprecedented level, showing the viability of these dynamical qubits for future quantum technologies.

When a composite Lindblad system consists of weakly coupled sub-systems with fast and slow timescales, the description of slow dynamics can be simplified by discarding fast degrees of freedom. This model reduction technique is called adiabatic elimination. While second-order perturbative expansion with respect to the timescale separation has revealed that the evolution of a reduced state is completely positive, this paper presents an example exhibiting complete positivity violation in the fourth-order expansion. Despite the non-uniqueness of slow dynamics parametrization, we prove that complete positivity cannot be ensured in any parametrization. The violation stems from correlation in the initial state.

A quantum system interacts with its environment—if ever so slightly—no matter how much care is put into isolating it1. Therefore, quantum bits undergo errors, putting dauntingly difficult constraints on the hardware suitable for quantum computation2. New strategies are emerging to circumvent this problem by encoding a quantum bit non-locally across the phase space of a physical system. Because most sources of decoherence result from local fluctuations, the foundational promise is to exponentially suppress errors by increasing a measure of this non-locality3,4. Prominent examples are topological quantum bits, which delocalize information over real space and where spatial extent measures non-locality. Here, we encode a quantum bit in the field quadrature space of a superconducting resonator endowed with a special mechanism that dissipates photons in pairs5,6. This process pins down two computational states to separate locations in phase space. By increasing this separation, we measure an exponential decrease of the bit-flip rate while only linearly increasing the phase-flip rate7. Because bit-flips are autonomously corrected, only phase-flips remain to be corrected via a one-dimensional quantum error correction code. This exponential scaling demonstrates that resonators with nonlinear dissipation are promising building blocks for quantum computation with drastically reduced hardware overhead8.

We provide a comprehensive impossibility result toward achieving string stability, i.e., keeping local relative errors in check with local controllers independently of the size of a chain of subsystems. We significantly extend the existing results, from the linear time-invariant (LTI) setting to any homogeneous controllers that can be nonlinear, time varying, and locally communicating. We prove this impossibility for a set of definitions with various norm choices, including the $L_2$ -type standard and a bounded-input implies bounded-output (BIBO) type criterion. All the results hold for a general discrete-time controller, which should cover most applications. [ABSTRACT FROM AUTHOR]

Adiabatic elimination is a perturbative model reduction technique based on timescale separation and often used to simplify the description of composite quantum systems. We here analyze a quantum experiment where the perturbative expansion can be carried out to arbitrary order, such that: (i) we can formulate in the end an exact reduced model in quantum form; (ii) as the series provides accuracy for ever larger parameter values, we can discard any condition on the timescale separation, thereby analyzing the intermediate regime where the actual experiment is performing best; (iii) we can clarify the role of some gauge degrees of freedom in this model reduction technique.

This paper deals with the problem of string stability in a chain of acceleration-controlled vehicles. It is known that string stability cannot be achieved, with any linear controller, when the vehicles’ control inputs are based only on relative distances to a fixed number of predecessors. We extend the set of characteristics under which string stability is impossible by including elements like dynamic sensor parts and local inter-vehicular communication, as in cooperative adaptive cruise control. It is also known that a weaker form of string stability is achievable by adding absolute velocity measurements (e.g. “time-headway” policy). We show that a stronger property can also be achieved, provided steady-state control gain is infinite e.g. by using integral control.

We address the standard quantum error correction using the three-qubit bit-flip code, yet in continuous-time. This entails rendering a target manifold of quantum states globally attractive. Previous feedback designs could feature spurious equilibria, or resort to discrete kicks pushing the system away from these equilibria to ensure global asymptotic stability. We present a new approach that consists of introducing controls driven by Brownian motions. Unlike the previous methods, the resulting closed-loop dynamics can be shown to stabilize the target manifold exponentially. We further present a reduced-order filter formulation with classical probabilities. The exponential property is important to quantify the protection induced by the closed-loop error-correction dynamics against disturbances. We study numerically the performance of this control law and of the reduced filter.

It is known that polynomial filtering can accelerate the convergence toward average consensus on an undirected network. In this paper, the gain of a second-order filtering is investigated in more detail. A set of graphs is determined for which consensus can be attained in finite time, and a preconditioner is proposed to adapt the undirected weights of any given graph to achieve fastest convergence with the polynomial filter. The corresponding cost function differs from the traditional spectral gap, as it favors grouping the eigenvalues in two clusters and can favor symmetry breaking. A possible loss of robustness of the polynomial filter is also highlighted.

We consider a quantum system composed of a fast quantum subsystem coupled to a slow one. We provide expressions of the approximate reduced model describing the slow subsystem (adiabatic elimination), based on an asymptotic expansion that we solve up to second order. The specificity of our expressions is to preserve the quantum structure in the reduced model: we provide the reduced dynamics in Lindblad form, and the mapping defining the slow manifold as a completely positive map in Kraus form.

This paper deals with the problem of string stability of interconnected systems with double-integrator open loop dynamics (e.g. acceleration-controlled vehicles). We analyze an asymmetric bidirectional linear controller, where each vehicle is coupled solely to its immediate predecessor and to its immediate follower with different gains in these two directions. We show that in this setting, unlike with unidirectional or symmetric bidirectional controllers, string stability can be recovered when disturbances act only on a small (TV-independent) set of leading vehicles. This improves existing results from the literature with this assumption. We also indicate that string stability with respect to arbitrarily distributed disturbances cannot be achieved with this controller.

Previous papers have proposed to add memory registers to the dynamics of discrete-time linear systems in order to accelerate their convergence. In particular, it has been proved that adding one memory slot per agent allows faster convergence towards average consensus. We here prove that this situation cannot be improved by adding more memory slots, when the knowledge about the self-adjoint linear map to be accelerated reduces to bounds on its extreme eigenvalues. [ABSTRACT FROM PUBLISHER]

This paper applies the recently developed framework for integral control on nonlinear spaces to two non-standard cases. First, we show that perfect target stabilization in presence of actuation bias holds also if this bias is state dependent. This might not be surprising, but in practice it provides an easy way to robustly cancel nonlinear dynamics of the uncontrolled plant. We specifically illustrate this for robust stabilization of a pendulum at arbitrary angle. Second, as previous work has been restricted to systems with as many control inputs as configuration dimensions, we here provide results for integral control of a non-holonomic system. More precisely, we design robust steering control of a rigid body under velocity bias.

Quantum dynamical decoupling is a procedure to cancel the effective coupling between two systems by applying sequences of fast actuations, under which the coupling Hamiltonian averages out to leading order(s). One of its prominent uses is to drive a target system in such a way as to decouple it from a less protected one. The present manuscript investigates the dual strategy: acting on a noisy "environment" subsystem, such as to decouple it from a target system. The target system only has a Hamiltonian coupling to this close environment which itself undergoes Lindbladian decoherence. The potential advantages are that actions on the environment commute with system operations, and that imprecisions in the decoupling actuation are harmless to the target. We consider two versions of environment-side decoupling: adding an imprecise Hamiltonian drive which stirs the environment components; and, increasing the decoherence rates on the environment. The latter can be viewed as driving the environment with pure noise and our conclusions establish how, maybe counterintuitively, isolating the environment from noise sources as much as possible is often not the best option. In this setting, we can explicitly analyze the induced decoherence on the target system, and focusing on the example of a two-level environment subsystem, we establish how the induced decoherence is influenced by the parameters in both cases. The analysis combines Lindbladian derivation, adiabatic elimination, and Floquet modeling in a way that may be of independent interest. [ABSTRACT FROM AUTHOR]

This paper extends the consensus framework, widely studied in the literature on distributed computing and control algorithms, to networks of quantum systems. We define consensus situations on the basis of invariance and symmetry properties, finding four different generalizations of classical consensus states. This new viewpoint can be directly used to study consensus for probability distributions, as these can be seen as a particular case of quantum statistical states: in this light, our analysis is also relevant for classical problems. We then extend the gossip consensus algorithm to the quantum setting and prove it converges to symmetric states while preserving the expectation of permutation-invariant global observables. Applications of the framework and the algorithms to estimation and control problems on quantum networks are discussed. [ABSTRACT FROM PUBLISHER]

We analyze a quantum reservoir engineering method, originally introduced by Sarlette et al. [Phys. Rev. Lett. 107, 010402 (2011)], for the stabilization of nonclassical field states in high-quality cavities. We generalize the method to the protection of mesoscopic entangled field states shared by two nondegenerate field modes. The reservoir consists of a stream of atoms consecutively interacting with the cavity. Each individual atom-cavity interaction follows the same time-varying Hamiltonian, combining resonant with nonresonant parts. We gain detailed insight into the competition between the engineered reservoir and decoherence. We show that the operation is quite insensitive to experimental imperfections and that it could thus be implemented in the near future in the context of microwave cavity or circuit quantum electrodynamics. [ABSTRACT FROM AUTHOR]

The present paper proposes a unified geometric framework for coordinated motion on Lie groups. It first gives a general problem formulation and analyzes ensuing conditions for coordinated motion. Then, it introduces a precise method to design control laws in fully actuated and underactuated settings with simple integrator dynamics. It thereby shows that coordination can be studied in a systematic way once the Lie group geometry of the configuration space is well characterized. Applying the proposed general methodology to particular examples allows to retrieve control laws that have been proposed in the literature on intuitive grounds. A link with Brockett's double bracket flows is also made. The concepts are illustrated on SO(3), SE(2) and SE(3). [ABSTRACT FROM AUTHOR]

We propose a scheme to measure the parity of two distant qubits, while ensuring that losses on the quantum channel between them does not destroy coherences within the parity subspaces. This capability enables deterministic preparation of highly entangled qubit states whose fidelity is not limited by the transmission loss. The key observation is that, for a probe electromagnetic field in a particular quantum state; namely, a superposition of two coherent states of opposite phases, the transmission loss stochastically applies a near-unitary backaction on the probe state. This leads to a parity measurement protocol where the main effect of the transmission losses is a decrease in the measurement strength. By repeating the nondestructive (weak) parity measurement, one achieves a high-fidelity entanglement in spite of a significant transmission loss. [ABSTRACT FROM AUTHOR]

A letter to the editor in response to the article "The Best Ways to Ease Your Knees" in the November-December 2014 issue is presented.

The fabrication of semiconductor devices can be complicated by various defectivity issues with respect to fabrication process steps, their interactions, the used materials and tool settings. In this paper we will focus on a defect type, called spire or cone defect. This conducting defect type is very common in the shallow trench isolation (STI) process. The presence of a single defect can be responsible for a device breakdown or reliability problems, which will result in a serious impact on the competitive edge for a product qualification. Spire defects, which can only be detected after etch, are observed on all our technology nodes using 248nm or 193nm exposure techniques. Bottom Anti-Reflection Coatings (BARC) impurities are considered to be the main root cause for the formation of spire defects. Therefore we focused our efforts on chemical filtration of the BARC material and related solvents, the usage of different BARC materials and the influence of the subsequent etch steps in order to reduce or overcome the spire defect problem. In this paper we will discuss the effectiveness of different filter materials, pore sizes and different BARC materials (organic and dielectric BARC) with respect to defect analysis and lithographic performance.

Among available lithography resolution enhancement techniques the Selective Inverse Lithography (SILT) approach recently introduced by authors [1] has been shown to provide the largest process window on lower-NA exposure tools for 65nm contact layer patterning. In present paper we attempt to harness the benefits of source mask optimization (SMO) approach as part of our hybrid RET. The application of source mask optimization techniques further extends the life-span of lower-NA 193nm exposure-tools in high volume manufacturing. By including SMO step in OPC flow, we show that model-based SRAF solution can be improved to approach SILT process variation (PV) band performance. Additionally to OPC, the complexity of embedded flash designs requires a high degree of exposure tool matching and a lithography process optimized for topographically different logic and flash areas. We present a method how SMO can be applied to scanner matching and topography-related optimization.

Histone deacetylases (HDACs) are important regulators of gene expression and cell differentiation. The HDAC inhibitors have recently been considered as potential novel neuroprotective drugs for the treatment of neurodegenerative diseases such as amyotrophic lateral sclerosis (ALS). A major limitation, however, lies in the broad spectrum of action of currently available HDAC inhibitors that may cause a variety of toxic side effects. The mRNA expression levels of the HDAC isoforms HDACs 1 to 11 have previously been characterized in rat brain but have not been studied in human tissue. Using in situ hybridization histochemistry and immunohistochemistry we assessed the distribution and expression levels of HDACs 1to 11 in postmortem ALS and control brain and spinal cord specimens (n = 6 cases each) to determine alterations in the mRNA expression pattern that could provide a basis for disease-specific therapies. We found a reduction of HDAC 11 mRNA and increased HDAC 2 levels in ALS brain and spinal cord compared with controls. A more precise knowledge of the disease-related expression pattern could lead to the development of more specific pharmacotherapeutic approaches.

Oxidative stress and inflammation are important pathogenetic mechanisms in amyotrophic lateral sclerosis (ALS). Nuclear erythroid 2-related factor 2 (Nrf2) is a basic region leucine-zipper transcription factor that binds to the antioxidant response element, thereby regulating the expression of many genes that are involved in cellular antioxidant and anti-inflammatory defense. Under normal conditions, Nrf2 activation is inhibited by Kelch-like ECH-associated protein 1 (Keap1). We investigated the potential involvement of the Nrf2/antioxidant response element signaling pathway in the selective degeneration of motor neurons in ALS. Nrf2 and Keap1 expression was analyzed in primary motor cortex and spinal cord postmortem tissue samples from ALS patients and controls by in situ hybridization histochemistry, quantitative real-time polymerase chain reaction, immunohistochemistry, and Western blot analysis. In ALS samples, there was a reduction of Nrf2 mRNA and protein expression in neurons, whereas Keap1 mRNA expression was increased in the motor cortex. These results suggest that alterations in this signaling cascade occur in motor neurons in ALS and that they may contribute to chronic motor neuron degeneration.

Tomography of a quantum state is usually based on a positive-operator-valued measure (POVM) and on their experimental statistics. Among the available reconstructions, the maximum-likelihood (MaxLike) technique is an efficient one. We propose an extension of this technique when the measurement process cannot be simply described by an instantaneous POVM. Instead, the tomography relies on a set of quantum trajectories and their measurement records. This model includes the fact that, in practice, each measurement could be corrupted by imperfections and decoherence, and could also be associated with the record of continuous-time signals over a finite amount of time. The goal is then to retrieve the quantum state that was present at the start of this measurement process. The proposed extension relies on an explicit expression of the likelihood function via the effective matrices appearing in quantum smoothing and solutions of the adjoint quantum filter. It allows us to retrieve the initial quantum state as in standard MaxLike tomography, but where the traditional POVM operators are replaced by more general ones that depend on the measurement record of each trajectory. It also provides, aside from the MaxLike estimate of the quantum state, confidence intervals for any observable. Such confidence intervals are derived, as the MaxLike estimate, from an asymptotic expansion of multidimensional Laplace integrals appearing in Bayesian mean estimation. A validation is performed on two sets of experimental data: photon(s) trapped in a microwave cavity subject to quantum nondemolition measurements relying on Rydberg atoms, and heterodyne fluorescence measurements of a superconducting qubit. [ABSTRACT FROM AUTHOR]