No abstract

The code capacity threshold for error correction using biased-noise qubits is known to be higher than with qubits without such structured noise. However, realistic circuit-level noise severely restricts these improvements. This is because gate operations, such as a controlled-NOT (CX) gate, which do not commute with the dominant error, unbias the noise channel. Here, we overcome the challenge of implementing a bias-preserving CX gate using biased-noise stabilized cat qubits in driven nonlinear oscillators. This continuous-variable gate relies on nontrivial phase space topology of the cat states. Furthermore, by following a scheme for concatenated error correction, we show that the availability of bias-preserving CX gates with moderately sized cats improves a rigorous lower bound on the fault-tolerant threshold by a factor of two and decreases the overhead in logical Clifford operations by a factor of five. Our results open a path toward high-threshold, low-overhead, fault-tolerant codes tailored to biased-noise cat qubits.

In quantum error correction, information is encoded in a high-dimensional system to protect it from the environment. A crucial step is to use natural, low-weight operations with an ancilla to extract information about errors without causing backaction on the encoded system. Essentially, ancilla errors must not propagate to the encoded system and induce errors beyond those which can be corrected. The current schemes for achieving this fault-tolerance to ancilla errors come at the cost of increased overhead requirements. An efficient way to extract error syndromes in a fault-tolerant manner is by using a single ancilla with strongly biased noise channel. Typically, however, required elementary operations can become challenging when the noise is extremely biased. We propose to overcome this shortcoming by using a bosonic-cat ancilla in a parametrically driven nonlinear cavity. Such a cat-qubit experiences only bit-flip noise and is stabilized against phase-flips. To highlight the flexibility of this approach, we illustrate the syndrome extraction process in a variety of codes such as qubit-based toric codes, bosonic cat-and Gottesman-Kitaev-Preskill (GKP) codes. Our results open a path for realizing hardware-efficient, fault-tolerant error syndrome extraction.

Manipulating the state of a logical quantum bit (qubit) usually comes at the expense of exposing it to decoherence. Fault-tolerant quantum computing tackles this problem by manipulating quantum information within a stable manifold of a larger Hilbert space, whose symmetries restrict the number of independent errors. The remaining errors do not affect the quantum computation and are correctable after the fact. Here we implement the autonomous stabilization of an encoding manifold spanned by Schrödinger cat states in a superconducting cavity. We show Zeno-driven coherent oscillations between these states analogous to the Rabi rotation of a qubit protected against phase flips. Such gates are compatible with quantum error correction and hence are crucial for fault-tolerant logical qubits. DOI: 10.1103/PhysRevX.8.021005 Subject Areas: Quantum Physics, Quantum InformationThe quantum Zeno effect (QZE) is the apparent freezing of a quantum system in one state under the influence of a continuous observation. This continuous observation can be performed by a dissipative environment [1][2][3]. It can be further generalized to the stabilization of a manifold spanned by multiple quantum states, an operation which requires a dissipation that is blind to the manifold observables [4]. Harnessing this effect is crucial for the design of quantum computation schemes, since autonomous stabilization is a form of the feedback needed for quantum error correction. When employing manifold QZE for correcting errors, motion inside the manifold can still subsist and can be driven by the combination of the dissipative stabilization and an external force [5][6][7][8][9][10]. Therefore, manifold QZE offers a pathway towards the realization of logical gates compatible with quantum error correction. An example of such a system is provided by a superconducting microwave cavity, in which a dissipative process that annihilates photons in pairs at rate κ 2 , acting together with a twophoton drive of strength ϵ 2 , projects the system onto the manifold spanned by Schrödinger cat states jCand N is a normalization factor [11][12][13]. Each one of these states has a well-defined photon number parity, which is conserved by the engineered dissipation. In this Schrödinger cat state manifold, the displacement operator DðαÞ ¼ expðαa † − α Ã aÞ (where a is the annihilation operator acting on the harmonic oscillator) has two effects: it changes the photon number parity and it changes the amplitude of its component coherent states. The engineered dissipation leaves the change in parity invariant and cancels the change in amplitude [ Fig. 1(a)]. The net result of this quantum Zeno dynamics is to continuously vary the parity of Schrödinger cat states.These parity oscillations constitute the basis of an X gate on a qubit encoded in the protected manifold j0/1i P ¼ N ðjα ∞ i AE j−α ∞ iÞ. Encoding quantum information in superpositions of Schrödinger cat states is compatible with quantum error correction realized with quantum nondemolition parity measurements [14]...

IntroductionMuscle ultrasound is emerging as a promising tool in the diagnosis of neuromuscular diseases. The current observational study evaluates the usefulness of muscle ultrasound in patients with severe sepsis for assessment of critical illness polyneuropathy and myopathy (CINM) in the intensive care unit.Methods28 patients with either septic shock or severe sepsis underwent clinical neurological examinations, muscle ultrasound, and nerve conduction studies on days 4 and 14 after onset of sepsis. 26 healthy controls of comparable age underwent clinical neurological evaluation and muscle ultrasound only.Results26 of the 28 patients exhibited classic electrophysiological characteristics of CINM, and all showed typical clinical signs. Ultrasonic echogenicity of muscles was graded semiquantitatively and fasciculations were evaluated in muscles of proximal and distal arms and legs. 75% of patients showed a mean echotexture greater than 1.5, which was the maximal value found in the control group. A significant difference in mean muscle echotexture between patients and controls was found at day 4 and day 14 (both p < 0.001). In addition, from day 4 to day 14, the mean grades of muscle echotexture increased in the patient group, although the values did not reach significance levels (p = 0.085). Controls revealed the lowest number of fasciculations. In the patients group, fasciculations were detected in more muscular regions (lower and upper arm and leg) in comparison to controls (p = 0.08 at day 4 and p = 0.002 at day 14).ConclusionsMuscle ultrasound represents an easily applicable, non-invasive diagnostic tool which adds to neurophysiological testing information regarding morphological changes of muscles early in the course of sepsis. Muscle ultrasound could be useful for screening purposes prior to subjecting patients to more invasive techniques such as electromyography and/or muscle biopsy.Trial registrationGerman Clinical Trials Register, DRKS-ID: DRKS00000642.

Ultrasound is useful for non-invasive visualization of focal nerve pathologies probably resulting from demyelination, remyelination, edema or inflammation. In patients with progressive muscle weakness, differentiation between multifocal motor neuropathy (MMN) and amyotrophic lateral sclerosis (ALS) is essential regarding therapy and prognosis. Therefore, the objective of this study was to investigate whether nerve ultrasound can differentiate between ALS and MMN. Systematic ultrasound measurements of peripheral nerves and the 6th cervical nerve root (C6) were performed in 17 patients with ALS, in 8 patients with MMN and in 28 healthy controls. Nerve conduction studies of corresponding nerves were undertaken in MMN and ALS patients. Electromyography was performed in ALS patients according to revised El-Escorial criteria. ANOVA and unpaired t test with Bonferroni correction revealed significant differences in cross-sectional areas (CSA) of different nerves and C6 diameter between the groups. Nerve enlargement was found significantly more frequently in MMN than in other groups (p < 0.001). Receiver operating characteristics analysis revealed detection of enlarged nerves/roots in at least four measurement points to serve as a good marker to differentiate MMN from ALS with a sensitivity of 87.5% and a specificity of 94.1%. Ultrasonic focal nerve enlargement in MMN was often not colocalized with areas of conduction blocks found in nerve conduction studies. Systematic ultrasound measurements in different nerves and nerve roots are valuable for detecting focal nerve enlargement in MMN, generally not found in ALS and thus could serve as a diagnostic marker to differentiate between both entities in addition to electrodiagnostic studies.

As reliable biomarkers of disease activity are lacking, monitoring of therapeutic response in chronic inflammatory demyelinating polyradiculoneuropathy (CIDP) remains a challenge. We sought to determine whether nerve ultrasound and electrophysiology scoring could close this gap. In CIDP patients (fulfilling EFNS/PNS criteria), we performed high-resolution nerve ultrasound to determine ultrasound pattern sum scores (UPSS) and predominant echotexture nerve conduction study scores (NCSS) as well as Medical Research Council sum scores (MRCSS) and inflammatory neuropathy cause and treatment disability scores (INCAT) at baseline and after 12 months of standard treatment. We retrospectively correlated ultrasound morphology with nerve histology when available. 72/80 CIDP patients featured multifocal nerve enlargement, and 35/80 were therapy-naïve. At baseline, clinical scores correlated with NCSS (r = 0.397 and r = 0.443, p < 0.01), but not or hardly with UPSS (Medical Research Council sum scores MRCSS r = 0.013, p = 0.332; inflammatory neuropathy cause and treatment disability scores INCAT r = 0.053, p = 0.048). Longitudinal changes in clinical scores, however, correlated significantly with changes in both UPSS and NCSS (r = 0.272-0.414, p < 0.0001). Combining nerve/fascicle size with echointensity and histology at baseline, we noted 3 distinct classes: 1) hypoechoic enlargement, reflecting active inflammation and onion bulbs; 2) nerve enlargement with additional hyperechogenic fascicles/perifascicular tissue in > 50% of measured segments, possibly reflecting axonal degeneration; and 3) almost no enlargement, reflecting "burned-out" or "cured" disease without active inflammation. Clinical improvement after 12 months was best in patients with pattern 1 (up to 75% vs up to 43% in pattern 2/3, Fisher's exact test p < 0.05). Nerve ultrasound has additional value not only for diagnosis, but also for classification of disease state and may predict treatment response.

No abstract