Time-crystalline eigenstate order on a quantum processor.

Quantum many-body systems display rich phase structure in their low-temperature equilibrium states1. However, much of nature is not in thermal equilibrium. Remarkably, it was recently predicted that out-of-equilibrium systems can exhibit novel dynamical phases2-8 that may otherwise be forbidden by equilibrium thermodynamics, a paradigmatic example being the discrete time crystal (DTC)7,9-15. Concretely, dynamical phases can be defined in periodically driven many-body-localized (MBL) systems via the concept of eigenstate order7,16,17. In eigenstate-ordered MBL phases, the entire many-body spectrum exhibits quantum correlations and long-range order, with characteristic signatures in late-time dynamics from all initial states. It is, however, challenging to experimentally distinguish such stable phases from transient phenomena, or from regimes in which the dynamics of a few select states can mask typical behaviour. Here we implement tunable controlled-phase (CPHASE) gates on an array of superconducting qubits to experimentally observe an MBL-DTC and demonstrate its characteristic spatiotemporal response for generic initial states7,9,10. Our work employs a time-reversal protocol to quantify the impact of external decoherence, and leverages quantum typicality to circumvent the exponential cost of densely sampling the eigenspectrum. Furthermore, we locate the phase transition out of the DTC with an experimental finite-size analysis. These results establish a scalable approach to studying non-equilibrium phases of matter on quantum processors.

Measurement of Small Photon Numbers in Circuit QED Resonators.

Off-resonant interaction of fluctuating photons in a resonator with a qubit increases the qubit dephasing rate. We use this effect to measure a small average number of intracavity photons that are coherently or thermally driven. For spectral resolution, we do this by subjecting the qubit to a Carr-Purcell-Meiboom-Gill sequence and record the qubit dephasing rate for various periods between qubit π pulses. The recorded data is then analyzed with formulas for the photon-induced dephasing rate derived for the non-Gaussian noise regime with an arbitrary ratio of the resonator dispersive shift to decay rate. We show that the presented Carr-Purcell-Meiboom-Gill dephasing rate formulas agree well with experimental results and demonstrate measurement of thermal and coherent photon populations at the level of a few 10^{-4}.

Mindfulness in primary care healthcare and teaching professionals and its relationship with stress at work: a multicentric cross-sectional study.

BACKGROUND: Work stress is a common problem among the health personnel of the Spanish National Health System. The objective of this paper is to assess the state of mindfulness among Spanish primary care providers and to evaluate its potential relationship with work stress and basic labor and sociodemographic characteristics. METHODS: Cross-sectional, multi-centric study. Primary care nurses, teachers, teaching collaborators and residents assigned to six Spanish Family Medicine/Family and Community Care Departments were invited to participate (n = 475). A template was designed in Google Forms, including sociodemographic and work-related variables. The state of mindfulness was measured with the Five Facet Mindfulness Questionnaire (FFMQ), while work-related stress was measured using an ordinal scale ranging from 0 to 10 points. Descriptive and inferential statistical analyses were carried out, as well as bivariate and multivariate statistics. RESULTS: The mean age of participants was 40,14 ± 13.12 (range:23-65 years); 66.9% were women, 42.5% internal medicine residents, 29.3% family physicians, and 20.2% nurses. More than half (54.5%) knew about mindfulness, with 24.0% have received training on it, and 22.5% were usual practitioners. The average level of mindfulness was 127.18 ± 15.45 (range: 89-177). The average score of stress at work was 6.00 ± 2.44; 49.9% (range: 0-10). 49.9% of participants scored 7 or more on the stress at work scale. There was an inverse correlation between the levels of mindfulness (FFMQ total score) and work-related stress (Spearman's r = - 0.155, p = 0.003). Significant relationships between the mindfulness practice and the level of mindfulness (F = 29.80, p < 0.001), as well as between the mindfulness practice and the level of work-related stress (F = 9.68, p = 0.042), were also found. CONCLUSIONS: Levels of mindfulness in primary care health providers were in line with those levels observed in other groups of health professionals. Half of all of the primary care providers suffered from a high degree of stress. Although weak, inverse relationships were observed between levels of mindfulness and stress at work, with lower values of stress at work among those who practiced mindfulness. TRIAL REGISTRATION: NCT03629457 .

Correlators Exceeding One in Continuous Measurements of Superconducting Qubits.

We consider the effect of phase backaction on the correlator ⟨I(t)I(t+τ)⟩ for the output signal I(t) from continuous measurement of a qubit. We demonstrate that the interplay between informational and phase backactions in the presence of Rabi oscillations can lead to the correlator becoming larger than 1, even though |⟨I⟩|≤1. The correlators can be calculated using the generalized "collapse recipe," which we validate using the quantum Bayesian formalism. The recipe can be further generalized to the case of multitime correlators and arbitrary number of detectors, measuring non-commuting qubit observables. The theory agrees well with experimental results for continuous measurement of a transmon qubit. The experimental correlator exceeds the bound of 1 for a sufficiently large angle between the amplified and informational quadratures, causing the phase backaction. The demonstrated effect can be used to calibrate the quadrature misalignment.

Controlled clinical trial comparing the effectiveness of a mindfulness and self-compassion 4-session programme versus an 8-session programme to reduce work stress and burnout in family and community medicine physicians and nurses: MINDUUDD study protocol.

BACKGROUND: Health personnel are susceptible to high levels of work stress and burnout due to the psychological and emotional demands of their work, as well as to other aspects related to the organisation of that work. This paper describes the rationale and design of the MINDUUDD study, the aim of which is to evaluate the effectiveness of a mindfulness and self-compassion 4-session programme versus the standard 8-session programme to reduce work stress and burnout in Family and Community Medicine and Nursing tutors and residents. METHODS: The MINDUDD study is a multicentre cluster randomised controlled trial with three parallel arms. Six Teaching Units will be randomised to one of the three study groups: 1) Experimental Group-8 (EG8); 2) Experimental Group-4 (EG4) Control group (CG). At least 132 subjects will participate (66 tutors/66 residents), 44 in the EG8, 44 in the EG4, and 44 in the CG. Interventions will be based on the Mindfulness-Based Stress Reduction (MBSR) program, including some self-compassion practices of the Mindful Self-Compassion (MSC) programme. The EG8 intervention will be implemented during 8 weekly face-to-face sessions of 2.5 h each, while the EG4 intervention will consist of 4 sessions of 2.5 h each. The participants will have to practice at home for 30 min/day in the EG8 and 15 min/day in the EG4. The Five Facet Mindfulness Questionnaire (FFMQ), Self-Compassion Scale (SCS), Perceived Stress Questionnaire (PSQ), Maslach Burnout Inventory (MBI), Jefferson Scale of Physician Empathy (JSPE), and Goldberg Anxiety-Depression Scale (GADS) will be administered. Measurements will be taken at baseline, at the end of the programs, and at three months after completion. The effect of the interventions will be evaluated by bivariate and multivariate analyses (Multiple Linear Regression). DISCUSSION: If the abbreviated mindfulness programme is at least as effective as the standard program, its incorporation into the curriculum and training plans will be easier and more appropriate. It will also be more easily applied and accepted by primary care professionals because of the reduced resources and means required for its implementation, and it may also extend beyond care settings to academic and teaching environments as well. TRIAL REGISTRATION: The study has been registered at ClinicalTrials.gov ( NCT03629457 ; date of registration: 13.08.2018).

Comparison of the Effectiveness of an Abbreviated Program versus a Standard Program in Mindfulness, Self-Compassion and Self-Perceived Empathy in Tutors and Resident Intern Specialists of Family and Community Medicine and Nursing in Spain.

Health professionals are among the most vulnerable to work stress and emotional exhaustion problems. These health professionals include tutors and resident intern specialists, due to the growing demand for the former and the high work overload of the latter. Mindfulness training programs can support these professionals during times of crisis, such as the current global pandemic caused by the coronavirus-19 disease. The objective of this study was to compare the effectiveness of an abbreviated Mindfulness-Based Stress Reduction (MBSR) and Mindful Self-Compassion (MSC) training program in relation to a standard training program on the levels of mindfulness, self-compassion, and self-perceived empathy in tutors and resident intern specialists of Family and Community Medicine and Nursing. A total of 112 professionals attached to six Spanish National Health System teaching units (TUs) participated in this randomized and controlled clinical trial. Experimental Group (GE) participants were included in the standard or abbreviated MBSR programs. The Five Facet Mindfulness Questionnaire (FFMQ), the Self-Compassion Scale short form (SCS-SF), and the Jefferson Scale of Physician Empathy (JSPE) were administered three times during the study: before, immediately after, and 3 months after the intervention. Adjusted covariance analysis (ANCOVA), using pretest scores as the covariate, showed a significant increase in mindfulness (F(2,91) = 3.271; p = 0.042; η2 = 0.067) and self-compassion (F(2,91) = 6.046; p = 0.003; η2 = 0.117) in the post-test visit, and in self-compassion (F(2,79) = 3.880; p = 0.025; η2 = 0.089) in the follow-up visit, attributable to the implementation of the standard training program. The standard MBSR and MSC training program improves levels of mindfulness and self-compassion, and promotes long-lasting effects in tutors and resident intern specialists. New studies are needed to demonstrate the effectiveness of abbreviated training programs.

Mindfulness-Based Program for Anxiety and Depression Treatment in Healthcare Professionals: A Pilot Randomized Controlled Trial.

In primary health care, the work environment can cause high levels of anxiety and depression, triggering relevant expert and individual change. Mindfulness-Based Stress Reduction (MBSR) programs reduce signs of anxiety and depression. The purpose of this sub-analysis of the total project, was to equate the effectiveness of the standard MBSR curriculum with the abbreviated version in minimizing anxiety and depression. This randomized controlled clinical trial enrolled 112 mentors and resident specialists from Family and Community Medicine and Nurses (FCMN), distributed across six teaching units (TU) of the Spanish National Health System (SNHS). Experimental group participants received a MBRS training (abbreviated/standard). Depression and anxiety levels were measured with the Goldberg Anxiety and Depression Scale (GADS) at three different time periods during the analysis: before (pre-test) and after (post-test) participation, as well as 3 months after the completion of intervention. Taking into account the pre-test scores as the covariate, an adjusted analysis of covariance (ANCOVA) showed significant depletion in anxiety and depression in general (F (2.91) = 4.488; p = 0.014; η2 = 0.090) and depression in particular (F (2, 91) = 6.653; p = 0.002; η2 = 0.128 at the post-test visit, maintaining their effects for 3 months (F (2.79) = 3.031; p = 0.050; η2 = 0.071-F (2.79) = 2.874; p = 0.049; η2 = 0.068, respectively), which is associated with the use of a standard training program. The abbreviated training program did not have a significant effect on the level of anxiety and depression. The standard MBSR training program had a positive effect on anxiety and depression and promotes long-lasting effects in tutors and resident practitioners. New research is needed to demonstrate the effectiveness of abbreviated versions of training programs.

Effectiveness of a Mindfulness and Self-Compassion Standard Training Program versus an Abbreviated Training Program on Stress in Tutors and Resident Intern Specialists of Family and Community Medicine and Nursing in Spain.

Stress is one of the most common problems among healthcare professionals, as they are exposed to potentially stressful and emotionally challenging situations in the workplace. Mindfulness-based stress reduction (MBSR) training programs have been shown to decrease stress. The objective of this study was to compare the effectiveness of an abbreviated 4-weeks MBSR training program in relation to a standard 8-weeks one on the stress levels. A controlled and randomized clinical trial was designed, in which 112 tutors and resident intern specialists in Family and Community Medicine and Nursing of six Spanish National Health System teaching units (TUs) participated. Participants included in the experimental groups (EGs) received a MBRS training program (standard or abbreviated), while control group (CG) participants did not receive any intervention. The stress levels were assessed by the Perceived Stress Questionnaire (PSQ) in three different moments during the study: before, immediately after, and 3 months after the intervention. Adjusted covariance analysis (ANCOVA), using pretest scores as the covariate, showed a significant reduction in stress (F(2,91) = 5.165; p = 0.008; η2 = 0.102) in the post-test visit, attributable to the implementation of the standard training program, but without the maintenance of its effects over time. No significant impact of the abbreviated training program on stress levels was observed in the intergroup comparison. A standard 8-weeks MBSR training program aimed at tutors and resident intern specialists in Family and Community Medicine and Nursing produces significant improvements in stress levels compared with the abbreviated intervention and no intervention. New studies about abbreviated training programs are needed to provide effective treatments which improve well-being of these professionals.

Information scrambling in quantum circuits.

Interactions in quantum systems can spread initially localized quantum information into the exponentially many degrees of freedom of the entire system. Understanding this process, known as quantum scrambling, is key to resolving several open questions in physics. Here, by measuring the time-dependent evolution and fluctuation of out-of-time-order correlators, we experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We engineer quantum circuits that distinguish operator spreading and operator entanglement and experimentally observe their respective signatures. We show that whereas operator spreading is captured by an efficient classical model, operator entanglement in idealized circuits requires exponentially scaled computational resources to simulate. These results open the path to studying complex and practically relevant physical observables with near-term quantum processors.

Mass loading induced dephasing in nanomechanical resonators.

This paper presents a study of dephasing of an underdamped nanomechanical resonator subject to random mass loading of small particles. A frequency noise model is presented which describes dephasing due to the attachment and detachment of particles at random points and particle diffusion along the resonator. This situation is commonly encountered in current mass measurement experiments using nanoelectromechanical (NEM) resonators. The conditions which can lead to inhomogeneous broadening and fine structure in the modes' absorption spectra are discussed. It is also shown that the spectra of the higher-order cumulants of the (complex) vibrational mode amplitude are sensitive to the parameters characterizing the frequency noise process. Hence, measurement of these cumulants can provide information not only about the mass but also about other parameters of the particles (diffusion coefficient and attachment-detachment rates).

Continuum elastic modeling of graphene resonators.

Starting from an atomistic approach, we have derived a hierarchy of successively more simplified continuum elasticity descriptions for modeling the mechanical properties of suspended graphene sheets. We find that already for deflections of the order of 0.5 A a theory that correctly accounts for nonlinearities is necessary and that for many purposes a set of coupled Duffing-type equations may be used to accurately describe the dynamics of graphene membranes. The descriptions are validated by applying them to square graphene-based resonators with clamped edges and studying numerically their mechanical responses. Both static and dynamic responses are treated, and we find good agreement with recent experimental findings.