Formation of robust bound states of interacting microwave photons.

Systems of correlated particles appear in many fields of modern science and represent some of the most intractable computational problems in nature. The computational challenge in these systems arises when interactions become comparable to other energy scales, which makes the state of each particle depend on all other particles1. The lack of general solutions for the three-body problem and acceptable theory for strongly correlated electrons shows that our understanding of correlated systems fades when the particle number or the interaction strength increases. One of the hallmarks of interacting systems is the formation of multiparticle bound states2-9. Here we develop a high-fidelity parameterizable fSim gate and implement the periodic quantum circuit of the spin-½ XXZ model in a ring of 24 superconducting qubits. We study the propagation of these excitations and observe their bound nature for up to five photons. We devise a phase-sensitive method for constructing the few-body spectrum of the bound states and extract their pseudo-charge by introducing a synthetic flux. By introducing interactions between the ring and additional qubits, we observe an unexpected resilience of the bound states to integrability breaking. This finding goes against the idea that bound states in non-integrable systems are unstable when their energies overlap with the continuum spectrum. Our work provides experimental evidence for bound states of interacting photons and discovers their stability beyond the integrability limit.

Accurately computing the electronic properties of a quantum ring.

A promising approach to study condensed-matter systems is to simulate them on an engineered quantum platform1-4. However, the accuracy needed to outperform classical methods has not been achieved so far. Here, using 18 superconducting qubits, we provide an experimental blueprint for an accurate condensed-matter simulator and demonstrate how to investigate fundamental electronic properties. We benchmark the underlying method by reconstructing the single-particle band structure of a one-dimensional wire. We demonstrate nearly complete mitigation of decoherence and readout errors, and measure the energy eigenvalues of this wire with an error of approximately 0.01 rad, whereas typical energy scales are of the order of 1 rad. Insight into the fidelity of this algorithm is gained by highlighting the robust properties of a Fourier transform, including the ability to resolve eigenenergies with a statistical uncertainty of 10-4 rad. We also synthesize magnetic flux and disordered local potentials, which are two key tenets of a condensed-matter system. When sweeping the magnetic flux we observe avoided level crossings in the spectrum, providing a detailed fingerprint of the spatial distribution of local disorder. By combining these methods we reconstruct electronic properties of the eigenstates, observing persistent currents and a strong suppression of conductance with added disorder. Our work describes an accurate method for quantum simulation5,6 and paves the way to study new quantum materials with superconducting qubits.

Digitized adiabatic quantum computing with a superconducting circuit.

Quantum mechanics can help to solve complex problems in physics and chemistry, provided they can be programmed in a physical device. In adiabatic quantum computing, a system is slowly evolved from the ground state of a simple initial Hamiltonian to a final Hamiltonian that encodes a computational problem. The appeal of this approach lies in the combination of simplicity and generality; in principle, any problem can be encoded. In practice, applications are restricted by limited connectivity, available interactions and noise. A complementary approach is digital quantum computing, which enables the construction of arbitrary interactions and is compatible with error correction, but uses quantum circuit algorithms that are problem-specific. Here we combine the advantages of both approaches by implementing digitized adiabatic quantum computing in a superconducting system. We tomographically probe the system during the digitized evolution and explore the scaling of errors with system size. We then let the full system find the solution to random instances of the one-dimensional Ising problem as well as problem Hamiltonians that involve more complex interactions. This digital quantum simulation of the adiabatic algorithm consists of up to nine qubits and up to 1,000 quantum logic gates. The demonstration of digitized adiabatic quantum computing in the solid state opens a path to synthesizing long-range correlations and solving complex computational problems. When combined with fault-tolerance, our approach becomes a general-purpose algorithm that is scalable.

Resource requirements for reintroducing elective surgery during the COVID-19 pandemic: modelling study.

BACKGROUND: The COVID-19 response required the cancellation of all but the most urgent surgical procedures. The number of cancelled surgical procedures owing to Covid-19, and the reintroduction of surgical acivirt, was modelled. METHODS: This was a modelling study using Hospital Episode Statistics data (2014-2019). Surgical procedures were grouped into four urgency classes. Expected numbers of surgical procedures performed between 1 March 2020 and 28 February 2021 were modelled. Procedure deficit was estimated using conservative assumptions and the gradual reintroduction of elective surgery from the 1 June 2020. Costs were calculated using NHS reference costs and are reported as millions or billions of euros. Estimates are reported with 95 per cent confidence intervals. RESULTS: A total of 4 547 534 (95 per cent c.i. 3 318 195 to 6 250 771) patients with a pooled mean age of 53.5 years were expected to undergo surgery between 1 March 2020 and 28 February 2021. By 31 May 2020, 749 247 (513 564 to 1 077 448) surgical procedures had been cancelled. Assuming that elective surgery is reintroduced gradually, 2 328 193 (1 483 834 - 3 450 043) patients will be awaiting surgery by 28 February 2021. The cost of delayed procedures is €5.3 (3.1 to 8.0) billion. Safe delivery of surgery during the pandemic will require substantial extra resources costing €526.8 (449.3 to 633.9) million. CONCLUSION: As a consequence of the Covid-19 pandemic, provision of elective surgery will be delayed and associated with increased healthcare costs.

Quasi-steady uptake and bacterial community assembly in a mathematical model of soil-phosphorus mobility.

We mathematically model the uptake of phosphorus by a soil community consisting of a plant and two bacterial groups: copiotrophs and oligotrophs. Four equilibrium states emerge, one for each of the species monopolising the resource and dominating the community and one with coexistence of all species. We show that the dynamics are controlled by the ratio of chemical adsorption to bacterial death permitting either oscillatory states or quasi-steady uptake. We show how a steady state can emerge which has soil and plant nutrient content unresponsive to increased fertilization. However, the additional fertilization supports the copiotrophs leading to community reassembly. Our results demonstrate the importance of time-series measurements in nutrient uptake experiments.

Mortality after surgery with SARS-CoV-2 infection in England: a population-wide epidemiological study.

BACKGROUND: The COVID-19 pandemic has heavily impacted elective and emergency surgery around the world. We aimed to confirm the incidence of perioperative severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection and associated mortality after surgery. METHODS: Analysis of routine electronic health record data from NHS hospitals in England. We extracted data from Hospital Episode Statistics in England describing adult patients undergoing surgery between January 1, 2020 and February 28, 2021. The exposure was SARS-CoV-2 infection defined by International Classification of Diseases (ICD)-10 codes. The primary outcome measure was 90 day in-hospital mortality. Data were analysed using multivariable logistic regression adjusted for age, sex, Charlson Comorbidity Index, Index of Multiple Deprivation, presence of cancer, surgical procedure type and admission acuity. Results are presented as n (%) and odds ratios (OR) with 95% confidence intervals (CI). RESULTS: We identified 2 666 978 patients undergoing surgery of whom 28 777 (1.1%) had SARS-CoV-2 infection. In total, 26 364 (1.0%) patients died in hospital. SARS-CoV-2 infection was associated with a much greater risk of death (SARS-CoV-2: 6153/28 777 [21.4%] vs no SARS-CoV-2: 20 211/2 638 201 [0.8%]; OR=5.7 [95% CI, 5.5-5.9]; P<0.001). Amongst patients undergoing elective surgery, 2412/1 857 586 (0.1%) had SARS-CoV-2, of whom 172/2412 (7.1%) died, compared with 1414/1 857 586 (0.1%) patients without SARS-CoV-2 (OR=25.8 [95% CI, 21.7-30.9]; P<0.001). Amongst patients undergoing emergency surgery, 22 918/582 292 (3.9%) patients had SARS-CoV-2, of whom 5752/22 918 (25.1%) died, compared with 18 060/559 374 (3.4%) patients without SARS-CoV-2 (OR=5.5 [95% CI, 5.3-5.7]; P<0.001). CONCLUSIONS: The low incidence of SARS-CoV-2 infection in NHS surgical pathways suggests current infection prevention and control policies are highly effective. However, the high mortality amongst patients with SARS-CoV-2 suggests these precautions cannot be safely relaxed.

State preservation by repetitive error detection in a superconducting quantum circuit.

Quantum computing becomes viable when a quantum state can be protected from environment-induced error. If quantum bits (qubits) are sufficiently reliable, errors are sparse and quantum error correction (QEC) is capable of identifying and correcting them. Adding more qubits improves the preservation of states by guaranteeing that increasingly larger clusters of errors will not cause logical failure-a key requirement for large-scale systems. Using QEC to extend the qubit lifetime remains one of the outstanding experimental challenges in quantum computing. Here we report the protection of classical states from environmental bit-flip errors and demonstrate the suppression of these errors with increasing system size. We use a linear array of nine qubits, which is a natural step towards the two-dimensional surface code QEC scheme, and track errors as they occur by repeatedly performing projective quantum non-demolition parity measurements. Relative to a single physical qubit, we reduce the failure rate in retrieving an input state by a factor of 2.7 when using five of our nine qubits and by a factor of 8.5 when using all nine qubits after eight cycles. Additionally, we tomographically verify preservation of the non-classical Greenberger-Horne-Zeilinger state. The successful suppression of environment-induced errors will motivate further research into the many challenges associated with building a large-scale superconducting quantum computer.

Atto-Foxes and Other Minutiae.

This paper addresses the problem of extinction in continuous models of population dynamics associated with small numbers of individuals. We begin with an extended discussion of extinction in the particular case of a stochastic logistic model, and how it relates to the corresponding continuous model. Two examples of 'small number dynamics' are then considered. The first is what Mollison calls the 'atto-fox' problem (in a model of fox rabies), referring to the problematic theoretical occurrence of a predicted rabid fox density of [Formula: see text] (atto-) per square kilometre. The second is how the production of large numbers of eggs by an individual can reliably lead to the eventual survival of a handful of adults, as it would seem that extinction then becomes a likely possibility. We describe the occurrence of the atto-fox problem in other contexts, such as the microbial 'yocto-cell' problem, and we suggest that the modelling resolution is to allow for the existence of a reservoir for the extinctively challenged individuals. This is functionally similar to the concept of a 'refuge' in predator-prey systems and represents a state for the individuals in which they are immune from destruction. For what I call the 'frogspawn' problem, where only a few individuals survive to adulthood from a large number of eggs, we provide a simple explanation based on a Holling type 3 response and elaborate it by means of a suitable nonlinear age-structured model.

Demonstrating a Continuous Set of Two-Qubit Gates for Near-Term Quantum Algorithms.

Quantum algorithms offer a dramatic speedup for computational problems in material science and chemistry. However, any near-term realizations of these algorithms will need to be optimized to fit within the finite resources offered by existing noisy hardware. Here, taking advantage of the adjustable coupling of gmon qubits, we demonstrate a continuous two-qubit gate set that can provide a threefold reduction in circuit depth as compared to a standard decomposition. We implement two gate families: an imaginary swap-like (iSWAP-like) gate to attain an arbitrary swap angle, θ, and a controlled-phase gate that generates an arbitrary conditional phase, ϕ. Using one of each of these gates, we can perform an arbitrary two-qubit gate within the excitation-preserving subspace allowing for a complete implementation of the so-called Fermionic simulation (fSim) gate set. We benchmark the fidelity of the iSWAP-like and controlled-phase gate families as well as 525 other fSim gates spread evenly across the entire fSim(θ,ϕ) parameter space, achieving a purity-limited average two-qubit Pauli error of 3.8×10^{-3} per fSim gate.

Superconducting quantum circuits at the surface code threshold for fault tolerance.

A quantum computer can solve hard problems, such as prime factoring, database searching and quantum simulation, at the cost of needing to protect fragile quantum states from error. Quantum error correction provides this protection by distributing a logical state among many physical quantum bits (qubits) by means of quantum entanglement. Superconductivity is a useful phenomenon in this regard, because it allows the construction of large quantum circuits and is compatible with microfabrication. For superconducting qubits, the surface code approach to quantum computing is a natural choice for error correction, because it uses only nearest-neighbour coupling and rapidly cycled entangling gates. The gate fidelity requirements are modest: the per-step fidelity threshold is only about 99 per cent. Here we demonstrate a universal set of logic gates in a superconducting multi-qubit processor, achieving an average single-qubit gate fidelity of 99.92 per cent and a two-qubit gate fidelity of up to 99.4 per cent. This places Josephson quantum computing at the fault-tolerance threshold for surface code error correction. Our quantum processor is a first step towards the surface code, using five qubits arranged in a linear array with nearest-neighbour coupling. As a further demonstration, we construct a five-qubit Greenberger-Horne-Zeilinger state using the complete circuit and full set of gates. The results demonstrate that Josephson quantum computing is a high-fidelity technology, with a clear path to scaling up to large-scale, fault-tolerant quantum circuits.

Age of patients undergoing surgery.

BACKGROUND: Advancing age is independently associated with poor postoperative outcomes. The ageing of the general population is a major concern for healthcare providers. Trends in age were studied among patients undergoing surgery in the National Health Service in England. METHODS: Time trend ecological analysis was undertaken of Hospital Episode Statistics and Office for National Statistics data for England from 1999 to 2015. The proportion of patients undergoing surgery in different age groupings, their pooled mean age, and change in age profile over time were calculated. Growth in the surgical population was estimated, with associated costs, to the year 2030 by use of linear regression modelling. RESULTS: Some 68 205 695 surgical patient episodes (31 220 341 men, 45·8 per cent) were identified. The mean duration of hospital stay was 5·3 days. The surgical population was older than the general population of England; this gap increased over time (1999: 47·5 versus 38·3 years; 2015: 54·2 versus 39·7 years). The number of people aged 75 years or more undergoing surgery increased from 544 998 (14·9 per cent of that age group) in 1999 to 1 012 517 (22·9 per cent) in 2015. By 2030, it is estimated that one-fifth of the 75 years and older age category will undergo surgery each year (1·49 (95 per cent c.i. 1·43 to 1·55) million people), at a cost of €3·2 (3·1 to 3·5) billion. CONCLUSION: The population having surgery in England is ageing at a faster rate than the general population. Healthcare policies must adapt to ensure that provision of surgical treatments remains safe and sustainable.

Diabatic Gates for Frequency-Tunable Superconducting Qubits.

We demonstrate diabatic two-qubit gates with Pauli error rates down to 4.3(2)×10^{-3} in as fast as 18 ns using frequency-tunable superconducting qubits. This is achieved by synchronizing the entangling parameters with minima in the leakage channel. The synchronization shows a landscape in gate parameter space that agrees with model predictions and facilitates robust tune-up. We test both iswap-like and cphase gates with cross-entropy benchmarking. The presented approach can be extended to multibody operations as well.

Preoperative systemic inflammation and perioperative myocardial injury: prospective observational multicentre cohort study of patients undergoing non-cardiac surgery.

BACKGROUND: Systemic inflammation is pivotal in the pathogenesis of cardiovascular disease. As inflammation can directly cause cardiomyocyte injury, we hypothesised that established systemic inflammation, as reflected by elevated preoperative neutrophil-lymphocyte ratio (NLR) >4, predisposes patients to perioperative myocardial injury. METHODS: We prospectively recruited 1652 patients aged ≥45 yr who underwent non-cardiac surgery in two UK centres. Serum high sensitivity troponin T (hsTnT) concentrations were measured on the first three postoperative days. Clinicians and investigators were blinded to the troponin results. The primary outcome was perioperative myocardial injury, defined as hsTnT≥14 ng L-1 within 3 days after surgery. We assessed whether myocardial injury was associated with preoperative NLR>4, activated reactive oxygen species (ROS) generation in circulating monocytes, or both. Multivariable logistic regression analysis explored associations between age, sex, NLR, Revised Cardiac Risk Index, individual leukocyte subsets, and myocardial injury. Flow cytometric quantification of ROS was done in 21 patients. Data are presented as n (%) or odds ratio (OR) with 95% confidence intervals. RESULTS: Preoperative NLR>4 was present in 239/1652 (14.5%) patients. Myocardial injury occurred in 405/1652 (24.5%) patients and was more common in patients with preoperative NLR>4 [OR: 2.56 (1.92-3.41); P<0.0001]. Myocardial injury was independently associated with lower absolute preoperative lymphocyte count [OR 1.80 (1.50-2.17); P<0.0001] and higher absolute preoperative monocyte count [OR 1.93 (1.12-3.30); P=0.017]. Monocyte ROS generation correlated with NLR (r=0.47; P=0.03). CONCLUSIONS: Preoperative NLR>4 is associated with perioperative myocardial injury, independent of conventional risk factors. Systemic inflammation may contribute to the development of perioperative myocardial injury. CLINICAL TRIAL REGISTRATION: NCT01842568.

Fluctuations of Energy-Relaxation Times in Superconducting Qubits.

Superconducting qubits are an attractive platform for quantum computing since they have demonstrated high-fidelity quantum gates and extensibility to modest system sizes. Nonetheless, an outstanding challenge is stabilizing their energy-relaxation times, which can fluctuate unpredictably in frequency and time. Here, we use qubits as spectral and temporal probes of individual two-level-system defects to provide direct evidence that they are responsible for the largest fluctuations. This research lays the foundation for stabilizing qubit performance through calibration, design, and fabrication.

Microbial dormancy and boom-and-bust population dynamics under starvation stress.

We propose a model for the growth of microbial populations in the presence of a rate-limiting nutrient which accounts for the switching of cells to a dormant phase at low densities in response to decreasing concentration of a putative biochemical signal. We then show that in conditions of nutrient starvation, self-sustained oscillations can occur, thus providing a natural explanation for such phenomena as plankton blooms. However, unlike results of previous studies, the microbial population minima do not become unrealistically small, being buffered during minima by an increased dormant phase population. We also show that this allows microbes to survive in extreme environments for very long periods, consistent with observation. The mechanism provides a natural vehicle for other such sporadic outbreaks, such as viral epidemics.

The surgical safety checklist and patient outcomes after surgery: a prospective observational cohort study, systematic review and meta-analysis.

BACKGROUND: The surgical safety checklist is widely used to improve the quality of perioperative care. However, clinicians continue to debate the clinical effectiveness of this tool. METHODS: Prospective analysis of data from the International Surgical Outcomes Study (ISOS), an international observational study of elective in-patient surgery, accompanied by a systematic review and meta-analysis of published literature. The exposure was surgical safety checklist use. The primary outcome was in-hospital mortality and the secondary outcome was postoperative complications. In the ISOS cohort, a multivariable multi-level generalized linear model was used to test associations. To further contextualise these findings, we included the results from the ISOS cohort in a meta-analysis. Results are reported as odds ratios (OR) with 95% confidence intervals. RESULTS: We included 44 814 patients from 497 hospitals in 27 countries in the ISOS analysis. There were 40 245 (89.8%) patients exposed to the checklist, whilst 7508 (16.8%) sustained ≥1 postoperative complications and 207 (0.5%) died before hospital discharge. Checklist exposure was associated with reduced mortality [odds ratio (OR) 0.49 (0.32-0.77); P<0.01], but no difference in complication rates [OR 1.02 (0.88-1.19); P=0.75]. In a systematic review, we screened 3732 records and identified 11 eligible studies of 453 292 patients including the ISOS cohort. Checklist exposure was associated with both reduced postoperative mortality [OR 0.75 (0.62-0.92); P<0.01; I2=87%] and reduced complication rates [OR 0.73 (0.61-0.88); P<0.01; I2=89%). CONCLUSIONS: Patients exposed to a surgical safety checklist experience better postoperative outcomes, but this could simply reflect wider quality of care in hospitals where checklist use is routine.

Association of preoperative anaemia with postoperative morbidity and mortality: an observational cohort study in low-, middle-, and high-income countries.

BACKGROUND: Anaemia is associated with poor postoperative outcomes, but few studies have described the impact of preoperative anaemia in low- and middle- (LMICs), and high-income countries (HICs). METHODS: This was a planned analysis of data collected during an international 7 day cohort study of adults undergoing elective inpatient surgery. The primary outcome was in-hospital death, and the secondary outcomes were in-hospital complications. Anaemia was defined as haemoglobin <12 g dl-1 for females and <13 g dl-1 for males. Hierarchical three-level mixed-effect logistic regression models were constructed to examine the associations between preoperative anaemia and outcomes. RESULTS: We included 38 770 patients from 474 hospitals in 27 countries of whom 11 675 (30.1%) were anaemic. Of these, 6886 (17.8%) patients suffered a complication and 198 (0.5%) died. Patients from LMICs were younger with lower ASA physical status scores, but a similar prevalence of anaemia [LMIC: 5072 (32.5%) of 15 585 vs HIC: 6603 (28.5%) of 23 185]. Patients with moderate [odds ratio (OR): 2.70; 95% confidence interval (CI): 1.88-3.87] and severe anaemia (OR: 4.09; 95% CI: 1.90-8.81) were at an increased risk of death in both HIC and LMICs. Complication rates increased with the severity of anaemia. Compared with patients in LMICs, those in HICs experienced fewer complications after an interaction term analysis [LMIC (OR: 0.92; 95% CI: 0.87-0.97) vs HIC (OR: 0.86; 95% CI: 0.84-0.87); P<0.01]. CONCLUSIONS: One-third of patients undergoing elective surgery are anaemic. These patients have an increased risk of complications and death. The prevalence of anaemia is similar amongst patients in LMICs despite their younger age and lower risk profile. CLINICAL TRIAL REGISTRATION: ISRCTN51817007.

A systematic review and consensus definitions for standardised end-points in perioperative medicine: pulmonary complications.

BACKGROUND: There is a need for robust, clearly defined, patient-relevant outcome measures for use in randomised trials in perioperative medicine. Our objective was to establish standard outcome measures for postoperative pulmonary complications research. METHODS: A systematic literature search was conducted using MEDLINE, Web of Science, SciELO, and the Korean Journal Database. Definitions were extracted from included manuscripts. We then conducted a three-stage Delphi consensus process to select the optimal outcome measures in terms of methodological quality and overall suitability for perioperative trials. RESULTS: From 2358 records, the full texts of 81 manuscripts were retrieved, of which 45 met the inclusion criteria. We identified three main categories of outcome measure specific to perioperative pulmonary outcomes: (i) composite outcome measures of multiple pulmonary outcomes (27 definitions); (ii) pneumonia (12 definitions); and (iii) respiratory failure (six definitions). These were rated by the group according to suitability for routine use. The majority of definitions were given a low score, and many were imprecise, difficult to apply consistently, or both, in large patient populations. A small number of highly rated definitions were identified as appropriate for widespread use. The group then recommended four outcome measures for future use, including one new definition. CONCLUSIONS: A large number of postoperative pulmonary outcome measures have been used, but most are poorly defined. Our four recommended outcome measures include a new definition of postoperative pulmonary complications, incorporating an assessment of severity. These definitions will meet the needs of most clinical effectiveness trials of treatments to improve postoperative pulmonary outcomes.

Correction to: The Dynamics of Ascaris lumbricoides Infections.

In the original article, the second author's name was incorrect in the metadata. The given name is T. Déirdre, and the family name is Hollingsworth.

Observation of Classical-Quantum Crossover of 1/f Flux Noise and Its Paramagnetic Temperature Dependence.

By analyzing the dissipative dynamics of a tunable gap flux qubit, we extract both sides of its two-sided environmental flux noise spectral density over a range of frequencies around 2k_{B}T/h≈1 GHz, allowing for the observation of a classical-quantum crossover. Below the crossover point, the symmetric noise component follows a 1/f power law that matches the magnitude of the 1/f noise near 1 Hz. The antisymmetric component displays a 1/T dependence below 100 mK, providing dynamical evidence for a paramagnetic environment. Extrapolating the two-sided spectrum predicts the linewidth and reorganization energy of incoherent resonant tunneling between flux qubit wells.