Uncomputably complex renormalisation group flows

Renormalisation group methods are among the most important techniques for analysing the physics of many-body systems: by iterating a renormalisation group map, which coarse-grains the description of a system and generates a flow in the parameter space, physical properties of interest can be extracted. However, recent work has shown that important physical features, such as the spectral gap and phase diagram, may be impossible to determine, even in principle. Following these insights, we construct a rigorous renormalisation group map for the original undecidable many-body system that appeared in the literature, which reveals a renormalisation group flow so complex that it cannot be predicted. We prove that each step of this map is computable, and that it converges to the correct fixed points, yet the resulting flow is uncomputable. This extreme form of unpredictability for renormalisation group flows had not been shown before and goes beyond the chaotic behaviour seen previously

Fitting quantum noise models to tomography data

The presence of noise is currently one of the main obstacles to achieving large-scale quantum computation. Strategies to characterise and understand noise processes in quantum hardware are a critical part of mitigating it, especially as the overhead of full error correction and fault-tolerance is beyond the reach of current hardware. Non-Markovian effects are a particularly unfavourable type of noise, being both harder to analyse using standard techniques and more difficult to control using error correction. In this work we develop a set of efficient algorithms, based on the rigorous mathematical theory of Markovian master equations, to analyse and evaluate unknown noise processes. In the case of dynamics consistent with Markovian evolution, our algorithm outputs the best-fit Lindbladian, i.e., the generator of a memoryless quantum channel which best approximates the tomographic data to within the given precision. In the case of non-Markovian dynamics, our algorithm returns a quantitative and operationally meaningful measure of non-Markovianity in terms of isotropic noise addition. We provide a Python implementation of all our algorithms, and benchmark these on a range of 1- and 2-qubit examples of synthesised noisy tomography data, generated using the Cirq platform. The numerical results show that our algorithms succeed both in extracting a full description of the best-fit Lindbladian to the measured dynamics, and in computing accurate values of non-Markovianity that match analytical calculations

Randomized Benchmarking for Individual Quantum Gates

Any technology requires precise benchmarking of its components, and the quantum technologies are no exception. Randomized benchmarking allows for the relatively resource economical estimation of the average gate fidelity of quantum gates from the Clifford group, assuming identical noise levels for all gates, making use of suitable sequences of randomly chosen Clifford gates. In this work, we report significant progress on randomized benchmarking, by showing that it can be done for individual quantum gates outside the Clifford group, even for varying noise levels per quantum gate. This is possible at little overhead of quantum resources, but at the expense of a significant classical computational cost. At the heart of our analysis is a representation-theoretic framework that we develop here which is brought into contact with classical estimation techniques based on bootstrapping and matrix pencils. We demonstrate the functioning of the scheme at hand of benchmarking tensor powers of T-gates. Apart from its practical relevance, we expect this insight to be relevant as it highlights the role of assumptions made on unknown noise processes when characterizing quantum gates at high precision.Comment: 4+13 pages, 4 figures, small changes, references adde

Anthropic pressures on Nature 2000 Sites: recommendations and monitoring criteria for the pollution emergency response activities within the Orbetello lagoon

L’elevato valore naturalistico e socioeconomico di un Sito Natura 2000 richiede che tutte le attività antropiche che si svolgono al suo interno (es. pesca, turismo, trasporti, attività industriali, etc.) siano gestite in maniera tale da non pregiudicare le specie e gli habitat per i quali l’area è stata designata. Molti di questi Siti sono ambienti di transizione, ovvero zone che costituiscono il passaggio naturale tra terra e mare. La loro posizione di interfaccia tra questi due ambienti li rende ecosistemi unici e biologicamente molto produttivi, sede di meccanismi di regolazione dei processi interattivi della biosfera nelle due fasi, terrestre e marina. In alcuni Siti la presenza di attività antropiche diffuse e prolungate nel tempo ha portato al riscontro di stati di contaminazione elevata, fino all’inclusione di queste zone, o parti di esse, tra i Siti di bonifica di Interesse Nazionale (SIN). Il presente lavoro descrive le linee di indirizzo e le attività di monitoraggio da attuare per la salvaguardia della salute pubblica e dell’ambiente nel corso degli interventi di messa in sicurezza di emergenza predisposti nell’area lagunare antistante l’area industriale Ex Sitoco, all’interno della perimetrazione del SIN di Orbetello, incluso in un Sito di Importanza Comunitaria. Le matrici ambientali potenzialmente a rischio a causa dell’esecuzione di tali interventi sono: acqua, sedimento, biocenosi acquatiche, avifauna, uomo. È altresì importante valutare gli effetti che le ipotetiche modifiche su microscala, apportate a livello di ogni matrice, potrebbero causare nel lungo periodo su macroscala.The high naturalistic and socio-economic value of Natura 2000 sites requires that all human activities performed within their borders (e.g. fishing, tourism, transports, industrial activities) are regulated. Indeed, the site management should assure the effective safeguard of all species and habitats of European interest included in the protected area. A lot of such sites are located in transitional environments, that are areas characterised by a natural progression from the terrestrial to the water environments. Such environments include unique and very productive habitats, and they represent the regulation mechanisms of the interactive processes of the terrestrial and marine biosphere. In some sites, the presence of human activities that are distributed both in space and time has led to high levels of contamination, that in some cases even required their inclusion in Reclamation Sites of National Interest (SIN). The present study describes the planning and monitoring activities to be performed in order to safeguard human and environment health during the actions of MISE in the lagoonal area in front of the industrial area Ex Sitoco, within the borders of the Orbetello SIN, included in a SCI. The environmental parameters that are potentially at risk due to such activities are: water, sediment, water biocenosis, birds, humans. Furthermore, it is important to evaluate the effects that potential variations at the microscale level may cause at the macroscale level

Noise-mitigated randomized measurements and self-calibrating shadow estimation

Randomized measurements are increasingly appreciated as powerful tools to estimate properties of quantum systems, e.g., in the characterization of hybrid classical-quantum computation. On many platforms they constitute natively accessible measurements, serving as the building block of prominent schemes like shadow estimation. In the real world, however, the implementation of the random gates at the core of these schemes is susceptible to various sources of noise and imperfections, strongly limiting the applicability of protocols. To attenuate the impact of this shortcoming, in this work we introduce an error-mitigated method of randomized measurements, giving rise to a robust shadow estimation procedure. On the practical side, we show that error mitigation and shadow estimation can be carried out using the same session of quantum experiments, hence ensuring that we can address and mitigate the noise affecting the randomization measurements. Mathematically, we develop a picture derived from Fourier-transforms to connect randomized benchmarking and shadow estimation. We prove rigorous performance guarantees and show the functioning using comprehensive numerics. More conceptually, we demonstrate that, if properly used, easily accessible data from randomized benchmarking schemes already provide such valuable diagnostic information to inform about the noise dynamics and to assist in quantum learning procedures.Comment: 6+20 pages, 6 figure

Early intra-aortic balloon pumping following perioperative myocardial injury improves hospital and mid-term prognosis

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Estimating gate-set properties from random sequences

With quantum computing devices increasing in scale and complexity, there is a growing need for tools that obtain precise diagnostic information about quantum operations. However, current quantum devices are only capable of short unstructured gate sequences followed by native measurements. We accept this limitation and turn it into a new paradigm for characterizing quantum gate-sets. A single experiment - random sequence estimation - solves a wealth of estimation problems, with all complexity moved to classical post-processing. We derive robust channel variants of shadow estimation with close-to-optimal performance guarantees and use these as a primitive for partial, compressive and full process tomography as well as the learning of Pauli noise. We discuss applications to the quantum gate engineering cycle, and propose novel methods for the optimization of quantum gates and diagnosing cross-talk.Comment: 10+18 pages, two figures, substantially rewritten (made more intuitive, connected better to common experimental prescriptions, equipped with stronger numerical analysis

Distal Reoperations after Repair of Acute Type A Aortic Dissection—Incidence, Causes and Outcomes

Background and Aim of the Study: In patients with acute type A aortic dissection (A-AAD) whether initial repair should include also aortic arch replacement is still debated. We aimed to assess if extensive aortic repair prevents from reoperations patients with A-AAD. Methods: Outcomes after distal reoperation following repair of A-AAD (n = 285; 1977 to 2018) were analysed in 22 of 226 who underwent ascending aorta/hemiarch replacement (Group 1R) and 7 of 59 who had ascending aorta/arch replacement (Group 2R). Results: Distal reoperation was more common in Group 1R (n = 22) than in Group 2R (n = 0) (p < 0.001) while thoracic endovascular stenting was more frequent in Group 2R (7 vs 3, p < 0.001). Indications for reoperation were pseudoaneurysm at distal anastomosis (n = 4, 18%) and progression of aortic dissection (n = 18, 82%) in Group 1R. Indication for thoracic endovascular stenting was progressive aortic dissection in 3 patients of Group 1R and in 6 of Group 2R. Second reoperation was required in 2 patients from Group 1R (2%) during a mean follow-up of 5 years. Median follow-up was 4 years in Group 1R and 7 years in Group 2R (p = 0.36). Hospital mortality was 14% in Group 1R and 0% in Group 2R (p = 0.3). Actuarial survival is 68 ± 10%, and 62 ± 11% for Group 1R and 100% for Group 2R at 5 and 10 years (p = 0.076). Conclusions: Distal reoperations after A-AAD repair have an acceptable mortality. An extensive initial repair has lower rate of reoperation and better mid-term survival and should be indicated especially for young patients in experienced centers