On the Hidden Subgroup Problem as a Pivot in Quantum Complexity Theory

Quantum computing has opened the way to new algorithms that can efficiently solve problems that have always been deemed intractable. However, since quantum algorithms are hard to design, the necessity to find a generalization of these problems arises. Such necessity is satisfied by the hidden subgroup problem (HSP), an abstract problem of group theory which successfully generalizes a large number of intractable problems. The HSP plays a significant role in quantum complexity theory, as efficient algorithms that solve it can be employed to efficiently solve other valuable problems, such as integer factorization, discrete logarithms, graph isomorphism and many others. In this thesis we give a computational definition of the HSP. We then prove the reducibility of some of the aforementioned problems to the HSP. Lastly, we introduce some essential notions of quantum computing and we present two quantum algorithms that efficiently solve the HSP on Abelian groups

On Dynamic Lifting and Effect Typing in Circuit Description Languages

In the realm of quantum computing, circuit description languages represent a valid alternative to traditional QRAM-style languages. They indeed allow for finer control over the output circuit, without sacrificing flexibility nor modularity. We introduce a generalization of the paradigmatic lambda-calculus Proto-Quipper-M, which models the core features of the quantum circuit description language Quipper. The extension, called Proto-Quipper-K, is meant to capture a very general form of dynamic lifting. This is made possible by the introduction of a rich type and effect system in which not only computations, but also the very types are effectful. The main results we give for the introduced language are the classic type soundness results, namely subject reduction and progress

Circuit Width Estimation via Effect Typing and Linear Dependency (Long Version)

Circuit description languages are a class of quantum programming languages in which programs are classical and produce a description of a quantum computation, in the form of a quantum circuit. Since these programs can leverage all the expressive power of high-level classical languages, circuit description languages have been successfully used to describe complex and practical quantum algorithms, whose circuits, however, may involve many more qubits and gate applications than current quantum architectures can actually muster. In this paper, we present Proto-Quipper-R, a circuit description language endowed with a linear dependent type-and-effect system capable of deriving parametric upper bounds on the width of the circuits produced by a program. We prove both the standard type safety results and that the resulting resource analysis is correct with respect to a big-step operational semantics. We also show that our approach is expressive enough to verify realistic quantum algorithms.Comment: 21 pages (excluding references), 21 figure

Abstract Machine Semantics for Quipper

Quipper is a domain-specific programming language for the description of quantum circuits. Because it is implemented as an embedded language in Haskell, Quipper is a very practical functional language. However, for the same reason, it lacks a formal semantics and it is limited by Haskell's type-system. In particular, because Haskell lacks linear types, it is easy to write Quipper programs that violate the non-cloning property of quantum states. In order to formalize relevant fragments of Quipper in a type-safe way, the Proto-Quipper family of research languages has been introduced over the last years. In this thesis we first introduce Quipper and Proto-Quipper-M. Proto-Quipper-M is an instance of the Proto-Quipper family based on a categorical model for quantum circuits, which features a linear type-system that guarantees that the non-cloning property holds at compile time. We then derive a tentative small-step operational semantics from the big-step semantics of Proto-Quipper-M and we prove that the two are equivalent. After proving subject reduction and progress results for the tentative semantics, we build upon it to obtain a truly small-step semantics in the style of an abstract machine, which we eventually prove to be equivalent to the original semantics

Extended Adhesion-Sparing Liver Eversion during Kasai Portoenterostomy for Infants with Biliary Atresia

Background: Despite the fact that Kasai portoenterostomy (KPE) is the primary treatment for biliary atresia (BA), liver transplantation (LT) remains the ultimate surgery for two-thirds of these patients. Their true survival rate with the native liver reflects the original KPE and the burden of post-operative complications. We report an original modification of the adhesion-sparing liver eversion (ASLE) technique during KPE that facilitates the total native hepatectomy at time of transplantation. Methods: All consecutive patients with BA who underwent KPE at our department and subsequent LT at Paediatric Liver Transplant Centre at Papa Giovanni XXIII Hospital between 2010-2018 were retrospectively enrolled. All patients underwent ASLE during KPE. Patients' demographic data, type of KPE, total transplant time (TTT), hepatectomy time (HT), intra-operative packed red blood cells and plasma transfusions, intra- and post-operative complications were noted. Results: 44 patients were enrolled. Median TTT and HT were 337 and 57 min, respectively. The median volume of packed red blood cell transfusion was 95 mL. No patients presented bowel perforation during the procedure or in the short post-operative course. No mortality after LT was recorded. Conclusions: In addition to the well-known advantages of the standard liver eversion technique, ASLE reduces the formation of intra-abdominal adhesions, lowering significantly the risk of bowel perforation and bleeding when liver transplantation is performed for failure of KPE

Pharmacokinetics of prolonged-release tacrolimus versus immediate-release tacrolimus in de novo liver transplantation: A randomized phase III substudy

Background With the same dose of tacrolimus, lower systemic exposure on the first day of dosing has been reported for prolonged-release tacrolimus compared with immediate-release tacrolimus, prompting investigation of differing initial doses. Methods This sub-study of a double-blind, randomized, phase III trial in de novo liver transplant recipients compared the pharmacokinetics of once-daily prolonged-release tacrolimus (initial dose: 0.2mg/kg/day) versus twice-daily immediate-release tacrolimus (initial dose: 0.1mg/kg/day) during the first 2 weeks post-transplant. Results Pharmacokinetic data were analysed from patients receiving prolonged-release tacrolimus (n=13) and immediate-release tacrolimus (n=12). Mean systemic exposure (AUC0–24) was higher with prolonged-release versus immediate-release tacrolimus. Dose-normalized AUC0–24 (normalized to 0.1mg/kg/day) showed generally lower exposure with prolonged-release tacrolimus versus immediate-release tacrolimus. There was good correlation between AUC0–24 and concentration at 24 hours after the morning dose (r=0.96 and r=0.86, respectively), and the slope of the line of best fit was similar for both formulations. Conclusions Doubling the initial starting dose of prolonged-release tacrolimus compared with immediate-release tacrolimus overcompensated for lower exposure on Day 1. A 50% higher starting dose of prolonged-release tacrolimus than immediate-release tacrolimus may be required for similar systemic exposure. However, doses of both formulations can be optimized using the same trough-level monitoring system. (ClinicalTrials . gov number: NCT00189826) Discipline liver transplantation/hepatology, immunosuppression/immune modulation. This article is protected by copyright. All rights reserved

Evolution of minimally invasive techniques and surgical outcomes of ALPPS in Italy: a comprehensive trend analysis over 10 years from a national prospective registry

BackgroundSince 2012, Associating Liver Partition and Portal vein ligation for Staged hepatectomy (ALPPS) has encountered several modifications of its original technique. The primary endpoint of this study was to analyze the trend of ALPPS in Italy over a 10-year period. The secondary endpoint was to evaluate factors affecting the risk of morbidity/mortality/post-hepatectomy liver failure (PHLF).MethodsData of patients submitted to ALPPS between 2012 and 2021 were identified from the ALPPS Italian Registry and evaluation of time trends was performed.ResultsFrom 2012 to 2021, a total of 268 ALPPS were performed within 17 centers. The number of ALPPS divided by the total number of liver resections performed by each center slightly declined (APC = - 2.0%, p = 0.111). Minimally invasive (MI) approach significantly increased over the years (APC = + 49.5%, p = 0.002). According to multivariable analysis, MI completion of stage 1 was protective against 90-day mortality (OR = 0.05, p = 0.040) as well as enrollment within high-volume centers for liver surgery (OR = 0.32, p = 0.009). Use of interstage hepatobiliary scintigraphy (HBS) and biliary tumors were independent predictors of PHLF.ConclusionsThis national study showed that use of ALPPS only slightly declined over the years with an increased use of MI techniques, leading to lower 90-day mortality. PHLF still remains an open issue

Improved survival in liver transplant recipients receiving prolonged-release tacrolimus in the European liver transplant registry

This study was a retrospective analysis of the European Liver Transplant Registry (ELTR) performed to compare long-term outcomes with prolonged-release tacrolimus versus tacrolimus BD in liver transplantation (January 2008-December 2012). Clinical efficacy measures included univariate and multivariate analyses of risk factors influencing graft and patient survival at 3 years posttransplant. Efficacy measures were repeated using propensity score-matching for baseline demographics. Patients with <1 month of follow-up were excluded from the analyses. In total, 4367 patients (prolonged-release tacrolimus: n = 528; BD: n = 3839) from 21 European centers were included. Tacrolimus BD treatment was significantly associated with inferior graft (risk ratio: 1.81; p = 0.001) and patient survival (risk ratio: 1.72; p = 0.004) in multivariate analyses. Similar analyses performed on the propensity score-matched patients confirmed the significant survival advantages observed in the prolonged-release tacrolimus- versus tacrolimus BD-treated group. This large retrospective analysis from the ELTR identified significant improvements in long-term graft and patient survival in patients treated with prolonged-release tacrolimus versus tacrolimus BD in primary liver transplant recipients over 3 years of treatment. However, as with any retrospective registry evaluation, there are a number of limitations that should be considered when interpreting these data