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Recently, great attention has been devoted to the problem of the undecidability of specific questions in quantum mechanics. In this context, it has been shown that the problem of the existence of a spectral gap, i.e., energy difference between the ground state and the first excited state, is algorithmically undecidable. Using this result herein proves that the existence of a quantum phase transition, as inferred from specific microscopic approaches, is an undecidable problem, too. Indeed, some methods, usually adopted to study quantum phase transitions, rely on the existence of a spectral gap. Since there exists no algorithm to determine whether an arbitrary quantum model is gapped or gapless, and there exist models for which the presence or absence of a spectral gap is independent of the axioms of mathematics, it infers that the existence of quantum phase transitions is an undecidable problem.

We present a detailed analysis and optimization of the variational quantum algorithms required to find the ground state of a correlated electron model, using several types of variational ansatz. Specifically, we apply our approach to the atomic limit of the Anderson model, which is widely studied in condensed matter physics since it can simulate fundamental physical phenomena, ranging from magnetism to superconductivity. The method is developed by presenting efficient state preparation circuits that exhibit total spin, spin projection, particle number and time-reversal symmetries. These states contain the minimal number of variational parameters needed to fully span the appropriate symmetry subspace allowing to avoid irrelevant sectors of Hilbert space. Then, we show how to construct quantum circuits, providing explicit decomposition and gate count in terms of standard gate sets. We test these quantum algorithms looking at ideal quantum computer simulations as well as implementing quantum noisy simulations. We finally perform an accurate comparative analysis among the approaches implemented, highlighting their merits and shortcomings.

Abstract Biallelic variants in nuclear gene NDUFA2 have been reported so far in only three children with variable presentations including Leigh syndrome or leukoencephalopathy. Herein, we report a further female child affected by NDUFA2‐related disorder presenting with cavitating and tigroid‐like pattern of leukodystrophy and without systemic biochemical abnormalities of mitochondrial disorders.

Abstract Background In GM1 gangliosidosis the lack of function of β‐galactosidase results in an accumulation of GM1 ganglioside and related glycoconjugates in visceral organs, and particularly in the central nervous system, leading to severe disability and premature death. In the type 2 form of the disease, early intervention would be important to avoid precocious complications. To date, there are no effective therapeutic options in preventing progressive neurological deterioration. Substrate reduction therapy with Miglustat, a N‐alkylated sugar that inhibits the enzyme glucosylceramide synthase, has been proposed for the treatment of several lysosomal storage disorders such as Gaucher type 1 and Niemann Pick Type C diseases. However, data on Miglustat therapy in patients with GM1 gangliosidosis are still scarce. Methods We report here the results of Miglustat administration in four Italian children (average age: 55 months, range 20–125) affected by GM1 gangliosidosis type 2 treated in three different Italian pediatric hospitals specialized in metabolic diseases. Conclusion This treatment was safe and relatively well tolerated by all patients, with stabilization and/or slowing down of the neurological progression in three subjects.

We study the tight-binding dispersion of the recently discovered superconductor K2Cr3As3, obtained from Wannier projection of Density Functional Theory (DFT) results. In order to establish quantitatively the actual degree of quasi-one-dimensionality of this compound, we analyze the electronic band structure for two reduced sets of hopping parameters: one restricted to the Cr-As tubes and another one retaining a minimal number of in-plane hoppings. The corresponding total and local density of states of the compound are also computed with the aim of assessing the tight-binding results with respect to the DFT ones. We find a quite good agreement with the DFT results for the more extended set of hopping parameters, especially for what concerns the orbitals that dominate at the Fermi level. Therefore, we conclude that one cannot avoid taking into account in-plane hoppings up to the next-nearest-neighbors cells even only to describe correctly the Fermi surface cuts and the populations along the kz direction. Such a choice of a minimal number of hopping parameters directly reflects in the possibility of correctly describing correlations and magnetic interactions.

We present a systematic derivation of a minimal five-band tight-binding model for the description of the electronic structure of the recently discovered quasi-one-dimensional superconductor K _2 Cr _3 As _3 . Taking as a reference the density-functional theory (DFT) calculation, we use the outcome of a Löwdin procedure to refine a Wannier projection and fully exploit the predominant weight at the Fermi level of the states having the same symmetry of the crystal structure. Such states are described in terms of five quasi-atomic d orbitals: four planar orbitals, two d _xy and two ${d}_{{x}^{2}-{y}^{2}}$ , and a single out-of-plane one, ${d}_{{z}^{2}}$ . We show that this minimal model reproduces with great accuracy the DFT band structure in a broad energy window around the Fermi energy. Moreover, we derive an explicit simplified analytical expression of such model, which includes three nearest-neighbor (NN) hopping terms along the z direction and one NN term within the xy plane. This model captures very efficiently the energy spectrum of the system and, consequently, can be used to study transport properties, superconductivity and dynamical effects in this novel class of superconductors.