Combining Topological Hardware and Topological Software: Color Code Quantum Computing with Topological Superconductor Networks

We present a scalable architecture for fault-tolerant topological quantum computation using networks of voltage-controlled Majorana Cooper pair boxes, and topological color codes for error correction. Color codes have a set of transversal gates which coincides with the set of topologically protected gates in Majorana-based systems, namely the Clifford gates. In this way, we establish color codes as providing a natural setting in which advantages offered by topological hardware can be combined with those arising from topological error-correcting software for full-fledged fault-tolerant quantum computing. We provide a complete description of our architecture including the underlying physical ingredients. We start by showing that in topological superconductor networks, hexagonal cells can be employed to serve as physical qubits for universal quantum computation, and present protocols for realizing topologically protected Clifford gates. These hexagonal cell qubits allow for a direct implementation of open-boundary color codes with ancilla-free syndrome readout and logical $T$-gates via magic state distillation. For concreteness, we describe how the necessary operations can be implemented using networks of Majorana Cooper pair boxes, and give a feasibility estimate for error correction in this architecture. Our approach is motivated by nanowire-based networks of topological superconductors, but could also be realized in alternative settings such as quantum Hall-superconductor hybrids.Comment: 24 pages, 24 figure

The boundaries and twist defects of the color code and their applications to topological quantum computation

The color code is both an interesting example of an exactly solved topologically ordered phase of matter and also among the most promising candidate models to realize fault-tolerant quantum computation with minimal resource overhead. The contributions of this work are threefold. First of all, we build upon the abstract theory of boundaries and domain walls of topological phases of matter to comprehensively catalog the objects realizable in color codes. Together with our classification we also provide lattice representations of these objects which include three new types of boundaries as well as a generating set for all 72 color code twist defects. Our work thus provides an explicit toy model that will help to better understand the abstract theory of domain walls. Secondly, we discover a number of interesting new applications of the cataloged objects for quantum information protocols. These include improved methods for performing quantum computations by code deformation, a new four-qubit error-detecting code, as well as families of new quantum error-correcting codes we call stellated color codes, which encode logical qubits at the same distance as the next best color code, but using approximately half the number of physical qubits. To the best of our knowledge, our new topological codes have the highest encoding rate of local stabilizer codes with bounded-weight stabilizers in two dimensions. Finally, we show how the boundaries and twist defects of the color code are represented by multiple copies of other phases. Indeed, in addition to the well studied comparison between the color code and two copies of the surface code, we also compare the color code to two copies of the three-fermion model. In particular, we find that this analogy offers a very clear lens through which we can view the symmetries of the color code which gives rise to its multitude of domain walls

Color-Code Quantum Computing with Topological Superconductor Networks

We present a scalable architecture for fault-tolerant topological quantum computation using networks of voltage-controlled Majorana Cooper pair boxes and topological color codes for error correction. Color codes have a set of transversal gates which coincides with the set of topologically protected gates in Majorana-based systems, namely, the Clifford gates. In this way, we establish color codes as providing a natural setting in which advantages offered by topological hardware can be combined with those arising from topological error-correcting software for full-fledged fault-tolerant quantum computing. We provide a complete description of our architecture, including the underlying physical ingredients. We start by showing that in topological superconductor networks, hexagonal cells can be employed to serve as physical qubits for universal quantum computation, and we present protocols for realizing topologically protected Clifford gates. These hexagonal-cell qubits allow for a direct implementation of open-boundary color codes with ancilla- free syndrome read-out and logical T gates via magic-state distillation. For concreteness, we describe how the necessary operations can be implemented using networks of Majorana Cooper pair boxes, and we give a feasibility estimate for error correction in this architecture. Our approach is motivated by nanowire-based networks of topological superconductors, but it could also be realized in alternative settings such as quantum-Hall–superconductor hybrids

In Patients With Multiple Sclerosis, Both Objective and Subjective Sleep, Depression, Fatigue, and Paresthesia Improved After 3 Weeks of Regular Exercise

Background:; Multiple sclerosis (MS) patients suffer from various difficulties including sleep complaints, symptoms of depression and fatigue, paresthesia, and cognitive impairments. There is growing evidence that regular physical activity has a positive effect on both sleep and psychological functioning, though there is limited evidence of this kind for MS patients. The aim of the present study was therefore to investigate the impact on this patient group of a regular exercise program with respect to subjective and objective sleep, depression, paresthesia, fatigue, and cognitive performance.; Methods:; A total of 46 patients [mean age: 50.74 years; Expanded Disability Status Scale (EDSS): mean: 5.3, 78.4% females] completed this 3-week intervention study. At baseline and 3 weeks later, they answered questionnaires covering sociodemographic information, subjective sleep, depression, fatigue, paresthesia, and subjective physical activity. Objective sleep [sleep electroencephalogram (EEG) recordings] and cognitive performance were also assessed at both time points. Patients participated in a regular exercise activity every weekday for about 60 min.; Results:; Compared to the baseline, by the end of the study, objective sleep had significantly improved (sleep efficiency, sleep onset latency, and wake time after sleep onset), and symptoms of sleep complaints, depression, fatigue, and paresthesia were significantly reduced. Subjective physical activity (moderate and vigorous) and cognitive performance also increased over the course of the intervention.; Conclusions:; In patients with MS, participation in regular exercise impacted positively on their objective and subjective sleep, depression, paresthesia, fatigue, and cognitive performance

Among Persons With Multiple Sclerosis (MS), Objective Sleep, Psychological Functioning, and Higher Physical Activity Scores Remained Stable Over 2 Years-Results From a Small Study Under Naturalistic Conditions

Background:; Persons with multiple sclerosis (PwMS) are at increased risk to report poor sleep patterns and lower physical activity indices. To date, data on longitudinal objectively sleep assessment is missing. In the present study, we investigated the pattern of objective sleep and subjective physical activity indices over a period of 13.5 months, under naturalistic conditions.; Method:; 13.5 months after their first assessment, a total of 16 PwMS (mean age = 49.13 median EDSS score: 5; 11 females) were reassessed on their objective sleep via portable sleep-electroencephalogram (EEG-) devices, along with their subjective sleep patterns (symptoms of insomnia, restless legs syndrome (RLS), and sleep-disordered breathing), physical activity indices, psychological functioning (symptoms of depression, fatigue, daytime sleepiness), and MS-related information (fatigue, EDSS; disease-modifying treatments). While the baseline assessment was performed in a rehabilitation center, the follow-up assessment took place at participants' naturalistic and familiar setting.; Results:; Statistically, symptoms of depression and fatigue, subjective sleep, and physical activity levels did neither increase, nor decrease over time, although descriptively, both moderate and vigorous physical activity levels decreased, and fatigue and subjective insomnia increased. Time awake after sleep onset statistically significantly decreased, while light sleep duration increased by trend.; Conclusions:; Among a smaller sample of PwMS, objective sleep in their naturalistic setting remained fairly stable over a mean time lapse of 13.5 months after clinic discharge. Physical activity levels descriptively decreased. The present results are of clinical and practical importance for treatment counseling: PwMS can be reassured that their sleep quality does not deteriorate, once they have left a rehabilitation center. Further, they should be encouraged to keeping their physical activity levels as stable as possible

Major depressive disorder subtypes and depression symptoms in multiple sclerosis: What is different compared to the general population?

OBJECTIVE To compare and characterize major depressive disorder (MDD) subtypes (i.e., pure atypical, pure melancholic and mixed atypical-melancholic) and depression symptoms in persons with multiple sclerosis (PwMS) with persons without MS (Pw/oMS) fulfilling the DSM-5 criteria for a past 12-month MDD. METHODS MDD in PwMS (n = 92) from the Swiss Multiple Sclerosis Registry was compared with Pw/oMS (n = 277) from a Swiss community-based study. Epidemiological MDD diagnoses were based on the Mini-SPIKE (shortened form of the Structured Psychopathological Interview and Rating of the Social Consequences for Epidemiology). Logistic and multinomial regression analyses (adjusted for sex, age, civil status, depression and severity) were computed for comparisons and characterization. Latent class analysis (LCA) was conducted to empirically identify depression subtypes in PwMS. RESULTS PwMS had a higher risk for the mixed atypical-melancholic MDD subtype (OR = 2.22, 95% CI = 1.03-4.80) compared to Pw/oMS. MDD in PwMS was specifically characterized by a higher risk of the two somatic atypical depression symptoms 'weight gain' (OR = 6.91, 95% CI = 2.20-21.70) and 'leaden paralysis' (OR = 3.03, 95% CI = 1.35-6.82) and the symptom 'irritable/angry' (OR = 3.18, 95% CI = 1.08-9.39). CONCLUSIONS MDD in PwMS was characterized by a higher risk for specific somatic atypical depression symptoms and the mixed atypical-melancholic MDD subtype. The pure atypical MDD subtype, however, did not differentiate between PwMS and Pw/oMS. Given the high phenomenological overlap with MS symptoms, the mixed atypical-melancholic MDD subtype represents a particular diagnostic challenge

Left Shifting of Language Related Activity Induced by Bihemispheric tDCS in Postacute Aphasia Following Stroke

Both anodal transcranial direct current stimulation (tDCS) of the left IFG and cathodal stimulation of the right IFG were shown to improve rehabilitation of stroke patients with Broca’s aphasia. The study aimed at assessing the impact of a bihemispheric IFG stimulation compared to sham on postacute non-fluent aphasia. Twelve patients with non-fluent aphasia were included at least 4 weeks following cerebral stroke. Ten daily sessions of 2 mA bihemispheric verum or sham tDCS (anode on left IFG and cathode on right IFG) were performed concomitantly with individual language therapy in a double-blinded randomized controlled study with parallel group design. Language functions [i.e., communication (ANELT), picture naming and the Aachen aphasia test (AAT)] were assessed up to 1 month following tDCS. The picture naming task significantly improved (increased number of nouns) at the end of the tDCS procedure in the verum but not sham group. Improvements in the picture naming task and the communication task of the AAT at 4 weeks after tDCS procedure were only seen in the verum group. In patients with postacute cerebral stroke, repeated sessions of tDCS applied on both IFG concomitantly with language therapy were able to induce immediate effects on picture naming presumably due to an early left shift of language-associated function that maintained for 4 weeks. Effects on clinically relevant communicative abilities are likely

In Patients With Multiple Sclerosis, Both Objective and Subjective Sleep, Depression, Fatigue, and Paresthesia Improved After 3 Weeks of Regular Exercise

Background: Multiple sclerosis (MS) patients suffer from various difficulties including sleep complaints, symptoms of depression and fatigue, paresthesia, and cognitive impairments. There is growing evidence that regular physical activity has a positive effect on both sleep and psychological functioning, though there is limited evidence of this kind for MS patients. The aim of the present study was therefore to investigate the impact on this patient group of a regular exercise program with respect to subjective and objective sleep, depression, paresthesia, fatigue, and cognitive performance.Methods: A total of 46 patients [mean age: 50.74 years; Expanded Disability Status Scale (EDSS): mean: 5.3, 78.4% females] completed this 3-week intervention study. At baseline and 3 weeks later, they answered questionnaires covering sociodemographic information, subjective sleep, depression, fatigue, paresthesia, and subjective physical activity. Objective sleep [sleep electroencephalogram (EEG) recordings] and cognitive performance were also assessed at both time points. Patients participated in a regular exercise activity every weekday for about 60 min.Results: Compared to the baseline, by the end of the study, objective sleep had significantly improved (sleep efficiency, sleep onset latency, and wake time after sleep onset), and symptoms of sleep complaints, depression, fatigue, and paresthesia were significantly reduced. Subjective physical activity (moderate and vigorous) and cognitive performance also increased over the course of the intervention.Conclusions: In patients with MS, participation in regular exercise impacted positively on their objective and subjective sleep, depression, paresthesia, fatigue, and cognitive performance