Quantum Information Encoding, Protection, and Correction from Trace-Norm Isometries

We introduce the notion of trace-norm isometric encoding and explore its implications for passive and active methods to protect quantum information against errors. Beside providing an operational foundations to the "subsystems principle" [E. Knill, Phys. Rev. A 74, 042301 (2006)] for faithfully realizing quantum information in physical systems, our approach allows additional explicit connections between noiseless, protectable, and correctable quantum codes to be identified. Robustness properties of isometric encodings against imperfect initialization and/or deviations from the intended error models are also analyzed.Comment: 10 pages, 1 figur

Brachistochrone of Entanglement for Spin Chains

We analytically investigate the role of entanglement in time-optimal state evolution as an appli- cation of the quantum brachistochrone, a general method for obtaining the optimal time-dependent Hamiltonian for reaching a target quantum state. As a model, we treat two qubits indirectly cou- pled through an intermediate qubit that is directly controllable, which represents a typical situation in quantum information processing. We find the time-optimal unitary evolution law and quantify residual entanglement by the two-tangle between the indirectly coupled qubits, for all possible sets of initial pure quantum states of a tripartite system. The integrals of the motion of the brachistochrone are determined by fixing the minimal time at which the residual entanglement is maximized. Entan- glement plays a role for W and GHZ initial quantum states, and for the bi-separable initial state in which the indirectly coupled qubits have a nonzero value of the 2-tangle.Comment: 9 pages, 4 figure

Generation and propagation of entanglement in driven coupled-qubit systems

In a bipartite system subject to decoherence from two separate reservoirs, the entanglement is typically destroyed faster than for single reservoirs. Surprisingly however, the existence of separate reservoirs can also have a beneficial entangling effect: if the qubits are coupled and driven externally by a classical field, the system ends up in a stationary state characterized by a finite degree of entanglement. This phenomenon occurs only in a certain region of the parameter space and the structure of the stationary state has a universal form which does not depend on the initial state or on the specific physical realization of the qubits. We show that the entanglement thus generated can be propagated within a quantum network using simple local unitary operations. We suggest the use of such systems as "batteries of entanglement" in quantum circuits.Comment: 14 pages, 7 figure

A novel nonsense ATP7A pathogenic variant in a family exhibiting a variable occipital horn syndrome phenotype

We report on a family with occipital horn syndrome (OHS) diagnosed in the proband's late fifties. A novel ATP7A pathogenic variant (c.4222A > T, p.(Lys1408*)), representing the first nonsense variant and the second late truncation causing OHS rather than classic Menkes disease, was found to segregate in the family. The predicted maintenance of transmembrane domains is consistent with a residual protein activity, which may explain the mild clinical presentation

Novel mutations support a role for Profilin 1 in the pathogenesis of ALS

AbstractMutations in the gene encoding profilin 1 (PFN1) have recently been shown to cause amyotrophic lateral sclerosis (ALS), a fatal neurodegenerative disorder. We sequenced the PFN1 gene in a cohort of ALS patients (n = 485) and detected 2 novel variants (A20T and Q139L), as well as 4 cases with the previously identified E117G rare variant (∼ 1.2%). A case-control meta-analysis of all published E117G ALS+/− frontotemporal dementia cases including those identified in this report was significant p = 0.001, odds ratio = 3.26 (95% confidence interval, 1.6–6.7), demonstrating this variant to be a susceptibility allele. Postmortem tissue from available patients displayed classic TAR DNA-binding protein 43 pathology. In both transient transfections and in fibroblasts from a patient with the A20T change, we showed that this novel PFN1 mutation causes protein aggregation and the formation of insoluble high molecular weight species which is a hallmark of ALS pathology. Our findings show that PFN1 is a rare cause of ALS and adds further weight to the underlying genetic heterogeneity of this disease

Reverse quantum state engineering using electronic feedback loops

We propose an all-electronic technique to manipulate and control interacting quantum systems by unitary single-jump feedback conditioned on the outcome of a capacitively coupled electrometer and in particular a single-electron transistor. We provide a general scheme to stabilize pure states in the quantum system and employ an effective Hamiltonian method for the quantum master equation to elaborate on the nature of stabilizable states and the conditions under which state purification can be achieved. The state engineering within the quantum feedback scheme is shown to be linked with the solution of an inverse eigenvalue problem. Two applications of the feedback scheme are presented in detail: (i) stabilization of delocalized pure states in a single charge qubit and (ii) entanglement stabilization in two coupled charge qubits. In the latter example we demonstrate the stabilization of a maximally entangled Bell state for certain detector positions and local feedback operations.Comment: 23 pages, 6 figures, to be published by New Journal of Physics (2013

Quantum Feedback Control: How to use Verification Theorems and Viscosity Solutions to Find Optimal Protocols

While feedback control has many applications in quantum systems, finding optimal control protocols for this task is generally challenging. So-called "verification theorems" and "viscosity solutions" provide two useful tools for this purpose: together they give a simple method to check whether any given protocol is optimal, and provide a numerical method for finding optimal protocols. While treatments of verification theorems usually use sophisticated mathematical language, this is not necessary. In this article we give a simple introduction to feedback control in quantum systems, and then describe verification theorems and viscosity solutions in simple language. We also illustrate their use with a concrete example of current interest.Comment: 12 pages, revtex

Association of Variants in the SPTLC1 Gene with Juvenile Amyotrophic Lateral Sclerosis

Importance: Juvenile amyotrophic lateral sclerosis (ALS) is a rare form of ALS characterized by age of symptom onset less than 25 years and a variable presentation. Objective: To identify the genetic variants associated with juvenile ALS. Design, Setting, and Participants: In this multicenter family-based genetic study, trio whole-exome sequencing was performed to identify the disease-associated gene in a case series of unrelated patients diagnosed with juvenile ALS and severe growth retardation. The patients and their family members were enrolled at academic hospitals and a government research facility between March 1, 2016, and March 13, 2020, and were observed until October 1, 2020. Whole-exome sequencing was also performed in a series of patients with juvenile ALS. A total of 66 patients with juvenile ALS and 6258 adult patients with ALS participated in the study. Patients were selected for the study based on their diagnosis, and all eligible participants were enrolled in the study. None of the participants had a family history of neurological disorders, suggesting de novo variants as the underlying genetic mechanism. Main Outcomes and Measures: De novo variants present only in the index case and not in unaffected family members. Results: Trio whole-exome sequencing was performed in 3 patients diagnosed with juvenile ALS and their parents. An additional 63 patients with juvenile ALS and 6258 adult patients with ALS were subsequently screened for variants in the SPTLC1 gene. De novo variants in SPTLC1 (p.Ala20Ser in 2 patients and p.Ser331Tyr in 1 patient) were identified in 3 unrelated patients diagnosed with juvenile ALS and failure to thrive. A fourth variant (p.Leu39del) was identified in a patient with juvenile ALS where parental DNA was unavailable. Variants in this gene have been previously shown to be associated with autosomal-dominant hereditary sensory autonomic neuropathy, type 1A, by disrupting an essential enzyme complex in the sphingolipid synthesis pathway. Conclusions and Relevance: These data broaden the phenotype associated with SPTLC1 and suggest that patients presenting with juvenile ALS should be screened for variants in this gene.

FUS and TARDBP but Not SOD1 Interact in Genetic Models of Amyotrophic Lateral Sclerosis

Mutations in the SOD1 and TARDBP genes have been commonly identified in Amyotrophic Lateral Sclerosis (ALS). Recently, mutations in the Fused in sarcoma gene (FUS) were identified in familial (FALS) ALS cases and sporadic (SALS) patients. Similarly to TDP-43 (coded by TARDBP gene), FUS is an RNA binding protein. Using the zebrafish (Danio rerio), we examined the consequences of expressing human wild-type (WT) FUS and three ALS–related mutations, as well as their interactions with TARDBP and SOD1. Knockdown of zebrafish Fus yielded a motor phenotype that could be rescued upon co-expression of wild-type human FUS. In contrast, the two most frequent ALS–related FUS mutations, R521H and R521C, unlike S57Δ, failed to rescue the knockdown phenotype, indicating loss of function. The R521H mutation caused a toxic gain of function when expressed alone, similar to the phenotype observed upon knockdown of zebrafish Fus. This phenotype was not aggravated by co-expression of both mutant human TARDBP (G348C) and FUS (R521H) or by knockdown of both zebrafish Tardbp and Fus, consistent with a common pathogenic mechanism. We also observed that WT FUS rescued the Tardbp knockdown phenotype, but not vice versa, suggesting that TARDBP acts upstream of FUS in this pathway. In addition we observed that WT SOD1 failed to rescue the phenotype observed upon overexpression of mutant TARDBP or FUS or upon knockdown of Tardbp or Fus; similarly, WT TARDBP or FUS also failed to rescue the phenotype induced by mutant SOD1 (G93A). Finally, overexpression of mutant SOD1 exacerbated the motor phenotype caused by overexpression of mutant FUS. Together our results indicate that TARDBP and FUS act in a pathogenic pathway that is independent of SOD1