Compressed sensing quantum process tomography for superconducting quantum gates

We apply the method of compressed sensing (CS) quantum process tomography (QPT) to characterize quantum gates based on superconducting Xmon and phase qubits. Using experimental data for a two-qubit controlled-Z gate, we obtain an estimate for the process matrix $\chi$ with reasonably high fidelity compared to full QPT, but using a significantly reduced set of initial states and measurement configurations. We show that the CS method still works when the amount of used data is so small that the standard QPT would have an underdetermined system of equations. We also apply the CS method to the analysis of the three-qubit Toffoli gate with numerically added noise, and similarly show that the method works well for a substantially reduced set of data. For the CS calculations we use two different bases in which the process matrix $\chi$ is approximately sparse, and show that the resulting estimates of the process matrices match each ther with reasonably high fidelity. For both two-qubit and three-qubit gates, we characterize the quantum process by not only its process matrix and fidelity, but also by the corresponding standard deviation, defined via variation of the state fidelity for different initial states.Comment: 16 pages, 11 figure

On the NP-Hardness of Approximating Ordering Constraint Satisfaction Problems

We show improved NP-hardness of approximating Ordering Constraint Satisfaction Problems (OCSPs). For the two most well-studied OCSPs, Maximum Acyclic Subgraph and Maximum Betweenness, we prove inapproximability of $14/15+\epsilon$ and $1/2+\epsilon$. An OCSP is said to be approximation resistant if it is hard to approximate better than taking a uniformly random ordering. We prove that the Maximum Non-Betweenness Problem is approximation resistant and that there are width-$m$ approximation-resistant OCSPs accepting only a fraction $1 / (m/2)!$ of assignments. These results provide the first examples of approximation-resistant OCSPs subject only to P $\neq$ \NP

Inferring the effective thickness of polyelectrolytes from stretching measurements at various ionic strengths: applications to DNA and RNA

By resorting to the thick-chain model we discuss how the stretching response of a polymer is influenced by the self-avoidance entailed by its finite thickness. The characterization of the force versus extension curve for a thick chain is carried out through extensive stochastic simulations. The computational results are captured by an analytic expression that is used to fit experimental stretching measurements carried out on DNA and single-stranded RNA (poly-U) in various solutions. This strategy allows us to infer the apparent diameter of two biologically-relevant polyelectrolytes, namely DNA and poly-U, for different ionic strengths. Due to the very different degree of flexibility of the two molecules, the results provide insight into how the apparent diameter is influenced by the interplay between the (solution-dependent) Debye screening length and the polymers' ``bare'' thickness. For DNA, the electrostatic contribution to the effective radius, $\Delta$, is found to be about 5 times larger than the Debye screening length, consistently with previous theoretical predictions for highly-charged stiff rods. For the more flexible poly-U chains the electrostatic contribution to $\Delta$ is found to be significantly smaller than the Debye screening length.Comment: iopart, 14 pages, 13 figures, to appear in J. Phys.: Condens. Matte

Spectral signatures of many-body localization with interacting photons

Statistical mechanics is founded on the assumption that a system can reach thermal equilibrium, regardless of the starting state. Interactions between particles facilitate thermalization, but, can interacting systems always equilibrate regardless of parameter values\,? The energy spectrum of a system can answer this question and reveal the nature of the underlying phases. However, most experimental techniques only indirectly probe the many-body energy spectrum. Using a chain of nine superconducting qubits, we implement a novel technique for directly resolving the energy levels of interacting photons. We benchmark this method by capturing the intricate energy spectrum predicted for 2D electrons in a magnetic field, the Hofstadter butterfly. By increasing disorder, the spatial extent of energy eigenstates at the edge of the energy band shrink, suggesting the formation of a mobility edge. At strong disorder, the energy levels cease to repel one another and their statistics approaches a Poisson distribution - the hallmark of transition from the thermalized to the many-body localized phase. Our work introduces a new many-body spectroscopy technique to study quantum phases of matter

Exercise-Induced Changes in Metabolic Intermediates, Hormones, and Inflammatory Markers Associated With Improvements in Insulin Sensitivity

OBJECTIVE: To understand relationships between exercise training-mediated improvements in insulin sensitivity (S(I)) and changes in circulating concentrations of metabolic intermediates, hormones, and inflammatory mediators. RESEARCH DESIGN AND METHODS: Targeted mass spectrometry and enzyme-linked immunosorbent assays were used to quantify metabolic intermediates, hormones, and inflammatory markers at baseline, after 6 months of exercise training, and 2 weeks after exercise training cessation (n = 53). A principal components analysis (PCA) strategy was used to relate changes in these intermediates to changes in S(I). RESULTS: PCA reduced the number of intermediates from 90 to 24 factors composed of biologically related components. With exercise training, improvements in S(I) were associated with reductions in by-products of fatty acid oxidation and increases in glycine and proline (P < 0.05, R² = 0.59); these relationships were retained 15 days after cessation of exercise training (P < 0.05, R² = 0.34). CONCLUSIONS: These observations support prior observations in animal models that exercise training promotes more efficient mitochondrial β-oxidation and challenges current hypotheses regarding exercise training and glycine metabolism

Role of a single noncoding nucleotide in the evolution of an epidemic African clade of Salmonella

Salmonella enterica serovar Typhimurium ST313 is a relatively newly emerged sequence type that is causing a devastating epidemic of bloodstream infections across sub-Saharan Africa. Analysis of hundreds ofSalmonellagenomes has revealed that ST313 is closely related to the ST19 group ofSTyphimurium that cause gastroenteritis across the world. The core genomes of ST313 and ST19 vary by only ∼1,000 SNPs. We hypothesized that the phenotypic differences that distinguish AfricanSalmonellafrom ST19 are caused by certain SNPs that directly modulate the transcription of virulence genes. Here we identified 3,597 transcriptional start sites of the ST313 strain D23580, and searched for a gene-expression signature linked to pathogenesis ofSalmonellaWe identified a SNP in the promoter of thepgtEgene that caused high expression of the PgtE virulence factor in AfricanS.Typhimurium, increased the degradation of the factor B component of human complement, contributed to serum resistance, and modulated virulence in the chicken infection model. We propose that high levels of PgtE expression by AfricanSTyphimurium ST313 promote bacterial survival and dissemination during human infection. Our finding of a functional role for an extragenic SNP shows that approaches used to deduce the evolution of virulence in bacterial pathogens should include a focus on noncoding regions of the genome

Ventrolateral Origin of Each Cycle of Rhythmic Activity Generated by the Spinal Cord of the Chick Embryo

BACKGROUND: The mechanisms responsible for generating rhythmic motor activity in the developing spinal cord of the chick embryo are poorly understood. Here we investigate whether the activity of motoneurons occurs before other neuronal populations at the beginning of each cycle of rhythmic discharge. METHODOLOGY/PRINCIPAL FINDINGS: The spatiotemporal organization of neural activity in transverse slices of the lumbosacral cord of the chick embryo (E8-E11) was investigated using intrinsic and voltage-sensitive dye (VSD) imaging. VSD signals accompanying episodes of activity comprised a rhythmic decrease in light transmission that corresponded to each cycle of electrical activity recorded from the ipsilateral ventral root. The rhythmic signals were widely synchronized across the cord face, and the largest signal amplitude was in the ventrolateral region where motoneurons are located. In unstained slices we recorded two classes of intrinsic signal. In the first, an episode of rhythmic activity was accompanied by a slow decrease in light transmission that peaked in the dorsal horn and decayed dorsoventrally. Superimposed on this signal was a much smaller rhythmic increase in transmission that was coincident with each cycle of discharge and whose amplitude and spatial distribution was similar to that of the VSD signals. At the onset of a spontaneously occurring episode and each subsequent cycle, both the intrinsic and VSD signals originated within the lateral motor column and spread medially and then dorsally. By contrast, following a dorsal root stimulus, the optical signals originated within the dorsal horn and traveled ventrally to reach the lateral motor column. CONCLUSIONS/SIGNIFICANCE: These findings suggest that motoneuron activity contributes to the initiation of each cycle of rhythmic activity, and that motoneuron and/or R-interneuron synapses are a plausible site for the activity-dependent synaptic depression that modeling studies have identified as a critical mechanism for cycling within an episode