Proposal for Quantum Simulation via All-Optically Generated Tensor Network States

We devise an all-optical scheme for the generation of entangled multimode photonic states encoded in temporal modes of light. The scheme employs a nonlinear down-conversion process in an optical loop to generate one- and higher-dimensional tensor network states of light. We illustrate the principle with the generation of two different classes of entangled tensor network states and report on a variational algorithm to simulate the ground-state physics of many-body systems. We demonstrate that state-of-the-art optical devices are capable of determining the ground-state properties of the spin-1/2 Heisenberg model. Finally, implementations of the scheme are demonstrated to be robust against realistic losses and mode mismatch.Comment: 6 pages main text plus 6 pages Supplementary Material and many figures. Updated to published version. Comments welcom

Combination of tag SNP alleles defining each haplotype and frequencies

<p>Haplotype tagging SNPs are indicated in bold. (0) indicates the allele with major frequency, (1) the allele with minor frequency.</p

Means and standard deviations of visual early contingent negative variation (CNV) amplitudes by DAT1 and COMT.

<p>Means and standard deviations of visual early contingent negative variation (CNV) amplitudes by DAT1 and COMT.</p

PIk3R1 SNPs: position and minor allele frequencies

<p>PIk3R1 SNPs: position and minor allele frequencies</p

Genetic influences on reaction times and reaction time variability (± standard deviation).

1<p>RTSD = intraindividual standard deviation of reaction times (reaction time variability).</p

Effects of DAT1 haplotype and COMT on the lateralized motor PINV – linear regression models¹.

1<p>B = regression coefficient; SE B = standard error of the regression coefficient; beta = standardized regression coefficient.</p

UCSC genome browser generated view of genomic region of <i>PIK3R1</i> including exons 2 to 7.

<p>Coding exons are represented by blocks connected by horizontal lines representing introns. The 5′ untranslated regions (UTRs) are displayed as thinner blocks on the leading ends of the aligning regions. Arrowheads on the connecting intron lines indicate the direction of transcription. Position of CpG islands, putative promoter and transcription start sites are indicated. Location of transcription factor binding sites conserved in the human/mouse/rat alignment is indicated. Conservation of binding sites in all 3 species is computed with the Transfac Matrix Database (v7.0). Evolutionary conservation in 17 vertebrates, including mammalian, amphibian, bird, and fish species was scored by the phastCons program following MULTIZ alignments. Conservation scores are displayed as wiggle, where the height reflects the size of the score. Pairwise alignments of each species to the human genome are displayed below as a “wiggle” that indicates alignment quality.</p

Association of <i>PIK3R1</i> SNPs with alcohol consumption patterns in adolescents (TDT)

<p>T = transmitted, U untransmitted</p>a<p>Subject has never been drunk vs. has been drunk</p>b<p>Median split at 16 g alcohol</p

Demographic and clinical characteristics in male and female adolescents

1<p>“enriched” family adversity index as proposed by Rutter and Quinton measuring the presence of 11 adverse family factors covering characteristics of the parents, the partnership, and the family environment during a period of one year prior to birth</p>2<p>obstetric adversity score counting the presence of 9 adverse conditions during pregnancy, delivery, and postnatal period such as preterm labor, asphyxia or seizures</p

Effects of <i>DAT1</i> haplotype and <i>COMT</i> on visual early contingent negative variation (CNV).

<p>The error bars indicate the 95% confidence intervals.</p