General-Purpose Parallel Simulator for Quantum Computing

With current technologies, it seems to be very difficult to implement quantum computers with many qubits. It is therefore of importance to simulate quantum algorithms and circuits on the existing computers. However, for a large-size problem, the simulation often requires more computational power than is available from sequential processing. Therefore, the simulation methods using parallel processing are required. We have developed a general-purpose simulator for quantum computing on the parallel computer (Sun, Enterprise4500). It can deal with up-to 30 qubits. We have performed Shor's factorization and Grover's database search by using the simulator, and we analyzed robustness of the corresponding quantum circuits in the presence of decoherence and operational errors. The corresponding results, statistics and analyses are presented.Comment: 15 pages, 15 figure

Tackling Systematic Errors in Quantum Logic Gates with Composite Rotations

We describe the use of composite rotations to combat systematic errors in single qubit quantum logic gates and discuss three families of composite rotations which can be used to correct off-resonance and pulse length errors. Although developed and described within the context of NMR quantum computing these sequences should be applicable to any implementation of quantum computation.Comment: 6 pages RevTex4 including 4 figures. Will submit to Phys. Rev.

Quantum computation in a Ising spin chain taking into account second neighbor couplings

We consider the realization of a quantum computer in a chain of nuclear spins coupled by an Ising interaction. Quantum algorithms can be performed with the help of appropriate radio-frequency pulses. In addition to the standard nearest-neighbor Ising coupling, we also allow for a second neighbor coupling. It is shown, how to apply the 2\pi k method in this more general setting, where the additional coupling eventually allows to save a few pulses. We illustrate our results with two numerical simulations: the Shor prime factorization of the number 4 and the teleportation of a qubit along a chain of 3 qubits. In both cases, the optimal Rabi frequency (to suppress non-resonant effects) depends primarily on the strength of the second neighbor interaction.Comment: 19 pages, 6 figure

Resonant tunneling and the multichannel Kondo problem: the quantum Brownian motion description

We study mesoscopic resonant tunneling as well as multichannel Kondo problems by mapping them to a first-quantized quantum mechanical model of a particle moving in a multi-dimensional periodic potential with Ohmic dissipation. From a renormalization group analysis, we obtain phase diagrams of the quantum Brownian motion model with various lattice symmetries. For a symmorphic lattice, there are two phases at T=0: a localized phase in which the particle is trapped in a potential minimum, and a free phase in which the particle is unaffected by the periodic potential. For a non-symmorphic lattice, however, there may be an additional intermediate phase in which the particle is neither localized nor completely free. The fixed point governing the intermediate phase is shown to be identical to the well-known multichannel Kondo fixed point in the Toulouse limit as well as the resonance fixed point of a quantum dot model and a double-barrier Luttinger liquid model. The mapping allows us to compute the fixed-poing mobility $\mu^*$ of the quantum Brownian motion model exactly, using known conformal-field-theory results of the Kondo problem. From the mobility, we find that the peak value of the conductance resonance of a spin-1/2 quantum dot problem is given by $e^2/2h$. The scaling form of the resonance line shape is predicted

Enhancement of the Two-channel Kondo Effect in Single-Electron boxes

The charging of a quantum box, coupled to a lead by tunneling through a single resonant level, is studied near the degeneracy points of the Coulomb blockade. Combining Wilson's numerical renormalization-group method with perturbative scaling approaches, the corresponding low-energy Hamiltonian is solved for arbitrary temperatures, gate voltages, tunneling rates, and energies of the impurity level. Similar to the case of a weak tunnel barrier, the shape of the charge step is governed at low temperatures by the non-Fermi-liquid fixed point of the two-channel Kondo effect. However, the associated Kondo temperature TK is strongly modified. Most notably, TK is proportional to the width of the level if the transmission through the impurity is close to unity at the Fermi energy, and is no longer exponentially small in one over the tunneling matrix element. Focusing on a particle-hole symmetric level, the two-channel Kondo effect is found to be robust against the inclusion of an on-site repulsion on the level. For a large on-site repulsion and a large asymmetry in the tunneling rates to box and to the lead, there is a sequence of Kondo effects: first the local magnetic moment that forms on the level undergoes single-channel screening, followed by two-channel overscreening of the charge fluctuations inside the box.Comment: 21 pages, 19 figure

Grover search with pairs of trapped ions

The desired interference required for quantum computing may be modified by the wave function oscillations for the implementation of quantum algorithms[Phys.Rev.Lett.84(2000)1615]. To diminish such detrimental effect, we propose a scheme with trapped ion-pairs being qubits and apply the scheme to the Grover search. It can be found that our scheme can not only carry out a full Grover search, but also meet the requirement for the scalable hot-ion quantum computing. Moreover, the ion-pair qubits in our scheme are more robust against the decoherence and the dissipation caused by the environment than single-particle qubits proposed before.Comment: RevTe

Quantum Effects in Coulomb Blockade

We review the quantum interference effects in a system of interacting electrons confined to a quantum dot. The review starts with a description of an isolated quantum dot. We discuss the status of the Random Matrix theory (RMT) of the one-electron states in the dot, present the universal form of the interaction Hamiltonian compatible with the RMT, and derive the leading corrections to the universal interaction Hamiltonian. Next, we discuss a theoretical description of a dot connected to leads via point contacts. Having established the theoretical framework to describe such an open system, we discuss its transport and thermodynamic properties. We review the evolution of the transport properties with the increase of the contact conductances from small values to values $\sim e^2/\pi\hbar$. In the discussion of transport, the emphasis is put on mesoscopic fluctuations and the Kondo effect in the conductance.Comment: 169 pages, 28 figures; several references and footnotes are added, and noticed typos correcte

Before and After: Comparison of Legacy and Harmonized TCGA Genomic Data Commons’ Data

We present a systematic analysis of the effects of synchronizing a large-scale, deeply characterized, multi-omic dataset to the current human reference genome, using updated software, pipelines, and annotations. For each of 5 molecular data platforms in The Cancer Genome Atlas (TCGA)—mRNA and miRNA expression, single nucleotide variants, DNA methylation and copy number alterations—comprehensive sample, gene, and probe-level studies were performed, towards quantifying the degree of similarity between the ‘legacy’ GRCh37 (hg19) TCGA data and its GRCh38 (hg38) version as ‘harmonized’ by the Genomic Data Commons. We offer gene lists to elucidate differences that remained after controlling for confounders, and strategies to mitigate their impact on biological interpretation. Our results demonstrate that the hg19 and hg38 TCGA datasets are very highly concordant, promote informed use of either legacy or harmonized omics data, and provide a rubric that encourages similar comparisons as new data emerge and reference data evolve. Gao et al. performed a systematic analysis of the effects of synchronizing the large-scale, widely used, multi-omic dataset of The Cancer Genome Atlas to the current human reference genome. For each of the five molecular data platforms assessed, they demonstrated a very high concordance between the ‘legacy’ GRCh37 (hg19) TCGA data and its GRCh38 (hg38) version as ‘harmonized’ by the Genomic Data Commons

The chromatin accessibility landscape of primary human cancers

We present the genome-wide chromatin accessibility profiles of 410 tumor samples spanning 23 cancer types from The Cancer Genome Atlas (TCGA).We identify 562,709 transposase-accessible DNA elements that substantially extend the compendium of known cis-regulatory elements. Integration of ATAC-seq (the assay for transposase-accessible chromatin using sequencing) with TCGA multi-omic data identifies a large number of putative distal enhancers that distinguish molecular subtypes of cancers, uncovers specific driving transcription factors via protein-DNA footprints, and nominates long-range gene-regulatory interactions in cancer. These data reveal genetic risk loci of cancer predisposition as active DNA regulatory elements in cancer, identify gene-regulatory interactions underlying cancer immune evasion, and pinpoint noncoding mutations that drive enhancer activation and may affect patient survival. These results suggest a systematic approach to understanding the noncoding genome in cancer to advance diagnosis and therapy