141 research outputs found
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 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 . 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 . 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
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