1,230 research outputs found
Monte Carlo sampling from the quantum state space. II
High-quality random samples of quantum states are needed for a variety of
tasks in quantum information and quantum computation. Searching the
high-dimensional quantum state space for a global maximum of an objective
function with many local maxima or evaluating an integral over a region in the
quantum state space are but two exemplary applications of many. These tasks can
only be performed reliably and efficiently with Monte Carlo methods, which
involve good samplings of the parameter space in accordance with the relevant
target distribution. We show how the Markov-chain Monte Carlo method known as
Hamiltonian Monte Carlo, or hybrid Monte Carlo, can be adapted to this context.
It is applicable when an efficient parameterization of the state space is
available. The resulting random walk is entirely inside the physical parameter
space, and the Hamiltonian dynamics enable us to take big steps, thereby
avoiding strong correlations between successive sample points while enjoying a
high acceptance rate. We use examples of single and double qubit measurements
for illustration.Comment: 11 pages, 4 figures, 12 reference
Monte Carlo sampling from the quantum state space. I
High-quality random samples of quantum states are needed for a variety of
tasks in quantum information and quantum computation. Searching the
high-dimensional quantum state space for a global maximum of an objective
function with many local maxima or evaluating an integral over a region in the
quantum state space are but two exemplary applications of many. These tasks can
only be performed reliably and efficiently with Monte Carlo methods, which
involve good samplings of the parameter space in accordance with the relevant
target distribution. We show how the standard strategies of rejection sampling,
importance sampling, and Markov-chain sampling can be adapted to this context,
where the samples must obey the constraints imposed by the positivity of the
statistical operator. For a comparison of these sampling methods, we generate
sample points in the probability space for two-qubit states probed with a
tomographically incomplete measurement, and then use the sample for the
calculation of the size and credibility of the recently-introduced optimal
error regions [see New J. Phys. 15 (2013) 123026]. Another illustration is the
computation of the fractional volume of separable two-qubit states.Comment: 13 pages, 5 figures, 1 table, 26 reference
Enhancing Hydrogen Generation Through Nanoconfinement of Sensitizers and Catalysts in a Homogeneous Supramolecular Organic Framework.
Enrichment of molecular photosensitizers and catalysts in a confined nanospace is conducive for photocatalytic reactions due to improved photoexcited electron transfer from photosensitizers to catalysts. Herein, the self-assembly of a highly stable 3D supramolecular organic framework from a rigid bipyridine-derived tetrahedral monomer and cucurbit[8]uril in water, and its efficient and simultaneous intake of both [Ru(bpy)3 ]2+ -based photosensitizers and various polyoxometalates, that can take place at very low loading, are reported. The enrichment substantially increases the apparent concentration of both photosensitizer and catalyst in the interior of the framework, which leads to a recyclable, homogeneous, visible light-driven photocatalytic system with 110-fold increase of the turnover number for the hydrogen evolution reaction
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