60,290 research outputs found
Sampling in a Quantum Population, and Applications
We propose a framework for analyzing classical sampling strategies for estimating the Hamming weight of a large string, when applied to a multi-qubit quantum system instead. The framework shows how to interpret such a strategy and how to define its accuracy when applied to a quantum system. Furthermore, we show how the accuracy of any strategy relates to its accuracy in its classical usage, which is well understood for the important examples. We show the usefulness of our framework by using it to obtain new and simple security proofs for the following quantum-cryptographic schemes: quantum oblivious-transfer from bit-commitment, and BB84 quantum-key-distribution
Algorithm for branching and population control in correlated sampling
Correlated sampling has wide-ranging applications in Monte Carlo
calculations. When branching random walks are involved, as commonly found in
many algorithms in quantum physics and electronic structure, population control
is typically not applied with correlated sampling due to technical
difficulties. This hinders the stability and efficiency of correlated sampling.
In this work, we study schemes for allowing birth/death in correlated sampling
and propose an algorithm for population control. The algorithm can be realized
in several variants depending on the application. One variant is a static
method that creates a reference run and allows other correlated calculations to
be added a posteriori. Another optimizes the population control for a set of
correlated, concurrent runs dynamically. These approaches are tested in
different applications in quantum systems, including both the Hubbard model and
electronic structure calculations in real materials.Comment: 10 pages, 8 figure
Secure certification of mixed quantum states with application to two-party randomness generation
We investigate sampling procedures that certify that an arbitrary quantum
state on subsystems is close to an ideal mixed state
for a given reference state , up to errors on a few positions. This
task makes no sense classically: it would correspond to certifying that a given
bitstring was generated according to some desired probability distribution.
However, in the quantum case, this is possible if one has access to a prover
who can supply a purification of the mixed state.
In this work, we introduce the concept of mixed-state certification, and we
show that a natural sampling protocol offers secure certification in the
presence of a possibly dishonest prover: if the verifier accepts then he can be
almost certain that the state in question has been correctly prepared, up to a
small number of errors.
We then apply this result to two-party quantum coin-tossing. Given that
strong coin tossing is impossible, it is natural to ask "how close can we get".
This question has been well studied and is nowadays well understood from the
perspective of the bias of individual coin tosses. We approach and answer this
question from a different---and somewhat orthogonal---perspective, where we do
not look at individual coin tosses but at the global entropy instead. We show
how two distrusting parties can produce a common high-entropy source, where the
entropy is an arbitrarily small fraction below the maximum (except with
negligible probability)
Ab initio computations of molecular systems by the auxiliary-field quantum Monte Carlo method
The auxiliary-field quantum Monte Carlo (AFQMC) method provides a
computational framework for solving the time-independent Schroedinger equation
in atoms, molecules, solids, and a variety of model systems. AFQMC has recently
witnessed remarkable growth, especially as a tool for electronic structure
computations in real materials. The method has demonstrated excellent accuracy
across a variety of correlated electron systems. Taking the form of stochastic
evolution in a manifold of non-orthogonal Slater determinants, the method
resembles an ensemble of density-functional theory (DFT) calculations in the
presence of fluctuating external potentials. Its computational cost scales as a
low-power of system size, similar to the corresponding independent-electron
calculations. Highly efficient and intrinsically parallel, AFQMC is able to
take full advantage of contemporary high-performance computing platforms and
numerical libraries. In this review, we provide a self-contained introduction
to the exact and constrained variants of AFQMC, with emphasis on its
applications to the electronic structure in molecular systems. Representative
results are presented, and theoretical foundations and implementation details
of the method are discussed.Comment: 22 pages, 11 figure
Population Monte Carlo algorithms
We give a cross-disciplinary survey on ``population'' Monte Carlo algorithms.
In these algorithms, a set of ``walkers'' or ``particles'' is used as a
representation of a high-dimensional vector. The computation is carried out by
a random walk and split/deletion of these objects. The algorithms are developed
in various fields in physics and statistical sciences and called by lots of
different terms -- ``quantum Monte Carlo'', ``transfer-matrix Monte Carlo'',
``Monte Carlo filter (particle filter)'',``sequential Monte Carlo'' and
``PERM'' etc. Here we discuss them in a coherent framework. We also touch on
related algorithms -- genetic algorithms and annealed importance sampling.Comment: Title is changed (Population-based Monte Carlo -> Population Monte
Carlo). A number of small but important corrections and additions. References
are also added. Original Version is read at 2000 Workshop on
Information-Based Induction Sciences (July 17-18, 2000, Syuzenji, Shizuoka,
Japan). No figure
Introduction to the variational and diffusion Monte Carlo methods
We provide a pedagogical introduction to the two main variants of real-space
quantum Monte Carlo methods for electronic-structure calculations: variational
Monte Carlo (VMC) and diffusion Monte Carlo (DMC). Assuming no prior knowledge
on the subject, we review in depth the Metropolis-Hastings algorithm used in
VMC for sampling the square of an approximate wave function, discussing details
important for applications to electronic systems. We also review in detail the
more sophisticated DMC algorithm within the fixed-node approximation,
introduced to avoid the infamous Fermionic sign problem, which allows one to
sample a more accurate approximation to the ground-state wave function.
Throughout this review, we discuss the statistical methods used for evaluating
expectation values and statistical uncertainties. In particular, we show how to
estimate nonlinear functions of expectation values and their statistical
uncertainties.Comment: Advances in Quantum Chemistry, 2015, Electron Correlation in
Molecules -- ab initio Beyond Gaussian Quantum Chemistry, pp.000
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