21,494 research outputs found
Entanglement-assisted weak value amplification
Large weak values have been used to amplify the sensitivity of a linear
response signal for detecting changes in a small parameter, which has also
enabled a simple method for precise parameter estimation. However, producing a
large weak value requires a low postselection probability for an ancilla degree
of freedom, which limits the utility of the technique. We propose an
improvement to this method that uses entanglement to increase the efficiency.
We show that by entangling and postselecting ancillas, the postselection
probability can be increased by a factor of while keeping the weak value
fixed (compared to uncorrelated attempts with one ancilla), which is the
optimal scaling with that is expected from quantum metrology. Furthermore,
we show the surprising result that the quantum Fisher information about the
detected parameter can be almost entirely preserved in the postselected state,
which allows the sensitive estimation to approximately saturate the optimal
quantum Cram\'{e}r-Rao bound. To illustrate this protocol we provide simple
quantum circuits that can be implemented using current experimental
realizations of three entangled qubits.Comment: 5 pages + 6 pages supplement, 5 figure
Discovering an active subspace in a single-diode solar cell model
Predictions from science and engineering models depend on the values of the
model's input parameters. As the number of parameters increases, algorithmic
parameter studies like optimization or uncertainty quantification require many
more model evaluations. One way to combat this curse of dimensionality is to
seek an alternative parameterization with fewer variables that produces
comparable predictions. The active subspace is a low-dimensional linear
subspace defined by important directions in the model's input space; input
perturbations along these directions change the model's prediction more, on
average, than perturbations orthogonal to the important directions. We describe
a method for checking if a model admits an exploitable active subspace, and we
apply this method to a single-diode solar cell model with five input
parameters. We find that the maximum power of the solar cell has a dominant
one-dimensional active subspace, which enables us to perform thorough parameter
studies in one dimension instead of five
An alternative solution to the model structure selection problem
An alternative solution to the model structure selection problem is introduced by conducting a forward search through the many possible candidate model terms initially and then performing an exhaustive all subset model selection on the resulting model. An example is included to demonstrate that this approach leads to dynamically valid nonlinear model
BQP-completeness of Scattering in Scalar Quantum Field Theory
Recent work has shown that quantum computers can compute scattering
probabilities in massive quantum field theories, with a run time that is
polynomial in the number of particles, their energy, and the desired precision.
Here we study a closely related quantum field-theoretical problem: estimating
the vacuum-to-vacuum transition amplitude, in the presence of
spacetime-dependent classical sources, for a massive scalar field theory in
(1+1) dimensions. We show that this problem is BQP-hard; in other words, its
solution enables one to solve any problem that is solvable in polynomial time
by a quantum computer. Hence, the vacuum-to-vacuum amplitude cannot be
accurately estimated by any efficient classical algorithm, even if the field
theory is very weakly coupled, unless BQP=BPP. Furthermore, the corresponding
decision problem can be solved by a quantum computer in a time scaling
polynomially with the number of bits needed to specify the classical source
fields, and this problem is therefore BQP-complete. Our construction can be
regarded as an idealized architecture for a universal quantum computer in a
laboratory system described by massive phi^4 theory coupled to classical
spacetime-dependent sources.Comment: 41 pages, 7 figures. Corrected typo in foote
A Space Communications Study Final Report, Sep. 15, 1965 - Sep. 15, 1966
Reception of frequency modulated signals passed through deterministic and random time-varying channel
The Surface Laplacian Technique in EEG: Theory and Methods
This paper reviews the method of surface Laplacian differentiation to study
EEG. We focus on topics that are helpful for a clear understanding of the
underlying concepts and its efficient implementation, which is especially
important for EEG researchers unfamiliar with the technique. The popular
methods of finite difference and splines are reviewed in detail. The former has
the advantage of simplicity and low computational cost, but its estimates are
prone to a variety of errors due to discretization. The latter eliminates all
issues related to discretization and incorporates a regularization mechanism to
reduce spatial noise, but at the cost of increasing mathematical and
computational complexity. These and several others issues deserving further
development are highlighted, some of which we address to the extent possible.
Here we develop a set of discrete approximations for Laplacian estimates at
peripheral electrodes and a possible solution to the problem of multiple-frame
regularization. We also provide the mathematical details of finite difference
approximations that are missing in the literature, and discuss the problem of
computational performance, which is particularly important in the context of
EEG splines where data sets can be very large. Along this line, the matrix
representation of the surface Laplacian operator is carefully discussed and
some figures are given illustrating the advantages of this approach. In the
final remarks, we briefly sketch a possible way to incorporate finite-size
electrodes into Laplacian estimates that could guide further developments.Comment: 43 pages, 8 figure
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