This work aims to introduce and analyze an adaptive stabilized finite element method to solve a nonlinear Darcy equation with a pressure-dependent viscosity and mixed boundary conditions. We stated ...the discrete problem’s well-posedness and optimal error estimates, in natural norms, under standard assumptions. Next, we introduce and analyze a residual-based a posteriori error estimator for the stabilized scheme. Finally, we present some two- and three-dimensional numerical examples which confirm our theoretical results.
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Abstract
In this paper, bayes estimators for the shape parameter (θ) of Exponentiated Gumbel distribution have been derived using Singly type II censored data under two priors distributions Proposed ...and Chi-square with two loss functions Quadratic and De-Groot, and using mean squared error, a simulation study was conducted to evaluate the performance of the four different estimators in six assumption experiments for various parameter values and sample sizes
In this paper, the permeability of sandstone, mudstone, gangue, and limestone under the condition of initial elastic deformation is obtained by transient method test. Mercury intrusion test is ...carried out on the four kinds of rock samples to obtain the initial permeability of the rock samples. The results show that the magnitude of permeability obtained by mercury intrusion test and transient method test is completely consistent. The measurement error is analyzed. The relative error of permeability in this paper is less than 6.0%. It can be showed that the use of transient method to measure the permeability of rock samples is reasonable and reliable.
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We present an improved determination of the Hubble constant from Hubble Space Telescope (HST) observations of 70 long-period Cepheids in the Large Magellanic Cloud (LMC). These were obtained with the ...same WFC3 photometric system used to measure extragalactic Cepheids in the hosts of SNe Ia. Gyroscopic control of HST was employed to reduce overheads while collecting a large sample of widely separated Cepheids. The Cepheid period-luminosity relation provides a zero-point-independent link with 0.4% precision between the new 1.2% geometric distance to the LMC from detached eclipsing binaries (DEBs) measured by Pietrzy ski et al. and the luminosity of SNe Ia. Measurements and analysis of the LMC Cepheids were completed prior to knowledge of the new DEB LMC distance. Combined with a refined calibration of the count-rate linearity of WFC3-IR with 0.1% precision, these three improved elements together reduce the overall uncertainty in the geometric calibration of the Cepheid distance ladder based on the LMC from 2.5% to 1.3%. Using only the LMC DEBs to calibrate the ladder, we find H0 = 74.22 1.82 km s−1 Mpc−1 including systematic uncertainties, 3% higher than before for this particular anchor. Combining the LMC DEBs, masers in NGC 4258, and Milky Way parallaxes yields our best estimate: H0 = 74.03 1.42 km s−1 Mpc−1, including systematics, an uncertainty of 1.91%-15% lower than our best previous result. Removing any one of these anchors changes H0 by less than 0.7%. The difference between H0 measured locally and the value inferred from Planck CMB and ΛCDM is 6.6 1.5 km s−1 Mpc−1 or 4.4 (P = 99.999% for Gaussian errors) in significance, raising the discrepancy beyond a plausible level of chance. We summarize independent tests showing that this discrepancy is not attributable to an error in any one source or measurement, increasing the odds that it results from a cosmological feature beyond ΛCDM.
Time-varying feedback particle filter Chen, Xiuqiong; Kang, Jiayi; Yau, Stephen S.-T.
Automatica (Oxford),
September 2024, 2024-09-00, Volume:
167
Journal Article
Peer reviewed
Feedback particle filter is a novel Monte Carlo algorithm with identically distributed particles evolving under feedback control structure, such that the Kullback–Leibler divergence between the ...actual posterior of the state and the common posterior of any particle can be minimized. In this work, we consider the time-varying linear systems and explicitly analyze the errors between the optimal solution obtained by Kalman filter and the estimates given by feedback particle filter and the optimal transportation particle filter, respectively. These theoretical analyses are also supported by the numerical simulation, where we compare the performances of particle filter, feedback particle filter, optimal transportation particle filter and Kalman filter.
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A quantum computer can solve hard problems, such as prime factoring, database searching and quantum simulation, at the cost of needing to protect fragile quantum states from error. Quantum error ...correction provides this protection by distributing a logical state among many physical quantum bits (qubits) by means of quantum entanglement. Superconductivity is a useful phenomenon in this regard, because it allows the construction of large quantum circuits and is compatible with microfabrication. For superconducting qubits, the surface code approach to quantum computing is a natural choice for error correction, because it uses only nearest-neighbour coupling and rapidly cycled entangling gates. The gate fidelity requirements are modest: the per-step fidelity threshold is only about 99 per cent. Here we demonstrate a universal set of logic gates in a superconducting multi-qubit processor, achieving an average single-qubit gate fidelity of 99.92 per cent and a two-qubit gate fidelity of up to 99.4 per cent. This places Josephson quantum computing at the fault-tolerance threshold for surface code error correction. Our quantum processor is a first step towards the surface code, using five qubits arranged in a linear array with nearest-neighbour coupling. As a further demonstration, we construct a five-qubit Greenberger-Horne-Zeilinger state using the complete circuit and full set of gates. The results demonstrate that Josephson quantum computing is a high-fidelity technology, with a clear path to scaling up to large-scale, fault-tolerant quantum circuits.
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The magnon cat state represents a macroscopic quantum superposition of collective magnetic excitations of large number spins that not only provides fundamental tests of macroscopic quantum effects ...but also finds applications in quantum metrology and quantum computation. In particular, remote generation and manipulation of Schrödinger cat states are particularly interesting for the development of long-distance and large-scale quantum information processing. Here, we propose an approach to remotely prepare magnon even or odd cat states by performing local non-Gaussian operations on the optical mode that is entangled with the magnon mode through pulsed optomagnonic interaction. By evaluating key properties of the resulting cat states, we show that for experimentally feasible parameters, they are generated with both high fidelity and nonclassicality, as well as with a size large enough to be useful for quantum technologies. Furthermore, the effects of experimental imperfections such as the error of projective measurements and dark count when performing single-photon operations have been discussed, where the lifetime of the created magnon cat states is expected to be t ∼ 1 μ s .
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High-quality two-qubit gate operations are crucial for scalable quantum information processing. Often, the gate fidelity is compromised when the system becomes more integrated. Therefore, a ...low-error-rate, easy-to-scale two-qubit gate scheme is highly desirable. Here, we experimentally demonstrate a new two-qubit gate scheme that exploits fixed-frequency qubits and a tunable coupler in a superconducting quantum circuit. The scheme requires less control lines, reduces cross talk effect, and simplifies calibration procedures, yet produces a controlled-Z gate in 30 ns with a high fidelity of 99.5%, derived from the interleaved randomized benchmarking method. Error analysis shows that gate errors are mostly coherence limited. Our demonstration paves the way for large-scale implementation of high-fidelity quantum operations.
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Quantum error correction protects fragile quantum information by encoding it into a larger quantum system
. These extra degrees of freedom enable the detection and correction of errors, but also ...increase the control complexity of the encoded logical qubit. Fault-tolerant circuits contain the spread of errors while controlling the logical qubit, and are essential for realizing error suppression in practice
. Although fault-tolerant design works in principle, it has not previously been demonstrated in an error-corrected physical system with native noise characteristics. Here we experimentally demonstrate fault-tolerant circuits for the preparation, measurement, rotation and stabilizer measurement of a Bacon-Shor logical qubit using 13 trapped ion qubits. When we compare these fault-tolerant protocols to non-fault-tolerant protocols, we see significant reductions in the error rates of the logical primitives in the presence of noise. The result of fault-tolerant design is an average state preparation and measurement error of 0.6 per cent and a Clifford gate error of 0.3 per cent after offline error correction. In addition, we prepare magic states with fidelities that exceed the distillation threshold
, demonstrating all of the key single-qubit ingredients required for universal fault-tolerant control. These results demonstrate that fault-tolerant circuits enable highly accurate logical primitives in current quantum systems. With improved two-qubit gates and the use of intermediate measurements, a stabilized logical qubit can be achieved.
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