A simple closed-form approximation for the cumulative distribution function of the composite error of stochastic frontier models

We investigate quantum error correction using continuous parity measurements to correct bit-flip errors with the three-qubit code. Continuous monitoring of errors brings the benefit of a continuous stream of information, which facilitates passive error tracking in real time. It reduces overhead from the standard gate-based approach that periodically entangles and measures additional ancilla qubits. However, the noisy analog signals from continuous parity measurements mandate more complicated signal processing to interpret syndromes accurately. We analyze the performance of several practical filtering methods for continuous error correction and demonstrate that they are viable alternatives to the standard ancilla-based approach. As an optimal filter, we discuss an unnormalized (linear) Bayesian filter, with improved computational efficiency compared to the related Wonham filter introduced by Mabuchi [New J. Phys. 11, 105044 (2009)]. We compare this optimal continuous filter to two practical variations of the simplest periodic boxcar-averaging-and-thresholding filter, targeting real-time hardware implementations with low-latency circuitry. As variations, we introduce a non-Markovian ``half-boxcar'' filter and a Markovian filter with a second adjustable threshold; these filters eliminate the dominant source of error in the boxcar filter, and compare favorably to the optimal filter. For each filter, we derive analytic results for the decay in average fidelity and verify them with numerical simulations.

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“…(39) when a = 0. It can be derived using the approximation erfc(x) ≈ exp(−c 1 x − c 2 x 2 ) valid for x > 0 with c 1 ≈ 1.1 and c 2 ≈ 0.76 [56].…”

Section: (B) One Misidentification and One Bit Flipmentioning

confidence: 99%

Always-On Quantum Error Tracking with Continuous Parity Measurements

Mohseninia

Yang

Siddiqi

et al. 2020

Quantum

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“…FQ that cannot be exactly known.Moreover,Tsay et al (2013) verified that the finite sample performance of the ML estimators of CSF based on…”

mentioning

confidence: 82%

“…Consequently, the result inferred from Equation 7will not be correct. In this paper, we attempt to solve this difficulty by introducing the censored stochastic frontier model (CSF), proposed by Tsay et al (2013), as CSF allows for truncation of the dependent variable in (6) at a constant value, say c. The CSF model must be estimated by maximum likelihood, and so the Vol. Amemiya (1985), the log-likelihood function of the CSF model can be expressed as follows:…”

Section: Herementioning

confidence: 99%

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Competition Conditions in Taiwan’s Public Accounting Industry

Chang¹,

Huang²,

Wang³

2016

AFR

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This paper investigates the degree of market competition in the public accounting industry of Taiwan over the period 1994-2008, using the ‘H statistic’ proposed by Panzar & Rosse (1987). Differing from previous works, this paper applies a newly developed model, i.e., the censored stochastic frontier (CSF) model, to test whether the audit market has achieved its long-run equilibrium. The model is superior to the conventional model that requires researchers adding a unity to the dependent variable of returns on assets (ROA) for all observations, forcing the transformed dependent variable to be non-negative. One can then take the natural logarithm of this dependent variable. Evidence shows that Taiwan’s accounting industry is characterized as monopolistic competition with a trend towards perfect competition. The result will help to build up the empirical model for public accounting industry. The CSF model confirms that this industry is already in a long-run equilibrium in the second half of the sample, which validates the use of the Panzar-Rosse model. Conversely, the employment of the conventional approach leads to a rejection of the long-run equilibrium over the entire sample period.

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“…Instead, the numerical comparison of the signal distortion for a constant T and T opt is given in Figure . To derive T opt , an approximation such that

erfc false(x false) = e^{- c_{1} x - c_{2} x^{2}}

, where c 1 =1.09500814703333 and c 2 =0.75651138383854, is used . Furthermore, it is assumed that

e^{- c_{1} z - false(c_{2} + 1 false) z^{2}} \approx e^{- c_{1} z - false(c_{2} + 2 false) z^{2}}

e^{- 2 c_{1} z - 2 c_{2} z^{2}} \approx e^{- 2 c_{1} z - false(2 c_{2} + 2 false) z^{2}}

e^{- 2 c_{1} z - false(2 c_{2} + 1 false) z^{2}} \approx e^{- 2 c_{1} z - false(2 c_{2} + 2 false) z^{2}}

to solve the equation for T opt .…”

Section: Receiver Nanomachine Designmentioning

confidence: 99%

Signal reconstruction in diffusion‐based molecular communication

Atakan

Gulec

2019

Trans Emerging Tel Tech

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Molecular communication (MC) is an important nanoscale communication paradigm, which is employed for the interconnection of the nanomachines (NMs) to form nanonetworks. A transmitter NM (TN) sends the information symbols by emitting molecules into the transmission medium and a receiver NM (RN) receives the information symbols by sensing the molecule concentration.In this paper, a model of how an RN measures and reconstructs the molecular signal is proposed. The signal around the RN is assumed to be a Gaussian random process instead of the less realistic deterministic approach. After the reconstructed signal is derived as a doubly stochastic poisson process, the distortion between the signal around the RN and the reconstructed signal is derived as a new performance parameter in MC systems. The derived distortion, which is a function of system parameters such as RN radius, sampling period, and the diffusion coefficient of the channel, is shown to be valid by employing random walk simulations. Then, it is shown that the original signal can be satisfactorily reconstructed with a sufficiently low level of distortion. Finally, optimum RN design parameters, namely, RN radius, sampling period, and sampling frequency, are derived by minimizing the signal distortion. The simulation results reveal that there is a trade-off among the RN design parameters which can be jointly set for a desired signal distortion.Trans Emerging Tel Tech. 2019;30:e3699.wileyonlinelibrary.com/journal/ett

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A simple closed-form approximation for the cumulative distribution function of the composite error of stochastic frontier models

Cited by 31 publications

References 11 publications

Always-On Quantum Error Tracking with Continuous Parity Measurements

Always-On Quantum Error Tracking with Continuous Parity Measurements

Competition Conditions in Taiwan’s Public Accounting Industry

Signal reconstruction in diffusion‐based molecular communication

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