\begin{algorithmic}[1]

    \Procedure{AdaptiveEstimation}{$n$, $p_0$, $N$, $a_{LW}$, $t_{RS}$}
    \State draw $\lbrace x_k \rbrace$ from $p_0(x)$
    \State $\lbrace \omega_k \rbrace \gets \lbrace 1/K \rbrace$
    
    \For{$i \in 1.. N$}
        \State $\hat{T}_{\chi} \gets \sum_j \omega_k \cdot x_k$ 
        \State $\tau \gets \xi \cdot \hat{T}_{\chi}$
        \For{$j \in 1.. R$}
            \State $m_j \gets \mbox{EXPERIMENT} (\tau)$
        \EndFor
        \State $r_i \gets \sum_{j=1}^R m_j$

        \State $\lbrace \omega_k \rbrace \gets \lbrace \omega_k \cdot p \left(r_i|T_{\chi}, R \right) \rbrace$
        \State $\lbrace \omega_k \rbrace \gets \lbrace \omega_k/\left(\sum_k \omega_k\right) \rbrace$
        
        \If {$1/ \sum \omega_k^2 < n \cdot t_{RS}$}  
        \State $\lbrace x_k \rbrace \gets \mbox{RESAMPLE} (\lbrace x_k \rbrace, \lbrace \omega_k \rbrace, a_{LW})$
        \State $\lbrace \omega_k \rbrace \gets \lbrace 1/K \rbrace$
    \EndIf
    \EndFor
    \\
    \Return $\hat{T}_{\chi}$

    \EndProcedure
    \\
    \Procedure{RESAMPLE}{$\lbrace x_k \rbrace$, $\lbrace \omega_k \rbrace$, $a_{LW}$}
    \State $\mu \gets \sum_k x_k \cdot \omega_k$
    \State $\sigma^2 \gets \sum_k x_k^2 \cdot \omega_k - \mu^2$
    \State $\mu' \gets a_{LW} \cdot x_k + (1-a_{LW})\cdot \mu$
    \State $\lbrace x_k \rbrace \gets \mbox{NORMAL} (\mu', \sigma^2)$
    \\
    \Return $\lbrace x_k \rbrace$
    \EndProcedure
    \end{algorithmic}

\begin{algorithmic}
[1]
\Procedure{AdaptiveEstimation}{$n$, $p_0$, $N$, $a_{LW}$, $t_{RS}$}
\State draw $\lbrace x_k \rbrace$ from $p_0(x)$
\State $\lbrace \omega_k \rbrace \gets \lbrace 1/K \rbrace$
\For{$i \in 1.. N$}
\State $\hat{T}_{\chi} \gets \sum_j \omega_k \cdot x_k$
\State $\tau \gets \xi \cdot \hat{T}_{\chi}$
\For{$j \in 1.. R$}
\State $m_j \gets \mbox{EXPERIMENT} (\tau)$
\EndFor
\State $r_i \gets \sum_{j=1}^R m_j$
\State $\lbrace \omega_k \rbrace \gets \lbrace \omega_k \cdot p \left(r_i|T_{\chi}, R \right) \rbrace$
\State $\lbrace \omega_k \rbrace \gets \lbrace \omega_k/\left(\sum_k \omega_k\right) \rbrace$
\If {$1/ \sum \omega_k^2 < n \cdot t_{RS}$}
\State $\lbrace x_k \rbrace \gets \mbox{RESAMPLE} (\lbrace x_k \rbrace, \lbrace \omega_k \rbrace, a_{LW})$
\State $\lbrace \omega_k \rbrace \gets \lbrace 1/K \rbrace$
\EndIf
\EndFor
\\
\Return $\hat{T}_{\chi}$
\EndProcedure
\\
\Procedure{RESAMPLE}{$\lbrace x_k \rbrace$, $\lbrace \omega_k \rbrace$, $a_{LW}$}
\State $\mu \gets \sum_k x_k \cdot \omega_k$
\State $\sigma^2 \gets \sum_k x_k^2 \cdot \omega_k - \mu^2$
\State $\mu' \gets a_{LW} \cdot x_k + (1-a_{LW})\cdot \mu$
\State $\lbrace x_k \rbrace \gets \mbox{NORMAL} (\mu', \sigma^2)$
\\
\Return $\lbrace x_k \rbrace$
\EndProcedure
\end{algorithmic}
{
    "title": "real-time adaptive estimation of decoherence timescales for a single   qubit",
    "id": "2210.06103",
    "abstract": "characterising the time over which quantum coherence survives is critical for any implementation of quantum bits, memories and sensors. the usual method for determining a quantum system's decoherence rate involves a suite of experiments probing the entire expected range of this parameter, and extracting the resulting estimation in post-processing. here we present an adaptive multi-parameter bayesian approach, based on a simple analytical update rule, to estimate the key decoherence timescales ($t_1$, $t_2^*$ and $t_2$) and the corresponding decay exponent of a quantum system in real time, using information gained in preceding experiments. this approach reduces the time required to reach a given uncertainty by a factor up to an order of magnitude, depending on the specific experiment, compared to the standard protocol of curve fitting. a further speed-up of a factor $\\sim 2$ can be realised by performing our optimisation with respect to sensitivity as opposed to variance.",
    "categories": "quant-ph",
    "doi": "10.1103/physrevapplied.21.024026",
    "created": "2022-10-12",
    "updated": "2024-01-24",
    "authors": [
        "muhammad junaid arshad",
        "christiaan bekker",
        "ben haylock",
        "krzysztof skrzypczak",
        "daniel white",
        "benjamin griffiths",
        "joe gore",
        "gavin w. morley",
        "patrick salter",
        "jason smith",
        "inbar zohar",
        "amit finkler",
        "yoann altmann",
        "erik m. gauger",
        "cristian bonato"
    ],
    "affiliation": [],
    "url": "https://arxiv.org/abs/2210.06103"
}
{
    "ToxicityFilter": {
        "text_to_toxicity_attributes": {
            "Final_PhysRevApplied.tex": {
                "toxicity_score": 0.015644746,
                "severe_toxicity_score": 0.0021839142,
                "identity_attack_score": 0.002034882,
                "insult_score": 0.008595883,
                "profanity_score": 0.025360947,
                "threat_score": 0.0063497215,
                "sexually_explicit_score": 0.020052237,
                "flirtation_score": 0.4170283
            }
        },
        "reason": null
    }
}
{
    "num_done": {
        "figure": 0,
        "algorithm": 2,
        "plot": 0
    }
}
{
    "NonTrivialRenderingFilter": {
        "white_pixels_ratio": 93.47594991774477,
        "hash": "0f9f87878f1f0f0f",
        "most_frequent_color_ratio": 93.47594991774477
    }
}