Electronic Noise and Fluctuations in Solids by Sh. Kogan (1996, Hardcover)
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DOI: Download Citation: J. Electronic noise analyses on organic electronic devices Y.
Song and T. Lee, J. The gate fidelity is calculated using the state fidelity as defined in ref.
Furthermore, to separate the effects of different noise channels, we have simulated benchmarking with the Overhauser noise only for the results shown in Fig. We therefore focus on comparing the performances of uncorrected and corrected sequences for a given noise. The left column a,c,e includes the Overhauser noise only, whereas in the right column b,d,f we consider the charge noise only.
These results are as expected because for a noise close to the white noise, there are a lot of spectral weight in higher frequencies where supcode sequences are unable to perform correction. At the same time, the longer gate duration of the corrected sequences leads to an accumulation of error, causing corrected sequences to have larger gate error than the uncorrected ones. This observation is confirmed by the results shown in Fig. Similarly for the charge noise with the corresponding detuning noise having the same spectra, the fidelity of uncorrected gates drops down to below 0.
We see that the d v.
This is due to the fact that the leading order error is not completely cancelled for non-static noises and the error curve should show similar scaling between corrected and uncorrected cases. Nevertheless, the error resulted from corrected and uncorrected pulse sequences are consistent with what shown in Fig.
These are all consistent with qualitative consideration from the nature of supcode sequences and their response to time dependent noises. The average error per gate d is found via an exponential fit of the results of randomized benchmarking as described in the main text. The results in the left column a,c,e are calculated using only Overhauser noise with amplitude A h , while those in the right column b,d,f are calculated for the charge noise with amplitude A J only. Using the results of Fig.
Figure 5 a shows the results for Overhauser noise.
This is probably due to the fact that even at the limit of static noise the supcode sequences will not completely compensate errors to all orders 26 ; instead, it only cancels the leading order error and the improvement factor must saturate at the reciprocal ratio between the remaining part of the error and those resulting from uncorrected operations. Turning to Fig. The results of Fig. Recent experiments in a silicon system have shown that the gate fidelity is mostly affected by charge noises in the 10 kHz to 1 MHz range We have also find that although the filter transfer functions corresponding to the charge noise are defined in a slightly different way than the nuclear noise, their behaviors are largely the same after the control-dependent part of the charge noise has been appropriately treated.
Through Randomized Benchmarking, we have extracted the average error per gate for uncorrected pulses as well as the two types of the supcode pulses. In the experiment of ref. Figure 4 e indicates that the error will be at least one order of magnitude smaller if the full supcode is used, compared to the uncorrected case. Extrapolation of the curves in Fig. Further developments of supcode sequences and their benchmarking include optimization of supcode sequences specific to a given type of time-dependent noise 55 and extension to two-qubit as well as non-Clifford gates Spin qubits based on semiconductor quantum dots are one of the most promising candidates for scalable fault-tolerant quantum computing.
Dynamically corrected gates, in particular supcode sequences and related control protocols are among the most viable approaches to improve the gate fidelity, keeping the error below the quantum error correction threshold. In this paper we have studied how supcode sequences filter noises with a range of frequency spectra and have shown that under experimentally relevant circumstances supcode , when properly used, offers considerable error reduction. We therefore believe that experimental realization of supcode sequences in semiconductor quantum dot systems will be of great interest to spin-based quantum computation.
The power spectral density of certain noise [which is essentially a random process f t ] may be defined as.
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One is a standard way to generate such kind of noise, which is a weighted combination of Random Telegraph Noises RTN , which we briefly explain below. The power spectral density of RTN is. Where applicable, we compare the results from this method to those generated from the summation of RTNs to verify our results, and we have found good agreements. Here we briefly introduce the method: One first generate a noise in the frequency domain as.
How to cite this article : Yang, X. Noise filtering of composite pulses for singlet-triplet qubits. Author Contributions X. Both authors discussed the results and implications at all stages and wrote the paper. National Center for Biotechnology Information , U. Sci Rep. Published online Jul 7. Xu-Chen Yang 1 and Xin Wang a, 1. Author information Article notes Copyright and License information Disclaimer. Received Feb 25; Accepted Jun This work is licensed under a Creative Commons Attribution 4.
Abstract Semiconductor quantum dot spin qubits are promising candidates for quantum computing. Results We start with the control Hamiltonian for a singlet-triplet qubit, which can be expressed in the computational bases as 3 , Open in a separate window. Figure 1. Figure 2.
Electronic Noise and Fluctuations in Solids - Sh Kogan - Google книги
Pulse shapes and filter transfer functions of selective supcode gates. Figure 3. Figure 4. The average error per gate v. Figure 5. Additional Information How to cite this article : Yang, X. Footnotes Author Contributions X.