Fault-tolerant Coded Quantum Chemical Distributed Calculation

doi:10.6023/A23110496

Abstract

With the rise of cutting-edge applications such as large-scale simulation and machine learning, distributed computing has become more and more an important means of computational research. However, distributed computing will still have some problems in the application of scientific computing, machine learning and other fields due to the hardware and software limitations caused by multiple nodes. In this paper, we apply coded distributed computing to the field of quantum chemistry, by drawing on the gradient coding scheme, on the one hand, to solve the problem of dropped nodes in distributed quantum chemical computation; on the other hand, to increase the automatic error correction capability of quantum chemical distributed computation, to reduce the manpower and resources consumed in the computation process, with a view to realizing the automated fault-tolerant quantum chemical computation. In addition, we also propose the computational idea of coded multiplexing, which can simply and effectively use more computational resources to perform distributed computation on a set fault-tolerant capacity. We applied this computational scheme to calculate the binding energy of P38 protein and ligand by artificially specifying the use of four computational nodes for each fragment and allowing one dropout node, and compared the results obtained using coded computation with the real results, and found that the error was extremely small and negligible, and the correct results could be obtained even in the case of one dropout node or one node being miscalculated. In order to verify whether this scheme is suitable for larger scale distributed quantum chemical computation, we further randomly selected 10 fragments on the basis of coded multiplexing and performed the computation with 40 nodes at the same time, and found that the obtained results are also very accurate. Finally we calculated the binding energy of the P38 protein to the ligand, and the results obtained were consistent with previous literature, demonstrating the accuracy of this scheme and its potential for application in automated fault-tolerant quantum chemical calculations.

Key words: quantum chemical calculation, coded computing, gradient coding, fault-tolerant, automation, binding energy

Cite this article

Ning Li, Lina Xu, Guoyong Fang, Yingjin Ma. Fault-tolerant Coded Quantum Chemical Distributed Calculation[J]. Acta Chimica Sinica, 2024, 82(2): 138-145.

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Fig. & Tab. 9

Figure 1. The idea of gradient coding

算法1: 构造B矩阵
输入: n, s(s<n), 假设k=n 输出: $B ∈ R n × n$ , B矩阵的每一行有(s+1)个非零值 H=randn(s, n); H(:, n)=–sum(H(:, 1 : n–1), 2); B=zeros(n); for i=1 : n do j=mod(i–1 : s+i–1, n)+1; B(i, j)=[1; –H(:, j(2 : s+1))\H(:, j(1))]; end

算法1: 构造B矩阵
输入: n, s(s<n), 假设k=n 输出: $B ∈ R n × n$ , B矩阵的每一行有(s+1)个非零值 H=randn(s, n); H(:, n)=–sum(H(:, 1 : n–1), 2); B=zeros(n); for i=1 : n do j=mod(i–1 : s+i–1, n)+1; B(i, j)=[1; –H(:, j(2 : s+1))\H(:, j(1))]; end

算法2: 构造A矩阵
输入: 矩阵B 输出: 矩阵A for I ⊆ [n], \|I\|=(n–s) do a=zeros(1, n); x=ones(1, n)/B(I, :); a(I)=x; A=[A; a]; end

Figure 2. Illustration of the MFCC framework

Figure 3. The structure of P38 protein

碎片编号	参考值	梯度编码计算的能量/(a.u.)
0029	–6.94210e^-5	–6.94210e^-5
		–6.94210e^-5
		–6.94210e^-5
		–6.94210e^-5
0062	1.38461e^-4	1.38461e^-4
		(无结果)
		(无结果)
		(无结果)

Table 1. Compare the results between these computed by gradient encoding and those from ref. 49

碎片编号	参考值	梯度编码计算的能量/(a.u.)
0130	–6.76000e^-6	–0.01000
		0.02999
		0.01999
		–6.75999e^-6
0187	1.62210e^-5	1.62210e^-5
		1.62210e^-5
		1.62210e^-5
		1.62210e^-5
0262	–2.30730e^-5	–2.30730e^-5
		–2.30730e^-5
		–2.30730e^-5
		–2.30730e^-5
0337	–1.9320e^-6	–1.9320e^-6
		–1.9320e^-6
		–1.9320e^-6
		–1.9320e^-6

Table 2. Compare the results between these computed by gradient encoding and those from ref. 49

Figure 4. Related structures of 10 fragments and ligand (red)

Figure 5. Errors between encoded calculated values and reference values (absolute value) from ref. 49

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结合容错编码的量子化学分布式计算