From db6da64f221c86cb7a661db008cb392050404547 Mon Sep 17 00:00:00 2001 From: huanxiaoling <3174348550@qq.com> Date: Wed, 26 Oct 2022 11:41:12 +0800 Subject: [PATCH] modify the files in mindquantum --- .../source_en/vqe_for_quantum_chemistry.md | 156 ++++++++---------- .../vqe_for_quantum_chemistry.ipynb | 2 +- 2 files changed, 73 insertions(+), 85 deletions(-) diff --git a/docs/mindquantum/docs/source_en/vqe_for_quantum_chemistry.md b/docs/mindquantum/docs/source_en/vqe_for_quantum_chemistry.md index 1649cb38d8..4183f19106 100644 --- a/docs/mindquantum/docs/source_en/vqe_for_quantum_chemistry.md +++ b/docs/mindquantum/docs/source_en/vqe_for_quantum_chemistry.md @@ -36,8 +36,6 @@ In this tutorial, the following environments need to be installed: Import the modules on which this tutorial depends. ```python -import numpy as np -import mindquantum as mq from openfermion.chem import MolecularData from openfermionpyscf import run_pyscf from mindquantum.core.gates import X @@ -46,7 +44,6 @@ from mindquantum.core.operators import Hamiltonian from mindquantum.simulator import Simulator from mindquantum.algorithm.nisq import generate_uccsd import mindspore as ms -from mindspore.common.initializer import initializer ms.set_context(mode=ms.PYNATIVE_MODE, device_target="CPU") ``` @@ -99,6 +96,7 @@ Where $| \psi_{1} \psi_{2} \psi_{3} \dots \rangle$ represents the Nth-order dete The spin-orbit wave function $\psi_{i}$ may be further expanded with a set of basis functions in known forms: $$\psi_{i} = \phi_{i} \eta_{i}$$ + $$\phi_{i} = \sum_{\mu}{C_{\mu i} \chi_{\mu}}$$ $\{\chi_{\mu}\}$ is referred to as a basis function, and may be a Gaussian function or the like. @@ -113,7 +111,7 @@ $$ You can obtain the configuration interaction (CI) method: $$ -| \Psi_{CI} \rangle = C_{0} | \Psi_{HF} \rangle + \sum^{a\rightarrow\infty} _{i\in occ\\\\a\not\in occ}{C^{a} _{i} | \Psi^{a} _{i} \rangle } + \sum^{ab\rightarrow\infty} _{ij\in occ\\\\ab\not\in occ}{C^{ab} _{ij} | \Psi^{ab} _{ij} \rangle } +| \Psi_{CI} \rangle = C_{0} | \Psi_{HF} \rangle + \sum^{a\rightarrow\infty} _{i\in occ, a\not\in occ}{C^{a} _{i} | \Psi^{a} _{i} \rangle } + \sum^{ab\rightarrow\infty} _{ij\in occ, ab\not\in occ}{C^{ab} _{ij} | \Psi^{ab} _{ij} \rangle } $$ $| \Psi^{a}_{i} \rangle + \dots$ in the preceding formula represents a single excitation wave function of the electron from the orbit $i$ to the orbit $a$, and so on. A CI that considers only single excitation and double excitation is called a configuration interaction with singles and doubles (CISD). The CI that takes into account all the ground-state HF wave functions to N excitation wave functions is called full configuration interaction (FCI). The FCI wave function is the exact solution of the time-independent Schrödinger equation under the given basis function. @@ -123,16 +121,16 @@ $| \Psi^{a}_{i} \rangle + \dots$ in the preceding formula represents a single ex Under the second quantization expression, the Hamiltonian of the system has the following form: $$ -\hat{H} = \sum_{p, q}{h^{p} _ {q} E^{p} _ {q}} + \sum_{p, q, r, s}{\frac{1}{2} g^{pq} _ {rs} E^{pq} _ {rs} } +\hat{H} = \sum_{p, q}{h^p_q E^p_q} + \sum_{p, q, r, s}{\frac{1}{2} g^{pq} _ {rs} E^{pq}_{rs}} $$ $E^{p} _{q}$ and $E^{pq}_ {rs}$ are as follows: $$ -E^{p} _ {q} = a^{\dagger} _ {p} a_{q} -$$ -$$ -E^{pq} _ {rs} = a^{\dagger} _ {p} a^{\dagger} _ {q} a_{r} a_{s} +\begin{align*} +E^{pq} _{rs} &= a^{\dagger} _{p} a^{\dagger} _{q} a _ {r} a _ {s}\\ +E^p_q &= a^{\dagger}_pa_q +\end{align*} $$ $a^{\dagger} _{p}$ and $a_ {q}$ are creation operator and annihilation operator, respectively. @@ -140,7 +138,7 @@ $a^{\dagger} _{p}$ and $a_ {q}$ are creation operator and annihilation operator, The excited-state wave function can be expressed conveniently by using a second quantization expression method: $$ -| \Psi^{abc\dots} _ {ijk\dots} \rangle = a^{\dagger} _ {a} a^{\dagger} _ {b} a^{\dagger} _ {c} \dots a_{i} a_{j} a_{k} \dots | \Psi \rangle +| \Psi^{abc\dots} _ {ijk\dots} \rangle = a^{\dagger} _ {a} a^{\dagger} _ {b} a^{\dagger} _ {c} \dots a _ {i} a_{j} a_{k} \dots | \Psi \rangle $$ An improvement to the CI method is the coupled-cluster theory (CC). Exponential operators are introduced to CC: @@ -152,7 +150,7 @@ $$ The coupled-cluster operator $\hat{T}$ is the sum of excitation operators. $$ -\hat{T} = \sum_{p\not\in occ\\\\q\in occ}{\theta^{p} _ {q} E^{p} _ {q}} + \sum_{pq\not\in occ\\\\rs\in occ}{\theta^{pq} _ {rs} E^{pq} _ {rs}} + \dots +\hat{T} = \sum_{p\not\in occ, q\in occ}{\theta^{p} _ {q} E^{p} _ {q}} + \sum_{pq\not\in occ, rs\in occ}{\theta^{pq} _ {rs} E^{pq} _ {rs}} + \dots $$ $\theta$ is similar to $C$ in the CI method, and is the parameter to be solved. It is easy to know from the Taylor's expansion of the exponent that even if the coupled-cluster operator $\hat{T}$ includes only a low-order excitation term, the $\exp{(\hat{T})}$ may also implicitly include a high-order excitation term. This also makes a convergence speed of the CC method to the FCI wave function much faster than that of the CI. For truncation to K excitation, for example, K=2, the accuracy of the CCSD exceeds that of the CISD. @@ -280,12 +278,12 @@ print("Number of parameters: %d" % (len(ansatz_parameter_names))) ``` ```bash -==============================Circuit Summary============================== -|Total number of gates : 12612. | -|Parameter gates : 640. | -|with 44 parameters are : p40, p9, p8, p3, p32, p28, p15, p4, p18, p22... | -|Number qubit of circuit: 12 | -=========================================================================== +============================Circuit Summary============================ +|Total number of gates : 15172. | +|Parameter gates : 640. | +|with 44 parameters are : p0, p8, p1, p9, p2, p10, p3, p11, p4, p12...| +|Number qubit of circuit: 12 | +======================================================================= Number of parameters: 44 ``` @@ -308,10 +306,8 @@ The procedure for solving the molecular ground state by using the VQE is as foll In step 5, the derivative $\{ {\partial E} / {\partial \theta_{i}} \}$ of the energy about the parameter may be computed by using a parameter-shift rule on a quantum computer, or may be computed by simulating a parameter-shift rule or a finite difference method in a simulator. This is a relatively time-consuming process. Based on the MindSpore framework, MindQuantum provides the automatic derivation function similar to machine learning, which can efficiently compute the derivatives of variational quantum circuits in simulation. The following uses MindQuantum to build a parameterized UCCSD quantum circuit with an automatic derivation function: ```python -from mindquantum.simulator import Simulator sim = Simulator('projectq', total_circuit.n_qubits) -molecule_pqc = sim.get_expectation_with_grad(Hamiltonian(hamiltonian_QubitOp), - total_circuit) +molecule_pqc = sim.get_expectation_with_grad(Hamiltonian(hamiltonian_QubitOp), total_circuit) ``` You can obtain the energy $E(\theta)=\langle \Psi_{UCC}(\theta) | \hat{H} | \Psi_{UCC}(\theta) \rangle$ corresponding to the variational parameter and the derivative of each variational parameter by transferring a specific value of the parameter to `molecule_pqc`. @@ -320,21 +316,13 @@ Next, steps 5 to 7 in VQE optimization need to be performed, that is, parameteri ```python from mindquantum.framework import MQAnsatzOnlyLayer -class PQCNet(ms.nn.Cell): - def __init__(self, pqc): - super(PQCNet, self).__init__() - self.pqc = pqc - self.net = MQAnsatzOnlyLayer(self.pqc, weight='Zeros') - - def construct(self): - return self.net() -molecule_pqcnet = PQCNet(molecule_pqc) +molecule_pqcnet = MQAnsatzOnlyLayer(molecule_pqc, 'Zeros') ``` -Here, we manually build a basic `PQCNet` as a model example. This model can be used similar to a conventional machine learning model, for example, optimizing weights and calculating derivatives. A better choice is to use `MQAnsatzOnlyLayer` encapsulated in MindQuantum, which will be demonstrated later. +Here, we manually build a basic `MQAnsatzOnlyLayer` as a model example. This model can be used similar to a conventional machine learning model, for example, optimizing weights and calculating derivatives. -The built `PQCNet` uses the `"Zeros"` keyword to initialize all variational parameters to 0. The computing result of CCSD or second order Møller-Plesset perturbation theory (MP2) can also be used as the initial value of the variational parameters of unitary coupled-clusters. In this case, $E(\vec{0})=\langle \Psi_{UCC}(\vec{0}) | \hat{H} | \Psi_{UCC}(\vec{0}) \rangle = E_{HF}$. +The built `MQAnsatzOnlyLayer` uses the `"Zeros"` keyword to initialize all variational parameters to 0. The computing result of CCSD or second order Møller-Plesset perturbation theory (MP2) can also be used as the initial value of the variational parameters of unitary coupled-clusters. In this case, $E(\vec{0})=\langle \Psi_{UCC}(\vec{0}) | \hat{H} | \Psi_{UCC}(\vec{0}) \rangle = E_{HF}$. ```python initial_energy = molecule_pqcnet() @@ -345,7 +333,7 @@ print("Initial energy: %20.16f" % (initial_energy.asnumpy())) Initial energy: -7.8633575439453125 ``` -Finally, the Adam optimizer of MindSpore is used for optimization. The learning rate is set to $1\times 10^{-2}$, and the optimization termination standard is set to $\left.|\epsilon|\right.= \left.|E^{k+1} - E^{k}|\right. \le 1\times 10^{-8}$. +Finally, the Adam optimizer of MindSpore is used for optimization. The learning rate is set to $1\times 10^{-2}$, and the optimization termination standard is set to $\left.|\epsilon|\right. = \left.|E^{k+1} - E^{k}|\right. \le 1\times 10^{-8}$. ```python optimizer = ms.nn.Adagrad(molecule_pqcnet.trainable_params(), learning_rate=4e-2) @@ -365,7 +353,7 @@ while abs(energy_diff) > eps: print("Optimization completed at step %3d" % (iter_idx - 1)) print("Optimized energy: %20.16f" % (energy_i)) -print("Optimized amplitudes: \n", molecule_pqcnet.net.weight.asnumpy()) +print("Optimized amplitudes: \n", molecule_pqcnet.weight.asnumpy()) ``` ```bash @@ -375,28 +363,27 @@ Step 10 energy -7.8821778297424316 Step 15 energy -7.8822836875915527 Step 20 energy -7.8823199272155762 Step 25 energy -7.8823370933532715 -Step 30 energy -7.8823437690734863 -Step 35 energy -7.8618836402893066 -Step 40 energy -7.8671770095825195 -Step 45 energy -7.8751692771911621 -Step 50 energy -7.8822755813598633 -Step 55 energy -7.8812966346740723 -Step 60 energy -7.8823189735412598 -Step 65 energy -7.8823523521423340 -Optimization completed at step 67 -Optimized energy: -7.8823528289794922 +Step 30 energy -7.8815641403198242 +Step 35 energy -7.8786268234252930 +Step 40 energy -7.8778734207153320 +Step 45 energy -7.8808088302612305 +Step 50 energy -7.8819031715393066 +Step 55 energy -7.8821558952331543 +Step 60 energy -7.8823504447937012 +Optimization completed at step 63 +Optimized energy: -7.8823523521423340 Optimized amplitudes: - [ 2.3980068e-04 1.8912849e-03 3.5044324e-02 1.6005965e-02 - -1.9985158e-07 9.0940151e-04 1.6222824e-05 1.4160988e-02 - -1.1072063e-07 9.0867787e-04 1.3825165e-05 1.4166672e-02 - -5.4699212e-04 4.2679289e-04 2.8641545e-03 5.3817011e-02 - 2.3320253e-04 1.7034533e-07 6.6684343e-08 -2.7686235e-07 - 7.2332718e-08 1.2834757e-05 -1.0439425e-04 7.1826143e-08 - 3.6483241e-06 6.1677817e-08 3.1003920e-06 7.9770159e-04 - -5.4951470e-02 3.0904056e-03 -4.4321241e-05 8.5840838e-07 - -1.9589644e-08 -4.9430941e-08 8.6163556e-07 -2.5008637e-07 - 2.1493735e-08 -4.6331229e-06 3.0904033e-03 9.5311613e-08 - -4.8755901e-08 2.0483398e-08 -3.9453280e-06 3.7235476e-04] + [ 2.40339446e-04 1.89154677e-03 3.49554531e-02 1.59917790e-02 + 2.33248898e-07 9.09393420e-04 -1.79268172e-05 1.41595434e-02 + 6.28582342e-08 9.08669957e-04 -1.49387897e-05 1.41652254e-02 + -5.46666037e-04 4.26779327e-04 2.86067789e-03 5.38198128e-02 + 2.32545775e-04 -2.78862785e-07 -7.10907813e-08 -7.98562283e-08 + 7.00364581e-07 -9.21200325e-08 -6.73263187e-08 1.26236855e-05 + -1.04519488e-04 7.97090179e-04 -4.01437364e-06 -3.34858555e-06 + -5.49289174e-02 3.09006264e-03 7.01365061e-05 -1.36400865e-06 + -1.35536197e-06 4.63907739e-08 5.32547162e-08 -2.34681625e-08 + 3.92657455e-07 5.11744884e-06 3.09006032e-03 -2.05122589e-07 + 5.91138871e-08 -2.44064164e-08 4.26194856e-06 3.72134935e-04] ``` It can be seen that the computing result of unitary coupled-cluster is very close to that of FCI, and has good accuracy. @@ -450,12 +437,12 @@ total_circuit.summary() ``` ```bash -======================================Circuit Summary====================================== -|Total number of gates : 12612. | -|Parameter gates : 640. | -|with 44 parameters are : d1_3, d2_26, d2_6, d2_1, d2_2, d2_14, d1_1, s_1, d2_16, d2_11...| -|Number qubit of circuit: 12 | -=========================================================================================== +==================================Circuit Summary================================== +|Total number of gates : 15172. | +|Parameter gates : 640. | +|with 44 parameters are : s_0, d1_0, s_1, d1_1, s_2, d1_2, s_3, d1_3, s_4, d1_4...| +|Number qubit of circuit: 12 | +=================================================================================== ``` Next, you need to provide a reasonable initial value for the variational parameter. The `PQCNet` built in the preceding text uses 0 as the initial guess by default, which is feasible in most cases. However, using CCSD's computational data as a starting point for UCC may be better. Use the `uccsd_singlet_get_packed_amplitudes` function to extract CCSD parameters from `molecule_of`. @@ -469,9 +456,10 @@ init_amplitudes_ccsd = [init_amplitudes_ccsd[param_i] for param_i in ansatz_para `MQAnsatzOnlyLayer` can be used to easily obtain a machine learning model based on a variational quantum circuit by using a parameter and a quantum circuit: ```python -sim = Simulator('projectq', total_circuit.n_qubits) -grad_ops = sim.get_expectation_with_grad(Hamiltonian(hamiltonian_QubitOp.real), - total_circuit) +grad_ops = Simulator('projectq', total_circuit.n_qubits).get_expectation_with_grad( + Hamiltonian(hamiltonian_QubitOp.real), + total_circuit) + molecule_pqcnet = MQAnsatzOnlyLayer(grad_ops) ``` @@ -513,32 +501,32 @@ print("Optimized amplitudes: \n", molecule_pqcnet.weight.asnumpy()) ```bash eps: 1e-08 Step 0 energy -7.8173098564147949 -Step 5 energy -7.8740763664245605 +Step 5 energy -7.8740758895874023 Step 10 energy -7.8818783760070801 Step 15 energy -7.8821649551391602 Step 20 energy -7.8822622299194336 -Step 25 energy -7.8823084831237793 -Step 30 energy -7.8823180198669434 -Step 35 energy -7.8737111091613770 -Step 40 energy -7.8724455833435059 -Step 45 energy -7.8801403045654297 -Step 50 energy -7.8821926116943359 -Step 55 energy -7.8818311691284180 -Step 60 energy -7.8823456764221191 -Optimization completed at step 64 +Step 25 energy -7.8823080062866211 +Step 30 energy -7.8822288513183594 +Step 35 energy -7.8758554458618164 +Step 40 energy -7.8761253356933594 +Step 45 energy -7.8807921409606934 +Step 50 energy -7.8818383216857910 +Step 55 energy -7.8821811676025391 +Step 60 energy -7.8823504447937012 +Optimization completed at step 63 Optimized energy: -7.8823523521423340 Optimized amplitudes: - [-2.4216002e-04 1.8924323e-03 -3.4653045e-02 1.5943546e-02 - 3.6362690e-07 9.0936717e-04 -1.7181528e-05 1.4154296e-02 - -4.4650793e-08 9.0864423e-04 -2.6399141e-06 1.4159971e-02 - 5.4558384e-04 4.2672374e-04 -2.8494308e-03 5.3833455e-02 - 2.3033506e-04 1.2578158e-06 3.3855862e-08 7.3955505e-08 - -5.2005623e-07 2.9746575e-08 1.2325607e-08 1.1919828e-05 - -1.0492613e-04 7.9503102e-04 3.8478893e-06 5.9738107e-07 - -5.4855812e-02 3.0889052e-03 7.9252044e-05 -1.5384763e-06 - -1.5373821e-06 -3.0784176e-07 -3.5303248e-08 1.7360321e-08 - 4.4359115e-07 -4.9067144e-06 3.0889027e-03 1.3888703e-07 - -1.6715177e-08 6.3234533e-09 -7.5149819e-07 3.7140178e-04] + [-2.42472161e-04 1.89258391e-03 -3.46013680e-02 1.59353409e-02 + -8.40432079e-08 9.09362687e-04 2.01798011e-05 1.41534032e-02 + -2.81526667e-07 9.08639806e-04 2.00776722e-05 1.41590768e-02 + 5.45396935e-04 4.26715094e-04 -2.84755090e-03 5.38354851e-02 + 2.29954778e-04 9.55212727e-07 -1.24844689e-07 -9.20767249e-08 + -4.53033465e-07 -7.44455733e-08 -8.83169875e-08 1.17984437e-05 + -1.04996754e-04 7.94677646e-04 -4.50417019e-06 -4.49753043e-06 + -5.48430867e-02 3.08870710e-03 -6.50319926e-05 1.26427835e-06 + 1.25660222e-06 -2.82077963e-07 7.96948143e-08 -3.28978906e-08 + -3.63568660e-07 5.76087541e-06 3.08870478e-03 8.82309266e-08 + 5.73797401e-08 -2.53652850e-08 5.72846511e-06 3.71275470e-04] ``` ## Summary diff --git a/docs/mindquantum/docs/source_zh_cn/vqe_for_quantum_chemistry.ipynb b/docs/mindquantum/docs/source_zh_cn/vqe_for_quantum_chemistry.ipynb index 4e237b73f1..5bc23ea8fc 100644 --- a/docs/mindquantum/docs/source_zh_cn/vqe_for_quantum_chemistry.ipynb +++ b/docs/mindquantum/docs/source_zh_cn/vqe_for_quantum_chemistry.ipynb @@ -72,7 +72,7 @@ "source": [ "## 量子化学计算方法\n", "\n", - "量子化学的核心问题在于求解薛定谔方程（Schrödinger Equation）。一般来说，求解含时薛定谔方程（Time-dependent Schrödinger Equation)较为复杂，故引入玻恩-奥本海默近似（Born-Oppenheimer approximation, BO approximation）。BO近似认为，原子核质量远大于电子、运动速度远低于电子，故可以将两者进行分离变量，单独讨论原子核或电子的运动，于是可得到如下不含时的电子运动方程，也称为定态薛定谔方程：\n", + "量子化学的核心问题在于求解薛定谔方程（Schrödinger Equation）。一般来说，求解含时薛定谔方程（Time-dependent Schrödinger Equation）较为复杂，故引入玻恩-奥本海默近似（Born-Oppenheimer approximation, BO approximation）。BO近似认为，原子核质量远大于电子、运动速度远低于电子，故可以将两者进行分离变量，单独讨论原子核或电子的运动，于是可得到如下不含时的电子运动方程，也称为定态薛定谔方程：\n", "\n", "$$\n", "\\hat{H} |\\Psi\\rangle = E |\\Psi\\rangle\n", -- Gitee