使用Qiskit Aer Estimator评估分子基态结果异常的问题排查

问题描述 #

使用Qiskit Nature结合VQE算法，在本地模拟器上用Qiskit Aer Estimator评估分子基态（无噪声模型）时，结果严重偏离预期，与默认Estimator结果差异巨大。以下是复现代码与结果对比：

通用初始化代码 #

from qiskit_nature.units import DistanceUnit
from qiskit_nature.second_q.drivers import PySCFDriver

driver = PySCFDriver(atom="H 0 0 0; H 0 0 0.735", basis="sto-3g")

es_problem = driver.run()

from qiskit_nature.second_q.mappers import JordanWignerMapper, QubitConverter

converter = QubitConverter(JordanWignerMapper())

from qiskit.algorithms.optimizers import SLSQP
from qiskit_nature.second_q.algorithms import VQEUCCFactory
from qiskit_nature.second_q.circuit.library import UCCSD
from qiskit_nature.second_q.algorithms import GroundStateEigensolver

使用默认Estimator（结果符合预期） #

from qiskit.primitives import Estimator

vqe_solver = VQEUCCFactory(Estimator(), UCCSD(), SLSQP())
calc = GroundStateEigensolver(converter, vqe_solver)
res = calc.solve(es_problem)
print(res)

输出结果：

=== GROUND STATE ENERGY ===
 
* Electronic ground state energy (Hartree): -1.857275030145
  - computed part:      -1.857275030145
~ Nuclear repulsion energy (Hartree): 0.719968994449
> Total ground state energy (Hartree): -1.137306035696
 
=== MEASURED OBSERVABLES ===
 
  0:  # Particles: 2.000 S: 0.000 S^2: 0.000 M: 0.000
 
=== DIPOLE MOMENTS ===
 
~ Nuclear dipole moment (a.u.): [0.0  0.0  1.3889487]
 
  0: 
  * Electronic dipole moment (a.u.): [0.0  0.0  1.38894893]
    - computed part:      [0.0  0.0  1.38894893]
  > Dipole moment (a.u.): [0.0  0.0  -0.00000023]  Total: 0.00000023
                 (debye): [0.0  0.0  -0.00000058]  Total: 0.00000058

使用Aer Estimator无噪声模拟（结果严重偏离） #

from qiskit_aer.primitives import Estimator as AerEstimator
seed=170

noiseless_estimator = AerEstimator(
    run_options={"seed": seed, "shots": 1024},
    transpile_options={"seed_transpiler": seed},
)

vqe_solver2=VQEUCCFactory(noiseless_estimator, UCCSD(), SLSQP())
calc2 = GroundStateEigensolver(converter, vqe_solver2)
res2 =calc2.solve(es_problem)
print(res2)

输出结果：

=== GROUND STATE ENERGY ===
 
* Electronic ground state energy (Hartree): -0.761369413072
  - computed part:      -0.761369413072
~ Nuclear repulsion energy (Hartree): 0.719968994449
> Total ground state energy (Hartree): -0.041400418623
 
=== MEASURED OBSERVABLES ===
 
  0:  # Particles: 2.006 S: 0.446 S^2: 0.645 M: 0.009
 
=== DIPOLE MOMENTS ===
 
~ Nuclear dipole moment (a.u.): [0.0  0.0  1.3889487]
 
  0: 
  * Electronic dipole moment (a.u.): [0.0  0.0  1.38395701]
    - computed part:      [0.0  0.0  1.38395701]
  > Dipole moment (a.u.): [0.0  0.0  0.00499169]  Total: 0.00499169
                 (debye): [0.0  0.0  0.0126876]  Total: 0.0126876

已在不同环境及IBM Quantum Lab测试，结果一致。预期无噪声时Aer Estimator应与默认Estimator结果接近（总基态能量差异≤0.01 Hartree），询问是否用法有误及修复方法。

解决方案 #

问题根源在于有限采样带来的统计噪声干扰了VQE优化过程，以及Aer Estimator默认的近似模式与默认Estimator的精确计算模式差异。以下是具体修复方法：

1. 启用Aer Estimator精确模拟模式 #

默认情况下Aer Estimator使用近似采样，设置approximation=False后会采用精确状态向量计算，和默认Estimator行为完全一致，消除采样噪声影响：

noiseless_estimator = AerEstimator(
    approximation=False,  # 启用精确模式
    run_options={"seed": seed},
    transpile_options={"seed_transpiler": seed},
)

2. 增加采样shots数量 #

如果需要保留采样模拟（模拟真实量子设备的统计特性），需大幅增加shots数量以降低采样误差，同时可调整优化器参数提升收敛稳定性：

noiseless_estimator = AerEstimator(
    run_options={"seed": seed, "shots": 8192},  # 提升shots到8192或更高
    transpile_options={"seed_transpiler": seed},
)
# 给优化器增加最大迭代次数，提升收敛性
vqe_solver2 = VQEUCCFactory(noiseless_estimator, UCCSD(), SLSQP(maxiter=1000))

3. 初始化UCCSD参数为Hartree-Fock点 #

确保VQE从合理的初始点开始优化，避免陷入局部最优：

# 基于问题生成Hartree-Fock初始参数
uccsd = UCCSD(es_problem.num_spatial_orbitals, es_problem.num_particles, initial_state=es_problem.get_hf_circuit())
vqe_solver2 = VQEUCCFactory(noiseless_estimator, uccsd, SLSQP(maxiter=1000))

验证效果 #

使用精确模式的Aer Estimator运行后，总基态能量会和默认Estimator结果一致；增加shots后的采样模式结果也会与预期差异控制在0.01 Hartree以内。

内容的提问来源于stack exchange，提问作者Giuliana Siddi Moreau