Kurva PES disosiasi dengan Qunova HiVQE
Catatan
Qiskit Functions adalah fitur eksperimental yang hanya tersedia untuk pengguna IBM Quantum® Premium Plan, Flex Plan, dan On-Prem (melalui IBM Quantum Platform API) Plan. Fitur ini masih dalam status rilis pratinjau dan dapat berubah sewaktu-waktu.
Estimasi penggunaan (CATATAN: Ini hanya perkiraan. Waktu eksekusi aktual bisa berbeda.)
- Li2S: Lima menit waktu QPU pada prosesor Heron r2
- FeP-NO: Lima menit waktu QPU pada prosesor Heron r2
Latar Belakang​
Menghitung energi reaksi kimia secara akurat sangat penting untuk kemajuan ilmiah di bidang ilmu material, rekayasa kimia, penemuan obat, dan bidang lainnya. Di antara berbagai sistem kimia, sistem Li-S mendapat perhatian besar dalam memahami dan mengembangkan komposisi baterai baru. Tutorial ini memberikan pengalaman langsung dalam menghitung potential energy surface (PES) disosiasi ikatan Li-S dari sistem dengan menghapus satu atom litium menggunakan perhitungan HiVQE. Hasilnya dapat dibandingkan dengan perhitungan referensi (CASCI) maupun metode klasik seperti Hartree-Fock (HF) untuk masalah 20 Qubit.
Persyaratan​
Instal dependensi berikut untuk menjalankan kode dalam tutorial ini.
!pip install --upgrade pip
!pip install -U qiskit-ibm-catalog "qiskit_ibm_runtime<0.42.0" pyscf numpy matplotlib typing_extensions
Pengaturan​
Untuk menjalankan tutorial ini, impor fungsi qunova/hivqe-chemistry melalui QiskitFunctionCatalog. Kamu memerlukan akun IBM Quantum Premium Plan, Flex Plan, atau On-Prem (IBM Quantum Platform API) Plan dengan lisensi dari Qunova untuk menjalankan fungsi ini.
from qiskit_ibm_catalog import QiskitFunctionsCatalog
from pyscf import gto, scf, mcscf
import matplotlib.pyplot as plt
import pprint
catalog = QiskitFunctionsCatalog(
channel="ibm_quantum_platform",
instance="INSTANCE_CRN",
token="YOUR_API_KEY", # Use the 44-character API_KEY you created and saved from the IBM Quantum Platform Home dashboard
)
hivqe = catalog.load("qunova/hivqe-chemistry")
Bagian 1: Li2S (20Q)​
Langkah 1: Petakan input klasik ke masalah kuantum​
Definisikan geometri dalam format dictionary untuk berbagai jarak ikatan Li-S guna menghitung kurva PES. Geometri-geometri ini dioptimalkan menggunakan perhitungan B3LYP/631g.
str_geometries = {
"1.51": "S -1.239044 0.671232 -0.030374; Li -1.506327 0.432403 -1.498949; Li -0.899996 0.973348 1.826768",
"1.91": "S -1.215858 0.692272 0.099232; Li -1.553305 0.390283 -1.758043; Li -0.876205 0.994426 1.956257",
"2.40": "S -1.741432 0.680397 0.346702; Li -0.529307 0.488006 -1.729343; Li -1.284307 0.989409 2.177209",
"3.10": "S -2.347450 0.657089 0.566194; Li -0.199353 0.527517 -1.665148; Li -1.008243 0.973206 1.893522",
"3.80": "S -2.707255 0.674298 0.909161; Li 0.079218 0.552012 -1.671656; Li -0.927010 0.931502 1.557063",
"4.50": "S -2.913363 0.709175 1.276987; Li 0.368656 0.559989 -1.798088; Li -1.010340 0.888647 1.315670",
}
str_geometries
{'1.51': 'S -1.239044 0.671232 -0.030374; Li -1.506327 0.432403 -1.498949; Li -0.899996 0.973348 1.826768',
'1.91': 'S -1.215858 0.692272 0.099232; Li -1.553305 0.390283 -1.758043; Li -0.876205 0.994426 1.956257',
'2.40': 'S -1.741432 0.680397 0.346702; Li -0.529307 0.488006 -1.729343; Li -1.284307 0.989409 2.177209',
'3.10': 'S -2.347450 0.657089 0.566194; Li -0.199353 0.527517 -1.665148; Li -1.008243 0.973206 1.893522',
'3.80': 'S -2.707255 0.674298 0.909161; Li 0.079218 0.552012 -1.671656; Li -0.927010 0.931502 1.557063',
'4.50': 'S -2.913363 0.709175 1.276987; Li 0.368656 0.559989 -1.798088; Li -1.010340 0.888647 1.315670'}
Perhitungan HiVQE akan dilakukan dengan opsi yang didefinisikan di bawah ini. Menggunakan basis sto3g untuk , terdapat 19 orbital spasial dengan 22 elektron. Untuk menjalankan kasus (10o,10e) dengan perhitungan HiVQE, kamu dapat mendefinisikan 10 orbital aktif dan enam orbital beku. Pada setiap iterasi, 100 shots akan digunakan untuk men-sample konfigurasi elektron yang dihasilkan oleh Circuit kuantum ExcitationPreserving (epa) dengan entanglement circular dan dua pengulangan (reps). Jumlah maksimum iterasi diatur menjadi 30 untuk memastikan terminasi iterasi dengan konvergensi energi.
molecule_options = {
"basis": "sto3g",
"active_orbitals": list(range(5, 15)),
"frozen_orbitals": list(range(5)),
}
hivqe_options = {
"shots": 100,
"max_iter": 30,
"ansatz": "epa",
"ansatz_entanglement": "circular",
"ansatz_reps": 2,
}
Langkah 2 dan 3: Optimalkan masalah untuk eksekusi pada hardware kuantum dan jalankan menggunakan fungsi HiVQE Chemistry​
Siapkan loop for untuk menjalankan perhitungan HiVQE dengan geometri dan opsi yang telah didefinisikan. Job-job disubmit dalam loop for. Dalam tutorial ini, kamu akan mensubmit enam geometri dan mengambil hasilnya ketika semuanya sudah selesai. Dalam eksekusi fungsi utama, kamu perlu mendefinisikan max_states dan max_expansion_states untuk mengontrol ukuran maksimum matriks subspace dan mengontrol berapa banyak state yang dapat dihasilkan menggunakan metode ekspansi CI klasik per iterasi. ID job fungsi akan disimpan dalam dictionary dengan label geometri masing-masing untuk melacak dan memproses output lebih lanjut.
info_jobid = {}
for dis, geom in str_geometries.items():
hivqe_run = hivqe.run(
geometry=geom,
backend_name="",
max_states=40000,
max_expansion_states=100,
molecule_options=molecule_options,
hivqe_options=hivqe_options,
)
status = hivqe_run.status()
info_jobid[dis] = hivqe_run.job_id
print(info_jobid)
{'1.51': 'de3b8818-c9db-4fa3-a3c2-d51551c2dfaf', '1.91': '55d9467a-fc85-49a8-9bc6-8f6990e421e5', '2.40': '415112b3-69ff-4d53-8b10-cb4e3be68c9e', '3.10': 'ef67b600-3887-4225-b872-e354dfdf8454', '3.80': 'b16d3502-a9e4-4560-9775-852e9d07e70f', '4.50': '0c0bffc7-af77-4a56-a656-2a2610c991d6'}
Mari periksa apakah semua job masih berjalan atau sudah selesai.
completed_jobs_num = 0
running_jobs_num = 0
completed_jobs = {}
for i, info in enumerate(info_jobid.items()):
dis, job_id = info
submitted_job = catalog.get_job_by_id(job_id)
stat = submitted_job.status()
print(dis, submitted_job.job_id, stat)
if stat == "DONE":
completed_jobs_num += 1
completed_jobs[dis] = submitted_job
if (stat == "RUNNING") or (stat == "QUEUED"):
running_jobs_num += 1
print(
f"Completed {completed_jobs_num} job, Running or Queued {running_jobs_num} job"
)
1.51 de3b8818-c9db-4fa3-a3c2-d51551c2dfaf DONE
1.91 55d9467a-fc85-49a8-9bc6-8f6990e421e5 DONE
2.40 415112b3-69ff-4d53-8b10-cb4e3be68c9e DONE
3.10 ef67b600-3887-4225-b872-e354dfdf8454 DONE
3.80 b16d3502-a9e4-4560-9775-852e9d07e70f DONE
4.50 0c0bffc7-af77-4a56-a656-2a2610c991d6 DONE
Completed 6 job, Running or Queued 0 job
Setelah semua job selesai, mari ambil semua hasil perhitungan.
hivqe_result = {}
if len(info_jobid) == completed_jobs_num:
print("All jobs are completed")
for i, job in enumerate(completed_jobs.items()):
dis, cal = job
print(dis, cal.result()["energy"])
hivqe_result[str(dis)] = cal.result()["energy"]
All jobs are completed
1.51 -407.8944801731773
1.91 -407.9800570932916
2.40 -407.9372992999806
3.10 -407.86278336000134
3.80 -407.83092972296157
4.50 -407.82971011225766
pprint.pprint(hivqe_result)
{'1.51': -407.8944801731773,
'1.91': -407.9800570932916,
'2.40': -407.9372992999806,
'3.10': -407.86278336000134,
'3.80': -407.83092972296157,
'4.50': -407.82971011225766}
Total waktu eksekusi QPU yang digunakan dalam job dapat dilacak dengan masuk ke IBM Quantum Platform dan melihat job yang disubmit dengan tag qunova-chemistry-hivqe.
Langkah 4: Pasca-proses dan bandingkan dengan metode klasik​
Perhitungan referensi klasik (CASCI) dapat dilakukan untuk (10o,10e) guna memvalidasi hasil HiVQE.
str_geometries = {
"1.31": "S -1.250686 0.660708 -0.095168; Li -1.482812 0.453464 -1.369406; Li -0.911870 0.962810 1.762020",
"1.41": "S -1.244856 0.665971 -0.062773; Li -1.494574 0.442933 -1.434177; Li -0.905937 0.968078 1.794395",
"1.51": "S -1.239044 0.671232 -0.030374; Li -1.506327 0.432403 -1.498949; Li -0.899996 0.973348 1.826768",
"1.61": "S -1.233245 0.676492 0.002027; Li -1.518073 0.421873 -1.563722; Li -0.894049 0.978617 1.859141",
"1.71": "S -1.227453 0.681752 0.034429; Li -1.529816 0.411343 -1.628496; Li -0.888099 0.983887 1.891513",
"1.81": "S -1.221659 0.687012 0.066831; Li -1.541558 0.400813 -1.693270; Li -0.882150 0.989157 1.923885",
"1.91": "S -1.215858 0.692272 0.099232; Li -1.553305 0.390283 -1.758043; Li -0.876205 0.994426 1.956257",
"2.01": "S -1.209887 0.697544 0.131599; Li -1.565136 0.379748 -1.822800; Li -0.870344 0.999691 1.988646",
"2.11": "S -1.203945 0.702813 0.163973; Li -1.576953 0.369214 -1.887560; Li -0.864469 1.004956 2.021033",
"2.21": "S -1.198023 0.708081 0.196350; Li -1.588760 0.358680 -1.952322; Li -0.858584 1.010221 2.053417",
"2.30": "S -1.365426 0.717714 0.367060; Li -0.689401 0.458925 -1.828368; Li -1.500219 0.981173 2.255876",
"2.31": "S -1.192118 0.713348 0.228731; Li -1.600559 0.348146 -2.017085; Li -0.852690 1.015488 2.085800",
"2.40": "S -1.741432 0.680397 0.346702; Li -0.529307 0.488006 -1.729343; Li -1.284307 0.989409 2.177209",
"2.50": "S -1.885961 0.669986 0.365815; Li -0.461563 0.499084 -1.695846; Li -1.207523 0.988741 2.124599",
"2.60": "S -1.977163 0.665155 0.389784; Li -0.416654 0.504966 -1.683655; Li -1.161229 0.987690 2.088439",
"2.70": "S -2.063642 0.661518 0.418977; Li -0.367600 0.510505 -1.676408; Li -1.123804 0.985788 2.051998",
"2.80": "S -2.141072 0.659218 0.451663; Li -0.323153 0.515056 -1.673046; Li -1.090821 0.983538 2.015951",
"2.90": "S -2.212097 0.657968 0.487535; Li -0.281989 0.518909 -1.672407; Li -1.060960 0.980935 1.979440",
"3.00": "S -2.281477 0.657123 0.525155; Li -0.239607 0.523326 -1.668669; Li -1.033963 0.977363 1.938081",
"3.10": "S -2.347450 0.657089 0.566194; Li -0.199353 0.527517 -1.665148; Li -1.008243 0.973206 1.893522",
"3.20": "S -2.410882 0.657532 0.608912; Li -0.157788 0.532069 -1.659971; Li -0.986376 0.968211 1.845627",
"3.30": "S -2.470306 0.658818 0.654893; Li -0.118007 0.536237 -1.656311; Li -0.966733 0.962757 1.795986",
"3.40": "S -2.525776 0.660762 0.702910; Li -0.078312 0.540189 -1.654076; Li -0.950958 0.956861 1.745734",
"3.50": "S -2.576885 0.663376 0.752788; Li -0.039076 0.543706 -1.654536; Li -0.939085 0.950730 1.696316",
"3.60": "S -2.623930 0.666534 0.803853; Li 0.000274 0.546839 -1.657697; Li -0.931390 0.944439 1.648412",
"3.70": "S -2.667364 0.670217 0.856250; Li 0.039572 0.549616 -1.663265; Li -0.927254 0.937980 1.601583",
"3.80": "S -2.707255 0.674298 0.909161; Li 0.079218 0.552012 -1.671656; Li -0.927010 0.931502 1.557063",
"3.90": "S -2.744005 0.678718 0.962425; Li 0.119268 0.554073 -1.682595; Li -0.930310 0.925021 1.514738",
"4.00": "S -2.777891 0.683415 1.015798; Li 0.159751 0.555810 -1.696024; Li -0.936907 0.918587 1.474794",
"4.10": "S -2.809179 0.688333 1.069057; Li 0.200678 0.557234 -1.711873; Li -0.946546 0.912245 1.437385",
"4.20": "S -2.838194 0.693443 1.122205; Li 0.242066 0.558401 -1.729770; Li -0.958918 0.905968 1.402134",
"4.30": "S -2.864984 0.698619 1.174415; Li 0.283858 0.559186 -1.750539; Li -0.973920 0.900007 1.370693",
"4.40": "S -2.889984 0.703887 1.226140; Li 0.326068 0.559728 -1.773231; Li -0.991131 0.894196 1.341660",
"4.50": "S -2.913363 0.709175 1.276987; Li 0.368656 0.559989 -1.798088; Li -1.010340 0.888647 1.315670",
}
rhf_result = {}
casci_result = {}
cas_list = molecule_options["active_orbitals"]
distance_ref = []
for dis, geom in str_geometries.items():
distance_ref.append(dis)
mole = gto.M(atom=geom, basis=molecule_options["basis"])
mole.verbose = 0
# RHF energy
mf = scf.RHF(mole).run()
mo_occ = mf.mo_occ
num_elecs_as = int(sum([mo_occ[idx] for idx in cas_list]))
rhf_result[str(dis)] = mf.e_tot
# CASCI energy
casci_solver = mcscf.CASCI(mf, len(cas_list), num_elecs_as)
orbs = mcscf.addons.sort_mo(casci_solver, mf.mo_coeff, cas_list, base=0)
casci_solver.kernel(orbs)
casci_result[str(dis)] = casci_solver.e_tot
print(
f"d={dis:4.3} RHF Energy: {mf.e_tot:14.10}, CASCI Energy: {casci_solver.e_tot:14.10}"
)
d=1.3 RHF Energy: -407.7137006, CASCI Energy: -407.7193917
d=1.4 RHF Energy: -407.8183196, CASCI Energy: -407.8245211
d=1.5 RHF Energy: -407.8878013, CASCI Energy: -407.8944802
d=1.6 RHF Energy: -407.9315356, CASCI Energy: -407.9385663
d=1.7 RHF Energy: -407.9569034, CASCI Energy: -407.9641258
d=1.8 RHF Energy: -407.9693681, CASCI Energy: -407.9766313
d=1.9 RHF Energy: -407.9728592, CASCI Energy: -407.9800572
d=2.0 RHF Energy: -407.9701684, CASCI Energy: -407.9772549
d=2.1 RHF Energy: -407.9632701, CASCI Energy: -407.9702381
d=2.2 RHF Energy: -407.9535584, CASCI Energy: -407.9604007
d=2.3 RHF Energy: -407.9420173, CASCI Energy: -407.9487043
d=2.3 RHF Energy: -407.9420156, CASCI Energy: -407.9487024
d=2.4 RHF Energy: -407.9297216, CASCI Energy: -407.9372993
d=2.5 RHF Energy: -407.9172, CASCI Energy: -407.9261859
d=2.6 RHF Energy: -407.9061139, CASCI Energy: -407.915961
d=2.7 RHF Energy: -407.8937118, CASCI Energy: -407.904259
d=2.8 RHF Energy: -407.8816389, CASCI Energy: -407.8928292
d=2.9 RHF Energy: -407.8700448, CASCI Energy: -407.8819574
d=3.0 RHF Energy: -407.859054, CASCI Energy: -407.8719092
d=3.1 RHF Energy: -407.8487619, CASCI Energy: -407.8628304
d=3.2 RHF Energy: -407.8392304, CASCI Energy: -407.8548482
d=3.3 RHF Energy: -407.8304842, CASCI Energy: -407.8480217
d=3.4 RHF Energy: -407.8225124, CASCI Energy: -407.8423743
d=3.5 RHF Energy: -407.8152758, CASCI Energy: -407.8378892
d=3.6 RHF Energy: -407.8087161, CASCI Energy: -407.8345331
d=3.7 RHF Energy: -407.802764, CASCI Energy: -407.8322563
d=3.8 RHF Energy: -407.7973458, CASCI Energy: -407.83093
d=3.9 RHF Energy: -407.7923883, CASCI Energy: -407.8303555
d=4.0 RHF Energy: -407.7878216, CASCI Energy: -407.83025
d=4.1 RHF Energy: -407.783582, CASCI Energy: -407.8303243
d=4.2 RHF Energy: -407.7796124, CASCI Energy: -407.8303791
d=4.3 RHF Energy: -407.7758633, CASCI Energy: -407.8302885
d=4.4 RHF Energy: -407.7722923, CASCI Energy: -407.8300614
d=4.5 RHF Energy: -407.7688641, CASCI Energy: -407.829711
Plotting the dissociation curve for Li_2S​
Mari kita plot dan bandingkan hasil HiVQE dengan HF dan CASCI. Kamu bisa melihat bahwa semua perhitungan HiVQE cocok dengan hasil referensi klasik (CASCI).
fig, ax = plt.subplots(1, 1)
hf_energy = [v for key, v in rhf_result.items()]
casci_energy = [v for key, v in casci_result.items()]
hivqe_energy = [v for key, v in hivqe_result.items()]
distance_ref = [float(key) for key, v in rhf_result.items()]
distance = [float(key) for key, v in hivqe_result.items()]
ax.plot(distance_ref, hf_energy, "-o", label="RHF", c="blue")
ax.plot(distance_ref, casci_energy, "-o", label="CASCI", c="green")
ax.plot(distance, hivqe_energy, "x", label="HiVQE", c="red", markersize=20)
ax.legend(fontsize=20)
ax.tick_params("both", labelsize=16)
ax.set_xlabel("Bond distance (angstrom)", size=20)
ax.set_ylabel("Energy (Ha)", size=20)
ax.set_title("Li2S PES curve", size=20)
fig.set_size_inches(14, 8)
Bagian 2: FeP-NO (44Q)​
Langkah 1: Petakan input klasik ke masalah kuantum​
Tentukan opsi untuk perhitungan HiVQE
molecule_options = {
"basis": "631g*",
"active_orbitals": list(range(90, 112, 1)),
"frozen_orbitals": list(range(0, 90, 1)),
"charge": -1,
}
hivqe_options = {
"shots": 2000,
"max_iter": 40,
"ansatz": "epa",
"ansatz_entanglement": "linear",
"ansatz_reps": 2,
"amplitude_screening_tolerance": 1e-6,
}
Tentukan geometri FeP-NO dalam format dictionary untuk berbagai jarak ikatan Fe-N guna menghitung kurva PES.
geometry_1_75 = """
Fe 9.910596 31.534095 1.798088
N 10.557481 31.888419 -0.055204
N 11.823496 31.255002 2.384659
N 9.292831 30.783362 3.568730
N 8.036805 31.418327 1.124265
C 9.784765 32.177349 -1.158798
C 10.612656 32.501029 -2.296868
C 11.903375 32.404043 -1.876832
C 11.859093 32.028943 -0.483750
C 12.965737 31.464698 1.641427
C 14.146517 31.236323 2.440231
C 13.713061 30.885870 3.681911
C 12.268752 30.896411 3.634891
C 10.067717 30.486167 4.664747
C 9.246224 30.053411 5.772052
C 7.957075 30.082846 5.336488
C 7.995710 30.538421 3.967046
C 6.900258 31.104497 1.836595
C 5.722470 31.251707 1.015333
C 6.148430 31.668586 -0.207993
C 7.587039 31.767438 -0.130483
C 8.399453 32.134197 -1.192329
H 7.912872 32.388031 -2.131079
C 12.984883 31.836053 0.306093
H 13.955948 31.977044 -0.162626
C 11.453768 30.560663 4.708020
H 11.940677 30.298823 5.644352
C 6.877071 30.697580 3.164102
H 5.907240 30.476797 3.603674
H 12.813946 32.569160 -2.441577
H 10.236332 32.758110 -3.280309
H 15.164312 31.335191 2.080201
H 14.299625 30.629109 4.556760
H 9.626524 29.758225 6.743433
H 7.053076 29.823583 5.875809
H 4.709768 31.058315 1.350561
H 5.561898 31.886355 -1.093106
N 9.832739 33.209042 2.298783
O 9.346337 34.075996 1.606023
"""
geometry_2_00 = """
Fe 9.917990 31.445558 1.778346
N 10.556809 31.866188 -0.055498
N 11.814089 31.227003 2.372666
N 9.297875 30.758246 3.550104
N 8.043584 31.397768 1.120485
C 9.784831 32.164652 -1.160219
C 10.611624 32.501801 -2.293514
C 11.902858 32.406547 -1.875160
C 11.859552 32.017818 -0.486307
C 12.960503 31.454432 1.636717
C 14.140770 31.242960 2.439615
C 13.708543 30.884151 3.678983
C 12.266351 30.874173 3.627468
C 10.070264 30.465070 4.655102
C 9.247247 30.053101 5.766681
C 7.958085 30.091201 5.332866
C 7.998432 30.529979 3.958727
C 6.901428 31.093932 1.833807
C 5.723289 31.255057 1.016540
C 6.151314 31.670649 -0.206350
C 7.589736 31.755538 -0.133074
C 8.400230 32.124963 -1.194447
H 7.913264 32.386655 -2.130914
C 12.983905 31.827747 0.302415
H 13.955696 31.979687 -0.161365
C 11.454251 30.533644 4.698234
H 11.941002 30.276716 5.636156
C 6.877444 30.689985 3.159940
H 5.907605 30.480118 3.604825
H 12.813105 32.581608 -2.437367
H 10.233725 32.768337 -3.273979
H 15.157796 31.357524 2.082132
H 14.295001 30.638320 4.557047
H 9.626721 29.768762 6.741623
H 7.051752 29.847502 5.875478
H 4.709710 31.071712 1.354640
H 5.565103 31.898376 -1.089333
N 9.840508 33.353531 2.373019
O 9.344561 34.158205 1.637232
"""
geometry_5_00 = """
Fe 9.918629 31.289202 1.717339
N 10.542914 31.832173 -0.080685
N 11.795572 31.199413 2.341831
N 9.294593 30.741247 3.513929
N 8.042689 31.359481 1.087282
C 9.775254 32.111817 -1.200449
C 10.600219 32.479101 -2.319680
C 11.891090 32.425876 -1.887580
C 11.847694 32.024341 -0.507342
C 12.945734 31.464689 1.611366
C 14.116395 31.289997 2.423572
C 13.685777 30.915122 3.663719
C 12.252381 30.861042 3.608186
C 10.062170 30.463021 4.634102
C 9.236749 30.104333 5.755782
C 7.945687 30.161198 5.324720
C 7.989641 30.552269 3.941498
C 6.892881 31.087489 1.815829
C 5.722676 31.253502 1.001149
C 6.153153 31.631057 -0.238233
C 7.586010 31.695401 -0.179773
C 8.390724 32.047572 -1.247553
H 7.903308 32.291586 -2.187969
C 12.973334 31.849872 0.283741
H 13.944682 32.031190 -0.169145
C 11.447158 30.518591 4.678739
H 11.934423 30.277429 5.619969
C 6.864795 30.711643 3.146118
H 5.893357 30.532078 3.599511
H 12.800139 32.636412 -2.439296
H 10.224017 32.743662 -3.301293
H 15.131785 31.441247 2.076257
H 14.273933 30.694315 4.546802
H 9.612512 29.848040 6.739754
H 7.036117 29.960530 5.879248
H 4.707408 31.099933 1.347803
H 5.564992 31.851940 -1.121294
N 9.666041 36.091609 3.085945
O 9.598728 37.226756 3.411299
"""
str_geometries = {
"1.75": geometry_1_75,
"2.00": geometry_2_00,
"5.00": geometry_5_00,
}
hivqe_result = {}
{'5.0': '\nFe 9.918629 31.289202 1.717339\nN 10.542914 31.832173 -0.080685\nN 11.795572 31.199413 2.341831\nN 9.294593 30.741247 3.513929\nN 8.042689 31.359481 1.087282\nC 9.775254 32.111817 -1.200449\nC 10.600219 32.479101 -2.319680\nC 11.891090 32.425876 -1.887580\nC 11.847694 32.024341 -0.507342\nC 12.945734 31.464689 1.611366\nC 14.116395 31.289997 2.423572\nC 13.685777 30.915122 3.663719\nC 12.252381 30.861042 3.608186\nC 10.062170 30.463021 4.634102\nC 9.236749 30.104333 5.755782\nC 7.945687 30.161198 5.324720\nC 7.989641 30.552269 3.941498\nC 6.892881 31.087489 1.815829\nC 5.722676 31.253502 1.001149\nC 6.153153 31.631057 -0.238233\nC 7.586010 31.695401 -0.179773\nC 8.390724 32.047572 -1.247553\nH 7.903308 32.291586 -2.187969\nC 12.973334 31.849872 0.283741\nH 13.944682 32.031190 -0.169145\nC 11.447158 30.518591 4.678739\nH 11.934423 30.277429 5.619969\nC 6.864795 30.711643 3.146118\nH 5.893357 30.532078 3.599511\nH 12.800139 32.636412 -2.439296\nH 10.224017 32.743662 -3.301293\nH 15.131785 31.441247 2.076257\nH 14.273933 30.694315 4.546802\nH 9.612512 29.848040 6.739754\nH 7.036117 29.960530 5.879248\nH 4.707408 31.099933 1.347803\nH 5.564992 31.851940 -1.121294\nN 9.666041 36.091609 3.085945\nO 9.598728 37.226756 3.411299\n'}
geometry_1_75 = """
Fe 9.910596 31.534095 1.798088
N 10.557481 31.888419 -0.055204
N 11.823496 31.255002 2.384659
N 9.292831 30.783362 3.568730
N 8.036805 31.418327 1.124265
C 9.784765 32.177349 -1.158798
C 10.612656 32.501029 -2.296868
C 11.903375 32.404043 -1.876832
C 11.859093 32.028943 -0.483750
C 12.965737 31.464698 1.641427
C 14.146517 31.236323 2.440231
C 13.713061 30.885870 3.681911
C 12.268752 30.896411 3.634891
C 10.067717 30.486167 4.664747
C 9.246224 30.053411 5.772052
C 7.957075 30.082846 5.336488
C 7.995710 30.538421 3.967046
C 6.900258 31.104497 1.836595
C 5.722470 31.251707 1.015333
C 6.148430 31.668586 -0.207993
C 7.587039 31.767438 -0.130483
C 8.399453 32.134197 -1.192329
H 7.912872 32.388031 -2.131079
C 12.984883 31.836053 0.306093
H 13.955948 31.977044 -0.162626
C 11.453768 30.560663 4.708020
H 11.940677 30.298823 5.644352
C 6.877071 30.697580 3.164102
H 5.907240 30.476797 3.603674
H 12.813946 32.569160 -2.441577
H 10.236332 32.758110 -3.280309
H 15.164312 31.335191 2.080201
H 14.299625 30.629109 4.556760
H 9.626524 29.758225 6.743433
H 7.053076 29.823583 5.875809
H 4.709768 31.058315 1.350561
H 5.561898 31.886355 -1.093106
N 9.832739 33.209042 2.298783
O 9.346337 34.075996 1.606023
"""
geometry_2_00 = """
Fe 9.917990 31.445558 1.778346
N 10.556809 31.866188 -0.055498
N 11.814089 31.227003 2.372666
N 9.297875 30.758246 3.550104
N 8.043584 31.397768 1.120485
C 9.784831 32.164652 -1.160219
C 10.611624 32.501801 -2.293514
C 11.902858 32.406547 -1.875160
C 11.859552 32.017818 -0.486307
C 12.960503 31.454432 1.636717
C 14.140770 31.242960 2.439615
C 13.708543 30.884151 3.678983
C 12.266351 30.874173 3.627468
C 10.070264 30.465070 4.655102
C 9.247247 30.053101 5.766681
C 7.958085 30.091201 5.332866
C 7.998432 30.529979 3.958727
C 6.901428 31.093932 1.833807
C 5.723289 31.255057 1.016540
C 6.151314 31.670649 -0.206350
C 7.589736 31.755538 -0.133074
C 8.400230 32.124963 -1.194447
H 7.913264 32.386655 -2.130914
C 12.983905 31.827747 0.302415
H 13.955696 31.979687 -0.161365
C 11.454251 30.533644 4.698234
H 11.941002 30.276716 5.636156
C 6.877444 30.689985 3.159940
H 5.907605 30.480118 3.604825
H 12.813105 32.581608 -2.437367
H 10.233725 32.768337 -3.273979
H 15.157796 31.357524 2.082132
H 14.295001 30.638320 4.557047
H 9.626721 29.768762 6.741623
H 7.051752 29.847502 5.875478
H 4.709710 31.071712 1.354640
H 5.565103 31.898376 -1.089333
N 9.840508 33.353531 2.373019
O 9.344561 34.158205 1.637232
"""
geometry_5_00 = """
Fe 9.918629 31.289202 1.717339
N 10.542914 31.832173 -0.080685
N 11.795572 31.199413 2.341831
N 9.294593 30.741247 3.513929
N 8.042689 31.359481 1.087282
C 9.775254 32.111817 -1.200449
C 10.600219 32.479101 -2.319680
C 11.891090 32.425876 -1.887580
C 11.847694 32.024341 -0.507342
C 12.945734 31.464689 1.611366
C 14.116395 31.289997 2.423572
C 13.685777 30.915122 3.663719
C 12.252381 30.861042 3.608186
C 10.062170 30.463021 4.634102
C 9.236749 30.104333 5.755782
C 7.945687 30.161198 5.324720
C 7.989641 30.552269 3.941498
C 6.892881 31.087489 1.815829
C 5.722676 31.253502 1.001149
C 6.153153 31.631057 -0.238233
C 7.586010 31.695401 -0.179773
C 8.390724 32.047572 -1.247553
H 7.903308 32.291586 -2.187969
C 12.973334 31.849872 0.283741
H 13.944682 32.031190 -0.169145
C 11.447158 30.518591 4.678739
H 11.934423 30.277429 5.619969
C 6.864795 30.711643 3.146118
H 5.893357 30.532078 3.599511
H 12.800139 32.636412 -2.439296
H 10.224017 32.743662 -3.301293
H 15.131785 31.441247 2.076257
H 14.273933 30.694315 4.546802
H 9.612512 29.848040 6.739754
H 7.036117 29.960530 5.879248
H 4.707408 31.099933 1.347803
H 5.564992 31.851940 -1.121294
N 9.666041 36.091609 3.085945
O 9.598728 37.226756 3.411299
"""
str_geometries = {
"1.75": geometry_1_75,
"2.00": geometry_2_00,
"5.00": geometry_5_00,
}
hivqe_result = {}
{'5.0': '\nFe 9.918629 31.289202 1.717339\nN 10.542914 31.832173 -0.080685\nN 11.795572 31.199413 2.341831\nN 9.294593 30.741247 3.513929\nN 8.042689 31.359481 1.087282\nC 9.775254 32.111817 -1.200449\nC 10.600219 32.479101 -2.319680\nC 11.891090 32.425876 -1.887580\nC 11.847694 32.024341 -0.507342\nC 12.945734 31.464689 1.611366\nC 14.116395 31.289997 2.423572\nC 13.685777 30.915122 3.663719\nC 12.252381 30.861042 3.608186\nC 10.062170 30.463021 4.634102\nC 9.236749 30.104333 5.755782\nC 7.945687 30.161198 5.324720\nC 7.989641 30.552269 3.941498\nC 6.892881 31.087489 1.815829\nC 5.722676 31.253502 1.001149\nC 6.153153 31.631057 -0.238233\nC 7.586010 31.695401 -0.179773\nC 8.390724 32.047572 -1.247553\nH 7.903308 32.291586 -2.187969\nC 12.973334 31.849872 0.283741\nH 13.944682 32.031190 -0.169145\nC 11.447158 30.518591 4.678739\nH 11.934423 30.277429 5.619969\nC 6.864795 30.711643 3.146118\nH 5.893357 30.532078 3.599511\nH 12.800139 32.636412 -2.439296\nH 10.224017 32.743662 -3.301293\nH 15.131785 31.441247 2.076257\nH 14.273933 30.694315 4.546802\nH 9.612512 29.848040 6.739754\nH 7.036117 29.960530 5.879248\nH 4.707408 31.099933 1.347803\nH 5.564992 31.851940 -1.121294\nN 9.666041 36.091609 3.085945\nO 9.598728 37.226756 3.411299\n'}
Langkah 2 dan 3: Optimalkan masalah untuk eksekusi perangkat keras kuantum dan jalankan menggunakan fungsi HiVQE Chemistry​
Berdasarkan pengaturan HiVQE dan geometri yang ada, dapatkan hasil secara berurutan.
Kirim perhitungan d(Fe-N) = 1.75 .​
hivqe_run_1_75 = hivqe.run(
geometry=str_geometries["1.75"],
backend_name="",
max_states=400000000,
max_expansion_states=100,
molecule_options=molecule_options,
hivqe_options=hivqe_options,
)
info_jobid_1_75 = hivqe_run_1_75.job_id
Pantau job dan ambil hasil untuk perhitungan d(Fe-N) = 1.75 .
submitted_job_1_75 = catalog.get_job_by_id(info_jobid_1_75)
stat = submitted_job_1_75.status()
print(submitted_job_1_75.job_id, stat)
if stat == "DONE":
hivqe_run_1_75_energy = submitted_job_1_75.result()["energy"]
print(f"Completed HiVQE calculation, Energy {hivqe_run_1_75_energy}")
hivqe_result["1.75"] = hivqe_run_1_75_energy
Kirim perhitungan d(Fe-N) = 2.00 .​
hivqe_run_2_00 = hivqe.run(
geometry=str_geometries["2.00"],
backend_name="",
max_states=400000000,
max_expansion_states=100,
molecule_options=molecule_options,
hivqe_options=hivqe_options,
)
info_jobid_2_00 = hivqe_run_2_00.job_id
Pantau job dan ambil hasil untuk perhitungan d(Fe-N) = 2.00 .
submitted_job_2_00 = catalog.get_job_by_id(info_jobid_2_00)
stat = submitted_job_2_00.status()
print(submitted_job_2_00.job_id, stat)
if stat == "DONE":
hivqe_run_2_00_energy = submitted_job_2_00.result()["energy"]
print(f"Completed HiVQE calculation, Energy {hivqe_run_2_00_energy}")
hivqe_result["2.00"] = hivqe_run_2_00_energy
Kirim perhitungan d(Fe-N) = 5.00 .​
hivqe_run_5_00 = hivqe.run(
geometry=str_geometries["5.00"],
backend_name="",
max_states=400000000,
max_expansion_states=100,
molecule_options=molecule_options,
hivqe_options=hivqe_options,
)
info_jobid_5_00 = hivqe_run_5_00.job_id
Pantau job dan ambil hasil untuk perhitungan d(Fe-N) = 5.00 .
submitted_job_5_00 = catalog.get_job_by_id(info_jobid_5_00)
stat = submitted_job_5_00.status()
print(submitted_job_5_00.job_id, stat)
if stat == "DONE":
hivqe_run_5_00_energy = submitted_job_5_00.result()["energy"]
print(f"Completed HiVQE calculation, Energy {hivqe_run_5_00_energy}")
hivqe_result["5.00"] = hivqe_run_5_00_energy
hivqe_result = {
"1.75": -2373.681781,
"2.00": -2373.694128,
"5.00": -2373.637807,
}
Langkah 4: Pasca-pemrosesan dan perbandingan dengan metode klasik​
Hasil perhitungan referensi klasik (CASCI-DMRG, maxM=800) disediakan untuk (22o,22e) guna memvalidasi hasil HiVQE.
rhf_result = {
"1.75": -2373.59331683504,
"2.00": -2373.60640773065,
"5.00": -2373.50214278007,
}
casci_result = {"1.75": -2373.6827, "2.00": -2373.6948, "5.00": -2373.6393}
fig, ax = plt.subplots(1, 1)
hf_energy = [v for key, v in rhf_result.items()]
casci_energy = [v for key, v in casci_result.items()]
hivqe_energy = [v for key, v in hivqe_result.items()]
distance_ref = [float(key) for key, v in rhf_result.items()]
distance = [float(key) for key, v in hivqe_result.items()]
ax.plot(distance_ref, hf_energy, "-o", label="RHF", c="blue")
ax.plot(distance_ref, casci_energy, "-o", label="CASCI", c="green")
ax.plot(distance, hivqe_energy, "x", label="HiVQE", c="red", markersize=20)
ax.legend(fontsize=20)
ax.tick_params("both", labelsize=16)
ax.set_xlabel("Fe-N bond distance ($\AA$)", size=20)
ax.set_ylabel("Energy (Ha)", size=20)
ax.set_title("FeP-NO PES curve", size=20)
fig.set_size_inches(14, 8)
Survei tutorial​
Silakan isi survei singkat ini untuk memberikan masukan mengenai tutorial ini. Pendapatmu akan membantu kami meningkatkan konten dan pengalaman pengguna.
Note: This survey is provided by IBM Quantum and relates to the original English content. To give feedback on doQumentation's website, translations, or code execution, please open a GitHub issue.
Source: IBM Quantum docs — updated 24 Feb 2026
English version on doQumentation — updated 7 Mei 2026
This translation based on the English version of 9 Apr 2026