Mga kurba ng Dissociation PES gamit ang Qunova HiVQE
Note
Ang mga Qiskit Function ay isang eksperimentong feature na available lamang para sa mga user ng IBM Quantum® Premium Plan, Flex Plan, at On-Prem (via IBM Quantum Platform API) Plan. Ang mga ito ay nasa preview release status at maaaring magbago.
Tantiya ng paggamit (TANDAAN: Ito ay tantiya lamang. Maaaring mag-iba ang inyong runtime.)
- Li2S: Limang minutong QPU time sa isang Heron r2 processor
- FeP-NO: Limang minutong QPU time sa isang Heron r2 processor
Panimula​
Ang tumpak na pagkalkula ng mga enerhiya ng kemikal na reaksyon ay mahalaga para sa siyentipikong pag-unlad sa materials science, chemical engineering, drug discovery, at iba pang larangan. Sa iba't ibang kemikal na sistema, ang Li-S system ay nakakuha ng malaking interes para sa pag-unawa at pagbuo ng mga bagong komposisyon ng baterya. Ang tutorial na ito ay nagbibigay ng hands-on na karanasan sa pagkalkula ng Li-S bond dissociation potential energy surface (PES) ng isang system sa pamamagitan ng pag-alis ng isang lithium atom gamit ang mga kalkulasyon ng HiVQE. Ang mga resulta ay maaaring ikumpara sa reference calculation (CASCI) pati na rin sa mga klasikal na pamamaraan tulad ng Hartree-Fock (HF) para sa isang 20-qubit na problema.
Mga Kinakailangan​
I-install ang mga sumusunod na dependency upang patakbuhin ang code sa tutorial na ito.
!pip install --upgrade pip
!pip install -U qiskit-ibm-catalog "qiskit_ibm_runtime<0.42.0" pyscf numpy matplotlib typing_extensions
Pag-setup​
Upang patakbuhin ang tutorial na ito, i-import ang qunova/hivqe-chemistry function sa pamamagitan ng QiskitFunctionCatalog. Kailangan ninyo ng IBM Quantum Premium Plan, Flex Plan, o On-Prem (IBM Quantum Platform API) Plan account na may lisensya mula sa Qunova upang patakbuhin ang function na ito.
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")
Bahagi 1: Li2S (20Q)​
Hakbang 1: I-map ang mga klasikal na input sa isang quantum problem​
Tukuyin ang mga geometry sa dictionary format para sa iba't ibang bond distance ng Li-S upang kalkulahin ang PES curve. Ang mga geometry na ito ay na-optimize gamit ang mga kalkulasyon ng 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'}
Ang mga kalkulasyon ng HiVQE ay isasagawa gamit ang mga opsyon na tinukoy sa ibaba. Gamit ang sto3g basis para sa , mayroong 19 spatial orbital na may 22 elektron. Upang patakbuhin ang (10o,10e) case gamit ang HiVQE calculation, maaari ninyong tukuyin ang 10 active orbital at anim na frozen orbital. Sa bawat iteration, gagamitin ang 100 shot upang mag-sample ng electron configuration na nabuo ng ExcitationPreserving quantum circuit (epa) na may circular entanglement at dalawang repetition (reps). Ang maximum na bilang ng iteration ay nakatakda sa 30 upang masiguro ang pagtatapos ng iteration na may energy convergence.
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,
}
Hakbang 2 at 3: I-optimize ang problema para sa quantum hardware execution at isagawa gamit ang HiVQE Chemistry function​
I-setup ang for loop upang patakbuhin ang mga kalkulasyon ng HiVQE gamit ang mga geometry na may mga opsyon na tinukoy sa ibaba. Ang mga job ay isinusubmit sa for loop. Sa tutorial na ito, magsusubmit kayo ng anim na geometry at kukuhanin ang mga resulta kapag nakumpleto na ang lahat. Sa main function run, kailangan ninyong tukuyin ang max_states at max_expansion_states upang kontrolin ang maximum na laki ng subspace matrix at upang kontrolin kung ilang estado ang maaaring mabuo gamit ang mga klasikal na pamamaraan ng CI expansion bawat iteration. Ang mga function job ID ay iimbak sa dictionary na may bawat geometry label upang higit pang subaybayan at iproseso ang output.
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'}
Suriin natin kung ang lahat ng mga job ay tumatakbo pa o nakumpleto na.
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
Kapag nakumpleto na ang lahat ng mga job, kunin natin ang lahat ng mga resulta ng kalkulasyon.
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}
Ang kabuuang QPU runtime na ginamit sa job ay maaaring subaybayan sa pamamagitan ng pag-log in sa IBM Quantum Platform at pagtingin sa mga naisumiteng job na may qunova-chemistry-hivqe tag.
Hakbang 4: Post-process at ikumpara sa mga klasikal na pamamaraan​
Ang klasikal na reference calculation (CASCI) ay maaaring isagawa para sa (10o,10e) upang i-validate ang mga resulta ng 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
Pag-plot ng dissociation curve para sa Li_2S​
I-plot at ikumpara natin ang mga resulta ng HiVQE sa HF at CASCI. Makikita ninyo na ang lahat ng mga kalkulasyon ng HiVQE ay tumutugma nang mabuti sa klasikal na reference result (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)
Bahagi 2: FeP-NO (44Q)​
Hakbang 1: I-map ang mga klasikal na input sa isang quantum problem​
Tukuyin ang mga opsyon para sa mga kalkulasyon ng 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,
}
Tukuyin ang mga FeP-NO geometry sa dictionary format para sa iba't ibang bond distance ng Fe-N upang kalkulahin ang PES curve.
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'}
Hakbang 2 at 3: I-optimize ang problema para sa quantum hardware execution at isagawa gamit ang HiVQE Chemistry function​
Batay sa setup ng HiVQE at mga geometry, kunin ang mga resulta nang sunud-sunod.
Isumite ang d(Fe-N) = 1.75 calculation.​
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
Subaybayan ang job at kunin ang resulta para sa d(Fe-N) = 1.75 calculation.
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
Isumite ang d(Fe-N) = 2.00 calculation.​
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
Subaybayan ang job at kunin ang resulta para sa d(Fe-N) = 2.00 calculation.
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
Isumite ang d(Fe-N) = 5.00 calculation.​
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
Subaybayan ang job at kunin ang resulta para sa d(Fe-N) = 5.00 calculation.
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,
}
Hakbang 4: Post-process at ikumpara sa mga klasikal na pamamaraan​
Ang mga resulta ng klasikal na reference calculation (CASCI-DMRG, maxM=800) ay ibinigay para sa (22o,22e) upang i-validate ang mga resulta ng 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)
Survey ng tutorial​
Pakisagutan ang maikling survey na ito upang magbigay ng feedback sa tutorial na ito. Ang inyong mga pananaw ay makakatulong sa amin na mapabuti ang aming mga alok na nilalaman at karanasan ng user.