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QURI Chemistry: a Qiskit Function by QunaSys

Note

Qiskit Functions are an experimental feature available only to IBM Quantum™ Premium Plan users. They are in preview release status and subject to change.

Overview

This function helps you solve the quantum chemistry ground state estimation problem by using one of two algorithms based on the Quantum Selected Configuration Interaction (QSCI) algorithm:

  • QSCI
  • Optimization-based QSCI

The overall procedure for using this function is summarized in the following flow chart:

Workflow

Function description

The QSCI algorithm samples from a specific ansatz on quantum computers. Each sampled bitstring corresponds to an electron configuration, and the number of times a bitstring is sampled represents the importance of that electron configuration. Choose a number, RR, to select the RR most important electron configurations from the sample. The function constructs and diagonalizes the subspace Hamiltonian, depending on your choice of RR. The smallest eigenvalue is called "QSCI energy" and is the estimation of the QSCI algorithm's true ground state energy.

One important QSCI ingredient is its initial state preparations. Several possible initial state preparations are provided in this function. These include the hardware efficient, UCCSD, kUpCCGSD, and kuCJ ansatzes. A CCSD amplitude-based double excitation ansatz is provided specifically to be executed on near-term devices. Ansatz-specific settings are also provided for you to customize according to your needs.

In addition to returning the QSCI energy, the function also computes the estimated ground state wave function to help you identify the important electron configurations.

Get started

First, authenticate using your IBM Quantum™ API token and select the Qiskit Function as follows:

from qiskit_ibm_catalog import QiskitFunctionsCatalog
 
# If you have not previously saved your credentials, follow instructions at
# https://docs.quantum.ibm.com/guides/functions
# to authenticate with your API token.
catalog = QiskitFunctionsCatalog()
 
function = catalog.load("qunasys/quri-chemistry")

Inputs

The function is called with the following arguments:

function.run(
    method = ...,               # Allow only "QSCI" or "OPT_QSCI"
    molecule = ...,             # The molecule
    circuit_options = {...},    # Options for customizing the circuits
    qsci_setting = {...},       # Parameters of the QSCI algorithm
    mitigation_setting = {...}  # Specifies the error mitigation method
    max_iter = ...              # Maximum number of iterations when method = "OPT_QSCI".
    instance = ...              # The instance to use.
    backend_name = ...          # The backend name to use.
)

Each argument is described in following table.

NameTypeDescriptionRequiredDefaultExample
methodstrThe algorithm nameYes-“QSCI” or "OPT_QSCI"
molejsonThe molecule setting.YesThe molecule setting. See the examples that follow the table.
circuit_optionsjsonThe settings for the circuit.YesSee the examples following the table.
qsci_settingdict[str, int]Specify the number of shots and the size of the subspace. See the following section for details.YesSee the QSCI setting table
mitigation_settingjsonSettings for configuring error mitigation.NoNoneSee the mitigation section.
max_iterintThe maximum number of iterations when the method is "OPT_QSCI"No20005
backend_namestrThe backend name to useNoThe least busy one available“ibm_torino”
instancestrThe instance to useNo"hub1/group1/project1"
Note

Refer to the Specify an instance in your code guide to learn more.

molecule

Specify the details about the molecule here. The input is the same as the pyscf.gto.M with an additional active_space option. Detailed settings for configuring a molecule are summarized in the following table.

NameTypeDescriptionRequiredDefaultExample
atomstrThe list of atom coordinatesYes-“H 0 0 0; H 0 0 1”
basisstrThe basis set to represent the electronic wave function. Allowed values are the same as those supported by PySCFNo“sto-3g”“sto-3g”
spinfloatThe szs_z quantum number of the molecule. Only spin=0.0 is supportedNo0.00.0
chargeintThe total charge of the moleculeNo00
active_spacejsonThe active space you want to choose. Review the “Active space” table for more informationNoNoneReview the “Active space” table for more information

The active space settings are summarized below.

NameTypeDescriptionRequiredDefaultExample
n_active_eleintThe number of active electronsYes-4
n_active_orbintThe number of active spatial orbitalsYes-3
active_orbs_indiceslist[int]The list of active spatial orbital indicesNoNone[0, 1, 2]

The circuit_options field

The circuit_options field should be a dictionary containing detailed settings of the circuit for running the QSCI algorithm - for example, the state preparation settings. In general it should take this form:

"circuit_options": {
    "ansatz": ...,
    "state_prep_method": ...,
    "ansatz_setting": ...,
}
NameTypeDescriptionRequiredDefaultExample
ansatzstrThe name of the ansatz to use. Only “DoubleExcitation” and “UCCSD” are supported. DoubleExcitation is highly recommended to obtain a stable result, especially for systems larger than eight qubits.Yes“DoubleExcitation”Yes“DoubleExcitation”
state_prep_methodstrHow to prepare the circuit parameter of the ansatz. Only CCSD is allowed.No“CCSD"“CCSD”
ansatz_settingstrSpecific setting to configure the ansatz withNoNoneSee the examples following the table.

Each field is explained in the subsequent sections.

ansatz, state_prep_method and ansatz_setting

The ansatz string specifies the ansatz to use. This specifies a type of parametric circuit without specifying what the concrete circuit parameters are. state_prep_method specifies how the circuit parameter is prepared. Finally, the ansatz_setting lets you customize the ansatz.

AnsatzPreparation methodAnsatz Setting DefaultNote
Double ExcitationCCSD{n_amplitudes: 10}Lets you optimize from the result in the last example.
UCCSDCCSD (default), Random{use_singles: True, n_trotter: 1, reduce_parameter: True}Not recommended for systems with eight or more qubits.
KuCJRandom{k: 1}Recommended for system up to 16 qubits
KUpCCGSDRandom{k: 1, n_trotter: 1, reduce_parameter: False}
Hardware EfficientRandom{n_layers: depends on qubit size}
Caution

When method is "QSCI", only the "CCSD" preparation method is supported. The "Random" preparation method is only supported when method = "OPT_QSCI".

Note

Detailed settings for UCCSD ansatz can be found in the QURI Parts documentation. The reduce_parameter option is the same as the singlet_excitation option in the QURI Parts documentation.

Note

Detailed settings for KUpCCGSD ansatz can be found in the QURI Parts documentation.

qsci_setting

NameTypeDescriptionRequiredExample
n_shotsintThe total number of shots to sample from the ansatzYes100000
number_of_states_pick_outintThe size of the subspace Hamiltonian is RR. It affects the classical resource, where classical diagonalization of the R×RR \times R subspace Hamiltonian is performed if the number of bitstrings (nn) sampled from the ansatz is larger than RR. Otherwise, the n×nn \times n subspace matrix is diagonalized.Yes10000

mitigation_setting

Usually, the problem at hand needs to respect some symmetry, especially particle number and spin conservation. To restore symmetry, use symmetry post-selection or configuration recovery error mitigation. You can choose either of them with the mitigation_setting field in either algorithm. Symmetry post-selection is the default value.

post-selection removes the erroneous states completely, leaving only the basis states to construct the subspace Hamiltonian. This usually saves classical resources, but might miss many states. Configuration recovery attempts to flip individual bits in erroneous basis states with respect to some probability distribution. Using configuration recovery increases the number of basis states to build a larger subspace Hamiltonian, but it uses a lot more classical resources.

The options are explained in the following table.

NameTypeDescriptionRequiredDefault
particle_number_symmetryboolIf True, remove bitstrings that do not respect particle number conservation from sampling result.NoTrue
spin_symmetryboolIf True, remove bitstrings that do not respect szs_z conservation from the sampling result.NoTrue
configuration_recoveryUnion[bool, dict[str, int]]Activate configuration recovery if set to a value other than False. Refer to the configuration recovery section for dict[str, int] inputNoFalse
Caution

You cannot set spin symmetry to True when particle symmetry is False.

Symmetry post-selection

These keys control the symmetry post-selection: particle_number_symmetry and spin_symmetry. Setting particle_number_symmetry to True selects those states that conserve the total electron numbers. Setting spin_symmetry to True selects those states that conserve the szs_z quantum number. Currently only sz=0s_z = 0 is supported. The default is:

mitigation_setting = {
    "particle_number_symmetry": True,
    "spin_symmetry": True,
}

Configuration recovery

Instead of the symmetry post-selection, you can choose to do configuration recovery. To turn it on, set it to True, and optionally customize it with a dictionary containing the following parameters:

NameTypeDescriptionRequiredDefault
n_recover_iterationintThe number of recovery iterations.No5
n_batchintThe number of batches generated per iteration.No1
number_of_states_pick_outint or NoneThe dimension of the QSCI vector in the recovery process. If None, it is set to the same value that was used for QSCI.NoNone
recovery_r_multipleintThe multiplier for number_of_states_pick_out. This is the number of states selected from the raw sample.No10
# Use the default configuration recovery setting
default_mitigation_setting = {"configuration_recovery": True}
 
# Customized configuration recovery setting
customized_mitigation_setting = {
    "configuration_recovery": {
        "n_recover_iteration": 20,
        "n_batch": 10,
        "number_of_states_pick_out": 5000,
    }
}
Caution

Other error mitigations are not allowed when configuration recovery is turned on.

Outputs

The output of the function contains these fields:

NameTypeDescription
qsci_energyfloatThe QSCI energy that acts as the estimation of the ground state energy.
state_vectordictA dictionary representing the QSCI estimated ground state vector.

The state_vector field is a dictionary containing these fields:

NameTypeDescription
bitslist[int]A list of integers representing the electron configurations
realslist[float]Real parts of the amplitudes of the electron configurations at the corresponding positions
imagslist[float]Imaginary parts of the amplitudes of the electron configurations at the corresponding positions

Example

This example shows you how to compute the ground state energy of the water molecule using the QSCI algorithm.

Set up the molecule

First, configure the setting for a H2OH_2O molecule in JSON format. The coordinates of the water molecule can be loaded from OpenFermion.

molecule = {
    "atom": "O 0 0 0; H 0.2774 0.8929 0.2544; H 0.6068 -0.2383 -0.7169",
    "basis": "6-31g",  # default to "sto-3g"
    "spin": 0.0,  # default to 0.0. Current code forces spin = 0.0
    "charge": 0,  # default to 0
    "active_space": {  # default to None. Equivalent to no active space chosen.
        "n_active_ele": 10,
        "n_active_orb": 10,
        "active_orbs_indices": [i for i in range(10)],
    },
}

Execute algorithms

All the function input is in JSON format. You will set up a JSON string that specifies the options for running an algorithm. As stated previously, the two types of algorithms provided are "QSCI" and "OPT_QSCI".

QSCI

First, set up the number of shots and the maximum subspace Hamiltonian size with the qsci_setting field.

qsci_setting = {"n_shots": 1e5, "number_of_states_pick_out": 12000}

Next, set up the ansatz. This example uses the DoubleExcitation as the ansatz because it carries the most non-trivial information with the lowest circuit depth. You can specify how many excitation amplitudes to include with the n_amplitudes key in the ansatz_setting field. The default value is 10. The function sorts the CCSD amplitudes according to their magnitude and chooses the largest n_amplitudes to construct the ansatz. An example JSON dictionary using this ansatz follows:

qsci_double_exc_json = {
    "ansatz": "DoubleExcitation",
    "state_prep_method": "CCSD",  # This is optional with a default of "CCSD".
    "ansatz_setting": {
        "n_amplitudes": 20
    },  # This is optional with a default of {"n_amplitudes": 10}.
}

Turn on the configuration recovery algorithm for error mitigation.

mitigation_setting = {  # Refer to the "Error mitigation" section for details.
    "configuration_recovery": {"number_of_states_pick_out": 10000}
}

Finally, execute the function.

job = function.run(
    method="QSCI",
    molecule=molecule,
    circuit_options=qsci_double_exc_json,
    qsci_setting=qsci_setting,
    mitigation_setting=mitigation_setting,
    instance=instance,  # E.g. "ibm-q/open/main"
    backend_name=backend_name,  # E.g. "ibm_torino"
)

Print out the result from the run:

result = job.result()
print(result)

Output:

{'qsci_energy': -76.05069405129802, 'state_vector': {'bits': [1023, 131583, 66303, 2943, 9087, 9183, 5103, 3039, 9207, 525183, 5055, 525279, 263103, 2031, 3063, 33663, 263151, 133503, 1983, 17391, 139647, 33759, 17343, 5115, 525303, 12543, 6399, 133599, 655743, 139743, 2043, 68079, 196863, 655839, 164223, 3327, 33783, 263163, 264447, 24831, 133623, 164319, 528639, 11103, 70383, 141663, 527199, 37119, 68031, 9471, 18687, 74223, 270591, 328383, 17403, 70335, 67263, 533343, 135663, 139767, 786687, 74175, 655863, 68223, 74367, 14463, 67311, 540927, 525567, 11127, 135615, 328431, 663903, 590271, 6975, 49407, 11223, 590319, 82671, 164343, 35679, 13263, 13215, 70395, 132591, 132543, 98799, 135903, 393663, 295167, 135807, 41823, 68091, 6063, 172383, 657759, 267183, 536703, 7023, 13167, 557919, 132831, 74487, 147903, 7119, 99039, 74463, 82623, 13119, 166239, 3903, 14559, 393855, 3999, 527319, 197583, 529359, 268479, 529263, 264111, 37743, 147951, 35703, 68319, 530655, 265023, 527223, 271263, 590559, 10095, 274671, 197487, 533463, 68343, 6075, 7071, 198879, 67323, 21423, 272511, 141783, 529311, 788607, 28911, 10143, 198783, 590583, 143727, 34047, 529215, 197535, 21483, 265119, 536799, 526287, 25503, 393711, 395583, 132603, 268527, 137631, 557943, 527487, 45183, 74235, 7143, 50031, 141687, 533367, 271167, 37839, 41943, 7035, 41847, 137583, 76239, 148191, 279471, 787407, 13179, 10191, 6123, 530559, 657783, 541503, 132735, 204927, 98751, 7131, 526143, 137535, 26751, 39039, 328443, 18351, 271311, 541599, 25455, 13275, 295791, 14583, 549087, 271215, 135927, 7095, 148095, 663927, 28863, 541551, 98943, 274623, 548991, 82683, 721119, 267195, 21435, 135675, 4047, 200943, 265167, 25551, 19407, 13551, 265071, 664023, 3951, 264123, 794751, 10047, 590463, 37791, 458943, 11487, 295743, 393951, 19311, 25407, 197499, 688479, 99063, 86703, 558039, 303231, 787263, 393975, 137823, 26847, 22767, 143823, 19359, 264171, 76191, 148215, 272607, 39135, 393723, 147963, 57471, 7407, 50079, 526239, 76383, 13503, 13239, 794847, 788703, 145695, 787311, 11391, 590331, 527583, 592335, 787359, 49983, 205023, 271287, 35799, 542943, 98811, 45279, 19323, 197607, 51327, 19383, 4059, 172503, 529275, 529371, 295887, 332463, 37863, 57567, 35967, 267243, 10203, 10215, 72303, 140607, 344751, 140703, 526299, 71343, 790719, 134559, 78255, 271335, 76095, 37695, 25575, 401727, 721023, 166263, 11511, 541659, 529335, 657879, 69183, 659823, 143679, 535383, 526191, 395679, 536823, 72111, 598479, 265083, 78399, 42111, 106911, 18363, 917919, 529383, 15183, 542847, 140895, 591279, 13287, 592287, 197595, 295839, 401871, 533727, 198903, 3963, 200955, 72255, 330399, 78543, 279531, 50127, 197439, 39159, 688503, 34671, 10227, 819423, 659835, 53487, 529599, 852543, 395727, 592191, 271551, 26871, 561375, 134511, 299199, 12063, 598335, 76143, 137679, 299247, 45303, 34767, 279483, 37851, 100767, 401775, 10107, 34719, 47199, 790767, 794871, 106959, 137847, 69039, 7359, 271323, 206943, 397887, 137595, 19263, 168399, 530679, 140751, 265191, 156063, 7155, 541671, 787431, 34623, 541647, 13563, 156015, 533631, 397935, 140655, 115119, 149967, 72351, 4023, 273183, 229599, 86763, 53439, 197559, 10167, 529647, 143739, 172407, 561279, 592479, 573663, 280767, 330303, 917823, 107103, 598623, 803055, 688599, 45855, 78315, 27471, 665943, 69279, 200895, 271599, 303327, 541887, 55503, 803007, 100791, 100839, 787323, 83631, 672063, 136623, 84687, 273231, 397983, 37815, 659919, 106863, 197871, 529395, 659775, 25467, 75183, 526263, 132855, 541623, 594639, 100671, 174423, 18411, 43863, 395631, 796767, 100815, 297087, 296127, 581727, 667983, 102831, 594543, 143967, 143835, 401823, 541935, 168351, 402015, 286911, 15135, 75423, 143847, 531615, 134463, 148911, 265407, 45903, 90735, 789279, 4083, 917967, 134607, 149823, 656751, 71355, 72171, 205047, 787419, 166359, 398031, 199455, 134751, 8079, 229503, 69327, 622959, 201615, 78567, 535647, 397743, 180831, 276543, 199527, 12111, 140763, 149871, 38079, 38127, 149919, 594495, 156255, 592239, 265179, 544959, 156111, 534351, 4071, 659931, 37755, 180687, 594351, 14127, 787695, 526203, 230223, 332475, 84639, 137691, 336303, 156087, 672159, 563295, 531231, 78519, 660063, 545007, 13299, 460863, 25851, 656859, 42207, 145743, 561399, 296175, 819327, 276687, 50415, 287631, 787383, 622911, 329403, 106983, 38703, 180543, 90687, 275367, 672207, 99759, 84591, 329391, 598491, 25563, 25527, 541563, 266127, 295803, 787647, 852399, 549711, 149943, 202863, 394815, 286959, 723039, 403791, 592347, 76155, 14223, 600351, 51447, 180639, 269115, 592359, 395739, 168303, 656991, 136815, 332523, 14235, 149991, 143775, 28923, 29583, 275343, 136767, 15303, 303903, 152271, 22719, 297183, 426447, 623055, 84543, 271611, 330159, 274683, 76503, 110991, 29487, 75243, 533751, 537375, 51423, 42783, 295863, 265203, 19431, 690519, 268539, 526311, 107127, 7419, 47223, 136827, 265143, 23439, 134583, 151983, 336447, 176463, 537663, 25839, 592599, 55407, 368943, 271227, 271347, 428367, 143991, 656703, 199503, 137703, 788727, 573687, 136683, 180591, 537447, 58191, 78447, 721143, 72423, 59487, 917871, 297807, 721695, 527607, 197823, 336543, 672111, 534303, 925983, 103023, 395991, 280815, 672231, 115407, 34779, 19419, 34791, 25791, 623007, 71403, 295911, 209055, 100731, 399663, 528159, 598743, 57591, 545583, 674079, 72123, 207063, 134619, 919839, 36063, 598455, 598383, 75471, 39711, 692559, 80271, 307359, 426303, 553071, 680271, 27423, 266031, 395703, 201531, 221343, 108831, 165471, 606951, 276639, 336495, 394911, 330447, 15195, 106815, 796791, 458991, 268203, 15471, 530319, 594615, 8091, 281391, 69231, 795807, 136863, 303351, 531291, 330351, 551007, 795423, 297759, 198543, 265455, 594591, 656847, 75195, 50103, 410031, 426351, 34743, 19647, 14247, 9213, 526323, 138543, 574287, 209103, 265467, 538719, 209007, 205599, 657111, 143859, 15423, 288927, 789327, 659871, 90783, 426591, 80463, 805023, 796887, 467007, 272631, 206031, 50043, 38139, 361023, 72411, 661851, 807087, 100071, 76407, 562119, 434511, 459003, 106971, 273207, 142623, 560223, 146007, 233679, 558303, 15219, 542967, 23343, 543519, 266043, 22779, 361167, 45975, 205647, 152187, 15207, 90555, 197883, 90543, 39759, 152223, 280827, 213231, 721755, 103035, 541683, 100959, 275403, 337323, 37875, 52059, 156027, 725103, 269199, 528207, 573567, 723159, 426399, 202935, 725055, 397947, 551127, 789399, 819999, 917943, 145719, 165591, 203535, 152175, 144087, 84399, 594663, 180711, 39735, 275631, 12231, 667935, 78495, 661791, 403743, 156123, 467055, 537543, 115311, 104751, 106875, 55359, 170319, 170271, 150111, 344763, 659895, 623079, 624927, 90747, 538743, 799503, 215103, 103095, 460959, 537399, 108879, 819447, 42831, 591471, 92583, 46143, 100719, 530379, 208959, 215199, 336615, 168315, 27855, 852687, 152127, 795543, 330171, 606831, 72375, 549663, 119439, 727119, 558327, 591291, 76251, 165279, 141015, 84711, 19443, 115131, 299919, 72399, 791439, 205659, 151995, 230175, 50991, 76263, 410223, 75495, 102975, 205767, 7983, 3069, 280491, 295923, 658767, 205719, 737391, 753759, 168543, 919887, 199575, 537435, 631119, 44127, 313551, 77391, 534483, 550047, 405903, 168663, 27483, 598503, 558207, 789663, 672219, 137655, 656799, 46239, 103119, 237687, 402039, 600399, 137715, 566103, 395643, 311535, 69099, 594651, 672375, 395871, 273471, 205983, 528327, 137943, 155967, 919911, 23403, 165327, 199887, 792807, 26511, 182631, 36087, 788427, 168411, 599631, 394959, 661911, 275247, 406047, 26523, 531519, 202983, 798951, 614943, 689487, 591423, 167199, 336507, 399903, 80535, 8139, 606927, 231543, 134523, 303951, 410175, 276591, 304083, 59511, 394683, 26475, 140775, 459663, 330423, 918111, 198603, 198555, 269103, 197619, 598515, 58143, 75483, 467127, 213243, 188775, 721815, 136887, 661863, 156135, 463035, 410295, 401787, 398007, 606699, 45879, 14187, 795591, 50163, 791451, 201675, 12123, 795471, 83643, 34683, 165231, 51999, 983199, 206967, 659943, 73131, 201519, 403767, 270219, 658719, 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-9.541030732486924e-05, 3.054619574173801e-05, 1.5463671325285635e-11, -3.055938739998159e-05, -1.5511514017007016e-11, 2.800773299641902e-06, -1.225924088156057e-09, 1.2259156790368839e-09, -0.0005968716260040485, -0.0003456669493577969, -3.139409719589229e-11, 9.35719448667909e-05, 3.7118896006081897e-11, -5.28999292918467e-11, 9.179053453559835e-05, 8.271246575612983e-11, -0.00018520634609095805, 2.93214576683212e-11, -8.552043342278602e-12, 6.510877733915124e-11, -0.0002543117467145152, -0.0001102736957661947, 2.460199771739412e-11, -1.4401170899244096e-11, 0.0001455337804541825, 3.111041943949224e-05, -7.231848537307431e-05, 7.898294807369167e-05, -3.406193510163393e-05, -5.619476670428404e-11, -1.2615077012048177e-10, 5.3669429646808315e-05, -9.226870467319667e-11, -0.0001324648281067364, 3.3323854367918714e-11, 0.0001035639593142253, 1.6300552906960716e-11, -5.090580064638691e-05, 1.4418135710290948e-10, -3.415568415993609e-05, 1.1200352371399826e-10, -1.0394601001926161e-10, -6.965905933514025e-05, 8.683087987951588e-05, 2.3590340314827922e-11, -8.83009318030425e-12, -8.227757761036788e-11, 0.00019779461689454795, 4.447820677870685e-05, 3.481725572629829e-12, 0.00036986967539154753, 7.649649849257777e-11, -2.543941723581303e-11, -0.00029624206392609803, -7.365339771504106e-05, -1.900358756888232e-12, 8.313348589747688e-11, -0.00018530954529882013, -5.415721841943634e-11, 9.16872557835155e-05, 0.00017327734434793268, -7.995185645316653e-12, 3.9013065524794406e-05, 2.956480684691724e-11, -1.1754155071978494e-06, 6.511078410262327e-11, 0.0002541508394766667, -2.5835296535610352e-11, -3.0973420149183026e-11, 9.350925802693954e-05, 1.6427138631033757e-10, -5.622474169791539e-11, 3.130275523077011e-05, -7.224433345424201e-05, 4.476405755644026e-11, -6.47947877409895e-11, 4.985428486805699e-11, 1.5295196602768335e-05, -1.2971929152863143e-05, -6.880885111009792e-05, 1.1265160281421642e-10, -6.959203118452615e-05, 1.44489601425176e-10, -3.416023080320932e-05, 3.183761839071842e-05, -0.00011017450685604003, -3.452561549936053e-05, 9.287950550354598e-11, -0.0001979984788783047, -4.3300178181601385e-11, 1.1725336812655948e-11, -7.369880523585031e-05]}}

Use the "qsci_energy" key to see the QSCI energy:

CASCI_ENERGY = -76.0508056368444  # Exact result
qsci_energy = result["qsci_energy"]
print(f"CASCI energy: {CASCI_ENERGY} Ha")
print(f"QSCI energy: {qsci_energy} Ha")
print(f"Energy error: {(qsci_energy - CASCI_ENERGY) * 1000: .2e} mHa")

Output:

CASCI energy: -76.0508056368444 Ha
QSCI energy: -76.05069405129802 Ha
Energy error:  1.12e-01 mHa

The returned ground state energy estimation of an H2O\text{H}_2 \text{O} molecule is very close to the exact result!

The state_vector field contains three values: bits, reals, and imags. The bits value is a list of integers representing electron configurations. The ii-th position of the reals (imags) field represents the real (imaginary) part of the amplitude of the electron configuration on position ii. You can sort it by magnitude and print out the top 10 most important electron configurations.

import numpy as np
 
amps = np.array(result["state_vector"]["reals"]) + 1j * np.array(
    result["state_vector"]["imags"]
)
sort_idx = np.argsort(np.abs(amps))
 
for i, (bit, real, imag) in enumerate(
    zip(
        np.array(result["state_vector"]["bits"])[sort_idx][::-1],
        np.array(result["state_vector"]["reals"])[sort_idx][::-1],
        np.array(result["state_vector"]["imags"])[sort_idx][::-1],
    )
):
    if i > 20:
        break
    print(
        f"Electron configuration: {bin(bit)[2:].zfill(20)}, "
        f"amplitude: {real + 1j * imag: .3e}, "
        f"magnitude: {real**2 + imag**2: .3e}"
    )

Output:

Electron configuration: 00000000001111111111, amplitude: -6.114e-01+7.731e-01j, magnitude:  9.715e-01
Electron configuration: 00110000000011111111, amplitude:  3.561e-02-4.503e-02j, magnitude:  3.296e-03
Electron configuration: 00000011001111001111, amplitude:  2.643e-02-3.341e-02j, magnitude:  1.815e-03
Electron configuration: 00001100001111001111, amplitude:  1.789e-02-2.262e-02j, magnitude:  8.315e-04
Electron configuration: 00100001000111101111, amplitude: -1.717e-02+2.171e-02j, magnitude:  7.662e-04
Electron configuration: 00010010001011011111, amplitude: -1.713e-02+2.166e-02j, magnitude:  7.623e-04
Electron configuration: 00000001101101101111, amplitude: -1.577e-02+1.994e-02j, magnitude:  6.463e-04
Electron configuration: 00000010011110011111, amplitude: -1.575e-02+1.992e-02j, magnitude:  6.450e-04
Electron configuration: 11000000001111001111, amplitude:  1.548e-02-1.957e-02j, magnitude:  6.228e-04
Electron configuration: 00000000111100111111, amplitude:  1.536e-02-1.942e-02j, magnitude:  6.129e-04
Electron configuration: 00010001001011101111, amplitude:  1.417e-02-1.791e-02j, magnitude:  5.216e-04
Electron configuration: 00100010000111011111, amplitude:  1.404e-02-1.775e-02j, magnitude:  5.120e-04
Electron configuration: 00000000111111001111, amplitude:  1.291e-02-1.632e-02j, magnitude:  4.329e-04
Electron configuration: 00010000101011110111, amplitude: -1.267e-02+1.602e-02j, magnitude:  4.172e-04
Electron configuration: 11000000001100111111, amplitude:  1.266e-02-1.601e-02j, magnitude:  4.166e-04
Electron configuration: 00100000010111111011, amplitude: -1.260e-02+1.593e-02j, magnitude:  4.124e-04
Electron configuration: 10000001001101101111, amplitude: -1.225e-02+1.549e-02j, magnitude:  3.902e-04
Electron configuration: 10010000001001111111, amplitude: -1.222e-02+1.545e-02j, magnitude:  3.878e-04
Electron configuration: 01000010001110011111, amplitude: -1.217e-02+1.538e-02j, magnitude:  3.846e-04
Electron configuration: 01100000000110111111, amplitude: -1.215e-02+1.536e-02j, magnitude:  3.835e-04
Electron configuration: 00001001001111001111, amplitude: -1.141e-02+1.442e-02j, magnitude:  3.381e-04

Optimization-based QSCI

If you don't want to use CCSD as the state preparation method, or if you want to optimize further from the CCSD initial state, you can use the optimization-based QSCI. This algorithm gives you access to more chemistry-inspired ansatz with random initial parameters. For this algorithm, the QSCI energy is used as the cost function for the COBYLA optimizer. In each iteration, the circuit parameters are updated and the QSCI energy is evaluated with the circuit carrying the new set of circuit parameters.

The JSON dictionary used to run this algorithm is similar to that of QSCI. It only contains one additional field, "max_iter", which lets you limit the resource usage. The default is 2000 iterations.

Example of running this algorithm with the 1-uCJ ansatz:

opt_qsci_1ucj_json = {
    "ansatz": "KuCJ",
    "state_prep_method": "RANDOM",  # This is optional with a default of "RANDOM" for "KuCJ".
    "ansatz_setting": {
        "k": 1
    },  # This is optional with the default described in the previous table.
}
opt_job = function.run(
    method="OPT_QSCI",
    molecule=molecule,
    parameters=opt_qsci_1ucj_json,
    qsci_setting={"n_shots": 1e5, "number_of_states_pick_out": 5e4},
    mitigation_setting={
        "configuration_recovery": {"number_of_states_pick_out": 10000}
    },
    max_iter=5,
    instance=instance,  # E.g. "ibm-q/open/main"
    backend_name=backend_name,  # E.g. "ibm_strasbourg"
)

Print out the result.

opt_result = opt_job.result()
print(opt_result)

Output:

{'qsci_energy': -76.05051672600099, 'state_vector': {'bits': [1023, 1983, 2943, 33783, 3039, 263151, 33663, 2031, 5103, 9087, 525183, 33759, 2043, 17343, 9207, 9213, 525279, 17406, 131583, 5115, 525303, 263163, 525309, 17391, 9183, 3063, 263103, 66303, 3069, 2046, 17403, 263166, 5118, 33789, 5055, 67323, 133503, 70335, 264123, 655863, 67263, 279471, 139743, 6138, 67311, 655743, 133599, 139647, 11127, 164223, 267195, 527223, 18411, 18426, 533343, 558039, 82671, 21486, 264111, 267183, 11223, 328443, 328446, 70383, 328431, 35799, 533373, 6063, 527199, 11103, 6126, 21483, 533469, 18363, 279534, 67326, 41847, 533463, 279486, 655839, 533367, 133629, 70398, 11229, 21498, 558045, 11133, 82683, 21423, 41823, 139767, 527319, 35679, 557919, 264126, 164343, 10095, 35703, 267243, 655869, 267198, 21435, 328383, 279531, 527325, 271356, 6075, 18366, 83631, 164349, 264171, 557943, 271311, 83691, 139773, 527229, 6078, 133623, 13215, 82686, 6123, 68319, 41949, 279546, 35805, 21438, 18414, 270591, 279483, 18351, 271323, 13287, 164319, 70395, 264186, 533493, 41853, 557949, 41973, 529371, 82623, 6975, 541563, 541683, 529359, 7038, 196863, 6399, 10215, 529374, 86703, 541659, 527349, 267258, 264174, 295923, 265086, 535389, 141789, 98751, 34779, 295911, 265182, 529263, 25503, 98811, 329391, 41943, 688479, 35829, 283563, 271326, 132591, 393663, 43863, 34671, 37869, 787311, 295167, 13167, 786687, 558069, 50139, 295806, 526206, 74487, 25470, 43893, 172383, 4077, 295899, 135663, 99039, 141663, 37791, 25575, 197595, 657783, 332463, 265143, 74367, 166239, 525567, 4071, 535413, 25455, 264447, 7035, 141693, 11253, 132831, 529215, 10206, 68091, 166365, 657789, 68349, 271230, 526311, 7158, 688599, 10173, 13299, 590271, 3966, 19422, 7023, 19311, 74223, 34743, 10236, 34047, 83646, 19437, 268266, 267246, 25587, 271227, 271167, 13182, 529389, 526263, 657909, 529311, 19323, 4062, 83706, 265203, 344766, 271599, 393723, 3327, 132855, 43869, 25596, 50043, 132735, 529395, 74463, 13278, 4086, 663927, 172413, 7161, 10167, 68223, 787446, 529401, 141687, 83643, 529404, 10227, 35709, 295791, 265197, 540927, 4047, 526287, 37839, 657759, 332478, 526326, 265071, 10203, 135678, 295926, 148191, 590463, 529275, 135933, 526143, 664029, 526239, 172509, 787449, 787383, 50127, 590583, 13302, 13119, 664053, 174423, 329403, 19263, 283566, 541503, 787326, 528639, 332538, 559965, 265023, 197439, 198459, 271287, 50079, 135675, 12543, 559989, 541629, 4089, 172503, 37758, 271347, 37755, 329406, 7149, 788427, 590319, 690549, 74493, 229503, 295887, 665973, 345834, 10047, 37119, 197499, 68094, 265212, 393726, 98799, 135615, 34803, 4083, 10107, 657885, 541677, 34623, 68343, 535383, 4023, 86778, 166263, 197487, 37881, 265167, 135807, 590559, 787443, 4029, 3903, 332523, 688605, 7143, 7101, 7155, 25593, 74235, 13179, 50031, 13308, 143838, 268218, 271350, 295932, 37851, 34683, 90870, 348843, 401790, 541566, 688503, 541689, 526203, 268206, 663933, 25407, 99069, 19407, 7134, 50172, 529278, 3963, 197598, 344811, 19359, 86763, 265206, 25467, 688629, 7095, 135903, 526332, 22446, 197613, 197622, 787407, 295929, 526323, 19431, 34782, 197625, 545595, 19443, 10191, 394941, 666069, 265179, 295863, 25590, 37854, 34809, 526269, 37863, 137583, 9471, 7131, 426363, 83694, 25551, 25527, 147966, 134589, 24831, 795483, 13263, 38778, 426459, 295743, 197607, 50142, 529341, 332526, 344763, 271335, 393975, 688509, 348906, 280494, 37815, 141783, 690519, 197535, 526299, 393855, 344814, 787437, 787263, 295803, 787359, 590334, 132603, 19326, 529398, 663903, 98814, 393711, 136767, 530379, 198606, 52089, 3999, 696693, 329454, 34686, 3951, 132861, 787422, 143967, 590589, 287547, 34791, 140727, 50046, 528183, 36723, 51150, 656823, 533727, 86715, 71418, 19389, 397803, 71355, 541551, 295839, 49407, 147963, 172533, 199605, 213918, 787323, 348858, 10143, 25533, 271215, 271293, 592239, 283578, 49983, 37875, 34749, 50109, 7164, 656871, 19419, 10233, 197502, 271263, 134523, 690645, 591603, 541647, 329466, 397806, 344751, 166269, 143805, 265083, 103023, 46035, 560085, 34806, 134751, 280491, 197628, 200943, 90861, 168429, 10110, 531255, 37878, 527607, 594555, 75258, 528219, 143862, 25566, 12135, 295902, 660087, 789351, 76263, 71403, 333546, 665943, 68079, 296946, 13305, 303927, 541599, 558999, 344826, 19707, 788409, 791358, 272235, 22458, 295917, 265209, 71406, 271341, 141813, 166389, 566133, 268203, 7071, 535509, 345771, 134511, 296826, 13245, 529335, 548991, 172407, 275307, 19446, 99063, 98943, 657879, 794847, 265119, 304083, 143775, 14190, 549711, 336363, 38079, 566103, 38142, 531381, 52179, 459747, 529662, 106971, 38874, 12153, 917943, 69357, 918135, 336606, 287694, 90876, 76281, 545007, 544959, 543699, 795495, 205767, 134643, 10221, 199635, 147951, 721782, 165591, 75423, 42873, 19383, 132543, 197583, 574332, 7995, 330486, 266091, 13275, 918231, 15303, 168318, 205689, 25563, 42111, 526329, 168411, 141021, 558879, 265191, 75183, 541662, 672189, 50157, 13239, 393951, 27510, 336591, 197619, 566109, 166359, 592365, 787431, 393981, 330471, 534303, 789357, 606699, 140790, 52062, 199542, 559065, 287643, 280506, 12111, 541671, 794877, 76215, 591579, 526302, 132606, 558942, 459579, 42855, 401883, 401787, 230358, 590331, 20286, 147903, 84591, 664023, 265149, 135927, 37695, 296763, 197559, 721821, 68031, 90855, 394671, 136926, 591582, 205659, 788334, 545679, 591612, 273567, 205773, 594615, 275247, 534396, 789303, 534429, 299259, 168435, 11391, 659964, 75486, 567153, 100047, 791454, 213822, 538719, 75375, 201579, 330222, 299958, 791802, 819327, 20472, 820023, 199623, 87738, 312243, 143835, 330489, 395679, 360894, 558969, 268539, 272511, 100851, 591279, 537525, 528246, 53439, 69246, 672159, 869043, 69372, 45942, 10230, 536823, 69327, 789462, 38139, 27606, 104046, 312270, 75510, 623031, 562077, 721743, 273273, 311487, 205686, 134619, 788283, 789477, 296934, 104115, 598653, 156135, 559053, 803691, 78459, 459003, 12063, 336495, 20346, 426399, 148221, 299247, 658932, 198633, 330399, 795609, 156015, 297087, 534453, 598647, 53487, 528348, 168567, 12141, 201720, 149883, 594414, 345774, 198507, 272334, 852723, 15483, 562125, 4059, 34767, 72435, 51099, 39159, 852543, 75507, 58206, 592605, 43989, 273372, 537447, 852399, 543705, 19449, 598749, 7119, 269229, 90813, 197565, 559959, 13293, 45183, 78567, 721119, 45915, 266127, 275403, 803055, 201675, 269235, 197823, 14235, 18687, 273267, 13503, 27423, 361167, 394734, 143727, 592311, 803826, 140667, 34797, 137823, 50163, 76275, 54126, 591471, 534366, 115431, 140655, 530286, 852669, 527583, 463086, 72429, 795486, 134775, 345786, 36702, 917919, 852603, 336543, 534381, 136911, 22506, 790767, 156063, 29607, 158031, 526191, 591342, 304092, 303903, 297807, 592350, 795513, 395643, 531291, 69039, 534390, 39711, 149238, 29547, 689757, 722886, 341610, 137973, 19647, 296175, 149967, 639687, 273213, 102975, 656751, 198447, 459630, 199455, 174453, 410355, 12261, 144867, 414123, 45855, 591543, 434646, 115179, 110193, 106998, 541686, 713052, 205662, 39039, 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The returned result has the same fields as the one in the QSCI example.

CASCI_ENERGY = -76.0508056368444  # Exact result
opt_qsci_energy = opt_result["qsci_energy"]
print(f"CASCI energy: {CASCI_ENERGY} Ha")
print(f"QSCI energy: {opt_qsci_energy} Ha")
print(f"Energy error: {(opt_qsci_energy - CASCI_ENERGY) * 1000: .2e} mHa")
print()
print("Top 20 important configurations:")
amps = np.array(opt_result["state_vector"]["reals"]) + 1j * np.array(
    opt_result["state_vector"]["imags"]
)
sort_idx = np.argsort(np.abs(amps))
 
for i, (bit, real, imag) in enumerate(
    zip(
        np.array(opt_result["state_vector"]["bits"])[sort_idx][::-1],
        np.array(opt_result["state_vector"]["reals"])[sort_idx][::-1],
        np.array(opt_result["state_vector"]["imags"])[sort_idx][::-1],
    )
):
    if i > 20:
        break
    print(
        f"Electron configuration: {bin(bit)[2:].zfill(20)}, "
        f"amplitude: {real + 1j * imag: .3e}, "
        f"magnitude: {real**2 + imag**2: .3e}"
    )

Output:

CASCI energy: -76.0508056368444 Ha
QSCI energy: -76.05051672600099 Ha
Energy error:  2.89e-01 mHa

Top 20 important configurations:
Electron configuration: 00000000001111111111, amplitude: -1.934e-01-9.664e-01j, magnitude:  9.713e-01
Electron configuration: 00110000000011111111, amplitude:  1.127e-02+5.629e-02j, magnitude:  3.295e-03
Electron configuration: 00000011001111001111, amplitude:  8.434e-03+4.214e-02j, magnitude:  1.847e-03
Electron configuration: 00001100001111001111, amplitude:  5.640e-03+2.818e-02j, magnitude:  8.258e-04
Electron configuration: 00010010001011011111, amplitude: -5.445e-03-2.721e-02j, magnitude:  7.698e-04
Electron configuration: 00100001000111101111, amplitude: -5.418e-03-2.707e-02j, magnitude:  7.622e-04
Electron configuration: 00000010011110011111, amplitude: -5.053e-03-2.524e-02j, magnitude:  6.628e-04
Electron configuration: 00000001101101101111, amplitude: -5.023e-03-2.510e-02j, magnitude:  6.551e-04
Electron configuration: 00000000111100111111, amplitude:  4.978e-03+2.487e-02j, magnitude:  6.434e-04
Electron configuration: 11000000001111001111, amplitude:  4.918e-03+2.457e-02j, magnitude:  6.280e-04
Electron configuration: 00100010000111011111, amplitude:  4.486e-03+2.241e-02j, magnitude:  5.224e-04
Electron configuration: 00010001001011101111, amplitude:  4.458e-03+2.227e-02j, magnitude:  5.160e-04
Electron configuration: 00000000111111001111, amplitude:  4.109e-03+2.053e-02j, magnitude:  4.383e-04
Electron configuration: 00010000101011110111, amplitude: -4.008e-03-2.002e-02j, magnitude:  4.170e-04
Electron configuration: 11000000001100111111, amplitude:  4.006e-03+2.001e-02j, magnitude:  4.166e-04
Electron configuration: 00100000010111111011, amplitude: -4.002e-03-1.999e-02j, magnitude:  4.157e-04
Electron configuration: 01000010001110011111, amplitude: -3.889e-03-1.943e-02j, magnitude:  3.927e-04
Electron configuration: 01100000000110111111, amplitude: -3.856e-03-1.927e-02j, magnitude:  3.860e-04
Electron configuration: 10010000001001111111, amplitude: -3.856e-03-1.927e-02j, magnitude:  3.860e-04
Electron configuration: 10000001001101101111, amplitude: -3.848e-03-1.923e-02j, magnitude:  3.845e-04
Electron configuration: 00000110001111001111, amplitude:  3.611e-03+1.804e-02j, magnitude:  3.386e-04

Performance

N2 dissociation curve

As a performance benchmark, the 20-qubit N2\text{N}_2 dissociation curve is shown.

N2_dissociation

The red curve in the plot is generated by the QSCI method with the DoubleExcitation ansatz. You can reproduce it by using the following code with different choices of d, the distance between the nitrogen atoms.

d = 1.0
 
job = function.run(
    method="QSCI",
    molecule={"atom": f"N 0 0 0; N 0 0 {d}"},
    parameters={"ansatz": "DoubleExcitation", "state_prep_method": "CCSD"},
    qsci_setting={"n_shots": 100000, "number_of_states_pick_out": 50000},
    mitigation_setting={"configuration_recovery": True},
    instance=instance,  # E.g. "ibm-q/open/main"
    backend_name=backend_name,  # E.g. "ibm_strasbourg"
)

Note that each point typically takes about one minute of QPU usage. On the classical side, where RR is chosen to be 50000, it doesn't necessarily mean that diagonalization of a 50000×5000050000 \times 50000 matrix is done. The number of samples after configuration recovery in this case is approximately 5000 - 7000, which sets the dimension of the subspace Hamiltonian. Thus, the classical diagonalization cost is much smaller than that of typical FCI computation.

The key takeaway of this result is that QSCI with suitable configuration recovery outperforms scalable classical methods such as Hartree-Fock (HF), CCSD, and CISD at all choices of d. This implies that at a scale where FCI energy is no longer available, QSCI serves as a reliable method to estimate the ground state energy at all distances. For example, using the 6-31g basis, a 36-qubit N2\text{N}_2 dissociation curve produced by QURI Function QSCI is given by

N2_dissociation

Here, the FCI curve is not available on a typical laptop (M2 Pro Chip, 16G RAM). However, QSCI can produce a qualitatively correct dissociation curve compared to the classical methods on the same machine with the assistance of the ibm_strasbourg quantum computer.

Azobenzene

Azobenzene has two isomers, trans-azobenzene and cis-azobenzene. The energy difference between the ground states of the two isomers plays an important role in the photoisomerization of azobenzene. This example benchmarks the ground state energy difference between QSCI and FCI with different active space settings up to 28 qubits. With configuration recovery, QURI Function QSCI yields error less than 5 mHa with only 10510^5 shots, 30 to 40 seconds of QPU usage, and under 10 minutes of classical post-processing time per point.

Azobenzene

Support

For running systems larger than 20 qubits, please contact sales@qunasys.com.

Next steps

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