QURI Chemistry: a Qiskit Function by QunaSys

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 functions is summarized in the flow chart below:

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 time a bitstring is sampled represents the importance of that electron configuration. Choose a number, $R$ , to select the $R$ most important electron configurations from the sample. The function constructs and diagonalizes the subspace Hamiltonian, depending on your choice of $R$ . The smallest eigenvalue is termed "QSCI energy", which 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:

[1] :

from qiskit_ibm_runtime import QiskitRuntimeService
from qiskit_ibm_catalog import QiskitFunctionsCatalog
 
token = QiskitRuntimeService.saved_accounts()["default-ibm-quantum"]["token"]
catalog = QiskitFunctionsCatalog(token=token)
 
function = catalog.load("qunasys/quri-chemistry")

Call the function with the following arguments:

function.run(
    method = ...,       # Allow only "QSCI" or "OPT_QSCI"
    parameters = {...}, # A JSON dictionary representing all the algorithm setting
    instance = ...,     # Your instance string.
    backend = ...       # The backend name you want to use.
)

A detailed description of each argument is summarized in the following table.

Name	Type	Description	Required	Default	Example
method	str	The algorithm name	Yes	-	“QSCI”
parameters	json	Details settings of the algorithm	Yes	-
instance	str	Your instance name	No	Your default instance saved on disk	“ibm-q/open/main”
backend	str	The backend name you want to use	No	The least busy one available	“ibm_torino”

Set up the molecule

Here, you will learn how to build a molecule. The input is exactly the same as the pyscf.gto.M with an additional active_space option. The following summarizes the detailed settings for configuring a molecule.

Name	Type	Description	Required	Default	Example
atom	str	The list of atom coordinates	Yes	-	“H 0 0 0; H 0 0 1”
basis	str	The basis set to represent the electronic wave function. Allowed values are the same those supported by PySCF	No	“sto-3g”	“sto-3g”
spin	float	The $s_z$ quantum number of your molecule. Only spin=0.0 is supported	No	0.0	0.0
charge	int	The total charge of your molecule	No	0	0
active_space	json	The active space you want to choose. See the “active space” table that follows for more information	No	None	See the “active space” table that follows for more information

The active space settings are summarized below.

Name	Type	Description	Required	Default	Example
n_active_ele	int	The number of active electrons	Yes	-	4
n_active_orb	int	The number of active spatial orbitals	Yes	-	3
active_orbs_indices	list[int]	The list of active spatial orbital indices	No	None	[0, 1, 2]

As an example, you can configure the setting for a $H_2O$ molecule in JSON format:

[3] :

mole = {
    "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".

QURI Chemistry

In QURI Chemistry, you need to specify an ansatz, its settings, the state preparation method, and the QSCI setting. Typical QSCI input example:

algo_input = {
    "mole": mole,
    "ansatz": ...,
    "state_prep_method": ...,
    "ansatz_setting": ...,
    "qsci_setting": {"n_shots": ..., "number_of_states_pick_out": ...},
    "mitigation_setting": {}
},

Name	Type	Description	Required	Default	Example
mole	json	The molecule setting. See the table for setting molecules above	Yes		The molecule setting. See the table for setting molecules above
ansatz	str	The name of the ansatz you want 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”
state_prep_method	str	The way you want to prepare the circuit parameter of your ansatz. Only CCSD is allowed	No	“CCSD"	“CCSD”
ansatz_setting	str	Specific setting you want to configure your ansatz with	No	None	See the following examples
qsci_setting	dict[str, int]	Specify the number of shots and the size of the subspace. See the following section for details	Yes		See the QSCI setting table
mitigation_setting	json	Settings for configuring error mitigation	No	None	See the mitigation section below

QSCI algorithm parameter

The parameters for setting the QSCI algorithm is summarized in this table.

Name	Type	Description	Required	Example
n_shots	int	The total number of shots to sample from the ansatz	Yes	100000
number_of_states_pick_out	int	Represents the size of the subspace Hamiltonian $R$ . It affects the classical resource, where classical diagonalization of the $R \times R$ subspace Hamiltonian is performed if the number of bitstrings ( $n$ ) sampled from the ansatz is larger than $R$ . Otherwise, the $n \times n$ subspace matrix is diagonalized	Yes	10000

This example demonstrates the following setting:

[4] :

qsci_setting = {"n_shots": 1e5, "number_of_states_pick_out": 1e4}

QURI Chemistry with UCCSD

UCCSD is a common chemistry-inspired ansatz. In the QURI Chemistry function, you can customize it with the ansatz_setting key. Options for customizing UCCSD is summarized in the table.

Name	Type	Description	Required	Default	Example
use_singles	bool	If True, all the single excitation modes are included. Otherwise, they are all turned off	No	True	True
n_trotter	int	The number of Trotter steps for the exponentiated excitation operator	No	1	1
reduce_parameter	bool	Only True is allowed for QSCI. refer to the `singlet_excitation` field in the QURI Parts documentation	No	True	True

A dictionary for running QURI Chemistry with UCCSD:

[ ] :

qsci_uccsd_json = {
    "mole": mole,
    "ansatz": "UCCSD",
    "state_prep_method": "CCSD",    # this is optional and defaulted to "CCSD".
    "ansatz_setting": {"use_singles": False},   # this is optional and defaulted to the list above.
    "qsci_setting": {"n_shots": 1e5, "number_of_states_pick_out": 1e4},
}

QURI Chemistry with double excitation ansatz

When DoubleExcitation is chosen as the ansatz, 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 for constructing the ansatz. An example JSON dictionary using this ansatz follows:

[5] :

qsci_double_exc_json = {
    "mole": mole,
    "ansatz": "DoubleExcitation",
    "state_prep_method": "CCSD",    # this is optional and defaulted to "CCSD".
    "ansatz_setting": {"n_amplitudes": 20}, # this is optional and defaulted to {"n_amplitudes": 10}.
    "qsci_setting": {"n_shots": 1e5, "number_of_states_pick_out": 5e4},
    "mitigation_setting": {     # please refer to the "error mitigation" section of this tutorial.
        "configuration_recovery": {
            "number_of_states_pick_out": 10000
        }
    }
}

Execute QSCI

Example of running the QSCI algorithm:

[30] :

import datetime
import time
job = function.run(
    method="QSCI",
    parameters=qsci_double_exc_json,
    instance="INSTANCE",
    backend="ibm_strasbourg",
)
 
while True:
    try:
        print(datetime.datetime.now(), job.status())
        time.sleep(10)
        if job.status() in ["ERROR", "DONE"]:
            break
    except:
        print("Retrieve job status failed.")
        pass
 
result = job.result()

Output:

2024-08-27 23:01:36.090958 QUEUED
2024-08-27 23:01:49.358961 QUEUED
2024-08-27 23:02:02.713788 QUEUED
2024-08-27 23:02:15.481531 RUNNING
2024-08-27 23:02:28.200317 RUNNING
2024-08-27 23:02:41.446378 RUNNING
2024-08-27 23:02:54.563686 RUNNING
2024-08-27 23:03:07.706745 RUNNING
2024-08-27 23:03:20.400988 RUNNING
2024-08-27 23:03:33.708046 RUNNING
2024-08-27 23:03:46.656525 RUNNING
2024-08-27 23:03:59.385160 RUNNING
2024-08-27 23:04:12.528769 RUNNING
2024-08-27 23:04:25.625868 RUNNING
2024-08-27 23:04:38.718299 RUNNING
2024-08-27 23:04:51.828514 RUNNING
2024-08-27 23:05:04.745142 RUNNING
2024-08-27 23:05:17.727985 RUNNING
2024-08-27 23:05:31.061746 RUNNING
2024-08-27 23:05:43.821970 RUNNING
2024-08-27 23:05:56.897187 RUNNING
2024-08-27 23:06:10.088404 RUNNING
2024-08-27 23:06:22.959995 RUNNING
2024-08-27 23:06:35.873720 RUNNING
2024-08-27 23:06:48.798231 RUNNING
2024-08-27 23:07:02.731781 RUNNING
2024-08-27 23:07:15.819290 RUNNING
2024-08-27 23:07:29.360154 RUNNING
2024-08-27 23:07:42.341557 RUNNING
2024-08-27 23:07:55.720916 RUNNING
2024-08-27 23:08:09.072428 RUNNING
2024-08-27 23:08:22.077443 RUNNING
2024-08-27 23:08:35.038400 RUNNING
2024-08-27 23:08:47.958711 RUNNING
2024-08-27 23:09:00.828232 RUNNING
2024-08-27 23:09:14.713651 RUNNING
2024-08-27 23:09:28.076111 RUNNING
2024-08-27 23:09:41.481971 RUNNING
2024-08-27 23:09:54.650976 RUNNING
2024-08-27 23:10:07.775569 RUNNING
2024-08-27 23:10:20.951318 RUNNING
2024-08-27 23:10:33.815651 RUNNING
2024-08-27 23:10:46.684406 RUNNING

You can print out the result from the run:

[41] :

print(result)

Output:

{'qsci_energy': -76.05077853515165, 'state_vector': {'bits': [1023, 131583, 3039, 3063, 2943, 33663, 263163, 9087, 2043, 33759, 66303, 525183, 263151, 17403, 2031, 525303, 263103, 9207, 1983, 5115, 33783, 9183, 5055, 5103, 17343, 17391, 525279, 139647, 70383, 18411, 67311, 164319, 139767, 655839, 164343, 655743, 267243, 527319, 6123, 533367, 133623, 11127, 41847, 279531, 82683, 67263, 533343, 82671, 133503, 264171, 11103, 35703, 41823, 67323, 527199, 164223, 133599, 35679, 393855, 328383, 533463, 264111, 328431, 279483, 267183, 132735, 21483, 139743, 557919, 328443, 265083, 18351, 41943, 35799, 132591, 557943, 141687, 11223, 197595, 21423, 50043, 527223, 655863, 21435, 279471, 558039, 82623, 6075, 6063, 98943, 70335, 70395, 141663, 25455, 265179, 10107, 6399, 267195, 393723, 148191, 197583, 197439, 7131, 18363, 295923, 3963, 535383, 265203, 25407, 526239, 329403, 264447, 590331, 196863, 270591, 688503, 526287, 344763, 25467, 19359, 787323, 148095, 132855, 43863, 34047, 393951, 265071, 197619, 197535, 83691, 264123, 166263, 787407, 4047, 19323, 86763, 74463, 541563, 7155, 174423, 393975, 34803, 19263, 265023, 526191, 271335, 265119, 10227, 13179, 541551, 34767, 74367, 166239, 3903, 7035, 99039, 71355, 71343, 68343, 135675, 295911, 148215, 295803, 271227, 657759, 541659, 332523, 135807, 526299, 295791, 566103, 688479, 526203, 37875, 787431, 6975, 98751, 3327, 13215, 68091, 19419, 590463, 271167, 197607, 271347, 528639, 526323, 7023, 74487, 657879, 132831, 166359, 22443, 74235, 74223, 786687, 329391, 393711, 132543, 590319, 271215, 7143, 230247, 132603, 197487, 34623, 83643, 657783, 295743, 265143, 3999, 329451, 590271, 68319, 147963, 49983, 265191, 172503, 10047, 295887, 197559, 71403, 49407, 34671, 135927, 529275, 10191, 9471, 590559, 4071, 19311, 787419, 213963, 265167, 393663, 280491, 135903, 10095, 147903, 13167, 34743, 18687, 147951, 13275, 24831, 4083, 68223, 787359, 13299, 135663, 98799, 68031, 19407, 690519, 98811, 10215, 271263, 663927, 664023, 230223, 12543, 50031, 197499, 526311, 271323, 172383, 25575, 526263, 37755, 135615, 37119, 787383, 83631, 663903, 50139, 295863, 90603, 266091, 787263, 13263, 37743, 37851, 34779, 8043, 34683, 50079, 295839, 25563, 50103, 50127, 19695, 525567, 25527, 141783, 25551, 68079, 7095, 100071, 559959, 10143, 688599, 213867, 3951, 13119, 19431, 283563, 787311, 74175, 25503, 10203, 50163, 34791, 140607, 198603, 86703, 665943, 541671, 19707, 529395, 99063, 198447, 529359, 410271, 34719, 590583, 37815, 332475, 344811, 529335, 295167, 789327, 574311, 344751, 134751, 917871, 395871, 541683, 86715, 4059, 268203, 25587, 13239, 526143, 19443, 198783, 165351, 165495, 312219, 199503, 558963, 100839, 27471, 7119, 591339, 529371, 426459, 72303, 201519, 12147, 10167, 541599, 149871, 58203, 100719, 548991, 541647, 533631, 271287, 137535, 149115, 311547, 26475, 395991, 201579, 295899, 201531, 266151, 397887, 541503, 530355, 345771, 529383, 75387, 7071, 13287, 271311, 69243, 69351, 426483, 297087, 156255, 37863, 99963, 272631, 459627, 150135, 672123, 75327, 37791, 158031, 197883, 156111, 12111, 149055, 458991, 100983, 272175, 134583, 395895, 134559, 426615, 4023, 199539, 143727, 140919, 50151, 172407, 529263, 402015, 395763, 149103, 787695, 269115, 395643, 180855, 395583, 76263, 656799, 787443, 45927, 136935, 410331, 852687, 272607, 180831, 819447, 558303, 229503, 265467, 152127, 330351, 140763, 167379, 75483, 50415, 531303, 99999, 529311, 205023, 52023, 529215, 395751, 136815, 540927, 265407, 394983, 205779, 401775, 168663, 789363, 311487, 394995, 394863, 303975, 401883, 199623, 7419, 11391, 622971, 394875, 542691, 545715, 20367, 394731, 534387, 173415, 398055, 287595, 165243, 598431, 19383, 148971, 143847, 69231, 410043, 15315, 197871, 273183, 672351, 180603, 213915, 198555, 134463, 426591, 149223, 87723, 299883, 273267, 598623, 401727, 721743, 606927, 149979, 69099, 38823, 280815, 149151, 85563, 134523, 198627, 394671, 143835, 156147, 15219, 199575, 205647, 14463, 156027, 274683, 273255, 459687, 395727, 152175, 165183, 26535, 541623, 535647, 140703, 529659, 394959, 78459, 152307, 721767, 410175, 917991, 213927, 542847, 180711, 42867, 100731, 84723, 213243, 591423, 84699, 52083, 152187, 37695, 794871, 107103, 165327, 75375, 140655, 75495, 199515, 150111, 332463, 42783, 348843, 72315, 12135, 696663, 789303, 788283, 26595, 545643, 168303, 269223, 531231, 788703, 659775, 337467, 273231, 269211, 594663, 140775, 542571, 42207, 200955, 459723, 29547, 273303, 534363, 286959, 99903, 591471, 272295, 207687, 275403, 197823, 527607, 42231, 76143, 205659, 983859, 168435, 137595, 398043, 26847, 558207, 803787, 152295, 27423, 140895, 13551, 336447, 136683, 205623, 330399, 303987, 14283, 402039, 622911, 13503, 26751, 27495, 303351, 528219, 36663, 205671, 917967, 397935, 269199, 180723, 84603, 280827, 528243, 213819, 199455, 8163, 592503, 528207, 917979, 545019, 606951, 134631, 140727, 213807, 459567, 721755, 397983, 297783, 134643, 360879, 401895, 297759, 108891, 917943, 426303, 336603, 788607, 312111, 361167, 156015, 530283, 658767, 78255, 789459, 403815, 11487, 275259, 558903, 90555, 22719, 330447, 542967, 156087, 231183, 23343, 90735, 51999, 36723, 530223, 672375, 39135, 88779, 721815, 200943, 426711, 336495, 75447, 296763, 296907, 57471, 852603, 852591, 275307, 38859, 269163, 136827, 168255, 788271, 58191, 29595, 426447, 103143, 106863, 85551, 297843, 143799, 594495, 52047, 659835, 819423, 803643, 591579, 803691, 36759, 106959, 656871, 76239, 296175, 721023, 7995, 549687, 137655, 534375, 791403, 149991, 136767, 531279, 27507, 58167, 333483, 198567, 296187, 411243, 213183, 150003, 152271, 426399, 721143, 189015, 230235, 100023, 428631, 115263, 167511, 594411, 303327, 143739, 168399, 820047, 143859, 101079, 336507, 201627, 820119, 77511, 753759, 198579, 299259, 84711, 410031, 57567, 165591, 272187, 562023, 20379, 543603, 563295, 330363, 149175, 287535, 410343, 795423, 401871, 336591, 170355, 205947, 76383, 397947, 395703, 658887, 51087, 58323, 659943, 100083, 397803, 137943, 51423, 39735, 674079, 76407, 530679, 198507, 167367, 296859, 401787, 950643, 54159, 42111, 23403, 75471, 115383, 76095, 199635, 542607, 78579, 536703, 427635, 51051, 103119, 394815, 28911, 287715, 14559, 533727, 69339, 103035, 198879, 672207, 14187, 281451, 360939, 232275, 820083, 144087, 42963, 38763, 27483, 102975, 721695, 149199, 100791, 137679, 592191, 213903, 789339, 69279, 336615, 594555, 346683, 78267, 50991, 51111, 459663, 549663, 201651, 401823, 361071, 37839, 42951, 395739, 36711, 534351, 50427, 27603, 14235, 201615, 39159, 399783, 90867, 211155, 304971, 14583, 69327, 115323, 536799, 657111, 918111, 656703, 134871, 134511, 919839, 273615, 803631, 427719, 291051, 168543, 116379, 272331, 660063, 549111, 47895, 299931, 545595, 721983, 459747, 234255, 531315, 15423, 39759, 298143, 26571, 231519, 268479, 658803, 45939, 39831, 20283, 362163, 188787, 160467, 26511, 103155, 100959, 287643, 537375, 592287, 527583, 22767, 205047, 117099, 134607, 188775, 15207, 795543, 72111, 395679, 721119, 180639, 401907, 230259, 426471, 184863, 234339, 274623, 574287, 287547, 543567, 28863, 136923, 820071, 7983, 591603, 205767, 459675, 76503, 42843, 672063, 99951, 394971, 137583, 106911, 230175, 541935, 623199, 36699, 592251, 549087, 12231, 215823, 36807, 155967, 35967, 820059, 107127, 549711, 165471, 152283, 275247, 592347, 404055, 330219, 561279, 530331, 23355, 545763, 25791, 23439, 530559, 721719, 723063, 459579, 180699, 198903, 459699, 136887, 58143, 397743, 45855, 45879, 148923, 200895, 461019, 394935, 58311, 301179, 153231, 156375, 658791, 656859, 722127, 661875, 491763, 141015, 729927, 214827, 8139, 231267, 153255, 528159, 213939, 622959, 442683, 51099, 704919, 142647, 137703, 434463, 852711, 19647, 102843, 807723, 137823, 266127, 173391, 659919, 461763, 232263, 269259, 85707, 606939, 550011, 94635, 215907, 791787, 154215, 230199, 230355, 75195, 169359, 115311, 266187, 593499, 20403, 598743, 426363, 54123, 182631, 215259, 54507, 562035, 156135, 791499, 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-2.0620818415554217e-11, 4.047193064858568e-05, -5.2394529339616075e-06, 2.310504362764662e-06, -4.4698476666846376e-11, -0.0002784922027604092, 4.853571399615967e-12, -9.208787896130126e-13, 3.7140558079825307e-06, -4.386948491320108e-12, -3.534971991537902e-11, -4.659127102538709e-06, 4.371839991447424e-08, -4.058131080404112e-05, 4.041982964368624e-11, -1.380288887211012e-11, -1.011559424814583e-06, -9.532184765520113e-11, -4.639675921276945e-11, -1.1324022980787864e-09, 7.751466532515781e-11, -5.805760825387381e-06, -4.988259179029357e-11, 4.5873192844598096e-08, -1.5255871137440962e-11, 4.7716567025461156e-11, -4.410693280286326e-06, 3.384234495657588e-05, -2.206363529811746e-08, 4.472425649396903e-07, -6.190928605640262e-13, -2.088555779892738e-05, -1.8870077979689036e-12, 8.219285259711854e-12, -3.960076970698413e-06, 8.122588646740704e-05, 4.61523696411709e-11, 2.484132185866386e-08, -8.103386423814208e-07, -3.282336954598928e-11, 3.7777728370177037e-07, -9.75974130616127e-07, -4.3885592407813645e-12, -1.0785712375518336e-06, 8.952711617727018e-05, -0.00014135659478841658, 1.7959950197641953e-11, -6.921363370800604e-11, 0.00021085095601651102, -1.8019205031906847e-11, 6.925015068765851e-11, -0.00021084182387660222, -9.880863249199306e-05, 3.1627870919492185e-05, 1.6143874981541312e-11, -3.166771274872585e-05, -1.6157859723873765e-11, 2.951369546414511e-06, -1.2704529728731665e-09, 1.270508452653431e-09, -0.000618467218152875, -0.00035818873930901164, -2.51665182110114e-11, 2.0417176074203426e-05, -4.347260079118874e-12, -4.801934042904417e-05, 4.044075031405339e-05, 3.070477575317882e-11, -6.090401399641853e-05, -8.641201369235034e-12, 1.4645389228612985e-06, 6.776146783085193e-11, -0.000553427822649513, 2.5630800617655394e-11, 0.00015093564902808967, -7.480099265027651e-05, 4.675513612730203e-11, 8.186724139260635e-05, 5.1084659381866076e-11, 1.582028023662844e-05, -6.739818480588933e-11, -9.459947901873748e-11, -1.3383801918034959e-05, -0.00013745477919467034, -2.5695726760813725e-11, 0.00010788444276538016, -3.549914294217215e-05, -7.222976991660531e-05, 9.005089324669424e-05, -0.0001139342394683422, 2.4720214187889084e-11, 3.300878598354061e-05, -8.298073895718403e-12, 3.569284985785835e-05, -8.435478949335761e-11, 4.6509644865551134e-05, -6.084494054224754e-11, 0.0003837615051845544, -0.00027947082208384634, -2.5533919980999483e-11, 1.1960820222842184e-11, -0.00030694487724480254, 3.9149814860970686e-11, 0.0001795011112941255, -6.078293223557838e-05, -8.553080415845784e-12, 4.0538039711532894e-05, 3.055581833488156e-11, 6.745677791859861e-11, -5.607061182628839e-11, 2.0448012886922793e-05, -3.796453602553546e-12, 1.6925502474314435e-10, 8.181343646604791e-05, -3.531195127828667e-05, -5.86451447122632e-11, 3.2211593600277175e-05, -7.489185422952422e-05, 1.3099830305679585e-10, -6.78361704466336e-11, 5.179969308808939e-11, 1.5859956995522072e-05, 9.39903588383956e-11, -3.474769878351711e-11, -0.00011436479385821033, 2.5501012166629397e-11, -7.146362504903478e-05, 5.2955397641808184e-05, 1.1584010105088123e-10, -1.0782689927956465e-10, -7.219044410904031e-05, -6.891900656017862e-11, 1.492378090446776e-10, -9.002383810038543e-05, 3.298982191774063e-05, -8.785877717804639e-12, 2.5293395221351567e-11, 9.752011212880049e-11, -0.00020502843108378014, -4.613040502578271e-05, -9.251988508181929e-05, 7.76006164133319e-11, -7.645812652445647e-05, -6.038015457875619e-11, 3.770776007216538e-12, 0.0003833563054196569]}}

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

[48] :

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: -76.05077853515165 Ha
Energy error:  2.71e-02 mHa

The returned ground state energy estimation of an $\text{H}_2 \text{O}$ 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 $i$ -th position of the reals (imags) field represents the real (imaginary) part of the amplitude of the electron configuration on position $i$ . You can sort it by magnitude and print out the top 10 most important electron configurations.

[66] :

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: -7.671e-01+6.185e-01j, magnitude:  9.710e-01
Electron configuration: 00110000000011111111, amplitude:  4.492e-02-3.622e-02j, magnitude:  3.330e-03
Electron configuration: 00000011001111001111, amplitude:  3.379e-02-2.724e-02j, magnitude:  1.884e-03
Electron configuration: 00001100001111001111, amplitude:  2.247e-02-1.812e-02j, magnitude:  8.333e-04
Electron configuration: 00100001000111101111, amplitude: -2.172e-02+1.751e-02j, magnitude:  7.780e-04
Electron configuration: 00010010001011011111, amplitude: -2.171e-02+1.750e-02j, magnitude:  7.775e-04
Electron configuration: 00000001101101101111, amplitude: -2.006e-02+1.617e-02j, magnitude:  6.637e-04
Electron configuration: 00000010011110011111, amplitude: -2.005e-02+1.617e-02j, magnitude:  6.636e-04
Electron configuration: 00000000111100111111, amplitude:  1.980e-02-1.596e-02j, magnitude:  6.467e-04
Electron configuration: 11000000001111001111, amplitude:  1.950e-02-1.572e-02j, magnitude:  6.275e-04
Electron configuration: 00010001001011101111, amplitude:  1.782e-02-1.437e-02j, magnitude:  5.242e-04
Electron configuration: 00100010000111011111, amplitude:  1.781e-02-1.436e-02j, magnitude:  5.233e-04
Electron configuration: 00000000111111001111, amplitude:  1.632e-02-1.316e-02j, magnitude:  4.396e-04
Electron configuration: 00010000101011110111, amplitude: -1.592e-02+1.284e-02j, magnitude:  4.183e-04
Electron configuration: 00100000010111111011, amplitude: -1.592e-02+1.284e-02j, magnitude:  4.183e-04
Electron configuration: 11000000001100111111, amplitude:  1.590e-02-1.282e-02j, magnitude:  4.171e-04
Electron configuration: 10000001001101101111, amplitude: -1.544e-02+1.245e-02j, magnitude:  3.935e-04
Electron configuration: 01000010001110011111, amplitude: -1.542e-02+1.243e-02j, magnitude:  3.925e-04
Electron configuration: 01100000000110111111, amplitude: -1.534e-02+1.237e-02j, magnitude:  3.882e-04
Electron configuration: 10010000001001111111, amplitude: -1.532e-02+1.235e-02j, magnitude:  3.874e-04
Electron configuration: 00001001001111001111, amplitude: -1.439e-02+1.160e-02j, magnitude:  3.418e-04

Optimization-based QSCI

If you don't want to use CCSD as the state preparation method, or 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. The following is a table of ansatz and their corresponding supported state preparation methods:

Ansatz	Preparation method	Ansatz Setting Default	Note
Double Excitation	CCSD	`{n_amplitudes: 10}`	Lets you optimize from the result in the last example
UCCSD	CCSD (default), Random	`{use_singles: True, n_trotter: 1, reduce_parameter: True}`	Not recommended for systems with eight or more qubits
KuCJ	Random	`{k: 1}`	Recommended for system up to 16 qubits
KUpCCGSD	Random	`{k: 1, n_trotter: 1, reduce_parameter: False}`
Hardware Efficient	Random	`{n_layers: depend on qubit size}`

If you don't specify the preparation method and the ansatz setting, default values are used. 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 contains one additional field, "max_iter", for limiting the resource usage. The default is 2000 iterations.

The follwing is an example of running this algorithm with the 1-uCJ ansatz:

[86] :

opt_qsci_1ucj_json = {
    "mole": mole,
    "ansatz": "KuCJ",
    "state_prep_method": "RANDOM",  # this is optional and defaulted to "RANDOM" for "KuCJ".
    "ansatz_setting": {"k": 1},     # this is optional and defaulted to the table above.
    "qsci_setting": {
        "n_shots": 1e5, "number_of_states_pick_out": 5e4
    },
    "max_iter": 5,                  # Default to 2000. Choose 5 iteration for demonstration.
    "mitigation_setting": {         # Refer to the "error mitigation" section.
        "configuration_recovery": {
            "number_of_states_pick_out": 10000
        }
    }
}

[ ] :

import time
opt_job = function.run(
    method="OPT_QSCI",
    parameters="opt_qsci_1ucj_json",
    instance="ibm_strasbourg",
)
start = time.time()
 
while True:
    try:
        print(datetime.datetime.now(), opt_job.status())
        time.sleep(10)
        if opt_job.status() in ["ERROR", "DONE"]:
            break
    except:
        print("Retrieve job status failed.")
        pass
 
opt_result = opt_job.result()

You can print out the result.

[80] :

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, 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1.6388625144058112e-06, -8.971303674548776e-13, 1.4899076943777008e-08, -1.1235372415331323e-06, -2.436048189241456e-12, -3.6706298376206096e-07, -2.3945600982112606e-12, -7.3383601444916644e-09, 5.970878264571742e-07, -2.4356241649766475e-12, -7.897573582142336e-05, 1.0780066075746075e-10, -2.309537118929899e-06, 9.322513610090804e-11, 5.056223081269228e-11, 2.691437093584705e-12, 2.1811550205874504e-11, 4.4314451651603185e-07, 8.396471096006516e-10, 2.4578189123986272e-06, 1.2991959129870485e-09, -1.2425438777719932e-12, -1.489694161038826e-07, -5.535710037002405e-07, 3.620752443720627e-11, 6.089153483783467e-13, 1.1154095989605927e-07, 1.3415454510859514e-10, -1.97978458066399e-11, -1.396106558508142e-07, -7.06500506973941e-13, 4.864507991233162e-11, -1.117288266315848e-06, 1.3873546634845525e-05, -2.44744147475109e-10, 7.067757576930161e-13, 1.3093818573205843e-07, 1.3100880249671438e-12, 3.973076339425331e-07, -1.0378597893553206e-06, -1.6934483802036148e-08, 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3.590421991769529e-12, 5.342580808419347e-12, 2.009879912147823e-12, -4.134176023637082e-10, 6.976602234041744e-08, -3.952966936331898e-09, -6.356303066884324e-12, 2.180964288080103e-08]}}

The returned result has the same fields as the one in the QSCI example.

[91] :

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

Error mitigation

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.

Name	Type	Description	Required	Default
particle_number_symmetry	bool	If True, remove bitstrings that do not respect particle number conservation from sampling result	No	TRUE
spin_symmetry	bool	If True, remove bitstrings that do not respect $s_z$ conservation from sampling result.	No	TRUE
configuration_recovery	Union[bool, dict[str, int]]	Activate configuration recovery if set to values other than False. Refer to the configuration recovery section for dict[str, int] input	No	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 $s_z$ quantum number. Currently, only $s_z = 0$ is supported. The default is:

[ ] :

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

Note

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

Configuration recovery

Instead of the symmetry post-selection, you can also choose to do configuration recovery. The most general sets of configuration recovery are summarized in the table below.

Name	Type	Description	Required	Default
n_recover_iteration	int	The number of recovery iterations	No	5
n_batch	int	The number of batches generated per iteration	No	1
number_of_states_pick_out	int or None	The dimension of the QSCI vector in the recovery process. If None, it is set to the same as the value used for QSCI	No	None
recovery_r_multiple	int	The multiplier for number_of_states_pick_out. This is the number of states selected from the raw sample	No	10

To activate configuration recovery, specify configuration_recovery = True in the error mitigation field, or customize any of the above fields. For example:

[ ] :

# Use default configuration recovery setting
default_mitigation_setting = {
    "mitigation_setting": {
        "configuration_recovery": True
    }
}
 
# Customized configuration recovery setting
customized_mitigation_setting = {
    "mitigation_setting": {
        "configuration_recovery": {
            "n_recover_iteration": 20,
            "n_batch": 10,
            "number_of_states_pick_out": 5000
        }
    }
}

Note

You cannot enable any other mitigation methods when configuration_recovery is turned on.

Performance

$\text{N}_2$ dissociation curve

As a performance benchmark, we provide the 20-qubit $\text{N}_2$ dissociation curve as a demonstration.

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

[ ] :

d = 1.0
n2_dissociation_qsci = {
    "mole": {"atom": f"N 0 0 0; N 0 0 {d}",},
    "ansatz": "DoubleExcitation",
    "state_prep_method": "CCSD",
    "qsci_setting": {
        "n_shots": 100000, "number_of_states_pick_out": 50000
    },
    "mitigation_setting": {
        "configuration_recovery": True
    },
}
job = function.run(
    method="QSCI",
    parameters=n2_dissociation_qsci,
    backend="ibm_strasbourg"
)

Note that each point typically takes about one minute of QPU usage. On the classical side, while $R$ is chosen to be 50000, it doesn't necessarily mean that diagonalization of a $50000 \times 50000$ matrix is done. The number of samples after configuration recovery in this case is approximately 5000 to 7000, which sets the dimension of the subspace Hamiltonian. Thus, the classical diagonalization cost is much smaller than that of typical full configuration interaction (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 $\text{N}_2$ dissociation curve produced by QURI Chemistry is given by

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. As an example, we benchmark the ground state energy difference between QSCI and FCI, with different active space settings up to 28 qubits. With configuration recovery, QURI Chemistry yields error under 5 mHa with only $10^5$ shots, 30 to 40 seconds of QPU usage, and under 10 minutes of classical post-processing time per point.

Support

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

Next steps

Recommendations

QURI Chemistry: a Qiskit Function by QunaSys

Overview

Function description

Get started

Set up the molecule

Execute algorithms

QURI Chemistry

QSCI algorithm parameter

QURI Chemistry with UCCSD

QURI Chemistry with double excitation ansatz

Execute QSCI

Optimization-based QSCI

Error mitigation

Symmetry post-selection

Configuration recovery

Performance

N2\text{N}_2N2​ dissociation curve

Azobenzene

Support

Next steps

$\text{N}_2$ dissociation curve