1.2 Entanglement Entropy by Randomized Measurement#
Basic Usage#
a. Import the instances#
from qurry import EntropyMeasure
experiment_randomized = EntropyMeasure()
# It's default method. EntropyMeasure(method='randomized') also works
b. Preparing quantum circuit#
from qiskit import QuantumCircuit
from qurry.recipe import TrivialParamagnet, GHZ
sample01 = TrivialParamagnet(8)
print("| trivial paramagnet in 8 qubits:")
print(sample01)
| trivial paramagnet in 8 qubits:
┌───┐
q_0: ┤ H ├
├───┤
q_1: ┤ H ├
├───┤
q_2: ┤ H ├
├───┤
q_3: ┤ H ├
├───┤
q_4: ┤ H ├
├───┤
q_5: ┤ H ├
├───┤
q_6: ┤ H ├
├───┤
q_7: ┤ H ├
└───┘
sample02 = GHZ(8)
print("| GHZ in 8 qubits:")
print(sample02)
| GHZ in 8 qubits:
┌───┐
q_0: ┤ H ├──■────────────────────────────────
└───┘┌─┴─┐
q_1: ─────┤ X ├──■───────────────────────────
└───┘┌─┴─┐
q_2: ──────────┤ X ├──■──────────────────────
└───┘┌─┴─┐
q_3: ───────────────┤ X ├──■─────────────────
└───┘┌─┴─┐
q_4: ────────────────────┤ X ├──■────────────
└───┘┌─┴─┐
q_5: ─────────────────────────┤ X ├──■───────
└───┘┌─┴─┐
q_6: ──────────────────────────────┤ X ├──■──
└───┘┌─┴─┐
q_7: ───────────────────────────────────┤ X ├
└───┘
sample03 = QuantumCircuit(8)
sample03.x(range(0, 8, 2))
print("| Custom circuit:")
print(sample03)
| Custom circuit:
┌───┐
q_0: ┤ X ├
└───┘
q_1: ─────
┌───┐
q_2: ┤ X ├
└───┘
q_3: ─────
┌───┐
q_4: ┤ X ├
└───┘
q_5: ─────
┌───┐
q_6: ┤ X ├
└───┘
q_7: ─────
c. Execute the circuit#
i. Directly input the circuit#
After executing, it will return a uuid of experiment. You can use this uuid to get the result of the experiment.
exp1 = experiment_randomized.measure(sample01, times=100, shots=4096)
exp1
'9f38a452-20c8-4ee4-9454-aca9dbdf7a67'
Each experiment result will be stored in a container .exps.
experiment_randomized.exps[exp1]
<EntropyMeasureRandomizedExperiment(exp_id=9f38a452-20c8-4ee4-9454-aca9dbdf7a67,
EntropyMeasureRandomizedArguments(exp_name='experiment.N_U_100.qurrent_randomized', times=100, qubits_measured=[0, 1, 2, 3, 4, 5, 6, 7], registers_mapping={0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7}, actual_num_qubits=8, unitary_located=[0, 1, 2, 3, 4, 5, 6, 7], random_unitary_seeds=None),
Commonparams(exp_id='9f38a452-20c8-4ee4-9454-aca9dbdf7a67', target_keys=[0], shots=4096, backend=<AerSimulator('aer_simulator')>, run_args={}, transpile_args={}, tags=(), save_location=PosixPath('.'), serial=None, summoner_id=None, summoner_name=None, datetimes=DatetimeDict({'build': '2025-06-26 11:46:31', 'run.001': '2025-06-26 11:46:31'})),
unused_args_num=0,
analysis_num=0))>
And use this uuid to access the experiments to execute post-processing.
report01 = experiment_randomized.exps[exp1].analyze(
selected_qubits=[0, 1, 2, 3],
)
report01
<EMRAnalysis(
serial=0,
EMRAnalysisInput(num_qubits=8, selected_qubits=[0, 1, 2, 3], registers_mapping={0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7}, bitstring_mapping={0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7}, shots=4096, unitary_located=[0, 1, 2, 3, 4, 5, 6, 7]),
EMRAnalysisContent(purity=0.949187821149826, entropy=0.0752345051851161, and others)),
unused_args_num=0
)>
main01, side_product01 = report01.export()
main01
{'purity': np.float64(0.949187821149826),
'entropy': np.float64(0.0752345051851161),
'puritySD': np.float64(1.1297807965000461),
'entropySD': np.float64(1.7171829600886979),
'num_classical_registers': 8,
'classical_registers': [0, 1, 2, 3],
'classical_registers_actually': [0, 1, 2, 3],
'all_system_source': 'independent',
'purityAllSys': np.float64(0.8283185172080993),
'entropyAllSys': np.float64(0.2717424541749239),
'puritySDAllSys': np.float64(1.0545137966396507),
'entropySDAllSys': np.float64(1.8366628215541976),
'num_classical_registers_all_sys': 8,
'classical_registers_all_sys': None,
'classical_registers_actually_all_sys': [0, 1, 2, 3, 4, 5, 6, 7],
'errorRate': np.float64(0.0902498933821066),
'mitigatedPurity': np.float64(1.1338380088818045),
'mitigatedEntropy': np.float64(-0.18121453756701073),
'counts_num': 100,
'taking_time': 0.001040667,
'taking_time_all_sys': 0.01061373,
'counts_used': None,
'input': {'num_qubits': 8,
'selected_qubits': [0, 1, 2, 3],
'registers_mapping': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7},
'bitstring_mapping': {0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7},
'shots': 4096,
'unitary_located': [0, 1, 2, 3, 4, 5, 6, 7]},
'header': {'serial': 0, 'datetime': '2025-06-26 11:46:32', 'log': {}}}
ii. Add the circuits to container .waves, then call them later.#
Since we have executed an experiment, the circuit we input in exp1 is stored in the container .waves with serial number 0.
experiment_randomized.waves
WaveContainer({
0: <qurry.recipe.simple.paramagnet.TrivialParamagnet object at 0x71371d8c4590>})
But we can also add the circuit to the container .waves with a custom name.
The name should be unique, otherwise it will be overwritten.
The method add will return the actual name of the circuit in the container.
print(experiment_randomized.add(sample02, "ghz_8"))
print(experiment_randomized.waves["ghz_8"])
ghz_8
┌───┐
q_0: ┤ H ├──■────────────────────────────────
└───┘┌─┴─┐
q_1: ─────┤ X ├──■───────────────────────────
└───┘┌─┴─┐
q_2: ──────────┤ X ├──■──────────────────────
└───┘┌─┴─┐
q_3: ───────────────┤ X ├──■─────────────────
└───┘┌─┴─┐
q_4: ────────────────────┤ X ├──■────────────
└───┘┌─┴─┐
q_5: ─────────────────────────┤ X ├──■───────
└───┘┌─┴─┐
q_6: ──────────────────────────────┤ X ├──■──
└───┘┌─┴─┐
q_7: ───────────────────────────────────┤ X ├
└───┘
If there is a circuit with the same name, it will be replaced by the new one.
print(experiment_randomized.add(sample03, "ghz_8"))
print(experiment_randomized.waves["ghz_8"])
ghz_8
┌───┐
q_0: ┤ X ├
└───┘
q_1: ─────
┌───┐
q_2: ┤ X ├
└───┘
q_3: ─────
┌───┐
q_4: ┤ X ├
└───┘
q_5: ─────
┌───┐
q_6: ┤ X ├
└───┘
q_7: ─────
Otherwise, you will need to use replace="duplicate" to prevent it from being replaced.
duplicated_case01 = experiment_randomized.add(sample02, "ghz_8", replace="duplicate")
print(duplicated_case01)
print(experiment_randomized.waves[duplicated_case01])
ghz_8.2
┌───┐
q_0: ┤ H ├──■────────────────────────────────
└───┘┌─┴─┐
q_1: ─────┤ X ├──■───────────────────────────
└───┘┌─┴─┐
q_2: ──────────┤ X ├──■──────────────────────
└───┘┌─┴─┐
q_3: ───────────────┤ X ├──■─────────────────
└───┘┌─┴─┐
q_4: ────────────────────┤ X ├──■────────────
└───┘┌─┴─┐
q_5: ─────────────────────────┤ X ├──■───────
└───┘┌─┴─┐
q_6: ──────────────────────────────┤ X ├──■──
└───┘┌─┴─┐
q_7: ───────────────────────────────────┤ X ├
└───┘
Now we have prepared the circuit and stored it in the container .waves.
experiment_randomized.waves
WaveContainer({
0: <qurry.recipe.simple.paramagnet.TrivialParamagnet object at 0x71371d8c4590>,
'ghz_8': <qiskit.circuit.quantumcircuit.QuantumCircuit object at 0x71371d8c10f0>,
'ghz_8.2': <qurry.recipe.simple.cat.GHZ object at 0x71371d8c63c0>})
Finally, we can execute the circuit and get the result.
exp2 = experiment_randomized.measure("ghz_8.2", times=100, shots=4096)
exp2
'ca554770-88a3-47c1-9546-73509f8abe76'
experiment_randomized.exps[exp2]
<EntropyMeasureRandomizedExperiment(exp_id=ca554770-88a3-47c1-9546-73509f8abe76,
EntropyMeasureRandomizedArguments(exp_name='experiment.N_U_100.qurrent_randomized', times=100, qubits_measured=[0, 1, 2, 3, 4, 5, 6, 7], registers_mapping={0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7}, actual_num_qubits=8, unitary_located=[0, 1, 2, 3, 4, 5, 6, 7], random_unitary_seeds=None),
Commonparams(exp_id='ca554770-88a3-47c1-9546-73509f8abe76', target_keys=['ghz_8.2'], shots=4096, backend=<AerSimulator('aer_simulator')>, run_args={}, transpile_args={}, tags=(), save_location=PosixPath('.'), serial=None, summoner_id=None, summoner_name=None, datetimes=DatetimeDict({'build': '2025-06-26 11:46:45', 'run.001': '2025-06-26 11:46:45'})),
unused_args_num=0,
analysis_num=0))>
report02 = experiment_randomized.exps[exp2].analyze(
selected_qubits=[0, 1, 2, 3],
)
report02
<EMRAnalysis(
serial=0,
EMRAnalysisInput(num_qubits=8, selected_qubits=[0, 1, 2, 3], registers_mapping={0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7}, bitstring_mapping={0: 0, 1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, 7: 7}, shots=4096, unitary_located=[0, 1, 2, 3, 4, 5, 6, 7]),
EMRAnalysisContent(purity=0.49372334241867066, entropy=1.0182252399732838, and others)),
unused_args_num=0
)>
d. Export them after all#
exp1_id, exp1_files_info = experiment_randomized.exps[exp1].write(
save_location=".", # where to save files
)
exp1_files_info
{'folder': 'experiment.N_U_100.qurrent_randomized.001',
'qurryinfo': 'experiment.N_U_100.qurrent_randomized.001/qurryinfo.json',
'args': 'experiment.N_U_100.qurrent_randomized.001/args/experiment.N_U_100.qurrent_randomized.001.id=9f38a452-20c8-4ee4-9454-aca9dbdf7a67.args.json',
'advent': 'experiment.N_U_100.qurrent_randomized.001/advent/experiment.N_U_100.qurrent_randomized.001.id=9f38a452-20c8-4ee4-9454-aca9dbdf7a67.advent.json',
'legacy': 'experiment.N_U_100.qurrent_randomized.001/legacy/experiment.N_U_100.qurrent_randomized.001.id=9f38a452-20c8-4ee4-9454-aca9dbdf7a67.legacy.json',
'tales.unitaryOP': 'experiment.N_U_100.qurrent_randomized.001/tales/experiment.N_U_100.qurrent_randomized.001.id=9f38a452-20c8-4ee4-9454-aca9dbdf7a67.unitaryOP.json',
'tales.randomized': 'experiment.N_U_100.qurrent_randomized.001/tales/experiment.N_U_100.qurrent_randomized.001.id=9f38a452-20c8-4ee4-9454-aca9dbdf7a67.randomized.json',
'reports': 'experiment.N_U_100.qurrent_randomized.001/reports/experiment.N_U_100.qurrent_randomized.001.id=9f38a452-20c8-4ee4-9454-aca9dbdf7a67.reports.json',
'reports.tales.purityCells': 'experiment.N_U_100.qurrent_randomized.001/tales/experiment.N_U_100.qurrent_randomized.001.id=9f38a452-20c8-4ee4-9454-aca9dbdf7a67.purityCells.reports.json',
'reports.tales.purityCellsAllSys': 'experiment.N_U_100.qurrent_randomized.001/tales/experiment.N_U_100.qurrent_randomized.001.id=9f38a452-20c8-4ee4-9454-aca9dbdf7a67.purityCellsAllSys.reports.json'}
Post-Process Availablities and Version Info#
from qurry.process import AVAIBILITY_STATESHEET
AVAIBILITY_STATESHEET
| Qurrium version: 0.13.0
---------------------------------------------------------------------------
### Qurrium Post-Processing
- Backend Availability ................... Python Cython Rust JAX
- randomized_measure
- entangled_entropy.entropy_core_2 ....... Yes Depr. Yes No
- entangle_entropy.purity_cell_2 ......... Yes Depr. Yes No
- entangled_entropy_v1.entropy_core ...... Yes Depr. Yes No
- entangle_entropy_v1.purity_cell ........ Yes Depr. Yes No
- wavefunction_overlap.echo_core_2 ....... Yes Depr. Yes No
- wavefunction_overlap.echo_cell_2 ....... Yes Depr. Yes No
- wavefunction_overlap_v1.echo_core ...... Yes Depr. Yes No
- wavefunction_overlap_v1.echo_cell ...... Yes Depr. Yes No
- hadamard_test
- purity_echo_core ....................... Yes No Yes No
- magnet_square
- magnsq_core ............................ Yes No Yes No
- string_operator
- strop_core ............................. Yes No Yes No
- classical_shadow
- rho_m_core ............................. Yes No No Yes
- utils
- randomized ............................. Yes Depr. Yes No
- counts_process ......................... Yes No Yes No
- bit_slice .............................. Yes No Yes No
- dummy .................................. Yes No Yes No
- test ................................... Yes No Yes No
---------------------------------------------------------------------------
+ Yes ...... Working normally.
+ Error .... Exception occurred.
+ No ....... Not supported.
+ Depr. .... Deprecated.
---------------------------------------------------------------------------
by <Hoshi>