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
'd3bf5830-5a87-4f7a-b999-a0d636c6cb07'
Each experiment result will be stored in a container .exps.
experiment_randomized.exps[exp1]
<EntropyMeasureRandomizedExperiment(exp_id=d3bf5830-5a87-4f7a-b999-a0d636c6cb07,
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='d3bf5830-5a87-4f7a-b999-a0d636c6cb07', 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': '2025-07-08 16:59:41', 'run.001': '2025-07-08 16:59:41'})),
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=1.0818525683879852, entropy=-0.11350390642180241, and others)),
unused_args_num=0
)>
main01, side_product01 = report01.export()
main01
{'purity': np.float64(1.0818525683879852),
'entropy': np.float64(-0.11350390642180241),
'puritySD': np.float64(0.9047121303994405),
'entropySD': np.float64(1.2064709574098542),
'num_classical_registers': 8,
'classical_registers': [0, 1, 2, 3],
'classical_registers_actually': [0, 1, 2, 3],
'all_system_source': 'independent',
'purityAllSys': np.float64(0.9814594411849975),
'entropyAllSys': np.float64(0.026999445341914383),
'puritySDAllSys': np.float64(1.2117104526181024),
'entropySDAllSys': np.float64(1.7811522184501039),
'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(0.009350347947765595),
'mitigatedPurity': np.float64(1.1011859063770018),
'mitigatedEntropy': np.float64(-0.13905805070709734),
'counts_num': 100,
'taking_time': 0.001137362,
'taking_time_all_sys': 0.010858034,
'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': '2025-07-08 16:59:42', '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 0x700e05c21130>})
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 0x700e05c21130>,
'ghz_8': <qiskit.circuit.quantumcircuit.QuantumCircuit object at 0x700e05afcc80>,
'ghz_8.2': <qurry.recipe.simple.cat.GHZ object at 0x700e05afc3e0>})
Finally, we can execute the circuit and get the result.
exp2 = experiment_randomized.measure("ghz_8.2", times=100, shots=4096)
exp2
'6c8ad942-ec28-4d7c-80bf-9f0875fb7540'
experiment_randomized.exps[exp2]
<EntropyMeasureRandomizedExperiment(exp_id=6c8ad942-ec28-4d7c-80bf-9f0875fb7540,
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='6c8ad942-ec28-4d7c-80bf-9f0875fb7540', 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': '2025-07-08 17:00:07', 'run.001': '2025-07-08 17:00:07'})),
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=0.45413352966308596, entropy=1.138811536889995, 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=d3bf5830-5a87-4f7a-b999-a0d636c6cb07.args.json',
'advent': 'experiment.N_U_100.qurrent_randomized.001/advent/experiment.N_U_100.qurrent_randomized.001.id=d3bf5830-5a87-4f7a-b999-a0d636c6cb07.advent.json',
'legacy': 'experiment.N_U_100.qurrent_randomized.001/legacy/experiment.N_U_100.qurrent_randomized.001.id=d3bf5830-5a87-4f7a-b999-a0d636c6cb07.legacy.json',
'tales.unitaryOP': 'experiment.N_U_100.qurrent_randomized.001/tales/experiment.N_U_100.qurrent_randomized.001.id=d3bf5830-5a87-4f7a-b999-a0d636c6cb07.unitaryOP.json',
'tales.randomized': 'experiment.N_U_100.qurrent_randomized.001/tales/experiment.N_U_100.qurrent_randomized.001.id=d3bf5830-5a87-4f7a-b999-a0d636c6cb07.randomized.json',
'reports': 'experiment.N_U_100.qurrent_randomized.001/reports/experiment.N_U_100.qurrent_randomized.001.id=d3bf5830-5a87-4f7a-b999-a0d636c6cb07.reports.json',
'reports.tales.purityCells': 'experiment.N_U_100.qurrent_randomized.001/tales/experiment.N_U_100.qurrent_randomized.001.id=d3bf5830-5a87-4f7a-b999-a0d636c6cb07.purityCells.reports.json',
'reports.tales.purityCellsAllSys': 'experiment.N_U_100.qurrent_randomized.001/tales/experiment.N_U_100.qurrent_randomized.001.id=d3bf5830-5a87-4f7a-b999-a0d636c6cb07.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>