2.2 Randomized Measurement#
WaveFunction Overlap#
This method is based on Probing Rényi entanglement entropy via randomized measurements with deplorizing error mitigation by Simple mitigation of global depolarizing errors in quantum simulations.
randomized_overlap_echo#
Here, we assume you already have the calculated data. You can call the function randomized_overlap_echo from qurry.process.randomized_measure to calculate the entropy.
This function requires only three arguments: shots, counts, and selected_classical_registers. All other arguments are optional.
Note that selected_classical_registers expects a list of bitstring indices, NOT qubit indices, as these are distinct.
The following is the arguments of the function:
def randomized_overlap_echo(
shots: int,
first_counts: list[dict[str, int]],
second_counts: list[dict[str, int]],
selected_classical_registers: Optional[Iterable[int]] = None,
backend: PostProcessingBackendLabel = DEFAULT_PROCESS_BACKEND,
pbar: Optional[tqdm.tqdm] = None,
) -> WaveFuctionOverlapResult:
"""Calculate wavefunction overlap
a.k.a. loschmidt echo when processes time evolution system.
Args:
shots (int):
Shots of the experiment on quantum machine.
first_counts (list[dict[str, int]]):
Counts of the experiment on quantum machine.
second_counts (list[dict[str, int]]):
Counts of the experiment on quantum machine.
selected_classical_registers (Optional[Iterable[int]], optional):
The list of **the index of the selected_classical_registers**.
backend (ExistingProcessBackendLabel, optional):
Backend for the process. Defaults to DEFAULT_PROCESS_BACKEND.
pbar (Optional[tqdm.tqdm], optional):
The progress bar API, you can use put a :cls:`tqdm` object here.
This function will update the progress bar description.
Defaults to None.
Returns:
WaveFuctionOverlapResult: A dictionary contains purity, entropy,
a list of each overlap, puritySD, degree, actual measure range, bitstring range.
"""
This function returns a dictionary that contains the echo, echoSD, and other relevant information.
The returned dict contains the following information:
class WaveFuctionOverlapResult(TypedDict):
"""The return type of the post-processing for wavefunction overlap."""
echo: np.float64
"""The overlap value."""
echoSD: np.float64
"""The overlap standard deviation."""
echoCells: dict[int, np.float64]
"""The overlap of each single count."""
num_classical_registers: int
"""The number of classical registers."""
classical_registers: Optional[list[int]]
"""The list of the index of the selected classical registers."""
classical_registers_actually: list[int]
"""The list of the index of the selected classical registers which is actually used."""
# refactored
counts_num: int
"""The number of first counts and second counts."""
taking_time: float
"""The calculation time."""
Dummy Data#
from qurry.capsule import quickRead
easy_dummy: dict[str, dict[str, int]] = quickRead("../easy-dummy.json")
large_dummy_list = [easy_dummy["0"] for _ in range(100)]
Simple Example#
from qurry.process.randomized_measure import randomized_overlap_echo
test_result_1_1_1 = randomized_overlap_echo(
4096, large_dummy_list, large_dummy_list, list(range(6))
)
from pprint import pprint
print("| result of randomized_overlap_echo except for purityCells")
pprint({k: v for k, v in test_result_1_1_1.items() if k != "echoCells"})
# "echoCells" is too long we skip it here
print("| result of randomized_overlap_echo[purityCells]")
print(test_result_1_1_1["echoCells"][0])
print(test_result_1_1_1["echoCells"][1])
| result of randomized_overlap_echo except for purityCells
{'classical_registers': [0, 1, 2, 3, 4, 5],
'classical_registers_actually': [0, 1, 2, 3, 4, 5],
'counts_num': 100,
'echo': np.float64(1.0627930164337158),
'echoSD': np.float64(0.0),
'num_classical_registers': 8,
'taking_time': 0.003986562}
| result of randomized_overlap_echo[purityCells]
1.0627930164337158
1.0627930164337158
Integration with your own progress bar#
from tqdm import tqdm
import time
all_counts_progress_01 = tqdm(
[
(4096, large_dummy_list, list(range(6))),
(4096, large_dummy_list, list(range(2, 8))),
(4096, large_dummy_list, list(range(7))),
(4096, large_dummy_list, list(range(0, 7))),
(4096, large_dummy_list, [0, 1, 2, 6, 7]),
(4096, large_dummy_list, [3, 4, 5, 6, 7, 0, 1]),
],
bar_format="| {desc} - {elapsed} < {remaining}",
)
test_result_1_1_2 = []
for tmp_shot, tmp_counts, tmp_partition in all_counts_progress_01:
print(tmp_partition)
test_result_1_1_2.append(
randomized_overlap_echo(
tmp_shot, tmp_counts, tmp_counts, tmp_partition, pbar=all_counts_progress_01
)
)
time.sleep(0.5)
| - 00:00 < ?
| Calculate selected classical registers: [0, 1, 2, 3, 4, 5]. - 00:00 < ?
[0, 1, 2, 3, 4, 5]
| Calculate selected classical registers: [0, 1, 2, 3, 4, 5]. - 00:00 < 00:02
| Calculate selected classical registers: [2, 3, 4, 5, 6, 7]. - 00:00 < 00:02
[2, 3, 4, 5, 6, 7]
| Calculate selected classical registers: [2, 3, 4, 5, 6, 7]. - 00:01 < 00:02
| Calculate selected classical registers: [0, 1, 2, 3, 4, 5, 6]. - 00:01 < 00:02
[0, 1, 2, 3, 4, 5, 6]
| Calculate selected classical registers: [0, 1, 2, 3, 4, 5, 6]. - 00:01 < 00:01
| Calculate selected classical registers: [0, 1, 2, 3, 4, 5, 6]. - 00:01 < 00:01
[0, 1, 2, 3, 4, 5, 6]
| Calculate selected classical registers: [0, 1, 2, 3, 4, 5, 6]. - 00:02 < 00:01
| Calculate selected classical registers: [0, 1, 2, 6, 7]. - 00:02 < 00:01
[0, 1, 2, 6, 7]
| Calculate selected classical registers: [0, 1, 2, 6, 7]. - 00:02 < 00:00
| Calculate selected classical registers: [3, 4, 5, 6, 7, 0, 1]. - 00:02 < 00:00
[3, 4, 5, 6, 7, 0, 1]
| Calculate selected classical registers: [3, 4, 5, 6, 7, 0, 1]. - 00:03 < 00:00
| Calculate selected classical registers: [3, 4, 5, 6, 7, 0, 1]. - 00:03 < 00:00
Using Python backend#
It will be slow. You’d better think twice before using it.
all_counts_progress_02 = tqdm(
[
(4096, large_dummy_list, list(range(6))),
(4096, large_dummy_list, list(range(2, 8))),
(4096, large_dummy_list, list(range(7))),
(4096, large_dummy_list, list(range(0, 7))),
(4096, large_dummy_list, [0, 1, 2, 6, 7]),
(4096, large_dummy_list, [3, 4, 5, 6, 7, 0, 1]),
],
bar_format="| {desc} - {elapsed} < {remaining}",
)
test_result_1_1_2 = []
for tmp_shot, tmp_counts, tmp_partition in all_counts_progress_02:
print(tmp_partition)
test_result_1_1_2.append(
randomized_overlap_echo(
tmp_shot,
tmp_counts,
tmp_counts,
tmp_partition,
pbar=all_counts_progress_02,
backend="Python",
)
)
time.sleep(0.5)
| - 00:00 < ?
| Calculate selected classical registers: [0, 1, 2, 3, 4, 5]. - 00:00 < ?
[0, 1, 2, 3, 4, 5]
| Calculate selected classical registers: [0, 1, 2, 3, 4, 5]. - 00:02 < 00:12
| Calculate selected classical registers: [2, 3, 4, 5, 6, 7]. - 00:02 < 00:12
[2, 3, 4, 5, 6, 7]
| Calculate selected classical registers: [2, 3, 4, 5, 6, 7]. - 00:05 < 00:12
| Calculate selected classical registers: [0, 1, 2, 3, 4, 5, 6]. - 00:05 < 00:12
[0, 1, 2, 3, 4, 5, 6]
| Calculate selected classical registers: [0, 1, 2, 3, 4, 5, 6]. - 00:09 < 00:10
| Calculate selected classical registers: [0, 1, 2, 3, 4, 5, 6]. - 00:09 < 00:10
[0, 1, 2, 3, 4, 5, 6]
| Calculate selected classical registers: [0, 1, 2, 3, 4, 5, 6]. - 00:13 < 00:07
| Calculate selected classical registers: [0, 1, 2, 6, 7]. - 00:13 < 00:07
[0, 1, 2, 6, 7]
| Calculate selected classical registers: [0, 1, 2, 6, 7]. - 00:17 < 00:03
| Calculate selected classical registers: [3, 4, 5, 6, 7, 0, 1]. - 00:17 < 00:03
[3, 4, 5, 6, 7, 0, 1]
| Calculate selected classical registers: [3, 4, 5, 6, 7, 0, 1]. - 00:21 < 00:00
| Calculate selected classical registers: [3, 4, 5, 6, 7, 0, 1]. - 00:21 < 00:00
Post-Process Availablities and Version Info#
from qurry.process.status 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>