Converting to probabilites

M3 natively works with quasi-probability distributions; distributions that contain negative values but nonetheless sum to one. This is useful for mitigating expectation values, but there could be situations where a true probability distribution is useful / needed. To this end, it is possible to find the closest probability distribution to a quasi-probability distribution in terms of \(L2\)-norm using: mthree.classes.QuasiDistribution.nearest_probability_distribution(). This conversion is done in linear time.

from qiskit import *
from qiskit_ibm_runtime.fake_provider import FakeCasablancaV2
import mthree

qc = QuantumCircuit(6)
qc.reset(range(6))
qc.h(3)
qc.cx(3,1)
qc.cx(3,5)
qc.cx(1,0)
qc.cx(5,4)
qc.cx(1,2)
qc.measure_all()

backend = FakeCasablancaV2()
mit = mthree.M3Mitigation(backend)
mit.cals_from_system(range(6))

trans_qc = transpile(qc, backend)
raw_counts = backend.run(trans_qc, shots=8192).result().get_counts()

quasis = mit.apply_correction(raw_counts, range(6))

# Here is where the conversion happens
quasis.nearest_probability_distribution()

{'011001': np.float32(4.707797e-05),
 '110100': np.float32(5.650698e-05),
 '101100': np.float32(6.83671e-05),
 '011100': np.float32(7.7837496e-05),
 '110001': np.float32(0.00010499917),
 '010100': np.float32(0.000108673004),
 '000101': np.float32(0.00012767228),
 '011011': np.float32(0.00019099959),
 '101101': np.float32(0.00026913657),
 '100111': np.float32(0.0003418473),
 '001110': np.float32(0.00037118915),
 '001000': np.float32(0.0010693646),
 '111101': np.float32(0.0013000557),
 '100000': np.float32(0.0015309765),
 '110000': np.float32(0.002023466),
 '011111': np.float32(0.0021256532),
 '000010': np.float32(0.0021290563),
 '010000': np.float32(0.002521949),
 '000110': np.float32(0.0030104595),
 '000001': np.float32(0.0032607021),
 '101111': np.float32(0.0033600668),
 '111110': np.float32(0.003680723),
 '000100': np.float32(0.004295373),
 '110111': np.float32(0.0047780294),
 '111011': np.float32(0.005021414),
 '001111': np.float32(0.005311705),
 '111001': np.float32(0.005769953),
 '000111': np.float32(0.005814682),
 '111000': np.float32(0.006640652),
 '111111': np.float32(0.46323493),
 '000000': np.float32(0.4713565)}