Usage

This section shows how to use quMeas library to compute expectation values of Pauli strings. See /examples for more.

Computing Expectation Values with Randomized Measurement and Cumulant Expansion

In the first example, we will use measurement basis and outcomes (basis, bits) that is already available from a quantum simulation. For complete example, check lihCumulantBits_expectation.py and lihRandom_expectation.py in /examples. Basically, basis is a list of Pauli strings, generated randomly and outcomes are list of classical bits from quantum measurement. Now, we will compute expectation values from classical shadow tomography and cumulant average expansion.:

from qumeas import PauliContainer, RandomShadow, QCumulant

# Get measurement basis and outcomes(basis, bits) from general quantum computing
# packages. See documentation & examples for more details

myPauli = PauliContainer(Nqubit=N, #Qubits
                         pauli_list=plist, # list of Pauli strings
                         pauli_list_coeff=clist) # list of coeffs for plist

# Compute expectation with classical shadow tomography
myRandom = RandomShadow(PauliObj=myPauli)
expectation_random = myRandom.compute_expectation(basis, bits)

# Compute expectation with cumulant expansion
myCumu = QCumulant(PauliObj=myPauli,
                   measure_basis=basis,
                   measure_outcome_bits=bits)
myCumu.generate_partitions(num_threads=4)
expectation_cumulant = myCumu.compute_expectation_bits()

In the next example, we will first perform randomized measurement (and get the expectation value as well). Then, we use cumulant expansion with the measurement bits from the randomized measurement to estimate expectation value of the Hamiltonian of water molecule. This example uses functionalities from qiskit and so qiskit, qiskit_nature, and qiskit_aer needs to be installed.:

from qumeas.qiskit_utils import Mole
from qumeas import RandomShadow, QCumulant

# Set up the molecule (H2O)
h2o_mol = Mole(atom='h2o')

# Initialize randomized measurements
random_measure = RandomShadow(h2o_mol)

# Perform randomized measurements
expectation_random = random_measure.measure(M=1000, nproc=1)
print(f'Randomized measurement expectation: {expectation_random:>12.8f}')

# Initialize cumulant expansion with random_measure
cumulant = QCumulant(protocol=random_measure)

# Generate non-crossing partitions (max block size of 4) and compute expectation
cumulant.generate_partitions(max_size=4, num_threads=4)
expectation_cumulant = cumulant.compute_expectation_bits()
print(f'Cumulant expansion expectation: {expectation_cumulant:>12.8f}')