qrisp.operators.fermionic.FermionicOperator.expectation_value#

FermionicOperator.expectation_value(state_prep, mapping_type='jordan_wigner', **measurement_kwargs)[source]#

The expectation value function allows to estimate the expectation value of a Hamiltonian for a state that is specified by a preparation procedure. This preparation procedure can be supplied via a Python function that returns a QuantumVariable.

Note that this method measures the hermitized version of the operator:

\[H = (O + O^\dagger)/2\]

Parameters:

state_prepcallable: A function returning a QuantumVariable. The expectation of the Hamiltonian for the state of this QuantumVariable will be measured. The state preparation function can only take classical values as arguments. This is because a quantum value would need to be copied for each sampling iteration, which is prohibited by the no-cloning theorem.
mapping_typestr, optional: The strategy on how to map the FermionicOperator to a QubitOperator. Default is jordan_wigner.
measurement_kwargsdict, optional: The keyword arguments of QubitOperator.expectation_value.

Returns:

callable: A function returning an array containing the expectaion value.

Examples

We define a Fermionic Hamiltonian, and measure its expectation value for the state of a QuantumFloat.

We prepare the state

\[\ket{\psi_{\theta}} = (\cos(\theta)\ket{0}+\sin(\theta)\ket{1})^{\otimes 2}\]

from qrisp import *
from qrisp.operators import a,c
import numpy as np

def state_prep(theta):
    qv = QuantumFloat(2)

    ry(theta,qv)

    return qv

And compute the expectation value of the Hamiltonion \(H=a_0^{\dagger}a_1+a_1^{\dagger}a_0\) for the state \(\ket{\psi_{\theta}}\)

H = c(0)*a(1) + c(1)*a(0)

ev_function = H.expectation_value(state_prep)

print(ev_function(np.pi/2))
# Yields: 0.5027499999999724

Similiarly, expectation values can be calculated with Jasp

@jaspify(terminal_sampling=True)
def main():

    H = c(0)*a(1) + c(1)*a(0)

    ev_function = H.expectation_value(state_prep)

    return ev_function(np.pi/2)

print(main())
# Yields: 0.5027499999999724