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Tfim simulation using 2 CNOT rather than 3 CNOT #94

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Tfim simulation using 2 CNOT rather than 3 CNOT #94

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1415670
added tfim_EvolutionOracle
shangtai Oct 23, 2024
9c729bf
added tfim_EvolutionOracle
shangtai Oct 23, 2024
7ad8b90
Update src/boostvqe/models/dbi/double_bracket_evolution_oracles.py
shangtai Nov 5, 2024
7a54540
yet to be done, make a over all qubits and load B_a. Currently made u…
shangtai Nov 10, 2024
1032637
Use commutivity to get rid of a for loop in steps. Thanks. Also, work…
shangtai Nov 12, 2024
c0a0f61
introduce steps in loop
shangtai Nov 13, 2024
6f2854a
apply product formula for TFIM
shangtai Nov 14, 2024
18a950b
fixing bug of RX not appearing in the circuit
shangtai Nov 15, 2024
bbd6928
still debugging.
shangtai Nov 19, 2024
109286b
still debugging.
shangtai Nov 19, 2024
a136991
removed comments.
shangtai Nov 20, 2024
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removed comments.
shangtai Nov 20, 2024
4353199
added tfim_2cnot_test.py
shangtai Nov 22, 2024
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40 changes: 40 additions & 0 deletions src/boostvqe/models/dbi/double_bracket_evolution_oracles.py
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Original file line number Diff line number Diff line change
Expand Up @@ -307,3 +307,43 @@ def circuit(self, t_duration, steps=None, order=None):
steps=steps,
order=order,
)


@dataclass
class tfim_EvolutionOracle(EvolutionOracle):
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steps: int = None
B_a: float = None

def circuit(self, a, t_duration, B_a, steps=None, order=None):
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Suggested change
def circuit(self, a, t_duration, B_a, steps=None, order=None):
def circuit(self, t_duration, steps=None, order=None):

This class must implement eo.circuit(0.1) without requiring other parameters.

What is a?

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@shangtai shangtai Nov 5, 2024 •
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I use the notation in the paper where a is an index and B_a is another parameter.

$$H^{(a)}=X_{a}X_{a+1}+B_{a}Z_{a}$$

if steps is None:
steps = self.steps

circuit = Circuit(self.h.nqubits) # Initialize the circuit with the number of qubits

# Add CNOT(a, a+1)
circuit.add(gates.CNOT(a, a + 1))

# Time evolution under the transverse field Ising model Hamiltonian
# exp(-i t (X(a) + B_a * Z(a)))
dt = t_duration / steps # Divide the time duration for Trotterization if needed
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Suggested change
dt = t_duration / steps # Divide the time duration for Trotterization if needed
dt = t_duration / steps # Divide the time duration for Trotterization if needed
for a in range(nqubits:
circuit.add(gates.CNOT(a, a + 1))
circuit += self._time_evolution_step(a, dt, B_a)
circuit.add(gates.CNOT(a, a + 1))

and then loop this over _ in range(steps)

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@shangtai shangtai Nov 20, 2024 •
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n_qubits = 3
h_coeff = 1
hamiltonian = SymbolicHamiltonian(nqubits=n_qubits)

oracle = TFIM_EvolutionOracle(h=hamiltonian, evolution_oracle_type="trotter", steps=1, B_a=0, order=2)

circuit = oracle.circuit(t_duration=1.0)

unitary = circuit.unitary()


from qibo import hamiltonians
from numpy.linalg import norm

def our_TFIM(nqubits, h: float = 0.0, dense: bool = True, backend=None):
        def multikron(matrix_list):
        """Calculates Kronecker product of a list of matrices."""
        return reduce(np.kron, matrix_list)

    from qibo.backends import matrices

    matrix = (
        - multikron([matrices.X, matrices.X]) - h * multikron([matrices.Z, matrices.I])
    )
    terms = [hamiltonians.terms.HamiltonianTerm(matrix, i, i + 1) for i in range(nqubits - 1)]
    terms.append(hamiltonians.terms.HamiltonianTerm(matrix, nqubits - 1, 0))
    ham = SymbolicHamiltonian(backend=backend)
    ham.terms = terms
    return ham

ham = our_TFIM(nqubits=n_qubits, h=h_coeff, dense=False)
truth = ham.exp(1)
verification_norm = []
for step in range(1, 21):
    oracle = TFIM_EvolutionOracle(h=hamiltonian, evolution_oracle_type="trotter", steps=step, B_a=h_coeff, order=2)
    circuit = oracle.circuit(t_duration=1.0)
    unitary = circuit.unitary()
    #print(norm(truth-unitary))
    verification_norm.append(norm(truth-unitary))

import matplotlib.pyplot as plt
x = np.array([i for i in range(1, 21)])
plt.plot(x, verification_norm, 'o')
plt.title("verification of TFIM 2 CNOT implementation")
plt.xlabel("steps")
plt.ylabel("norm of difference")

plt.show()

produces the following graph:

Screenshot 2024-11-20 at 3 19 27 PM


for _ in range(steps):
# Apply time evolution for X(a) + B_a * Z(a)
circuit += self._time_evolution_step(a, dt, B_a)
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This is commuting so it's equivalent to
circuit += self._time_evolution_step(a, t_duration, B_a)

Once you have for a in range(self.nqubits): (TFIM evolution oracle should be implemented for nqubits) then you need to do the CNOTs before every dt step here


# Add second CNOT(a, a+1)
circuit.add(gates.CNOT(a, a + 1))

return circuit

def _time_evolution_step(self, a: int, dt: float, B_a: float):
"""Apply a single Trotter step of the time evolution operator exp(-i dt (X(a) + B_a Z(a)))."""
step_circuit = Circuit(self.h.nqubits)

# Time evolution for X(a)
step_circuit.add(gates.RX(a, theta=-2 * dt)) # Apply exp(-i dt X(a))

# Time evolution for Z(a)
step_circuit.add(gates.RZ(a, theta=-2 * dt * B_a)) # Apply exp(-i dt B_a Z(a))

return step_circuit