Description

This circuit simulates the time evolution of the quantum Ising model under a transverse magnetic field.

Qiskit Circuit Code

```python
from qiskit import QuantumCircuit
from qiskit.circuit import Parameter

# Create circuit with 2 qubits and 2 classical bits
qc = QuantumCircuit(2, 2)

# Define parameters for coupling constant (J), transverse field (h), and time (t)
J = Parameter('J')  # Interaction strength between qubits
h = Parameter('h')  # Strength of transverse magnetic field
t = Parameter('t')  # Time evolution parameter

# Initialize qubits to superposition states
qc.h(0)
qc.h(1)

# Implement the Ising model Hamiltonian evolution using Trotterization
# First, apply the ZZ interaction term: exp(-i * J * t * Z ⊗ Z)
qc.cx(0, 1)
qc.rz(-2 * J * t, 1)
qc.cx(0, 1)

# Next, apply the transverse field term to both qubits: exp(-i * h * t * X)
qc.rx(-2 * h * t, 0)
qc.rx(-2 * h * t, 1)

# Measure the qubits
qc.measure([0, 1], [0, 1])
```

Quantum Execution Results

{
  "backend": "ibm_kyiv",
  "error": "The number of values (0) does not match the number of parameters (3) for the circuit. Note that if you want to run a single pub, you need to wrap it with `[]` like `sampler.run([(circuit, param_values)])` instead of `sampler.run((circuit, param_values))`.",
  "status": "failed"
}

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