Description

This circuit simulates the time evolution of a two-qubit system under a Hamiltonian H = X⊗X + Y⊗Y + Z⊗Z.

Qiskit Circuit Code

```python
from qiskit import QuantumCircuit
import numpy as np

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

# Initialize qubits in superposition
qc.h(0)
qc.h(1)

# Time parameter for Hamiltonian evolution
t = np.pi / 4  # You can adjust this value

# Simulate time evolution under a custom Hamiltonian H = X⊗X + Y⊗Y + Z⊗Z
# Using Trotter-Suzuki decomposition for e^{-iHt}

# XX interaction
qc.h([0, 1])
qc.cx(0, 1)
qc.rz(2 * t, 1)
qc.cx(0, 1)
qc.h([0, 1])

# YY interaction
qc.rx(np.pi / 2, [0, 1])
qc.cx(0, 1)
qc.rz(2 * t, 1)
qc.cx(0, 1)
qc.rx(-np.pi / 2, [0, 1])

# ZZ interaction
qc.cx(0, 1)
qc.rz(2 * t, 1)
qc.cx(0, 1)

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

Quantum Execution Results

{
  "backend": "ibm_kyiv",
  "error": "\u0027Failed to run program: \\\u0027409 Client Error: Conflict for url: https://api.quantum.ibm.com/runtime/jobs. {\"errors\":[{\"message\":\"You have reached the limit of 3 pending  jobs. Please wait for a job to complete or cancel one before submitting anything new.\",\"code\":3458,\"solution\":\"Wait until some previous jobs were finished. You can cancel pending jobs to run new jobs.\",\"more_info\":\"https://docs.quantum-computing.ibm.com/errors\"}]}\\\u0027\u0027",
  "status": "failed"
}

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