Consider a simple Hamiltonian coupling two qubits:

The eigenvectors are just the computational basis states , with eigenvalues . To implement the unitary which evolves by time , we need to build a gate with the following action on basis states:

As you will check in a moment, this can be done using the following (non-trivial) circuit involving CNOTs and a rotation:

where .

Implement the circuit drawn above, allowing for the specification of an initial computational basis state.

Tip. Try using qml.BasisState to prepare the basis state.

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Learning Objectives:

  • Describe the utility of diagonalizing a Hamiltonian for simulation, and diagonalize a simple case.
  • See how nontrivial computational problems can be encoded in ground states.