Generalize Hamiltonian

[zaqqwerty]

Dually to QuantumData, which is anything providing the context in which an expectation value of an operator can calculated, Hamiltonian should represent any operator whose expectation value can be calculated.

We probably don't want complete freedom in the representation, so I propose the following subclasses to address this:

• ModularHamiltonian for any diagonalized representation. Ingested by SampledQuantumInference
  • BitstringEnergy for diagonal
  • QuantumCircuit for diagonalizing unitary
  • num_samples to say how many samples to use for each expectation calculation
• AnalyticModularHamiltonian inheriting from ModularHamiltonian
  • has a list of converted cirq.PauliTerms which are in the Z basis; it is assumed that the QuantumCircuit already specifies the basis.
  • function to map expectation values of the terms to the overall expectation value. Thus this class only works for energy functions linear in the pauli terms Encapsulate cirq.PauliSum in Hamiltonian #164
• ModularHamiltonianSum for a sum of ModularHamiltonian #234