SymbolicHamiltonianEvolutionOracle

[marekgluza]

• Please fill in the pseudocode structure
  

  boostvqe/src/boostvqe/models/dbi/double_bracket_evolution_oracles.py

  Lines 267 to 293 in c6da8c5

  	##############################################
  	#pseudocode follows
  	@dataclass
  	class HamiltonianSimulation_EvolutionOracle(EvolutionOracle):
  	steps: int = None
  	order: int = None
  	delta: float = 0.5
  	@classmethod
  	def from_symbolic_hamiltonian(cls, h):
  	hamiltonian = h
  	...
  	return cls(
  	h=hamiltonian,
  	evolution_oracle_type=EvolutionOracleType.hamiltonian_simulation,
  	**kwargs,
  	)
  	def circuit(self, t_duration, steps=None, order=None):
  	c=self.h.circuit(dt)
  	for g in c.queue:
  	if g is two qubit
  	new_gate_list_add(two_qubit_decomposition(g)
  	c_recompiled_into_CNOT = ...collect...decompositions here
  	return reduce(__add__,c_recompiled_dt) #cf XXZ compiling

• key is to use something like this on h.circuit(dt)

import qibo
from qibo.symbols import *

from qibo.hamiltonians import SymbolicHamiltonian
from qibo.transpiler.unitary_decompositions import two_qubit_decomposition

nqubits = 2
delta = 0.5
hamiltonian = SymbolicHamiltonian(
X(0)*X(1)+Z(0)
,
nqubits=nqubits,
)

for g in hamiltonian.circuit(0.1).queue:
    two_qubit_decomposition(0,1,g.matrix())

• HamiltonianSimulation gives 1 Trotter step use this to multiply them up, @shangtai please help out with this too
  

  boostvqe/src/boostvqe/compiling_XXZ.py

  Lines 162 to 165 in c6da8c5

  	for _ in range(steps):
  	multi_layer += circuit
  	return multi_layer

• please make checks showing that the eo compiling agress with h.exp(0.5) if you cast your compiled circuit into a unitary . Here is an example how we checked the XXZ
  

  boostvqe/notebooks/compiling_XXZ_test.py

  Line 14 in c6da8c5

  print(np.linalg.norm(u-np.exp(nqubits*steps*1j*np.pi/4)*v))

• for the PR please make a plot like this https://github.com/qiboteam/boostvqe/blob/symbolic_hamiltonian_evolution_oracle/notebooks/docs_and_tutorial_ideas/example_comparison_XXZ_compiling_check.ipynb maybe in log scale to show the scaling

• please run this comparison for all models from New Hamiltonians #45 that are two local