Maintain Index Consistency When Using simplify=True in qubo_to_ising

[Jacomichi]

Description

Currently, using simplify=True in the qubo_to_ising function causes an index mismatch between QUBO and Ising models. We need to address this issue to ensure that simplify=True can be used safely without compromising index consistency.

Objectives

1. Maintain index consistency between QUBO and Ising models when using simplify=True in some cases.
   The test below is the case.
   

   Qamomile/tests/quri_parts/test_quri_transpiler.py

   Lines 179 to 194 in 27b4515

   	def test_coloring_sample_decode():
   	problem = graph_coloring_problem()
   	instance_data = graph_coloring_instance()
   	compiled_instance = jmt.compile_model(problem, instance_data)
   	initial_circuit = create_graph_coloring_operator_ansatz_initial_state(compiled_instance, instance_data['V'], instance_data['N'])
   	qaoa_converter = qm.qaoa.QAOAConverter(compiled_instance)
   	qaoa_converter.ising_encode(multipliers={"one-color": 1})
   	qp_transpiler = QuriPartsTranspiler()
   	sampler = create_qulacs_vector_sampler()
   	qp_circ = qp_transpiler.transpile_circuit(initial_circuit)
   	qp_result = sampler(qp_circ, 10)
   	sampleset = qaoa_converter.decode(qp_transpiler, (qp_result, initial_circuit.num_qubits))
   	assert sampleset[0].var_values["x"].values == {(0, 0): 1, (1, 0): 1, (2, 0): 1, (3, 0): 1}
   	assert sampleset[0].num_occurrences == 10

2. Provide a way for users to easily access the correct indices after simplification.

Current Behavior

• When simplify=True is used in qubo_to_ising, the resulting Ising model has different indices from the original QUBO model.
• This mismatch can lead to wrong decode when working with var_map or performing other operations that rely on consistent indexing.

Desired Behavior

• Using simplify=True should not break the index correspondence.
• Users should be able to work with simplified models without worrying about index mismatches.

Related PR

#67