Fixed MPS save failure when memory limit is ignored (#2248)

* Fixed MPS save failure when memory limit is ignored

* Release note

releasenotes/notes/fix_mps_save_without_memory_limit-64d927c4b4e1e2d4.yaml

@@ -0,0 +1,5 @@
+---
+fixes:
+  - |
+    Fixes a bug preventing the MPS simulator from running when its estimate
+    for the required memory is too large, even when `max_memory_mb=-1`.

src/simulators/circuit_executor.hpp

@@ -428,7 +428,7 @@ uint_t Executor<state_t>::get_max_parallel_shots(
     const Config &config, const Circuit &circ,
     const Noise::NoiseModel &noise) const {
   uint_t mem = required_memory_mb(config, circ, noise);
-  if (mem == 0)
+  if (mem == 0 || !check_required_memory_)
     return circ.shots * circ.num_bind_params;
 
   if (sim_device_ == Device::GPU && num_gpus_ > 0) {

test/terra/backends/aer_simulator/test_save_matrix_product_state.py

@@ -16,6 +16,9 @@
 import math
 import numpy as np
 from qiskit import QuantumCircuit, transpile
+from qiskit.circuit.library import PauliEvolutionGate
+from qiskit.quantum_info import SparsePauliOp
+from qiskit.synthesis import SuzukiTrotter
 from test.terra.backends.simulator_test_case import SimulatorTestCase, supported_methods
 
 
@@ -60,3 +63,32 @@ def test_save_matrix_product_state(self, method, device):
             self.assertTrue(np.allclose(val, target))
         for val, target in zip(value[1], target_lambda_reg):
             self.assertTrue(np.allclose(val, target))
+
+    @supported_methods(["automatic", "matrix_product_state"])
+    def test_save_matrix_product_state_memory_limit(self, method, device):
+        """Test save matrix_product_state instruction when max memory check is disabled"""
+        backend = self.backend(
+            method=method,
+            device=device,
+            matrix_product_state_max_bond_dimension=10,
+            max_memory_mb=-1,  # Disable memory limit check
+        )
+
+        L = 100
+        hamiltonian = SparsePauliOp.from_sparse_list([], num_qubits=L)
+        for x in range(L - 1):
+            hamiltonian += SparsePauliOp.from_sparse_list(
+                [
+                    ("XX", (x, x + 1), 1),
+                    ("YY", (x, x + 1), 1),
+                ],
+                num_qubits=L,
+            )
+        qc = QuantumCircuit(L)
+        qc.append(
+            PauliEvolutionGate(hamiltonian, synthesis=SuzukiTrotter(reps=100)), qargs=qc.qubits
+        )
+        qc = qc.decompose()
+        qc.save_matrix_product_state("mps")
+        result = backend.run(qc).result().data(0)
+        self.assertTrue("mps" in result)