fix: Handle Projection and Reset in DensityMatrixSimulation

[speller26]

Issue #, if available:

Description of changes:

Testing done:

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 100.00%. Comparing base (e12f376) to head (bf56dbc).

Additional details and impacted files

@@            Coverage Diff            @@
##              main      #376   +/-   ##
=========================================
  Coverage   100.00%   100.00%           
=========================================
  Files           49        49           
  Lines         4882      4897   +15     
  Branches       561       563    +2     
=========================================
+ Hits          4882      4897   +15     

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find the edge case

[yitchen-tim]

Found an edge case:

qreg = [8,13,17,18]

with EnableExperimentalCapability():
    circ = Circuit()
    circ.h(qreg[1])
    circ.measure_ff(qreg[1], 0)
    circ.cc_prx(qreg[2], 3.14159, 0, 0)
    circ.measure([qreg[1],qreg[2]])

print(circ)
res_cnot = qd.run(circ, shots=1000).result()
print(res_cnot.measurement_counts)

with error stack

File [~/Desktop/code/Github/amazon-braket-default-simulator-python/src/braket/default_simulator/density_matrix_simulation.py:50](http://localhost:8888/lab/tree/examples/experimental_capabilities/dynamic_circuits/~/Desktop/code/Github/amazon-braket-default-simulator-python/src/braket/default_simulator/density_matrix_simulation.py#line=49), in DensityMatrixSimulation.evolve(self, operations)
     49 def evolve(self, operations: list[GateOperation | KrausOperation]) -> None:
---> 50     self._density_matrix = DensityMatrixSimulation._apply_operations(
     51         self._density_matrix, self._qubit_count, operations
     52     )

File [~/Desktop/code/Github/amazon-braket-default-simulator-python/src/braket/default_simulator/density_matrix_simulation.py:152](http://localhost:8888/lab/tree/examples/experimental_capabilities/dynamic_circuits/~/Desktop/code/Github/amazon-braket-default-simulator-python/src/braket/default_simulator/density_matrix_simulation.py#line=151), in DensityMatrixSimulation._apply_operations(state, qubit_count, operations)
    150 original_shape = state.shape
    151 result = state.view()
--> 152 result.shape = [2] * 2 * qubit_count
    153 temp = np.zeros_like(result, dtype=complex)
    154 work_buffer1 = np.zeros_like(result, dtype=complex)

ValueError: maximum supported dimension for an ndarray is 32, found 36

I think there is something wrong in setting qubit_count. It should be only 2 qubits but it uses the max qubit index as qubit count (=18 qubits).

[speller26]

Found an edge case:

qreg = [8,13,17,18]

with EnableExperimentalCapability():
    circ = Circuit()
    circ.h(qreg[1])
    circ.measure_ff(qreg[1], 0)
    circ.cc_prx(qreg[2], 3.14159, 0, 0)
    circ.measure([qreg[1],qreg[2]])

print(circ)
res_cnot = qd.run(circ, shots=1000).result()
print(res_cnot.measurement_counts)

with error stack

File [~/Desktop/code/Github/amazon-braket-default-simulator-python/src/braket/default_simulator/density_matrix_simulation.py:50](http://localhost:8888/lab/tree/examples/experimental_capabilities/dynamic_circuits/~/Desktop/code/Github/amazon-braket-default-simulator-python/src/braket/default_simulator/density_matrix_simulation.py#line=49), in DensityMatrixSimulation.evolve(self, operations)
     49 def evolve(self, operations: list[GateOperation | KrausOperation]) -> None:
---> 50     self._density_matrix = DensityMatrixSimulation._apply_operations(
     51         self._density_matrix, self._qubit_count, operations
     52     )

File [~/Desktop/code/Github/amazon-braket-default-simulator-python/src/braket/default_simulator/density_matrix_simulation.py:152](http://localhost:8888/lab/tree/examples/experimental_capabilities/dynamic_circuits/~/Desktop/code/Github/amazon-braket-default-simulator-python/src/braket/default_simulator/density_matrix_simulation.py#line=151), in DensityMatrixSimulation._apply_operations(state, qubit_count, operations)
    150 original_shape = state.shape
    151 result = state.view()
--> 152 result.shape = [2] * 2 * qubit_count
    153 temp = np.zeros_like(result, dtype=complex)
    154 work_buffer1 = np.zeros_like(result, dtype=complex)

ValueError: maximum supported dimension for an ndarray is 32, found 36

I think there is something wrong in setting qubit_count. It should be only 2 qubits but it uses the max qubit index as qubit count (=18 qubits).

Fixed in #378