Unnecessary zero-probability states returned by Sampler, with different behaviour to Aer Sampler

Environment

• Qiskit Terra version: 0.23.0.dev0+ad07847
• Python version: 3.10.4
• Operating system: macOS Monterey 12.6 M1 2020

What is happening?

• Sampler returns a dictionary with every possible state, even if some states have a probability 0 of being sampled. As the number of qubits is increased, the size of this dictionary will scale exponentially.
• The behaviour is different to the qiskit_aer Sampler, which does not return states with probability 0. Importantly, since the number of qubits is not saved, this results in a faulty conversion to binary strings in qiskit_aer using the binary_probabilities() method. This is probably because the length of the binary strings is calculated based on the number of returned states instead of the number of qubits, which in Aer is a subset of all possible states.

How can we reproduce the issue?

from qiskit_aer.primitives import Sampler as aer_sampler
from qiskit.primitives import Sampler as terra_sampler

qc = QuantumCircuit(4)
qc.h(0)
qc.measure_all()

terra_job = terra_sampler().run([qc], [], shots=10)
terra_quasis = terra_job.result().quasi_dists[0]
terra_bin_probs = terra_quasis.binary_probabilities()
print('TERRA RESULTS:')
print('\n', terra_quasis)
print('\n', terra_bin_probs)

aer_job = aer_sampler(backend_options={"method": "statevector"}).run([qc], [], shots=100)
aer_quasis = aer_job.result().quasi_dists[0]
aer_bin_probs = aer_quasis.binary_probabilities()
print('\nAER RESULTS:')
print('\n', aer_quasis)
print('\n', aer_bin_probs)

TERRA RESULTS:

{0: 0.5, 1: 0.5, 2: 0.0, 3: 0.0, 4: 0.0, 5: 0.0, 6: 0.0, 7: 0.0, 8: 0.0, 9: 0.0, 10: 0.0, 11: 0.0, 12: 0.0, 13: 0.0, 14: 0.0, 15: 0.0}

{‘0000’: 0.5, ‘0001’: 0.5, ‘0010’: 0.0, ‘0011’: 0.0, ‘0100’: 0.0, ‘0101’: 0.0, ‘0110’: 0.0, ‘0111’: 0.0, ‘1000’: 0.0, ‘1001’: 0.0, ‘1010’: 0.0, ‘1011’: 0.0, ‘1100’: 0.0, ‘1101’: 0.0, ‘1110’: 0.0, ‘1111’: 0.0}

AER RESULTS:

{1: 0.54, 0: 0.46}

{‘1’: 0.54, ‘0’: 0.46}

What should happen?

We should see only the non-zero probability states in Terra, and a correct conversion to binary in Aer (i.e. matches the number of qubits):

TERRA RESULTS:

{0: 0.5, 1: 0.5}

{‘0000’: 0.5, ‘0001’: 0.5}

AER RESULTS:

{1: 0.54, 0: 0.46}

{‘0001’: 0.54, ‘0000’: 0.46}

Any suggestions?

• Since the "statevector" method in Aer doesn’t return zero probability states, the same steps could be applied to the Statevector in Terra (which is called by the Sampler).
• The number of qubits could be saved in the metadata of the SamplerResult, such that Aer can properly do the conversion to binary probabilities.

[ikkoham]

Also Terra’s Sampler should use probabilities_dict method instead of probabilities. https://github.com/Qiskit/qiskit-terra/blob/main/qiskit/quantum_info/states/quantum_state.py#L216

[t-imamichi]

Yes, it might be good to remove bits with 0 prob at QuasiDistribution side. It can be a good first issue too.