Got different probabilities if not placing measurement at the end

[wangzbo]

I am not quite sure if this is an issue, or it's working as design, or a use problem. I'll try to make it clear using an example:

I create a 4-qubit GHZ state circuit and measure all at the end of the circuit(import from openqasm), then call probabilities and measureAllMultishot:

  const circuit = new QuantumCircuit(4);
  circuit.importQASM('OPENQASM 2.0;\ninclude "qelib1.inc";\nqreg q[4];\ncreg c[4];\nh q[0];\ncx q[0], q[1];\ncx q[1], q[2];\ncx q[2], q[3];\nmeasure q[0] -> c[0];\nmeasure q[1] -> c[1];\nmeasure q[2] -> c[2];\nmeasure q[3] -> c[3];', function(errors: any) {
    console.log(errors);
  }, true);
  circuit.run();
  console.log(circuit.probabilities());
  console.log(circuit.measureAllMultishot(1024));

This is the result and it looks correct:
[0.5, 0.5, 0.5, 0.5]
{1111: 520, 0000: 504}

If change the circuit a little bit, and move some measurements to the front, the circuilt will be something like:

Then I import the circuit and call probabilities and measureAllMultishot:

  const circuit1 = new QuantumCircuit(4);
  circuit1.importQASM('OPENQASM 2.0;\ninclude "qelib1.inc";\nqreg q[4];\ncreg c[4];\nh q[0];\ncx q[0], q[1];\nmeasure q[0] -> c[0];\ncx q[1], q[2];\nmeasure q[1] -> c[1];\ncx q[2], q[3];\nmeasure q[2] -> c[2];\nmeasure q[3] -> c[3];', function(errors: any) {
    console.log(errors);
  }, true);
  circuit1.run();
  console.log(circuit1.probabilities());
  console.log(circuit1.measureAllMultishot(1024));

I got a different result from above:
[0, 0, 0, 0]
{0000: 1024}
Every run only produce one result.

As a comparison I also had a try with the second circuit using qiskit:

from qiskit import QuantumCircuit
from qiskit_aer.primitives import SamplerV2
qc1 = QuantumCircuit.from_qasm_str('OPENQASM 2.0;\ninclude "qelib1.inc";\nqreg q[4];\ncreg c[4];\nh q[0];\ncx q[0],q[1];\nmeasure q[0] -> c[0];\ncx q[1],q[2];\nmeasure q[1] -> c[1];\ncx q[2],q[3];\nmeasure q[2] -> c[2];\nmeasure q[3] -> c[3];')
sampler = SamplerV2()
job = sampler.run([qc1], shots=1024)
job_result = job.result()
print(f"counts : {job_result[0].data.c.get_counts()}")

counts : {'0000': 480, '1111': 544}
It returns almost half 0000 and half 1111.

[perak]

Hi @wangzbo sorry for late reply:

After you moved measurement in the middle of the circuit, following happens:

• After H gate and first CNOT gate, first two qubits are in equal superposition.
• Then first measurement executes and state "collapses" to one of two states (|0000> or |1100>).
• Now, there is no superposition anymore and second CNOT has either |0> or |1> at control qubit q[1].

If you run that circuit multiple times, sometimes you will get { "0000": 1024 }, and other times { "1111": 1024 }.

In original circuit, where measurement is at the end:

After all gates are executed, before any measurement, circuit is in equal superposition of 1/sqrt(2) (|0000> + |1111>), measurement it will collapse to either 0000 or 1111, so result will be { "0000": 512, "1111": 512 }.

Why Qiskit gives different output?

It executes entire circuit shot times. This is behavior of a quantum computer.
Our package executes circuit once, and simply samples state vector shot times.

Is this a bug?

Well, yes it is.

If measurement is not at the end of the circuit, you will get correct results only if you run circuit multiple times and collect results.

What we can do to fix?

Detect if there is any gate after measurement, and rerun circuit for every shot (instead simply sampling state vector shot times).

Thank you for reporting this!