How to implement controlled gate based on measurement (quantum teleportation)?

Question

I am implementing the teleportation algorithm on IBM Q Experience (GUI interface). Certain operations on the third qubit are only performed if the classical measurement result is 1, for example

if (c==1) x q[2];

However, it removes all the if statements after it is transpiled (lines 19 and 21). Do you know what I did wrong?

Answer 1

Currently IBM Q does not support IF statement on real quantum processor. The IF can be used on simulator only. However, there is a theorem stating that quantum gates controlled by classical register can be replaced by those controlled by qubits before measurement.

So, you can simply replace the statement

measure q[1] -> c[1];
if (c == 1) x q[2];

by

cx q[1], q[2];

i.e. qubit $q_1$ controls CNOT acting on $q_2$.

Similarly, you can do that for controlled $Z$ gate. In the end, you will get same results as with IF statement.

Answer 2

I contacted @fran-cabrera from the IBMQ team and he could reproduce the bug!

The problem is with the visualization of the transpiled circuit, not the execution (the result should be correct). The team is working on solving it and they expect to deploy a fix at the end of the week.

I ran you example in Qiskit and it seems to work

IBMQ.load_account()
provider = IBMQ.get_provider(group='open')
device = provider.get_backend('ibmq_16_melbourne')

qasm_string = """
OPENQASM 2.0;
include "qelib1.inc";
qreg q[3];
creg c[3];
h q[1];
cx q[1],q[2];
cx q[0],q[1];
h q[0];
measure q[1] -> c[1];
if(c==1) x q[2];
measure q[0] -> c[0];
if(c==1) z q[2];
measure q[2] -> c[2];
"""

circuit = QuantumCircuit.from_qasm_str(qasm_string)
circuit.draw('text')

                         ┌───┐┌─┐          
q_0: |0>─────────────■───┤ H ├┤M├──────────
        ┌───┐      ┌─┴─┐ └┬─┬┘└╥┘          
q_1: |0>┤ H ├──■───┤ X ├──┤M├──╫───────────
        └───┘┌─┴─┐ ├───┤  └╥┘  ║  ┌───┐ ┌─┐
q_2: |0>─────┤ X ├─┤ X ├───╫───╫──┤ Z ├─┤M├
             └───┘ └─┬─┘   ║   ║  └─┬─┘ └╥┘
                  ┌──┴──┐  ║   ║ ┌──┴──┐ ║ 
 c_0: 0 ══════════╡     ╞══╬═══╩═╡     ╞═╬═
                  │     │  ║     │     │ ║ 
 c_1: 0 ══════════╡ = 1 ╞══╩═════╡ = 1 ╞═╬═
                  │     │        │     │ ║ 
 c_2: 0 ══════════╡     ╞════════╡     ╞═╩═
                  └─────┘        └─────┘   

result = transpile(circuit,
                   backend=provider.get_backend('ibmq_16_melbourne'),
                   seed_transpiler=42)
result.draw('text', idle_wires=False)

                                            ┌──────────┐┌─┐             
q_0 -> 0 |0>────────────────────────■───────┤ U2(0,pi) ├┤M├─────────────
            ┌──────────┐          ┌─┴─┐     └───┬─┬────┘└╥┘             
q_1 -> 1 |0>┤ U2(0,pi) ├──■───────┤ X ├─────────┤M├──────╫──────────────
            └──────────┘┌─┴─┐┌────┴───┴────┐    └╥┘      ║ ┌────────┐┌─┐
q_2 -> 2 |0>────────────┤ X ├┤ U3(pi,0,pi) ├─────╫───────╫─┤ U1(pi) ├┤M├
                        └───┘└──────┬──────┘     ║       ║ └───┬────┘└╥┘
                                 ┌──┴──┐         ║       ║  ┌──┴──┐   ║ 
     c_0: 0 ═════════════════════╡     ╞═════════╬═══════╩══╡     ╞═══╬═
                                 │     │         ║          │     │   ║ 
     c_1: 0 ═════════════════════╡ = 1 ╞═════════╩══════════╡ = 1 ╞═══╬═
                                 │     │                    │     │   ║ 
     c_2: 0 ═════════════════════╡     ╞════════════════════╡     ╞═══╩═
                                 └─────┘                    └─────┘     

Based on this, I think your example should work in the IQX jupyter notebooks, included in the IBM Quantum Experience.