How to create a condition on only one classical bit when we have a total of 2 classic bits in the system

Question

I am trying to make a quantum circuit with one qubit and 2 classical bits for each measurment in the system below:

I want to make condition on the first bit: if the first collapse to zero so x operator is act on the circuit, else (one) nothing is acting on the circuit.

I am using qiskit language.

but when I try to create my circuit, there is always an error:

#definitions
q = QuantumRegister(1)
c = ClassicalRegister(2)
qc = QuantumCircuit(q,c)

# building the circuit
qc.h(q)
qc.measure(q[0],c[0])
qc.x(q[0]).c[0]_if(c[0], 0)
qc.measure(q[0],c[1])
circuit_drawer(qc)

and the error is:

  File "<ipython-input-4-66c70285946b>", line 3
    qc.x(q[0]).c[0]_if(c[0], 0)
                     ^
SyntaxError: invalid syntax

how to write it correctly?

When I try to change

qc.x(q[0]).c[0]_if(c[0], 0)

with:

qc.x(q).c_if(c, 0)

I succeed in building my circuit but I get circuit that I don`t want to work with:

I wish for help, thanks.

Answer 1

The controlled NOT gate does the opposite of what you want, it applies $X$ to the target qubit if the control qubit is 1, and does nothing if the control qubit is 0.

What you want is to apply $X$ when the control qubit is 0 and do nothing when it is 1. This can be accomplished by applying a NOT gate (i.e. an $X$ gate) before doing the CNOT.

In the IBM composer it would look like this:

The code for doing CNOT in quiskit is:

gate cx c,t {
 CX c,t; 
}

Since there is a specific gate for what you want to do, you do not need any "if statements"!

Answer 2

See the answer to this question for more on how the classical control works. Basically, your operations are controlled on the integer stored (in binary) across a register rather than on the individual bits themselves.

I also don't quite know the 'best practice' way of controlling on single bits, but I can tell you my workaround. Instead of creating a register with two bits, I create a list of two single qubit registers.

c = [ ClassicalRegister(1) for _ in range(2) ]

These can be added using the add method of a quantum circuit.

q = QuantumRegister(1)
qc = QuantumCircuit(q)
for register in c:
    qc.add_register( register )

Then it is possible to use your 'building the circuit' code can be done with

qc.h(q)
qc.measure(q,c[0])
qc.x(q[0]).c_if(c[0], 0)
qc.measure(q,c[1])
circuit_drawer(qc)

This works because c[0] now refers to a classical register, rather than a single bit from a classical register.