Efficiency of CNOT Gates in Quantum Circuit Design

[jimmycricket]

I'm constructing a quantum circuit that implements a gray code that connects the binary strings |0001> and |1110> using CNOT gates. Since the two strings are negations of each other, two equivalent circuits can be designed where the control qubit conditions are negated. My question is what is more efficient/ easier to construct: a CNOT where control qubit is set if it equals 0 or one where its set if it equals 1?

 

[Strilanc]

I'm constructing a quantum circuit that implements a gray code that connects the binary strings |0001> and |1110> using CNOT gates. Since the two strings are negations of each other, two equivalent circuits can be designed where the control qubit conditions are negated. My question is what is more efficient/ easier to construct: a CNOT where control qubit is set if it equals 0 or one where its set if it equals 1?

Given that no one has managed to make a large quantum computer at scale yet, your question won't be answerable in detail for years.

Most likely is that they would cost the same amount, since the roles of |0> and |1> are usually easily swapped (e.g. |0> being 'clockwise current' and |1> being 'counterclockwise current'). If they did differ, it would depend heavily on how the machine was actually implemented.

Here's a simulator you can use to test if your circuit works correctly.