## Trying to make irreversable operation in the quantum circuit

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I want to make a 2 qubit circuit such that the non-unitary program will transform the regular basis in the way that:

$$|0 0\rangle \to |00\rangle$$

$$|0 1\rangle \to |01\rangle$$

$$|10\rangle \to |01\rangle$$ (the only one that affected)

$$|11\rangle \to |11\rangle$$

The only way I think of doing it, is after measuring the circuit I will change the classical outcomes so it will fit the transformation, for example in the classic way I would code:

if c[0]==1 & c[1]==0
c[0]==0
c[1]==1


but I didn$$`$$t find a way to write it in Qiskit language, please help.

Just hint: first q-bit of result is logical product (AND) of both input q-bits, second one is logical sum (OR) of both inputs. AND and OR can be implemented with Toffoli gate. – Martin Vesely – 2019-11-12T17:13:27.927

2The use of "unreversible" and "ununitary" in your question is unusual. All operations on a quantum circuit must be unitary, and therefore reversible. – Jonathan Trousdale – 2019-11-12T20:55:12.557

1Daniel, I agree with @ChainedSymmetry - the question seems confusing. Do you have a classical circuit, and you are wondering how to realize it with quantum (unitary and reversible) gates? A classical circuit made of $\mathsf{AND}$ and $\mathsf{OR}$ gates, such as any bit of combinatorial logic, may be converted to a unitary, reversible circuit that uses Toffoli gates, as Martin mentions. – Mark S – 2019-11-12T21:36:18.720

1@ChainedSymmetry: It bring to my mind one question: What about reset gate? Naturaly, it is not reversible operation. How does this fit to the concept of quantum computation? – Martin Vesely – 2019-11-12T22:10:18.113

@MartinVesely It's a good question, and DaftWullie gives a good answer here (short answer, you have to take a measurement and possibly bit-flip). I'm guessing this is not easy to implement in hardware, which is why it's only available in IBM Q simulations.

– Jonathan Trousdale – 2019-11-13T03:03:35.297

## Answers

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I tried to implement your transformation on IBM Q. Here is the result:

Input is $$|00\rangle$$ in this case. You can set input values by application of $$X$$ gates on q-bits $$|q0\rangle$$ and $$|q1\rangle$$.

Please note that this circuit run on a simulator only as reset gate has not been implemented on real IBM Q quantum hardware. But it is possible to simply measure $$|q2\rangle$$ and $$|q3\rangle$$. In that case your transformation become reversible.

is that an image of a quantum circuit or quantum register and is there a textbook that shows how to read them with examples? – develarist – 2019-11-15T01:13:24.703

Initial state of a quantum register is on left hand side of the figure, a quantum circuit doing actual calculation (or quantum state transformation) follows. The right hand side of the figure contains measurement of the quantum register and record of the quantum state to a classic register. – Martin Vesely – 2019-11-15T05:45:33.867

See more inforation on how to read quantum circuits for example here https://en.wikipedia.org/wiki/Quantum_circuit.

– Martin Vesely – 2019-11-15T05:53:23.957

Why do you have q4 there not connected to anything? – AHusain – 2019-11-16T21:04:09.787

@AHusain: I just used implicit configuration on IBM Q and there is always 5 qbits unless you say otherwise. Qbit q4 is of course not necessary for correct work of the circuit. – Martin Vesely – 2019-11-16T23:14:24.123