Fig. 7: Circuits implementing the collisional model.
From: IBM Q Experience as a versatile experimental testbed for simulating open quantum systems
The top circuit shows the case of the collision with three ancillae in the separable \(\left|+++\right\rangle\) state, prepared by means of Hadamard gates. Each collision consists of a rotation around \(Z\) between two CNOTs. A final measurement in the \(X\) basis is performed in order to measure the coherence of the system qubit. The bottom circuit shows how, in the case of ancillae prepared in the correlated state, we can effectively simulate the map with three ancillae prepared in the GHZ state \((\left|000\right\rangle +\left|111\right\rangle )/\sqrt{2}\), by colliding alternately with two of them. Notice that, in principle, we could have always a collision with the same ancilla. This, however, would cause the compiler to remove consecutive CNOTs and join the rotations into a single gate, making the circuit trivial. The top circuit was run on ibmq_16_melbourne, while the bottom circit was run on ibmqx2.
