Help to understand QCNN?

[ghost]

Could anyone help to explain how this function works?

def two_qubit_pool(source_qubit, sink_qubit, symbols): """Make a Cirq circuit to do a parameterized 'pooling' operation, which attempts to reduce entanglement down from two qubits to just one."""

https://github.com/tensorflow/quantum/blob/master/docs/tutorials/qcnn.ipynb

 Thanks!

[MichaelBroughton]

This function is to recreate a cirq.Circuit that enacts something similar to the pooling operation used in https://arxiv.org/pdf/1810.03787.pdf . If you want more details than what we give in the tutorial I would recommend giving it a read :)

[ghost]

Thanks @MichaelBroughton ! In that paper, they showed a measurement so two qubits are reduced to one. But in this function, there is no measurement:

def two_qubit_pool(source_qubit, sink_qubit, symbols): """Make a Cirq circuit to do a parameterized 'pooling' operation, which attempts to reduce entanglement down from two qubits to just one.""" pool_circuit = cirq.Circuit() sink_basis_selector = one_qubit_unitary(sink_qubit, symbols[0:3]) source_basis_selector = one_qubit_unitary(source_qubit, symbols[3:6]) pool_circuit.append(sink_basis_selector) pool_circuit.append(source_basis_selector) pool_circuit.append(cirq.CNOT(control=source_qubit, target=sink_qubit)) pool_circuit.append(sink_basis_selector**-1) return pool_circuit

[MichaelBroughton]

Yes, instead of measuring we just discard the unused qubits and don't operate on them anymore (which in this context has the same effect).

[ghost]

Thanks @MichaelBroughton ! Which lines do the job of "discard the unused qubits"? Beacuse of cirq.CNOT(control=source_qubit, target=sink_qubit), the two lines are entangled. How do you discard the unused qubits?

[MichaelBroughton]

This happens in software. You can see later on in the tutorial that as we apply the conv and pool layers we operate on fewer and fewer qubits as the network gets deeper. Finally the fact that we don't measure or continue to operate on those qubits is how they get discarded.

If things are still unclear I would recommend examining the circuits and readout operators we are using in the QCNN tutorial and convincing yourself that these circuits are in fact (mostly) equivalent to what is happening in their paper.

Closing.

[ghost]

Hi @MichaelBroughton, Could you explain this comment: """Make a Cirq circuit to do a parameterized 'pooling' operation, which attempts to reduce entanglement down from two qubits to just one.""" What are the two and what is the one in this comment? Thanks!

[ghost]

Hi @MichaelBroughton, one of the consequences of pooling is to create nonlinear effect. If you do not take any measurement in the process, then I guess you do not have this effect? Thanks!