[Feature] Conditional feed-forward operations

[arthurfaria]

For my QGNN implementations, I need conditional operations since the quantum pooling layer relies on these types of gates [1]. As in CNNs, QCNNs consist of convolution layers that finds a new state and a pooling layer that reduces the size of the system. Below is an example:

Hence, for the quantum pooling layer, we need those conditional feed-forward operations, defined as follows [2]:

• Principle of deferred measurement: a controlled gate followed by a measurement of the controlled qubit results in the same as first performing the measurement and then applying a classically-controlled gate as in Fig. below

In addition, these conditional operations are a necessary ingredient for quantum error correction, such as in surface code schemes. They check for errors using measurements in ancillas and depending on the measurement results, the system either performs error correction or does not.

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ref. [1]: https://arxiv.org/pdf/2009.09423
ref. [2]: https://arxiv.org/pdf/2308.13065

[jpmoutinho]

Hey @arthurfaria, thanks for opening this! How urgently do you need it?

Doing a fully integrated implementation of conditional gates would likely require a bit of re-thinking of some core features of Qadence, like adding a classical register, a different measurement operation other than "sample", and implementing the control mechanism.

However, there should be sufficient tools in Qadence to replicate the circuit you want. For example, since the measured qubits are not reused, instead of measuring you can just do a normal control gate and then post-process the data at the end and post-select on the state of the ancilla qubits. That way each pooling layer will not "reduce" size of the system, but it will have the same effect. Well this is essentially just not doing the deferred measurement like you said.

[rajaiitp]

As far as the runtime, I think its gonna be identical as you would have to run thru all possible projections of the qubits being measured (subspace scaled down by 2^k, but additional 2^k simulations). If you are interested in specific projections alone, I presume a quicker hack would be is to use projector operator once all the controlled operations are performed and reuse the subspace output of interest for further simulations

[jpmoutinho]

Yes indeed @rajaiitp, and projectors are also available in Qadence (see here).

[Roland-djee]

@jpmoutinho @arthurfaria @rajaiitp It would be good to start on this I guess.