AmplitudeAnsatz for performing Amplitude Encoding - Feature request

[ACE07-Sev]

Description

The choice of the feature map is perhaps the most important choice a QML engineer can make, as it will directly dictate the size of the circuit required. There are four common encoding algorithms :

• Basis Encoding
• Angle Encoding
• Amplitude Encoding
• Arbitrary Encoding

There is a wide array of literature on each of the approaches mentioned, with each having its own list of algorithms. However, as a rule of thumb, amplitude encoders are more appropriate for large models given their logarithmic scaling in terms of number of qubits with respect to number of features to be embedded. Currently, Lambeq is using IQPAnsatz based on IQP Encoding which similarly to Angle encoding requires N qubits to encode N features. For now, we will ignore the depth scaling.

The challenge is to create a new encoder class called AmplitudeAnsatz based on amplitude encoding, with the motivation of the efficiency of amplitude encoders for high dimensional data.

Notes

• One can start by creating an ansatz that does amplitude encoding (i.e., RFV, FRQI, etc.)
• The amplitude encoder must take into consideration how Lambeq currently performs the feature embedding (i.e., using qubit count dedicated to each AtomicType)
• The implementation must take into consideration how Model is trained given the embedded circuits (going back to what Model is exactly)

See Also

https://cqcl.github.io/lambeq/tutorials/extend-lambeq.html#Creating-ans%C3%A4tze
https://arxiv.org/pdf/1804.11326.pdf
https://docs.pennylane.ai/en/stable/code/api/pennylane.IQPEmbedding.html
https://qiskit.org/documentation/stubs/qiskit.circuit.library.IQP.html
https://qiskit.org/ecosystem/machine-learning/tutorials/01_neural_networks.html