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In a free-fermionic circuit, each box is replaced by a matchgate under the Jordan-Wigner transformation. This allows us to efficiently evaluate the diagram using covariance matrices and quadratic Hamiltonians.
See "Fermionic Gaussian states: an introduction to numerical approaches"
The natural place to add fermionic circuits support in lambeq is a new module in the backend package, e.g. fermionic.py. This module will be similar in form with backend.grammar, backend.tensor and backend.quantum, and will include:
- A new class
backend.fermionic.Diagramwhich will inherit frombackend.quantum.Diagramand override any parts that are specific to fermionic circuits. Parts that remain the same can come from the base class unaltered. - New definitions for boxes (
backend.fermionic.Box) and types (backend.fermionic.Ty), inheriting from the corresponding quantum classes, if required. - New definitions for all quantum gates that change in the fermionic backend.
- New definitions for special boxes such as cups, caps, spiders, and swaps, when required.
- New
eval()method, if required. - New
to_tn(),to_tk(), andto_pennylane()methods, to make training with all available training backends possible.
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