From Fermions to Qubits: A ZX-Calculus Perspective
summary
Claims a unified graphical framework using the scalable ZX-calculus that maps fermionic encodings to qubit circuits, proving correspondence between linear encodings and phase-free ZX-diagrams and that every ternary-tree mapping yields a linear encoding. It gives a constructive translation of ternary trees to scalable ZX-diagrams, extracts CNOT-style encoder circuits, and provides an algorithm to compute the binary matrix for any ternary tree. The framework also yields encoder diagrams that match the fermionic interaction graph and exposes stabilizers; several proofs and constructions are formal and effective.
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chapters (11)
- 0:00Fermion to qubit mappings intro
- 1:09Studying fermionic systems
- 4:49Defining fermion mappings
- 7:39ZX calculus overview
- 9:47Scalable ZX for qubits
- 11:55Background recap
- 12:19Linear encodings in mappings
- 15:35Bravyi-Kitaev encoding
- 16:57Ternary tree mappings
- 18:00Ternary trees to ZX diagrams
- 20:29Q&A
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