A parity-aware graphical calculus extends the ZX diagram language to fermionic modes, covering Gaussian states, partial traces, purification, fermionization/bosonization, and fermionic error-correcting codes.
A graphical approach to measurement-based quantum computing
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abstract
Quantum computations are easily represented in the graphical notation known as the ZX-calculus, a.k.a. the red-green calculus. We demonstrate its use in reasoning about measurement-based quantum computing, where the graphical syntax directly captures the structure of the entangled states used to represent computations, and show that the notion of information flow within the entangled states gives rise to rewriting strategies for proving the correctness of quantum programs.
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Graphical Calculus for Fermionic Tensors
A parity-aware graphical calculus extends the ZX diagram language to fermionic modes, covering Gaussian states, partial traces, purification, fermionization/bosonization, and fermionic error-correcting codes.