Spectral interpretations of the Interlace polynomial

We relate the interlace polynomials of a graph to the spectra of a quadratic boolean function with respect to a strategic subset of local unitary transforms. By so doing we establish links between graph theory, cryptography, coding theory, and quantum entanglement. We establish the form of the interlace polynomial for certain functions, provide a new interlace polynomial, QHN , and propose a generalisation of the interlace polynomial to hypergraphs. We also prove some conjectures from [13] and equate certain spectral metrics with various evaluations of the interlace polynomial.

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