Here we present a first study of search spaces and fitness landscapes in the context of the evolution of quantum programs. We consider small instances of the Deutsch-Jozsa problem as a starting point for the exploration of search spaces of quantum algorithms and analyze the structure of mutation landscapes using autocorrelation functions and information measures for characterizing their behavio...

We study the space of biinvariants and zonal spherical functions associated to quantum symmetric pairs in the maximally split case. Under the obvious restriction map, the space of biinvariants is proved isomorphic to the Weyl group invariants of the character group ring associated to the restricted roots. As a consequence, there is either a unique set, or an (almost) unique two-parameter set of...

We show that the family of spectral triples for quantum projective spaces introduced by D’Andrea and Da̧browski, which have spectral dimension equal to zero, can be reconsidered as modular spectral triples by taking into account the action of the element K2ρ or its inverse. The spectral dimension computed in this sense coincides with the dimension of the classical projective spaces. The connecti...

We pursue the principles of duality and symmetry building upon Pratt’s idea of the Stone Gamut and Abramsky’s representations of quantum systems. In the first part of the paper, we first observe that the Chu space representation of quantum systems leads us to an operational form of state-observable duality, and then show via the Chu space formalism enriched with a generic concept of closure con...

A particularly simple and flexible mathematical framework for the study of probability theory classical, quantum and otherwise is the notion of a test space, i.e., a collection of (possibly overlapping) discrete sample spaces (as developed in the 1970s and 80s by D. J. Foulis, C. H. Randall and others). “Quantum logics” arise quite naturally as invariants of test spaces; however, the latter are...