The diagonalization method in quantum recursion theory

Abstract

As quantum parallelism allows the effective co-representation of classical mutually exclusive states, the diagonalization method of classical recursion theory has to be modified. Quantum diagonalization involves unitary operators whose eigenvalues are different from one.Comment: 15 pages, completely rewritte

Formal verification of communication protocols using quantized Horn clauses

“…There are four assumptions on Equation (30), which is a generalized form of Equation ( 27), required for applying the adiabatic elimination model reduction method and we list them now. For a more detailed treatment of this approximation and the assumptions involved we refer the reader to the work of Bouten et al It is important to note that the adiabatic approximations are applied to individual cavities and the composite system is constructed out of the two limiting systems.…”

“…Rigorous certification of quantum information is an active area of research as in formal verification of quantum processes [8], topological quantum computation [9], quantum lambda calculus based approaches [7], and quantum prolog where predicates are quantized using the annealing paradigm [33]. Formal methods also play a critical role in decidability of algorithms, either classical or quantum, as exemplified by the tools of partial recursive functions [30]. Recently, Schulman and Schreiber integrated mathematical logic and quantum field theory [11] using cohesive Homotopy type theory.…”