This paper introduces a new notion of quantum recursion of which the control flow of the computation is quantum rather than classical as in the notions of recursion considered in the previous studies of quantum programming. A typical example is recursive quantum walks, which are obtained by slightly modifying the construction of the ordinary quantum walks. The operational and denotational seman...

Resistive switching offers a promising route to universal electronic memory, potentially replacing current technologies that are approaching their fundamental limits. In many cases switching originates from the reversible formation and dissolution of nanometre-scale conductive filaments, which constrain the motion of electrons, leading to the quantisation of device conductance into multiples of...

After motivating why the study of asymptotically flat spaces is important in loop quantum gravity, we review the extension of the standard framework of this theory to the asymptotically flat sector detailed in [1]. In particular, we provide a general procedure for constructing new Hilbert spaces for loop quantum gravity on non-compact spatial manifolds. States in these Hilbert spaces can be int...

The known canonical quantum theory of a spherically symmetric pure (Schwarzschild) gravitational system describes isolated black holes by plane waves exp(−iMc2τ/h̄) with respect to their continuous masses M and the proper time τ of observers at spatial infinity. On the other hand Bekenstein and Mukhanov postulated discrete mass levels for such black holes in the spirit of the Bohr-Sommerfeld qua...

The algebraic theory of double product integrals and particularly its role in the quantisation of Lie bialgebras is described. When the underlying associative algebra is that of the Itô differentials of quantum stochastic calculus such product integrals are formally represented as operators which are infinite sums of iterated integrals in Fock space. In this paper we describe some of the analyt...

the rank-k numerical range has a close connection to the construction of quantum error correction code for a noisy quantum channel. for noisy quantum channel, a quantum error correcting code of dimension k exists if and only if the associated joint rank-k numerical range is non-empty. in this paper the notion of joint rank-k numerical range is generalized and some statements of [2011, generaliz...

Loop quantum gravity is a physical theory that aims at unifying general relativity and mechanics. It takes very seriously modifies it via quantisation. General describes in terms of geometry; therefore, quantising such must be equivalent to geometry what loop does. This sounds like mathematical task as well, thus, this paper we will present the mathematics gravity. We do from mathematician’s po...

This is a pedagogical and (almost) self-contained introduction into the Theorem of Groenewold and van Howe, which states that a naive transcription of Dirac’s quantisation rules cannot work. Some related issues in quantisation theory are also discussed. First-class constrained systems a briefly described in a slightly more ‘global’ fashion.1