Quantum weakest preconditions

Abstract

We develop a notion of predicate transformer and, in particular, the weakest precondition, appropriate for quantum computation. We show that there is a Stone-type duality between the usual state-transformer semantics and the weakest precondition semantics. Rather than trying to reduce quantum computation to probabilistic programming we develop a notion that is directly taken from concepts used in quantum computation. The proof that weakest preconditions exist for completely positive maps follows immediately from the Kraus representation theorem. As an example we give the semantics of Selinger's language in terms of our weakest preconditions. We also cover some specific situations and exhibit an interesting link with stabilizers.

Deriving the correctness of quantum protocols in the probabilistic logic for quantum programs

“…A significant recent development is the strengthening of quantum logic to be able to address quantum computation as well (Dunn et al 2013). This coincides with development to formalize the semantics of quantum programs (D'Hondt and Panangaden 2006b) and the development of model checkers and verification tools for quantum systems (Gay et al 2008;Feng et al 2013;Ying et al 2013).…”

Creating and preserving multi‐partite entanglement with spin chains

“…We illustrated this by showing how a tripartite W-state could be created and completely frozen in a very simple branched system. W-states are robust and immune against global dephasing [29]; research is on-going into specific applications of W-states, including in teleportation [30] secure communication [31] and leadership election protocols [32]. Generally, distributed entanglement provides a useful resource, for example for teleportation [24] or distributed quantum processing.…”

Natural Quantum Operational Semantics with Predicates

“…It the case where the support of F consists of only one atom, the corresponding quantum predicate E F is the same as that constructed in (D'Hondt and Panangaden, 2006). A generalisation of this result to the infinite dimension setting and a continuously supported POVM is presented elsewhere (Gielerak and Sawerwain, 2007).…”