Distributed Measurement-based Quantum Computation

Abstract

We develop a formal model for distributed measurement-based quantum computations, adopting an agent-based view, such that computations are described locally where possible. Because the network quantum state is in general entangled, we need to model it as a global structure, reminiscent of global memory in classical agent systems. Local quantum computations are described as measurement patterns. Since measurement-based quantum computation is inherently distributed, this allows us to extend naturally several concepts of the measurement calculus [DKP04], a formal model for such computations. Our goal is to define an assembly language, i.e. we assume that computations are well-defined and we do not concern ourselves with verification techniques. The operational semantics for systems of agents is given by a probabilistic transition system, and we define operational equivalence in a way that it corresponds to the notion of bisimilarity. With this in place, we prove that teleportation is bisimilar to a direct quantum channel, and this also within the context of larger networks.

Classical Knowledge for Quantum Cryptographic Reasoning

“…This paper assumes some familiarity with quantum computation and reasoning about knowledge -for the reader not familiar with these domains, we refer to the excellent [19] and [12]. The present paper is a continuation of earlier work by the authors [4,7,8]. We present only the basics of this earlier work here, and refer the reader to the references cited above for more detailed explanations.…”

“…Several formal languages for protocol specification were developed, either in the flavour of classical process calculi [17,13,4] or in terms of dynamic logic [1]. Some of these frameworks have been augmented with logical tools for protocol analysis: both [14] and [8] use meta-logic reasoning to assert correctness properties on top of non-logical base language, though only the latter defines epistemic operators.…”

“…At the base level the protocol to be analysed is specified in the language of quantum networks [4], a protocol specification language for distributed quantum computations with evaluation rules and a formal semantics. On top of this we have a epistemic-temporal logical framework suitable for meta-logic analysis of the protocol under consideration, first developed in [8].…”

Quantum Predicative Programming

“…It also provides semantics for the language of [30]. Other interesting work by the same authors include reasoning about knowledge in quantum systems ( [16]) and developing a formal model for distributed measurement-based quantum computation ( [12]). A similar work is introduced in [17], where a language CQP for modelling communication in quantum systems is defined.…”

Computing the Exit Complexity of Knowledge in Distributed Quantum Computers

“…imitative computations direct to an omnipresent design of 'fault merciful' counting, of which an auxiliary observe is ascribed by Preskill [ 29]. Their claim been numerous approaches at explicating quantum schemas in provisos of formulation transformers: in [30] a synthesis of quantum assesses, based on propositional energetic deduction is constructed, while in [31], a weakest precondition semantics for quantum considerations are corrected. additionally, a propositional cogitation conceived to explicate quantum determination at an operational category is embed obtrusive in [32].…”