Sectorial constaints in quantum physics

Level: M1 - M2

Contact: Augustin Vanrietvelde

Email: augustin.vanrietvelde [at] inria [dot] fr

Location: Laboratoire Méthodes Formelles, Université Paris-Saclay

Keywords: Quantum Information, Sectorial constraints, Quantum circuits

Read the detailed internship proposal in pdf.


Recent years have seen considerable progress in the reformulation of fundamental physics concepts in informational terms, building on the perspective and techniques of the field of quantum information. One trend, interconnected with the study of quantum computing, has been to model physical processes in terms of quantum circuits [ 1, 2, 3 ]. The goal is to attain a more general and pliable account of known physics in informational terms, but also to open the door to the analysis of potential new physics [ 4, 5 ].

Yet, this led to the discovery that standard quantum circuits were not sufficient to properly describe some physical situations [ 6, 7, 8 ]. The common feature of these situations is the presence of sectorial constraints: some of the operations cannot connect between some sectors (i.e. orthogonal subspaces) of their input and output spaces. Sectorial constraints arise form the physical specifics of the processes that are being modelled, for example from conservation laws. This led to the design of an extended framework, that of ‘routed quantum circuits’, in which sectorial constraints are explicitly described [ 9, 10 ]. This allows to properly capture some otherwise ill-defined scenarios[ 11 ] and to perform a detailed causal analysis of them [ 12 ].

The introduction of sectorial constraints can carry fundamental significance for our understanding of physics, because they allow for the presence of coherence between sectors: broadly, they don’t mean that one should lose track of the phase between different subspaces. In contrast, most past treatments of similar problems (typically, those appealing to a notion of superselection) implicitly assumed that they implied the loss of all coherence between sectors. In that sense, using sectorial constraints allows to spot new phenomena and structure that might have gone unnoticed before.

The project

There are good reasons to believe that many more examples of physical scenarios involving sectorial constraints exist. Identifying them, and analysing them using routed quantum circuits, could help uncover some of their fundamental and practical features. In particular, studying the consequences of the preservation of coherence between sectors might be a key to progress. The intern will explore this question, applying the framework to the study of different physical situations. More specifically, there are many possible research directions to pursue along these lines, ranging from safe projects (clear-cut applications, with certainty of an outcome) to more ambitious ones (which may yield very novel and interesting results, but with a risk of leading nowhere). A list can be found in the detailed proposal available here.