[PhD proposal] Diagrammatic language for the quantum computer.

Diagrammatic language for the quantum computer.

Supervision : Simon Perdrix (simon.perdrix@loria.fr), Emmanuel Jeandel (emmanuel.jeandel@loria.fr)

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Context

ZX-calculus is a powerful graphical language for quantum computing. This language captures fundamental quantum notions such as entanglement, complementarity, causality and how they interact. A major challenge in the development of ZX-calculus is to make it an intermediate language between high-level languages and specific targets. High level quantum languages, like Quipper or Liqui|>, can be used to program the quantum computer, quantum algorithm libraries have already been developed in these languages. The specific, low-level targets are: (i) architecture proposals for the quantum computer based on various technologies; (ii) specific models of quantum computation such as measurement-based quantum computation; or (iii) simulation on a classical computer. ZX-calculus is the right level of abstraction for an intermediate language, plus it is equipped with a powerful equational theory for deciding program equivalence, or doing program optimization.

Objectives

Using ZX-calculus diagrams as an intermediate language requires the development of a new diagram description language, if only because a high-level program will not be compiled to a single diagram but to a family of diagrams set by the size of the input.

  •  Based on recent results on programming languages for quantum circuits and string diagrams, the objective is to propose a programming language allowing the description of ZX-calculus diagrams. The management of classical control from quantum measurements will be an important theoretical point.
  • Propose a categorical axiomatization of the concept of controlled diagrams, a powerful tool for describing diagrams. The objective is, in particular, to characterise the categories that allow control.
  • Finally, the objective is also to take into account the constraints linked to an implementation on concrete quantum computer architectures. The constraints of implementation — like bounded size memory, topological constraints on the memory, or set of specific quantum operations — will be addresses using transformations of diagrams or specific formalisms.

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