TL;DR
This paper proposes a diagrammatic, intuitive formalism for quantum theory based on monoidal categories, aiming to simplify understanding, reasoning, and computation in quantum physics and related fields.
Contribution
It introduces a high-level diagrammatic approach to quantum mechanics that enhances intuition, simplifies calculations, and supports automation, based on recent mathematical developments in monoidal categories.
Findings
Provides diagrammatic proofs of quantum computational schemes
Analyzes the structural origin of quantum non-locality
Exposes limitations like the no-cloning theorem
Abstract
The quantum mechanical formalism doesn't support our intuition, nor does it elucidate the key concepts that govern the behaviour of the entities that are subject to the laws of quantum physics. The arrays of complex numbers are kin to the arrays of 0s and 1s of the early days of computer programming practice. In this review we present steps towards a diagrammatic `high-level' alternative for the Hilbert space formalism, one which appeals to our intuition. It allows for intuitive reasoning about interacting quantum systems, and trivialises many otherwise involved and tedious computations. It clearly exposes limitations such as the no-cloning theorem, and phenomena such as quantum teleportation. As a logic, it supports `automation'. It allows for a wider variety of underlying theories, and can be easily modified, having the potential to provide the required step-stone towards a deeper…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.