In 2020 our Oxford-based Quantinuum team performed Quantum Natural Language Processing (QNLP) on IBM quantum hardware [1, 2]. Key to having been able to achieve what is conceived as a heavily data-driven task, is the observation that quantum theory and natural language are governed by much of the same compositional structure -- a.k.a. tensor structure.
Hence our language model is in a sense quantum-native, and we provide an analogy with simulation of quantum systems in terms of algorithmic speed-up [forthcoming]. Meanwhile we have made all our software available open-source, and with support [github.com/CQCL/lambeq].
The compositional match between natural language and quantum extends to other domains than language, and argue that a new generation of AI can emerge when fully pushing this analogy, while exploiting the completeness of categorical quantum mechanics / ZX-calculus [3, 4, 5] for novel reasoning purposes that go hand-in-hand with modern machine learning.
[1] B. Coecke, G. De Felice, K. Meichanetzidis and A. Toumi (2020) Foundations for Near-Term Quantum Natural Language Processing. https://arxiv.org/abs/2012.03755
[2] R. Lorenz, A. Pearson, K. Meichanetzidis, D. Kartsaklis and B. Coecke (2020) QNLP in Practice: Running Compositional Models of Meaning on a Quantum Computer. https://arxiv.org/abs/2102.12846
[3] B. Coecke and A. Kissinger (2017) Picturing Quantum Processes. A first course on quantum theory and diagrammatic reasoning. Cambridge University Press.
[4] B. Coecke, D. Horsman, A. Kissinger and Q. Wang (2021) Kindergarten quantum mechanics graduates (...or how I learned to stop gluing LEGO together and love the ZX-calculus). https://arxiv.org/abs/2102.10984
[5] B. Coecke and S. Gogioso (2022) Quantum in Pictures. Quantinuum, 2023.
I will report onexperiments that were performed with superconducting microwave photoniccrystals, that is, flat resonators containing circular scatterers arranged on atriangular grid, so-called Dirac billiards (DBs). The eigenfrequencies of wavepropagation as function of the two quasimomentum components exhibit a bandstructure which comprises two Dirac points (DPs), where two bands touch eachother conically, and in between them a nearly flat band. This is reminiscent ofa combined Honeycomb-Kagome lattice. The high-precision measurements allowedthe determination of complete sequences of several thousands of eigenfrequencies.Around the DPs the density of states (DOS) of DBs is similar to that ofgraphene and well described by a finite tight-binding model which includesfirst-, second-, and third-nearest-neighbor couplings. At the band edges DBsare governed by the non-relativistic Schrödinger equation of the quantumbilliard, around the DPs by the Dirac equation of the graphene billiard ofcorresponding shape, respectively. We analyzed the spectral properties of DBsof various shapes and compare them to those of graphene billiards andrelativistic & non-relativistic quantum billiards.
