Abstract
We present a Matlab toolbox, called “FockBox”, handling Fock spaces and objects associated with Fock spaces: scalars, ket and bra vectors, and linear operators. We give brief application examples from computational linguistics, semantics processing, and quantum logic, demonstrating the use of the toolbox.
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Notes
- 1.
Here we adopt Dirac’s bra-ket-notation as “a neat and concise way of writing, in a single scheme, both the abstract quantities themselves and their coordinates.” [3].
- 2.
This is an actual problem, e.g., for semantic modeling (see Sect. 4.2) where a ket representing a feature-value relation comprising a moderate number of \(2^8=256\) different feature and value symbols would already exceed \(2^{64}\) row indexes for depths \(>\!8\).
- 3.
These operations are not “coordinate-free” in the sense that they are not compatible with a change of orthonormal basis of Hilbert space.
- 4.
Note that the representation of a sparse matrix \(\mathbf {x}\) in memory is just a list containing the elements of set x.
- 5.
The exact data are reported by Moore [13]. Busemeyer and Bruza use play data for their computations displaying only some tendency of the reported data.
- 6.
A model for quantum measurement is just a projection followed by a preparation.
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Wolff, M., Wirsching, G., Huber, M., beim Graben, P., Römer, R., Schmitt, I. (2018). A Fock Space Toolbox and Some Applications in Computational Cognition. In: Karpov, A., Jokisch, O., Potapova, R. (eds) Speech and Computer. SPECOM 2018. Lecture Notes in Computer Science(), vol 11096. Springer, Cham. https://doi.org/10.1007/978-3-319-99579-3_77
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