Kronecker Product in Circuits

leimao.github.io

35 points·keyboardman··5 comments

As a shameless plug, if you want to visualize Kronecker product in circuits, I wrote an open-source Vue-based tool for visualizing quantum states and operators (with strong support for the tensor structure):

https://github.com/Quantum-Game/bra-ket-vue

There is an example of CNOT on the front page, you can create and visualize other gates. Including Toffoli in a strange basis, https://twitter.com/QuantumGameIO/status/1231938026806353920.

If you want to use that, I am happy to help. (All operations you mentioned are easy implementable with BraKetVue + Quantum Tensors, so if you want to make an interactive demo, it should be straightforward.)

This is pretty nice! My first impulse was that could be visualized as a boolean matrix. Good going.

Unsurprisingly, this is applied for quantum circuits as well: https://vtomole.com/blog/2018/03/03/sd. It's the most popular way of introducing quantum computation.

Does anyone have a geometric intuition for Kronecker products? Or even any intuition for it? I've never been able to move beyond the formalism of it.

If you think of a binary matrix as the adjacency matrix of a graph, the kronecker product corresponds to the product of graphs, which is a 100% geometrical construct.

If your matrix has arbitrary weigths, this is the "weighted" graph product, where the weights of the edges are multiplied in the obvious manner (each edge in the product graph comes from a pair of edges of each input graph, and its weight is just the product of the two input weights).

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