Ilya Kondratyev | Searcharxiv

arXiv2024

Calculating HOMFLY-PT polynomials on a photonic processor

In this paper we discuss an approach to calculate knot polynomials on a photonic processor. Calculations of knot polynomials is a computationally difficult problem and therefore it is interesting to use new advanced calculation methods to find them. Here we present a proof of concept by calculating the simplest knot polynomial of the trefoil knot in fundamental representation. This approach, however, can easily be generalized to more complex knots and representations. Same operators can also be realized on a quantum computer with the same effect.

quant-ph↗

arXiv2019

Robust architecture for programmable universal unitaries

The decomposition of large unitary matrices into smaller ones is important, because it provides ways to realization of classical and quantum information processing schemes. Today, most of the methods use planar meshes of tunable two-channel blocks, however, the schemes turn out to be sensitive to fabrication errors. We study a novel decomposition method based on multi-channel blocks. We have shown that the scheme is universal even when the block`s transfer matrices are chosen at random, making it virtually insensitive to errors. Moreover, the placement of the variable elements can be arbitrary, so that the scheme is not bound to specific topologies. Our method can be beneficial for large-scale implementations of unitary transformations by techniques, which are not of wide proliferation today or yet to be developed.

quant-ph↗