Low-rank tensor decompositions of quantum circuits
- URL: http://arxiv.org/abs/2205.09882v3
- Date: Mon, 2 Jan 2023 11:10:31 GMT
- Title: Low-rank tensor decompositions of quantum circuits
- Authors: Patrick Gel{\ss}, Stefan Klus, Sebastian Knebel, Zarin Shakibaei,
Sebastian Pokutta
- Abstract summary: We show how MPOs can be used to express certain quantum states, quantum gates, and entire quantum circuits as low-rank tensors.
This enables the analysis and simulation of complex quantum circuits on classical computers.
- Score: 14.531461873576449
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Quantum computing is arguably one of the most revolutionary and disruptive
technologies of this century. Due to the ever-increasing number of potential
applications as well as the continuing rise in complexity, the development,
simulation, optimization, and physical realization of quantum circuits is of
utmost importance for designing novel algorithms. We show how matrix product
states (MPSs) and matrix product operators (MPOs) can be used to express
certain quantum states, quantum gates, and entire quantum circuits as low-rank
tensors. This enables the analysis and simulation of complex quantum circuits
on classical computers and to gain insight into the underlying structure of the
system. We present different examples to demonstrate the advantages of MPO
formulations and show that they are more efficient than conventional techniques
if the bond dimensions of the wave function representation can be kept small
throughout the simulation.
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