Quantum Tensor-Product Decomposition from Choi-State Tomography

Author:

Mansuroglu Refik1ORCID,Adil Arsalan2ORCID,Hartmann Michael J.1ORCID,Holmes Zoë3,Sornborger Andrew T.4

Affiliation:

1. Friedrich-Alexander Universität Erlangen-Nürnberg (FAU)

2. University of California, Davis

3. École Polytechnique Fédérale de Lausanne

4. Los Alamos National Laboratory

Abstract

The Schmidt decomposition is the go-to tool for measuring bipartite entanglement of pure quantum states. Similarly, it is possible to study the entangling features of a quantum operation using its operator-Schmidt or tensor-product decomposition. While quantum technological implementations of the former are thoroughly studied, entangling properties on the operator level are harder to extract in the quantum computational framework because of the exponential nature of sample complexity. Here, we present an algorithm for unbalanced partitions into a small subsystem and a large one (the environment) to compute the tensor-product decomposition of a unitary the effect of which on the small subsystem is captured in classical memory, while the effect on the environment is accessible as a quantum resource. This quantum algorithm may be used to make predictions about operator nonlocality and effective open quantum dynamics on a subsystem, as well as for finding low-rank approximations and low-depth compilations of quantum circuit unitaries. We demonstrate the method and its applications on a time-evolution unitary of an isotropic Heisenberg model in two dimensions. Published by the American Physical Society 2024

Funder

Sandoz Family Foundation-Monique de Meuron Program for Academic Promotion

German Federal Ministry of Education and Research, “Quantum Technologies – From Basic Research to Market”

Bavarian State Government, Hightech Agenda Bayern Plus, Munich Quantum Valley

U.S. Department of Energy (DOE), Los Alamos National Laboratory (LANL) Information Science and Technology Institute

Publisher

American Physical Society (APS)

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