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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

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Multiscale entanglement renormalization ansatz in two dimensions: quantum Ising model.

Lukasz Cincio¹, Jacek Dziarmaga, Marek M Rams

¹Institute of Physics and Centre for Complex Systems Research, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland.

Physical Review Letters

|July 23, 2008

Summary

We developed a new symmetric multiscale entanglement renormalization ansatz for 2D quantum systems. This method accurately finds ground states, demonstrated by precise results in the 2D quantum Ising model.

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Area of Science:

Quantum physics
Condensed matter theory
Computational physics

Background:

The multiscale entanglement renormalization ansatz (MERA) is a powerful tensor network method for simulating quantum systems.
Extending MERA to two spatial dimensions (2D) presents significant computational challenges.
Accurate determination of ground states is crucial for understanding quantum many-body systems.

Purpose of the Study:

To propose and implement a symmetric version of the 2D multiscale entanglement renormalization ansatz (MERA).
To utilize the symmetric 2D MERA to determine the ground state of a 2D quantum system.
To assess the accuracy and efficiency of the proposed symmetric 2D MERA.

Main Methods:

Development of a symmetric formulation for the 2D multiscale entanglement renormalization ansatz.
Application of the symmetric 2D MERA to the 2D quantum Ising model on an 8x8 square lattice.
Analysis of ground state properties using the developed ansatz.

Main Results:

The symmetric 2D MERA successfully found the unknown ground state of the 2D quantum system.
Highly accurate results were obtained for the 2D quantum Ising model.
Accuracy was maintained even with the smallest nontrivial truncation parameter.

Conclusions:

The symmetric 2D MERA is an effective and accurate method for finding ground states of 2D quantum systems.
This approach offers a promising direction for simulating complex quantum many-body problems in two dimensions.
The method demonstrates high precision, even with minimal computational resources (truncation parameter).