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Unifying variational methods for simulating quantum many-body systems.

C M Dawson¹, J Eisert, T J Osborne

¹Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW, United Kingdom.

Physical Review Letters

|June 4, 2008

Summary

We present a new variational method for quantum many-body systems using quantum circuits and flow equations. This approach efficiently simulates ground states for complex systems, including multiscale entanglement renormalization (MERA) states.

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Published on: December 4, 2017

Area of Science:

Quantum physics
Computational physics
Condensed matter theory

Background:

Simulating ground state properties of quantum many-body systems is computationally challenging.
Existing variational methods have limitations in representing complex quantum states.

Purpose of the Study:

To introduce a unified and flexible formulation for variational methods in quantum many-body simulations.
To develop a novel variational method over quantum circuits inspired by flow equations.

Main Methods:

A new variational method is proposed using infinitesimal unitary transformations on quantum circuits.
Variational classes are represented as efficiently contractible unitary networks.
This includes matrix-product states, multiscale entanglement renormalization (MERA) states, and others.

Main Results:

The method provides an efficient way to perform variational calculations over previously intractable state classes like MERA.
Numerical implementations on MERA, matrix-product states, and a new variational set demonstrate the method's functionality.
The scheme is flexible for hybridizing existing methods or creating new ones.

Conclusions:

The developed formulation offers a powerful and versatile tool for simulating quantum many-body systems.
It significantly advances the capabilities for studying ground state properties, particularly for systems with complex entanglement structures.
The approach opens new avenues for variational studies in quantum physics and related fields.