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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
PubMed
Summary
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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.

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.

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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.