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Improved Approximation Algorithms for Bounded-Degree Local Hamiltonians.

Anurag Anshu1, David Gosset2,3, Karen J Morenz Korol4

  • 1Department of EECS & Challenge Institute for Quantum Computation, University of California, Berkeley, California 94720, USA and Simons Institute for the Theory of Computing, Berkeley, California 94720, USA.

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Summary
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This study introduces shallow quantum circuits to efficiently approximate the ground state energy of quantum systems. The novel algorithm significantly improves energy estimation for interacting quantum systems, offering an extensive enhancement.

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Area of Science:

  • Quantum Computing
  • Computational Physics
  • Quantum Many-Body Systems

Background:

  • Approximating low-temperature properties of interacting quantum systems is computationally intensive.
  • Efficient algorithms for approximating ground state energies of quantum Hamiltonians are a key challenge.

Purpose of the Study:

  • To develop efficient algorithms for approximating the ground state energy of two-local quantum Hamiltonians.
  • To improve upon existing methods that optimize over product states.

Main Methods:

  • Proposing and analyzing a family of shallow quantum circuits.
  • Inputting an n-qubit product state with variance Var.
  • Extending results to k-local Hamiltonians and entangled initial states.

Main Results:

  • The algorithm improves the energy approximation by an amount proportional to Var²/n.
  • Achieves an extensive improvement in estimated ground state energy for typical cases.
  • Demonstrates applicability to k-local Hamiltonians and entangled states.

Conclusions:

  • Shallow quantum circuits offer a pathway to efficiently approximate ground state energies.
  • The proposed method provides a significant enhancement over existing product state optimization techniques.
  • This work advances the understanding of resource requirements for quantum system computations.