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Quantum computational complexity of the N-representability problem: QMA complete.

Yi-Kai Liu1, Matthias Christandl, F Verstraete

  • 1Computer Science and Engineering, University of California, San Diego, California, USA.

Physical Review Letters
|May 16, 2007
PubMed
Summary
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The N-representability problem in quantum chemistry is proven to be quantum Merlin-Arthur complete. This finding advances our understanding of the computational complexity of quantum systems.

Area of Science:

  • Quantum Chemistry
  • Computational Complexity Theory
  • Quantum Computing

Background:

  • The N-representability problem is central to quantum chemistry, determining if a given N-electron density corresponds to an actual quantum state.
  • Understanding its computational complexity is crucial for developing efficient quantum chemistry algorithms.

Purpose of the Study:

  • To determine the precise computational complexity class of the N-representability problem.
  • To establish a theoretical foundation for the difficulty of solving electronic structure problems.

Main Methods:

  • Mapping spin systems to fermionic systems.
  • Utilizing convex optimization techniques.
  • Reducing the ground-state problem to N-representability.

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Main Results:

  • The N-representability problem is shown to be quantum Merlin-Arthur complete.
  • This establishes a high level of computational difficulty for the problem within quantum complexity theory.

Conclusions:

  • The N-representability problem is computationally hard, even for quantum computers.
  • This complexity has significant implications for the feasibility of accurate quantum chemical simulations.