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Updated: Jun 14, 2026

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method
05:51

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method

Published on: July 19, 2019

Interacting boson problems can be QMA hard.

Tzu-Chieh Wei1, Michele Mosca, Ashwin Nayak

  • 1Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada.

Physical Review Letters
|April 7, 2010
PubMed
Summary
This summary is machine-generated.

Calculating the ground-state energy for interacting boson systems is QMA-hard, challenging previous assumptions. This finding suggests efficient quantum algorithms for these complex bosonic problems are unlikely.

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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

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Last Updated: Jun 14, 2026

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method
05:51

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Published on: July 19, 2019

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06:42

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Published on: June 8, 2018

Area of Science:

  • Quantum computing
  • Computational complexity theory
  • Quantum chemistry

Background:

  • Fermionic systems, particularly computing ground-state energies, are known to be computationally hard for quantum Merlin Arthur (QMA).
  • This hardness is often linked to the 'sign problem' inherent in fermionic simulations.
  • Bosonic systems were conventionally considered tractable, lacking the sign problem's complexity.

Purpose of the Study:

  • To investigate the computational complexity of interacting boson problems.
  • To determine if bosonic systems share the hardness observed in fermionic systems.
  • To analyze the complexity of the N-representability problem for bosons.

Main Methods:

  • Complexity theory analysis
  • Quantum Merlin Arthur (QMA) complexity class evaluation
  • Comparison of fermionic and bosonic system computational requirements

Main Results:

  • Interacting boson problems are demonstrated to be QMA-hard.
  • The bosonic version of the N-representability problem is shown to be QMA-complete.
  • These results challenge the conventional wisdom regarding the tractability of bosonic systems.

Conclusions:

  • Bosonic systems, like fermionic ones, present significant computational challenges.
  • The QMA-hardness of these problems implies that efficient quantum algorithms are unlikely to exist.
  • This research redefines the landscape of computational complexity in quantum many-body physics.