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Quantum advantage and stability to errors in analogue quantum simulators.

Rahul Trivedi1,2,3, Adrian Franco Rubio4,5, J Ignacio Cirac6,7

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Noisy quantum simulators can offer an advantage for complex many-body problems. This study proves stability in certain quantum systems, showing potential for quantum advantage even with errors and without full error correction.

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Area of Science:

  • Quantum computing
  • Condensed matter physics
  • Computational physics

Background:

  • Quantum hardware can function as analogue quantum simulators for many-body problems.
  • Errors in these systems raise questions about their advantage over classical computers.

Purpose of the Study:

  • To assess the potential of noisy analogue quantum simulators for quantum advantage.
  • To analyze the stability of these systems against errors in equilibrium and dynamic scenarios.

Main Methods:

  • Formulated a system-size independent notion of stability against extensive errors.
  • Proved stability for Gaussian fermion models and a restricted class of spin systems.
  • Analyzed the implications of stability for achieving quantum advantage.

Main Results:

  • Demonstrated stability for Gaussian fermion models, including critical models with long-range correlations.
  • Showed that stability can lead to a quantum advantage for computing thermodynamic limits.
  • This advantage is achievable with a constant error rate and without explicit error correction.

Conclusions:

  • Noisy analogue quantum simulators can provide a quantum advantage for specific many-body problems.
  • The demonstrated stability is key to overcoming limitations posed by errors.
  • This research advances the understanding of practical quantum computation with current hardware.