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Universal Cost Bound of Quantum Error Mitigation Based on Quantum Estimation Theory.

Kento Tsubouchi1, Takahiro Sagawa1,2, Nobuyuki Yoshioka1,3,4

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Quantum error mitigation costs grow exponentially with circuit depth and qubit count. Rescaling measurement results can saturate bounds for global depolarizing noise, offering insights into quantum computing limitations.

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Quantum Error Mitigation

Background:

  • Quantum error mitigation is crucial for reliable quantum computation.
  • Existing methods face challenges in scalability and cost-effectiveness.
  • Understanding the fundamental cost of these methods is essential.

Purpose of the Study:

  • To develop a unified approach for analyzing the cost of quantum error mitigation.
  • To derive bounds on measurement costs based on quantum estimation theory.
  • To investigate the impact of circuit depth and qubit count on mitigation costs.

Main Methods:

  • Utilized quantum estimation theory and the quantum Fisher information matrix.
  • Analyzed a virtual quantum circuit representing error mitigation operations.
  • Derived theoretical bounds for generic layered quantum circuits under Markovian noise.

Main Results:

  • Discovered exponential growth in measurement cost lower bounds with circuit depth for unbiased estimation.
  • Showed that for global depolarizing noise, bounds can be saturated by rescaling measurement results.
  • Proved exponential cost growth with qubit count for random circuits with local noise.

Conclusions:

  • Quantum error mitigation costs are fundamentally limited by exponential scaling with circuit depth and qubit count.
  • Rescaling techniques offer a viable strategy for mitigating costs in deep quantum circuits.
  • Provides a new framework and criterion for evaluating quantum error mitigation performance and physical limitations.