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Non-Pauli Errors Can Be Efficiently Sampled in Qudit Surface Codes.

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Surface codes offer promising fault-tolerant quantum computation. This study shows that even with non-Pauli errors, quantum error syndromes are efficiently samplable for qudit surface codes, simplifying decoding.

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Area of Science:

  • Quantum Information Science
  • Quantum Error Correction
  • Condensed Matter Theory

Background:

  • Surface codes are leading candidates for fault-tolerant quantum computation.
  • Current models often simplify errors to Pauli operators, potentially overlooking complex error dynamics.
  • Qudit-based quantum systems offer advantages over qubit systems but introduce more complex error models.

Purpose of the Study:

  • To quantify correlations remaining after syndrome measurement in a 2D surface code for qudit systems.
  • To analyze the impact of non-Pauli errors on the efficiency of syndrome sampling.
  • To assess the robustness of surface codes against a broader range of quantum errors.

Main Methods:

  • Utilizing percolation theory to model error propagation on the lattice.
  • Analyzing loop structures on the lattice to identify and quantify correlations.
  • Simulating syndrome measurement processes under non-Pauli error conditions.

Main Results:

  • Remaining correlations after syndrome measurement are sparse and locally constrained below the error correction threshold.
  • The efficiency of syndrome sampling is largely independent of the specific form of non-Pauli errors.
  • Percolation theory effectively captures the behavior of correlations in qudit surface codes.

Conclusions:

  • Qudit surface codes demonstrate resilience to non-Pauli errors.
  • Syndrome measurement in qudit surface codes is efficiently samplable, even with complex errors.
  • These findings support the viability of qudit surface codes for practical fault-tolerant quantum computing.