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Quantum EngineeringYear 2: Advanced Quantum ScienceMonth 34Day 941

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Year 2·Month 34·Week 3

Day 941: Probabilistic Error Cancellation - Quasi-Probability Decomposition

Day 941 of 2,016~18 min read

Learning Objectives

  • •**Derive quasi-probability decompositions** - Express ideal operations as linear combinations of noisy operations
  • •**Calculate sampling overhead** - Quantify the cost of PEC in terms of variance amplification
  • •**Implement noise inversion** - Construct inverse channels for common noise models
  • •**Apply Monte Carlo PEC** - Sample from quasi-probability distributions to cancel errors
  • •**Optimize PEC protocols** - Balance tomography cost vs mitigation benefit
  • •**Compare PEC to other methods** - Understand when PEC is preferred over ZNE

Today's Schedule (7 hours)

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On this page

1 Quasi-Probability Representation11 The PEC Principle12 Intuition from Classical Error Cancellation2 Noise Model and Inverse Channels21 Noisy Gate Model22 Inverse of Depolarizing Channel23 Quasi-Probability Decomposition3 Sampling Overhead31 Monte Carlo Implementation32 Variance Amplification33 Overhead Examples4 Gate-Level PEC Protocol41 Complete PEC Algorithm42 Noise Learning Requirements5 Practical Considerations51 When to Use PEC52 PEC vs ZNE Comparison53 Hybrid Approaches6 Two-Qubit Gate PEC61 CNOT with Depolarizing NoiseQuantum Computing ApplicationsVariational Algorithms with PECQuantum SimulationBenchmarking Applications
Day 940Day 941 of 2,016Day 942