Further Reading: Error Mitigation

Tagged Tier 1 (confident it exists and recommended) and Tier 2 (real and worth seeking, but verify the current version or URL).

The primary sources

• The qiskit-ibm-runtime documentation on resilience_level and the resilience options. What each level actually enables, and the individual switches (measure_mitigation, zne_mitigation, pec_mitigation, layer_noise_learning) underneath the dial. Essential, because §13.4 measured that these options are server-side and silently inert locally — the docs are the only way to know what you are turning on. Tier 1.
• The Qiskit transpiler.passes documentation for PadDynamicalDecoupling and the scheduling analysis passes. Read skip_reset_qubits and the ALAP/ASAP distinction carefully; Case Study 2 exists because their interaction silently disabled the pass. Tier 1.
• The M3 package documentation (mthree, Nation, Kang, Sundaresan, Gambetta). Matrix-free measurement mitigation: the practical answer to §13.3's $2^n$ problem, and what you should actually use past ten qubits. The accompanying paper, Scalable Mitigation of Measurement Errors on Quantum Computers (2021), explains the subspace trick clearly. Tier 1.

On zero-noise extrapolation

• Temme, Bravyi, and Gambetta, "Error Mitigation for Short-Depth Quantum Circuits" (2017), Physical Review Letters 119, 180509. The founding paper for both ZNE and PEC. Read it for the precise statement of what is being assumed about the noise — which is exactly what Case Study 1's readout floor violates. Tier 1.
• Li and Benjamin, "Efficient Variational Quantum Simulator Incorporating Active Error Minimization" (2017), Physical Review X 7, 021050. The independent, simultaneous derivation of extrapolation-based mitigation, from a variational-algorithms angle. Tier 1.
• Giurgica-Tiron et al., "Digital Zero Noise Extrapolation for Quantum Error Mitigation" (2020). Where gate folding is developed properly, including local versus global folding and non-integer scale factors — Exercise 13.13's subject. The reason you can do ZNE without pulse-level control. Tier 1.
• The mitiq documentation (Unitary Fund). A framework-agnostic mitigation library implementing ZNE, PEC, CDR, and more, with a genuinely good user guide. If you are doing more than one extrapolation, use this rather than the twenty lines in §13.5. Tier 1.

On probabilistic error cancellation and noise learning

• van den Berg, Minev, Kandala, and Temme, "Probabilistic error cancellation with sparse Pauli–Lindblad models on noisy quantum processors" (2023), Nature Physics. The technique behind the runtime's layer_noise_learning: how the noise model that PEC inverts is actually learned, layer by layer. The most practically important PEC paper. Tier 1.
• Wallman and Emerson, "Noise tailoring for scalable quantum computation via randomized compiling" (2016), Physical Review A 94, 052325. Twirling, done properly. Why converting coherent noise to stochastic noise is worth doing even though it does not reduce the error rate — §13.8's claim, with the argument. Tier 1.
• Any careful treatment of the sampling overhead $\gamma^{2d}$. The exponential that makes PEC exact and unaffordable, and the clearest quantitative statement of §13.1's "mitigation trades shots for accuracy at a worsening rate." Tier 2.

On the limits

• Takagi, Endo, Minagawa, and Gu, "Fundamental limits of quantum error mitigation" (2022), npj Quantum Information 8, 114. The theoretical result behind §13.1's Honest Assessment: the sampling cost of any mitigation strategy grows exponentially with circuit depth. Read this before describing mitigation as a route to advantage. Tier 1.
• Quek et al. and related work on exponentially-scaling mitigation overheads. The literature hardening the same conclusion from several directions. Tier 2 — an active area.
• Cai et al., "Quantum Error Mitigation" (2023), Reviews of Modern Physics. The comprehensive survey. If you want one document covering every technique in this chapter and a dozen more, with consistent notation, this is it. Tier 1.

On what DD needs that a simulator lacks

• Viola, Knill, and Lloyd, "Dynamical Decoupling of Open Quantum Systems" (1999), Physical Review Letters 82, 2417. The founding paper. Read the assumptions about the environment's correlation time — that is precisely the structure Case Study 2 found missing from a Markovian noise model. Tier 1.
• Any treatment of non-Markovian noise and $1/f$ dephasing in superconducting qubits. The physics DD addresses, and the reason it works on hardware and cannot work in Chapter 11's simulator. Tier 2.
• Ezzell et al., "Dynamical decoupling for superconducting qubits: a performance survey" (2023). An empirical comparison of DD sequences on real devices — the experiment §13.6 could not run. Tier 2.

Forward references

• Chapter 24 — where the mitigation stack meets an optimizer loop, and every cost in §13.9 gets multiplied by the iteration count.
• Chapter 25 — the other half of §13.1's table: actual error correction, in code.
• Chapter 30 — measuring noise parameters yourself, including the correlated noise this chapter could not simulate.
• Appendix G — the calibration fields the assignment matrix is built from.

Where to go next. If one thing: Takagi et al. on the fundamental limits. It is the paper that turns §13.1's Honest Assessment from an opinion into a theorem, and reading it will permanently change how you hear the phrase "error mitigation enables near-term quantum advantage."

If two: add Nation et al. on M3, because it is what you will actually run.

Then Chapter 14 — Part III, and a different framework, which is the fastest way to find out which of the last seven chapters was about Qiskit and which was about quantum computing.