What is Error Mitigation?

Overview

Error mitigation exists because today’s quantum devices are noisy, but we still want to extract useful information from them.

In NISQ settings, we often cannot fully prevent errors inside the circuit. Instead, we try to reduce the impact of noise on the final estimated quantities (like probabilities or expectation values) using extra experiments and smarter analysis.

This page clarifies:

• mitigation vs correction
• why mitigation is a core NISQ tool
• the main categories of mitigation techniques
• what mitigation can and cannot promise

Intuition

Mitigation vs correction (core distinction)

• Error correction (not covered in detail here) aims to actively protect quantum information during computation so that longer computations remain reliable.

• Error mitigation aims to estimate what the ideal result would have been from noisy runs, typically by:

  • repeating experiments
  • varying noise levels
  • exploiting symmetry
  • calibrating measurement errors

Mitigation is like improving the “measurement of the answer” rather than fixing the hardware mid-computation.

Why mitigation is necessary in NISQ

Even if you design a good algorithm:

• decoherence reduces coherence over time
• gates introduce small errors that accumulate
• measurement misclassifies outcomes

Mitigation acknowledges a practical truth:

• we can’t run deep fault-tolerant circuits yet
• but we can often afford extra shots and extra calibration circuits

So mitigation trades more experiments for better estimates.

Formal Description

We describe mitigation as a workflow.

What mitigation targets

Mitigation typically targets outputs like:

• an expectation value (e.g., average of a measurement outcome)
• a probability distribution over bitstrings

The goal is not “make every shot correct.” The goal is: “make the final estimated quantity closer to the ideal.”

General categories of mitigation techniques

1. Measurement mitigation

   • calibrate readout confusion
   • correct reported counts

2. Noise-scaling and extrapolation (e.g., ZNE)

   • deliberately increase noise
   • observe how results drift
   • extrapolate back to the zero-noise limit

3. Symmetry-based checks and post-selection

   • use known properties (conservation laws, parity constraints)
   • discard outcomes that violate them

4. Circuit-level tricks (conceptual category)

   • rewrite circuits to reduce error impact
   • compare equivalent circuits to estimate bias

We’ll focus on the first three categories in the next pages.

Honest limitations

Mitigation typically requires:

• extra shots (higher sampling cost)
• extra calibration circuits
• assumptions about how noise behaves

If the assumptions fail or the noise is too large, mitigation can become unstable or misleading.

Worked Example

Suppose you want to estimate the probability of measuring 1 on a qubit.

• Ideal answer: $p=0.40$
• Hardware readout flips 1→0 about 7% of the time

If you just report raw counts, you might observe something like $p_{\text{obs}}=0.37$.

Measurement mitigation can use a calibrated confusion matrix to estimate that the underlying probability was closer to 0.40.

This does not mean the device became noiseless. It means your estimate of the ideal quantity improved.

Turtle Tip

Common Pitfalls

Quick Check

What’s Next

Next we cover a central mitigation idea: Zero-Noise Extrapolation (ZNE). ZNE uses controlled noise scaling and curve fitting to estimate what a measurement would have been in the zero-noise limit.