Mitigation vs Correction

Error mitigation cleans up answers after noisy runs — by re-weighting, extrapolating, or discarding measurement results — without needing extra qubits; error correction prevents errors during the computation but demands large qubit overhead. Today's uncorrected devices rely on mitigation, and its costs grow exponentially with circuit size, which is exactly why the field is engineering its way toward correction.

What's the difference between mitigating and correcting an error?

Error correction, the subject of this course so far, prevents errors from corrupting a computation while it runs: encode into many physical qubits, check parities continuously, fix faults as they happen. It protects arbitrary computations — and costs hundreds to thousands of physical qubits per logical qubit (see the previous chapter).

Error mitigation accepts that today's devices run unprotected, and instead cleans up the results: run the noisy circuit (often many variants of it, many times), then use classical post-processing to estimate what a noiseless device would have returned. No extra qubits. The price is paid in samples — many more runs — and in scope: mitigation improves expectation values (averaged quantities like "the mean energy in a chemistry calculation"), not individual outputs. It cannot make an unreliable circuit reliably output a specific correct bitstring.

This is the working reality of the NISQ era — Noisy Intermediate-Scale Quantum, John Preskill's 2018 term for today's uncorrected machines, whose failure modes are catalogued in why qubits fail. The rule of thumb: mitigation spends shots; correction spends qubits. This chapter covers the four mitigation techniques you will actually meet, with one worked calculation you can reproduce by hand for each of the first two, and closes the course.