Mitigation vs Correction

Error mitigation cleans up answers after noisy runs. It re-weights, stretches back, or throws away measured results, and it needs no extra qubits. Error correction stops errors during the computation, but it needs a large number of extra qubits. Today's uncorrected devices rely on mitigation. Its costs grow exponentially as circuits get bigger. That is exactly why the field is working its way toward correction.

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

Error correction is what this course has covered so far. It stops errors from damaging a computation while it runs. You encode into many physical qubits, check parities all the time, and fix faults as they happen. It protects any computation. But it costs hundreds to thousands of physical qubits per logical qubit (see the previous chapter).

Error mitigation accepts that today's devices run unprotected. Instead, it cleans up the results. You run the noisy circuit — often many versions of it, many times. Then a normal computer does math on the results to estimate what a noise-free device would have given. No extra qubits are needed.

The price is paid in samples, meaning many more runs. There is also a limit on what it can do. Mitigation improves expectation values. Those are averages, like "the mean energy in a chemistry calculation." It does not improve single outputs. It cannot make an unreliable circuit reliably give one specific correct bitstring.

An everyday example: a blurry photo. Correction is like buying a steadier camera, so the photo is sharp when taken. Mitigation is like taking many blurry photos and using software to estimate the sharp one. Where the picture breaks: photo software can sometimes rebuild one sharp photo. Mitigation can only improve averages, never a single shot.

This is daily life in the NISQ era. NISQ stands for Noisy Intermediate-Scale Quantum. It is John Preskill's 2018 term for today's uncorrected machines. Their failure modes are listed in why qubits fail. The rule of thumb: mitigation spends shots; correction spends qubits. This chapter covers the four mitigation methods you will actually meet. It includes a worked calculation you can redo by hand for each of the first two. Then it closes the course.