Why is error mitigation different from full error correction in quantum

Quantum error mitigation and full quantum error correction differ fundamentally in how they handle noise, the physical requirements they demand, and the computational trade-offs involved. Error mitigation uses the outputs of ensembles of circuits to reduce or eliminate the effect of noise when estimating expectation values, operating somewhat like noise-cancelling headphones by working on average rather than correcting errors shot-by-shot ^[1]. Because powerful mitigation techniques can come with an exponential overhead where execution time increases rapidly with problem size and circuit depth, users balance these accuracy demands against the acceptable overhead ^[2]. In contrast, quantum error correction aims to achieve fault-tolerant computation by building redundancies into the hardware so that the system returns accurate answers even when physical qubits experience errors ^[3]. Quantum error correction encodes single qubit values, called logical qubits, across multiple physical qubits and uses an error correction code consisting of specific operations and measurements to detect and correct errors ^[4]. While full error correction requires hardware error rates to fall below a specific threshold and demands a large physical qubit overhead for each logical qubit, error mitigation serves as the near-term path to usefulness on current noisy hardware, with potential hybrid techniques envisioned for larger scales ^[5].

For developers today, these distinctions mean that near-term algorithms can leverage a portfolio of error mitigation methods—such as probabilistic error cancellation, zero-noise extrapolation, and readout error extinction—to calculate unbiased expectation values despite hardware noise, while keeping an eye toward eventual fault-tolerant error correction as hardware codes and physical error rates improve ^[6].

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