An error-mitigated quantum circuit implements $R_x(\theta)$ using a single gate regardless of $\theta$, while the number of gates required for a fault-tolerant implementation actually depends on $\theta$.īased on the first bullet above, QEC is the only promising approach out of the two. Clifford T) to approximate arbitrary logical operations (with some overhead - see Solovay-Kitaev). Gate restrictions: EM usually doesn't impose restrictions on the types of gates available in the circuit, while QEC uses fault-tolerant gates (in a restricted gateset, e.g.Logical qubits: QEC involves protecting qubits by encoding them into larger groups of qubits (logical qubits), EM generally does not. Given any nonzero error rate, no one reasonably expects EM to work for arbitrarily wide or deep circuits. Without QEC, the failure probability increases with the size of the circuit, and the role of EM is to reduce this rate of increase with respect to circuit size/depth. Fault-tolerance: It is widely believed that with QEC, for low enough error rates you can arbitrarily reduce the failure probability of a circuit with additional gate overhead i.e. The basic difference is that QEC involves the detection and correction of errors that occur during computation, while EM schemes allow errors to occur and try to compensate for the negative effects of these uncorrected errors in various ways.Ī few high-level differences between QEC and EM are:
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