What determines the ultimate precision of a quantum computer

摘要

A quantum error correction (QEC) code uses N_c quantum bits to construct one “logical” quantum bit of better quality than the original “physical” ones. QEC theory predicts that the failure probability pL of logical qubits decreases exponentially with Nc provided the failure probability p of the physical qubit is below a certain threshold p < pth . In particular, QEC theorems imply that the logical qubits can be made arbitrarily precise by simply increasing Nc. In this article, we search for physical mechanisms that lie outside of the hypothesis of QEC theorems and set a limit ηL to the precision of the logical qubits (irrespectively of N_c). η_L directly controls the maximum number of operations ∝ 1/η_L~2 that can be performed before the logical quantum state gets randomized, hence the depth of the quantum circuits that can be considered. We identify a type of error-silent stabilizer failure-as a mechanism responsible for finite ηL and discuss its possible causes. Using the example of the topological surface code, we show that a single local event can provoke the failure of the logical qubit, irrespectively of N_c.