quantum error correction and quantum foundation

This theorem seems to present an obstacle to formulating a theory of quantum error correction. Similar to classical error correction, QEC codes do not always correctly decode logical qubits, but their use reduces the effect of noise.Ĭopying quantum information is not possible due to the no-cloning theorem. In this example, the logical information was a single bit in the one state, the physical information are the three copied bits, and determining what logical state is encoded in the physical state is called decoding. It is possible that a double-bit error occurs and the transmitted message is equal to three zeros, but this outcome is less likely than the above outcome. Assuming that noisy errors are independent and occur with some sufficiently low probability p, it is most likely that the error is a single-bit error and the transmitted message is three ones. Suppose further that a noisy error corrupts the three-bit state so that one of the copied bits is equal to zero but the other two are equal to one. suppose we copy a bit in the one state three times. The idea is to store the information multiple times, and-if these copies are later found to disagree-take a majority vote e.g.

The simplest albeit inefficient approach is the repetition code. Ĭlassical error correction employs redundancy. This would allow algorithms of greater circuit depth. Quantum error correction is theorised as essential to achieve fault tolerant quantum computing that can reduce the effects of noise on stored quantum information, faulty quantum gates, faulty quantum preparation, and faulty measurements. Quantum error correction ( QEC) is used in quantum computing to protect quantum information from errors due to decoherence and other quantum noise.

Quantum error correction and quantum foundation