With the distance of the CWS code being equal to the distance of the classicalĬode. We construct a CWS code from a given classical code, Secondly, we prove hardness results for the problem of finding theĭistance of a CWS code. Using this result, first we give necessary conditions for a CWS code to beĭegenerate. Of the graphs in our sufficient class achieve the upper bound of δ+1. This paper, we give sufficient conditions on a graph such that a CWS codeĬonstructed from it has diagonal distance at least δ, and in fact most It is known that the diagonal distance of such a code is upper boundedīy δ+1, where δ is the minimum degree of the associated graph. In the CWS framework introduced by Cross, Smith, SmolinĪnd Zeng (2009), a quantum code is constructed using a classical code and a Degeneracy is a property unique to quantum codes, which allows quantumĬodes, unlike their classical counterparts, to correct more errors than theyĬan uniquely identify. Quantum error-correcting code that characterizes whether the code is degenerate Lastly, there is one more quantum error correction method: stabilizer measurements.The diagonal distance or graph distance is an important parameter of a For example, \(|00\rangle\) has a different parity than \(|01\rangle\) in both regard to 0 and 1 there are even numbers of 0’s in the initial codeword while there is an odd number of zeroes in the final codeword. On the other hand, if \(s = 01\) then qubit 3 was flipped. For example, for a \(s = 00\) error syndrome, there was no error. These two respective \(s\)’s will be 1 depending on if their parity is incorrect. These two qubits are represented by \(s = s_0 + s_1\) where \(s_0\) is qubit 4 and \(s_1\) is qubit 2. At this point, qubits 2 and 4 are error qubits. First, the code applies a SWAP gate between qubits 2 and 3 so that now the codeword is stored in qubits 0, 1, 3 (I was personally confused what the purpose of the SWAP gate was but turns out it is just for physical limitations such as wires). Firstly, assume that qubits 0, 1, 2 contain the codeword 000. The third is the encoder with bit-flip code and parity checks. The second is a bit flip encoder and decoder. Luckily, the probability of two errors is quite small at just 1% error rate, the error rate for 2 errors would be less than 0.03%. However, if two errors occur, then clearly the correction code would not work. For example, if a bit flip error occurs and a \(|0\rangle\) becomes a \(|1\rangle\) and thus the codeword \(|000\rangle\) becomes \(|010\rangle\), then simply the code takes the majority value of the three qubits (which would be 0) and corrects \(|010\rangle\) to \(|000\rangle\). From here, there are three main implementations of quantum repetition code. For example, \(|0\rangle\) would be assigned a “codeword” of \|000\rangle\) which would utilize three qubits. The first step to quantum repetition code is repeating the state of a qubit multiple times. For example, quantum repetition code is very widespread. These errors do inevitable occur, however, and thus quantum error correction strategies have come into existence. Qubits generally stay coherent for just 0.0001 seconds (as of 2015). But still, it is very short relative to our normal frames of time. In fact, coherence time (the time in which the qubit stays coherent) has been increasing exponentially. Dephasing collapses the qubits into just \(|0\rangle\) and \(|1\rangle\)īut, the effects of these are being minimized with the ever-advancing technology. There are two main types of decoherence: energy relaxation and dephasing.Įnergy relaxation: \(|1\rangle\) state decays towards \(|0\rangle\) state.ĭephasing: If you look at this quick segment: Quantum decoherence, at the end there is a density matrix describing the actions of the system and the small blurb afterwards explains it quite well. Any environmental disturbances, called “noise”, can disturb the superposition and cause decoherence.ĭecoherence: loss of information due to environmental disturbances Qubits are strongly affected by the environment.
0 Comments
Leave a Reply.AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |