![]() ![]() Lastly, there is one more quantum error correction method: stabilizer measurements. 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. #QUANTUM ERROR CORRECTION COURSE U OF A CODE#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. The rub, of course, is that quantum mechanics is different than classical. 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%. ory of fault-tolerant quantum error correction (FTQEC) is rather daunt. 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 One assignment to be completed per week with personalised feedback.Qubits are strongly affected by the environment. Time commitment: Two weekly 1 hour live interactive small group classes.Content: 18 hours recorded material and supporting notes.Dates: Quantum Computation course 3rd Oct - 2nd Dec 2022, second iteration of Quantum Information spring 2023.Noise and the framework of quantum channels.The quantum Fourier transform and periodicity.Grover's algorithm and its generalisations.Classical and quantum compuational complexity.You will also learn about quantum Fourier transform and phase estimation, quantum error correction and noise and quantum channels. Course introduces the concepts of quantum communication, quantum computing and quantum error correction. By the end of this course you will understand the key algorithms and their applications, such as Shor's and Grover's algorithms and quantum simulation. This course builds upon quantum information course to describe the concepts underpinning quantum computation. ![]()
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