![]() ![]() There are two distinct types of error suppression technologies: quantum error correction (QEC) and quantum error mitigation (QEM). Since superposition states are quite fragile against environmental noise, the biggest challenge towards the realization of quantum computers is the suppression of noise and the improvement of computation accuracy. Because quantum computing may solve prime number factorization and simulate chemical materials much more efficiently than classical computers, it has been extensively studied over the globe. Quantum computing is a new paradigm that performs computation by exploiting "qubits", which have unique properties of quantum mechanics such as superposition and quantum entanglement. This novel method allows for the reduction of the size of quantum computers required for practical applications by up to 80%. Lastly, there is one more quantum error correction method: stabilizer measurements.Researchers at Nippon Telegraph and Telephone Corporation (NTT head office: Chiyoda-ku, Tokyo president: Jun Sawada hereinafter "NTT"), in collaboration with the Center for Quantum Information and Quantum Biology, Osaka University (QIQB), have proposed a hybrid quantum error reduction technique, consisting of quantum error correction and quantum error mitigation. 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. #Types of quantum error codeFirst, 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. ![]()
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