- #Clifford group quantum error correction full
- #Clifford group quantum error correction code
- #Clifford group quantum error correction trial
Unfortunately, the regularized entropy of magic is not feasible to compute. One can then ask, which qutrit state is most magic? To answer this question, a natural measure to use is the regularized entropy of magic, which is defined as the relative entropy between a large supply of qutrits in the candidate magic state and the nearest multi-qutrit stabilizer state. By analogy, any (pure) state that is not a stabilizer state is defined to be magic. What constitutes a magic state for a qutrit? In the entanglement theory, any state that is not a separable state is defined to be entangled. An open problem is to design a distillation protocol with as high a threshold as possible. This process is only successful if the noise level of the low-fidelity input qudits is below a particular threshold associated with the particular distillation protocol employed. Using many low-fidelity magic states, it is sometimes possible to distil a small number of high-fidelity magic states via protocols involving only Clifford unitaries and stabilizer measurements. To approximate a universal quantum computer within this model, we require arbitrarily pure magic states, which can be used to implement non-Clifford gates via state injection. In addition, the computer is able to prepare ancilla qudits in certain non-stabilizer states, called magic states but these states are produced with limited fidelity.
A quantum computer with only these capabilities is classically simulable and therefore not sufficient for universal quantum computation.
#Clifford group quantum error correction full
In the magic state model, a fault-tolerant quantum computer has the ability to measure and initialize states without error in the computational basis and act without error on these states with a discrete subgroup of the full set of unitary operators known as the Clifford group. However, for the most part, qudit fault-tolerant quantum computing appears relatively unexplored although attractive experimental realizations of qutrits do exist, e.g. In the past few years, magic state distillation for qudits of (typically odd prime) dimensions other than two has attracted some interest and notably has been used to identify contextuality as an essential resource for universal quantum computation. Magic state distillation is a leading approach to fault-tolerant quantum computing.
#Clifford group quantum error correction code
Here, we observe that the 11-qutrit Golay code is remarkably well suited for a promising approach to fault-tolerant quantum computing known as magic state distillation. Applications of the 23-qubit Golay code to fault-tolerant quantum computing exist, but the 11-qutrit Golay code has apparently never been studied. Ĭan the Golay codes provide us better ways to protect quantum information from noise? Through the CSS construction, the Golay codes can be used to construct 2 and 3 quantum error correcting codes.
#Clifford group quantum error correction trial
While they were discovered through a computer search (and independently by a Finnish football enthusiast, apparently via trial and error), their discovery led to profound advancements in the theory of coding as well as the mathematical theory of finite groups. These codes are unique, in that they are the only linear perfect classical error correcting codes other than the Hamming codes.
Two Golay codes exist-the 23-bit binary Golay code and the 11-trit ternary Golay code. The classical Golay codes are amongst the first and most beautiful ways discovered to protect classical information.