![alexei kitaev quantum error correction alexei kitaev quantum error correction](https://lifeboat.com/blog.images/error-transparent-operations-on-a-logical-qubit-protected-by-quantum-error-correction.jpg)
#Alexei kitaev quantum error correction code#
In the surface code 3, 30, 31, 32, qubits follow a 2D chequerboard pattern of measure and data qubits, with n qubits = 2 d 2 − 1. Each measure qubit checks the parity of its two neighbours, and all measure qubits check the same basis so that the logical qubit is protected from either X or Z errors, but not both. In the repetition code, qubits alternate between measure and data qubits in a 1D chain, and the number of qubits for a given code distance is n qubits = 2 d − 1. In this work, we run two stabilizer codes. Moreover, exponential error suppression has not previously been demonstrated with cyclic stabilizer measurements, which are a key requirement for fault-tolerant computing but introduce error mechanisms such as state leakage, heating and data qubit decoherence during measurement 21, 29. However, these results cannot be extrapolated to exponential error suppression in large systems unless non-idealities such as crosstalk are well understood. Many previous experiments have demonstrated the principles of stabilizer codes in various platforms such as nuclear magnetic resonance 22, 23, ion traps 24, 25, 26 and superconducting qubits 19, 21, 27, 28. Instead, quantum processors must be benchmarked by measuring Λ. More realistic error models cannot be characterized by a single error rate p or a single threshold value p th.
![alexei kitaev quantum error correction alexei kitaev quantum error correction](https://jqi.umd.edu/sites/default/files/styles/article_lead/public/images/qec_2017_image-ps.jpg)
Here, Λ ∝ p th/ p is the exponential error suppression factor, C is a fitting constant and d is the code distance, defined as the minimum number of physical errors required to generate a logical error, and increases with the number of physical qubits 3, 21. In the simplest model, if the physical error per operation p is below a certain threshold p th determined by quantum computer architecture, chosen QEC code and decoder, then the probability of logical error per round of error correction ( ε L) should scale as:
![alexei kitaev quantum error correction alexei kitaev quantum error correction](https://lifeboat.com/blog.images/quantum-error-correction-and-universal-gate-set-operation-on-a-binomial-bosonic-logical-qubit.jpg)
#Alexei kitaev quantum error correction software#
For the purpose of maintaining a logical quantum memory in the codes presented in this work, these errors can be compensated in classical software 3. The stream of parity values can then be decoded to determine the most likely physical errors that occurred. These projective stabilizer measurements turn undesired perturbations of the data qubit states into discrete errors, which we track by looking for changes in parity. Additional physical qubits known as measure qubits are interlaced with the data qubits and are used to periodically measure the parity of chosen data qubit combinations. Many quantum error-correction (QEC) architectures are built on stabilizer codes 20, where logical qubits are encoded in the joint state of multiple physical qubits, which we refer to as data qubits. These experimental demonstrations provide a foundation for building a scalable fault-tolerant quantum computer with superconducting qubits. Finally, we perform error detection with a small logical qubit using the 2D surface code on the same device 18, 19 and show that the results from both one- and two-dimensional codes agree with numerical simulations that use a simple depolarizing error model. We also introduce a method for analysing error correlations with high precision, allowing us to characterize error locality while performing quantum error correction. Crucially, this error suppression is stable over 50 rounds of error correction. Here we implement one-dimensional repetition codes embedded in a two-dimensional grid of superconducting qubits that demonstrate exponential suppression of bit-flip or phase-flip errors, reducing logical error per round more than 100-fold when increasing the number of qubits from 5 to 21. Errors on the encoded logical qubit state can be exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold and stable over the course of a computation. Quantum error correction 15, 16, 17 promises to bridge this divide by distributing quantum logical information across many physical qubits in such a way that errors can be detected and corrected. 2, 3, 4, 5, 6, 7, 8, 9), but state-of-the-art quantum platforms typically have physical error rates near 10 −3 (refs. Many applications call for error rates as low as 10 −15 (refs. Realizing the potential of quantum computing requires sufficiently low logical error rates 1.