Related papers: Efficient Decoding of Topological Color Codes
Topological quantum error-correcting codes are defined by geometrically local checks on a two-dimensional lattice of quantum bits (qubits), making them particularly well suited for fault-tolerant quantum information processing. Here, we…
Color coding is an algorithmic technique used in parameterized complexity theory to detect "small" structures inside graphs. The idea is to derandomize algorithms that first randomly color a graph and then search for an easily-detectable,…
Polar codes are a new class of capacity-achieving error-correcting codes with low encoding and decoding complexity. Their low-complexity decoding algorithms rendering them attractive for use in software-defined radio applications where…
Concurrent coding is an encoding scheme with "holographic" type properties that are shown here to be robust against a significant amount of noise and signal loss. This single encoding scheme is able to correct for random errors and burst…
Efficient high-performance decoding of topological stabilizer codes has the potential to crucially improve the balance between logical failure rates and the number and individual error rates of the constituent qubits. High-threshold…
We describe a fault-tolerant one-way quantum computer on cluster states in three dimensions. The presented scheme uses methods of topological error correction resulting from a link between cluster states and surface codes. The error…
Topological quantum codes are intrinsically fault-tolerant to local noise, and underlie the theory of topological phases of matter. We explore geometry to enhance the performance of topological quantum codes by rotating the four dimensional…
Quantum error correction is believed to be essential for scalable quantum computation, but its implementation is challenging due to its considerable space-time overhead. Motivated by recent experiments demonstrating efficient manipulation…
Quantum error correction (QEC) is required for large-scale computation, but incurs a significant resource overhead. Recent advances have shown that by jointly decoding logical qubits in algorithms composed of transversal gates, the number…
Quantum error correction is an essential technique for constructing a scalable quantum computer. In order to implement quantum error correction with near-term quantum devices, a fast and near-optimal decoding method is demanded. A decoder…
We consider the problem of optimally decoding a quantum error correction code -- that is to find the optimal recovery procedure given the outcomes of partial "check" measurements on the system. In general, this problem is NP-hard. However,…
Machine learning has the potential to become an important tool in quantum error correction as it allows the decoder to adapt to the error distribution of a quantum chip. An additional motivation for using neural networks is the fact that…
A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate $R\in[0,1]$. An efficient interpolation-based decoding…
The strongly correlated systems we use to realise quantum error-correcting codes may give rise to high-weight, problematic errors. Encouragingly, we can expect local quantum error-correcting codes with no string-like logical operators $-$…
A quantum error correction code is assessed over its ability to correct errors in noisy quantum circuits. This task requires extensive simulations of faulty quantum circuits, which are often made tractable by considering stochastic Pauli…
A critical milestone for quantum computers is to demonstrate fault-tolerant computation that outperforms computation on physical qubits. The tesseract subsystem color code protects four logical qubits in 16 physical qubits, to distance…
This work constructs codes that are efficiently decodable from a constant fraction of \emph{worst-case} insertion and deletion errors in three parameter settings: (i) Binary codes with rate approaching 1; (ii) Codes with constant rate for…
Quantum error correction (QEC) is critical for scalable fault-tolerant quantum computing. Topological codes, such as the toric code, offer hardware-efficient architectures but their Tanner graphs contain many girth-4 cycles that degrade the…
A scheme for linear optical implementation of fault-tolerant quantum computation is proposed, which is based on an error-detecting code. Each computational step is mediated by transfer of quantum information into an ancilla system embedding…
Topological quantum memory can protect information against local errors up to finite error thresholds. Such thresholds are usually determined based on the success of decoding algorithms rather than the intrinsic properties of the mixed…