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Codes based on sparse matrices have good performance and can be efficiently decoded by belief-propagation (BP). Decoding binary stabilizer codes needs a quaternary BP for (additive) codes over GF(4), which has a higher check-node complexity…
This work presents a hardware-efficient and fully parallelizable decoder for quantum LDPC codes that leverages belief propagation (BP) with a speculative post-processing strategy inspired by classical Chase decoding algorithm. By monitoring…
Fault tolerance is a prerequisite for scalable quantum computing. Architectures based on 2D topological codes are effective for near-term implementations of fault tolerance. To obtain high performance with these architectures, we require a…
Stabilizer codes lie at the heart of modern quantum-error-correcting codes (QECC). Of particular importance is a class called Calderbank-Shor-Steane (CSS) codes, which includes many important examples such as toric codes, color codes, and…
The highest information rate at which quantum error-correction schemes work reliably on a channel, which is called the quantum capacity, is proven to be lower bounded by the limit of the quantity termed coherent information maximized over…
Quantum data is susceptible to decoherence induced by the environment and to errors in the hardware processing it. A future fault-tolerant quantum computer will use quantum error correction (QEC) to actively protect against both. In the…
Quantum error correction is an essential ingredient for reliable quantum computation for theoretically provable quantum speedup. Topological color codes, one of the quantum error correction codes, have an advantage against the surface codes…
Ternary channels can be used to model the behavior of some memory devices, where information is stored in three different levels. In this paper, error correcting coding for a ternary channel where some of the error transitions are not…
Quantum computers require error correction to achieve universal quantum computing. However, current decoding of quantum error-correcting codes relies on classical computation, which is slower than quantum operations in superconducting…
Topological color codes defined by the 4.8.8 semiregular lattice feature geometrically local check operators and admit transversal implementation of the entire Clifford group, making them promising candidates for fault-tolerant quantum…
A classical coding across a block of logical qubits is presented. We characterize subgroups of the product stabilizer group on a block of logical qubits corresponding to dual codes of classical error correcting codes. We prove conditions on…
Quantum error correcting codes protect quantum information, allowing for large quantum computations provided that physical error rates are sufficiently low. We combine post-selection with surface code error correction through the use of a…
We investigate cat codes that can correct multiple excitation losses and identify two types of logical errors: bit-flip errors due to excessive excitation loss and dephasing errors due to quantum back-action from the environment. We show…
Quantum error correction (QEC) is essential for scalable quantum computing. However, it requires classical decoders that are fast and accurate enough to keep pace with quantum hardware. While quantum low-density parity-check codes have…
Quantum error-correcting codes so far proposed have not worked in the presence of noise which introduces more than one bit of entropy per qubit sent through a quantum channel, nor can any code which identifies the complete error syndrome.…
One of the main challenge for an efficient implementation of quantum information technologies is how to counteract quantum noise. Quantum error correcting codes are therefore of primary interest for the evolution towards quantum computing…
Bit flipping can be used as a postprocessing technique to further improve the performance for successive cancellation list (SCL) decoding of polar codes. However, the number of bit-flipping trials could increase the decoding latency…
Quantum error correction is instrumental in protecting quantum systems from noise in quantum computing and communication settings. Pauli channels can be efficiently simulated and threshold values for Pauli error rates under a variety of…
Quantum error correction is necessary to perform large-scale quantum computations in the presence of noise and decoherence. As a result, several aspects of quantum error correction have already been explored. These have been primarily…
The discovery of new quantum error-correcting codes that encode several logical qubits into relatively few physical qubits motivates the development of efficient and accurate methods of decoding these systems. Here, we adopt the…