Related papers: On the logical error rate of sparse quantum codes
Quantum error correction is expected to be essential in large-scale quantum technologies. However, the substantial overhead of qubits it requires is thought to greatly limit its utility in smaller, near-term devices. Here we introduce a new…
It has recently been shown that there are efficient algorithms for quantum computers to solve certain problems, such as prime factorization, which are intractable to date on classical computers. The chances for practical implementation,…
The development of practical, high-performance decoding algorithms reduces the resource cost of fault-tolerant quantum computing. Here we propose a decoder for the surface code that finds low-weight correction operators for errors produced…
A method for concatenating quantum error-correcting codes is presented. The method is applicable to a wide class of quantum error-correcting codes known as Calderbank-Shor-Steane (CSS) codes. As a result, codes that achieve a high rate in…
Accurate decoding of quantum error-correcting codes is a crucial ingredient in protecting quantum information from decoherence. It requires characterizing the error channels corrupting the logical quantum state and providing this…
Quantum computation promises significant computational advantages over classical computation for some problems. However, quantum hardware suffers from much higher error rates than in classical hardware. As a result, extensive quantum error…
Logical qubits encoded into a quantum code exhibit improved error rates when the physical error rates are sufficiently low, below the pseudothreshold. Logical error rates and pseudothresholds can be estimated for specific circuits and noise…
Designing quantum error correcting codes that promise a high error threshold, low resource overhead and efficient decoding algorithms is crucial to achieve large-scale fault-tolerant quantum computation. The concatenated quantum Hamming…
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…
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…
Recent progress in quantum computing has enabled systems with tens of reliable logical qubits, built from thousands of noisy physical qubits. However, many impactful applications demand quantum computations with millions of logical qubits,…
Quantum error correction (QEC) will be essential to achieve the accuracy needed for quantum computers to realise their full potential. The field has seen promising progress with demonstrations of early QEC and real-time decoded experiments.…
We introduce a decoding framework for correlated errors in quantum LDPC codes under circuit-level noise. The core of our approach is a graph augmentation and rewiring for interference (GARI) method, which modifies the correlated detector…
Erasures are the primary type of errors in physical systems dominated by leakage errors. While quantum error correction (QEC) using stabilizer codes can combat erasure errors, it remains unknown which constructions achieve capacity…
Color code is a promising topological code for fault-tolerant quantum computing. Insufficient research on the color code has delayed its practical application. In this work, we address several key issues to facilitate practical…
We present a nonintrusive method for reliably estimating the noise level during quantum computation and quantum communication protected by quantum error-correcting codes. As preprocessing of quantum error correction, our scheme estimates…
We introduce a convergent iterative algorithm for finding the optimal coding and decoding operations for an arbitrary noisy quantum channel. This algorithm does not require any error syndrome to be corrected completely, and hence also finds…
Recent progress in fault-tolerant quantum computing suggests that leveraging error-syndrome information at the logical layer can substantially improve performance, including the estimation of logical observables from noisy states. In this…
Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical…
Fault-tolerant quantum computing demands many qubits with long lifetimes to conduct accurate quantum gate operations. However, external noise limits the computing time of physical qubits. Quantum error correction codes may extend such…