Related papers: Single-shot and two-shot decoding with generalized…
We study the performance of Bacon-Shor codes, quantum subsystem codes which are well suited for applications to fault-tolerant quantum memory because the error syndrome can be extracted by performing two-qubit measurements. Assuming…
Given a quantum error correcting code, an important task is to find encoded operations that can be implemented efficiently and fault-tolerantly. In this Letter we focus on topological stabilizer codes and encoded unitary gates that can be…
Codeword stabilized (CWS) codes are a general class of quantum codes that includes stabilizer codes and many families of non-additive codes with good parameters. For such a non-additive code correcting all t-qubit errors, we propose an…
The hypergraph product creates a quantum stabilizer code from two input classical linear codes; a paradigmatic example being the surface code as a hypergraph product of two classical repetition codes. Many properties of the hypergraph…
Quantum error correction (QEC) codes are traditionally defined and searched for without specifying the manner in which its syndrome extraction circuits are executed using elementary gates and measurements. We show how morphing circuits…
Bivariate bicycle codes are promising candidates for high-threshold, low-overhead fault-tolerant quantum memories. Meanwhile, color codes are the most prominent self-dual CSS codes, supporting transversal Clifford gates that have been…
The essential insight of quantum error correction was that quantum information can be protected by suitably encoding this quantum information across multiple independently erred quantum systems. Recently it was realized that, since the most…
In this article we address the computational hardness of optimally decoding a quantum stabilizer code. Much like classical linear codes, errors are detected by measuring certain check operators which yield an error syndrome, and the…
We propose a general method for preparing stabilizer states with reduced two-qubit gate count and depth compared to the state of the art. The method starts from a graph state representation of the stabilizer state and iteratively reduces…
We introduce a new family of erasure codes, called group decodable code (GDC), for distributed storage system. Given a set of design parameters {\alpha; \beta; k; t}, where k is the number of information symbols, each codeword of an…
We show that within any quantum stabilizer code there lurks a classical binary linear code with similar error-correcting capabilities, thereby demonstrating new connections between quantum codes and classical codes. Using this result --…
Typical studies of quantum error correction assume probabilistic Pauli noise, largely because it is relatively easy to analyze and simulate. Consequently, the effective logical noise due to physically realistic coherent errors is relatively…
Quantum error correcting code can diagnose potential errors and correct them based on measured outcomes by leveraging syndrome measurement. However, mid-circuit measurement has been technically challenging for early fault-tolerant quantum…
Understanding error mechanisms in two-qubit gate operations is essential for building high-fidelity quantum processors. While prior studies predominantly treat dephasing noise as either Markovian or predominantly low-frequency, realistic…
Quantum low-density parity-check codes are promising candidates for low-overhead fault-tolerant quantum computing, but degeneracy is known to impair the convergence of belief-propagation (BP) decoding of these codes. In this work, we show…
In this work, we introduce a technique for reducing the length of a quantum stabilizer code, and we call this deflation of the code. Deflation can be seen as a generalization of the well-known puncturing and shortening techniques in cases…
Quantum errors are primarily detected and corrected using the measurement of syndrome information which itself is an unreliable step in practical error correction implementations. Typically, such faulty or noisy syndrome measurements are…
Topological codes have many desirable properties that allow fault-tolerant quantum computation with relatively low overhead. A core challenge for these codes, however, is to achieve a low-overhead universal gate set with limited…
We study single-copy stabilizer learning, the problem of identifying a stabilizer group of dimension $n-t$ from an $n$-qubit quantum state $\rho$. We obtain two complementary results. First, in the average case, logarithmic-depth local…
In previous work, we have shown that pseudocodewords can be used to characterize the behavior of decoders not only for classical codes but also for quantum stabilizer codes. With the insights obtained from this pseudocodewords-based…