Related papers: Quantum XYZ Product Codes
Three-dimensional (3D) quantum XYZ product can construct a class of non-CSS quantum codes by using three classical codes. However, there has been limited study on their error-correcting performance so far and whether this code construction…
We present new constructions of quantum codes of linear or close-to-linear distance and dimension with low-weight stabilizers. Only a few constructions of such codes were previously known, and were primarily based on a specific operation…
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…
We develop a topological theory for fault-tolerant quantum computation in quantum low-density parity-check (qLDPC) codes. We show that there exist hidden simplicial or CW complex structures encoding the topological data for all qLDPC and…
Hypergraph product (HGP) codes are one of the most popular family of quantum low-density parity-check (LDPC) codes. Circuit-level simulations show that they can achieve the same logical error rate as surface codes with a reduced qubit…
Several notions of code products are known in quantum error correction, such as hyper-graph products, homological products, lifted products, balanced products, to name a few. In this paper we introduce a new product code construction which…
In this paper, we introduce a new family of stabilizer quantum LDPC codes derived from the classical linear codes $L_k$ and $L_k^{+}$, defined via sub-exceding functions. In previous work, these codes demonstrated strong performance in…
Quantum codes with low-weight stabilizers known as LDPC codes have been actively studied recently due to their simple syndrome readout circuits and potential applications in fault-tolerant quantum computing. However, all families of quantum…
Single-shot error correction outperforms conventional approaches by requiring only one round of stabilizer measurements for decoding, even in the presence of measurement errors. This capability relates to the confinement property of codes,…
We study parallel fault-tolerant quantum computing for families of homological quantum low-density parity-check (LDPC) codes defined on 3-manifolds with constant or almost-constant encoding rate. We derive generic formula for a transversal…
CSS codes are in one-to-one correspondance with length 3 chain complexes. The latter are naturally endowed with a tensor product $\otimes$ which induces a similar operation on the former. We investigate this operation, and in particular its…
We introduce a "hyperbicycle" ansatz for quantum codes which gives the hypergraph-product (generalized toric) codes by Tillich and Z\'emor and generalized bicycle codes by MacKay et al. as limiting cases. The construction allows for both…
The hypergraph product (HGP) construction of quantum error-correcting codes (QECC) offers a general and explicit method for building a QECC from two classical codes, thereby paving the way for the discovery of good quantum low-density…
Quasi-cyclic (QC) low-density parity-check (LDPC) codes are an important instance of proto-graph-based LDPC codes. In this paper we present upper bounds on the minimum Hamming distance of QC LDPC codes and study how these upper bounds…
The hypergraph product (HGP) is a famous code construction technique with an equally famous canonical visualisation. This visual perspective provides much more than simply a way to build intuition: HGP codes can be defined graphically,…
Existence of quantum low-density parity-check (LDPC) codes whose minimal distance scales linearly with the number of qubits is a major open problem in quantum information. Its practical interest stems from the need to protect information in…
Quantum low-density parity-check (LDPC) codes are an important class of quantum error correcting codes. In such codes, each qubit only affects a constant number of syndrome bits, and each syndrome bit only relies on some constant number of…
We continue the study of classical and quantum low-density parity check (LDPC) codes from a physical perspective. We focus on constructive approaches and formulate a general framework for systematically constructing codes with various…
Product codes are a class of quantum error correcting codes built from two or more constituent codes. They have recently gained prominence for a breakthrough yielding quantum low-density parity-check (qLDPC) codes with favorable scaling of…
Quantum error correction (QEC) is critical for practical realization of fault-tolerant quantum computing, and recently proposed families of quantum low-density parity-check (QLDPC) code are prime candidates for advanced QEC hardware…