相关论文: Balanced Product Quantum Codes

Transversal gates are the ideal gates in a fault-tolerant scenario; relatively easy to implement, and minimally error propagating. Their availability will maximise fault tolerant thresholds, enabling universal quantum computation in a wider…

In this paper, we present a new construction of asymmetric quantum codes (AQCs) by combining classical concatenated codes (CCs) with tensor product codes (TPCs), called asymmetric quantum concatenated and tensor product codes (AQCTPCs)…

In this paper, we prove a lower bound on the soundness of quantum locally testable codes under the distance balancing construction of Evra et al. arXiv:2004.07935 [quant-ph]. Our technical contribution is that the new soundness of the…

Due to their fast decoding algorithms, quantum generalizations of low-density parity check, or LDPC, codes have been investigated as a solution to the problem of decoherence in fragile quantum states. However, the additional twisted inner…

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…

Quantum error correction is critical to the design and manufacture of scalable quantum computing systems. Recently, there has been growing interest in quantum low-density parity-check codes as a resource-efficient alternative to surface…

We discuss error-correction properties for families of quantum low-density parity check (LDPC) codes with relative distance that tends to zero in the limit of large blocklength. In particular, we show that any family of LDPC codes, quantum…

Utility-scale quantum computing requires quantum error correction (QEC) to protect quantum information against noise. Currently, superconducting hardware is a promising candidate for achieving fault tolerance due to its fast gate times and…

Quantum computers hold the potential to surpass classical computers in solving complex computational problems. However, the fragility of quantum information and the error-prone nature of quantum operations make building large-scale,…

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…

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 LDPC codes may provide a path to build low-overhead fault-tolerant quantum computers. However, as general LDPC codes lack geometric constraints, na\"ive layouts couple many distant qubits with crossing connections which could be…

Constant-rate low-density parity-check (LDPC) codes are promising candidates for constructing efficient fault-tolerant quantum memories. However, if physical gates are subject to geometric-locality constraints, it becomes challenging to…

Qudits offer significant advantages over qubit-based architectures, including more efficient gate compilation, reduced resource requirements, improved error-correction primitives, and enhanced capabilities for quantum communication and…

For any positive integer $g \ge 2$, we derive general condition for the existence of a $2g$-cycle in the Tanner graph of two-dimensional ($2$-D) classical quasi-cyclic (QC) low-density parity-check (LDPC) codes. Depending on whether $p$ is…

The promise of high-rate low-density parity check (LDPC) codes to substantially reduce the overhead of fault-tolerant quantum computation depends on constructing efficient, fault-tolerant implementations of logical gates on such codes.…

The techniques of distance verification known for general linear codes are re-applied to quantum stabilizer codes. Then distance verification is addressed for classical and quantum LDPC codes. New complexity bounds for distance verification…

Quantum error-correcting codes (QECCs) sit between noisy quantum hardware and reliable computation, so the code parameters used in practice must be trustworthy. The single number that summarizes a code's strength is its distance, yet…

We present an efficient decoding algorithm for constant rate quantum hypergraph-product LDPC codes which provably corrects adversarial errors of weight $\Omega(\sqrt{n})$ for codes of length $n$. The algorithm runs in time linear in the…

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…