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For an arbitrary degree distribution pair (DDP), we construct a sequence of low-density parity-check (LDPC) code ensembles with girth growing logarithmically in block-length using Ramanujan graphs. When the DDP has minimum left degree at…
We propose fault-tolerant encoders for quantum low-density parity check (LDPC) codes. By grouping qubits within a quantum code over contiguous blocks and applying preshared entanglement across these blocks, we show how transversal…
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…
An algorithm is proposed to encode low-density parity-check (LDPC) codes into codewords with a non-uniform distribution. This enables power-efficient signalling for asymmetric channels. We show gains of 0.9 dB for additive white Gaussian…
We present a unifying approach to quantum error correcting code design that encompasses additive (stabilizer) codes, as well as all known examples of nonadditive codes with good parameters. We use this framework to generate new codes with…
The quantum capacity of a memoryless channel is often used as a single figure of merit to characterize its ability to transmit quantum information coherently. The capacity determines the maximal rate at which we can code reliably over…
Recently, a lot of effort has been devoted towards designing erasure qubits in which dominant physical noise excites leakage states whose population can be detected and returned to the qubit subspace. Interest in these erasure qubits has…
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…
Two methods for constructing quantum LDPC codes are presented. We explain how to overcome the difficulty of finding a set of low weight generators for the stabilizer group of the code. Both approaches are based on some graph representation…
We derive exact analytical expressions for the quantum capacity of a broad subclasses of generalized dephasing channels of the form $\Lambda(\rho)=(1-x)\rho + x D(\rho)$, where $D(\rho)$ represents a structured decoherence process. These…
The non-local interactions in several quantum device architectures allow for the realization of more compact quantum encodings while retaining the same degree of protection against noise. Anticipating that short to medium-length codes will…
We study the super dense coding capacity in the presence of quantum channels with correlated noise. We investigate both the cases of unitary and non-unitary encoding. Pauli channels for arbitrary dimensions are treated explicitly. The super…
We show that a quantum architecture with an error correction procedure limited to geometrically local operations incurs an overhead that grows with the system size, even if arbitrary error-free classical computation is allowed. In…
Quantum error correction is rapidly seeing first experimental implementations, but there is a significant gap between asymptotically optimal error-correcting codes and codes that are experimentally feasible. Quantum LDPC codes range from…
The low coding rate of quantum stabilizer codes results in formidable physical qubit overhead when realizing quantum error correcting in engineering. In this letter, we propose a new class of hypergraph-product code called…
We consider the problem of implementing two-party interactive quantum communication over noisy channels, a necessary endeavor if we wish to fully reap quantum advantages for communication. For an arbitrary protocol with $n$ messages,…
The iterative decoding threshold of low-density parity-check (LDPC) codes over the binary erasure channel (BEC) fulfills an upper bound depending only on the variable and check nodes with minimum distance 2. This bound is a consequence of…
We first present a useful characterization of additive (stabilizer) quantum error-correcting codes. Then we present several examples of We first present a useful characterization of additive (stabilizer) quantum error--correcting codes.…
We give new dequantization and hardness results for estimating spectral sums of matrices, such as the log-determinant. Recent quantum algorithms have demonstrated that the logarithm of the determinant of sparse, well-conditioned, positive…
The successive cancellation list decoder (SCL) is an efficient decoder for classical polar codes with low decoding error, approximating the maximum likelihood decoder (MLD) for small list sizes. Here we adapt the SCL to the task of decoding…