Related papers: Quantum error correcting codes based on privacy am…
For a quantum error correcting code to be used in practice, it needs to be equipped with an efficient decoding algorithm, which identifies corrections given the observed syndrome of errors.Hypergraph product codes are a promising family of…
Classical communication through quantum channels may be enhanced by sharing entanglement. Superdense coding allows the encoding, and transmission, of up to two classical bits of information in a single qubit. In this paper, the maximum…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
We consider the problem of decoding corrupted error correcting codes with NC$^0[\oplus]$ circuits in the classical and quantum settings. We show that any such classical circuit can correctly recover only a vanishingly small fraction of…
Quantum error correction is essential for realizing scalable quantum computation. Among various approaches, low-density parity-check codes over higher-order Galois fields have shown promising performance due to their structured sparsity and…
We prove a one-shot "minimax" converse bound for quantum channel coding assisted by positive partial transpose channels between sender and receiver. The bound is similar in spirit to the converse by Polyanskiy, Poor, and Verdu [IEEE Trans.…
Standard approaches to quantum error correction for fault-tolerant quantum computing are based on encoding a single logical qubit into many physical ones, resulting in asymptotically zero encoding rates and therefore huge resource…
Implementing robust quantum error correction (QEC) is imperative for harnessing the promise of quantum technologies. We introduce a framework that takes {\it any} classical code and explicitly constructs the corresponding QEC code. Our…
Entanglement purification provides a unifying framework for proving the security of quantum key distribution schemes. Nonetheless, up till now, a local commutability constraint in the CSS code construction means that the error correction…
Quantum error correction codes based on continuous variables play an important role for the implementation of quantum communication systems. A natural application of such codes occurs within quantum repeater systems which are used to combat…
Error correcting codes with a universal set of transversal gates are a desideratum for quantum computing. Such codes, however, are ruled out by the Eastin-Knill theorem. Moreover, the theorem also rules out codes which are covariant with…
The overheads of classical decoding for quantum error correction on superconducting quantum systems grow rapidly with the number of logical qubits and their correction code distance. Decoding at room temperature is bottle-necked by…
We propose quaternion-based strategies for quantum error correction by extending quantum mechanics into quaternionic Hilbert spaces. Building on the properties of quaternionic quantum states, we define quaternionic analogues of Pauli…
A central challenge for the scaling of quantum computing systems is the need to control all qubits in the system without a large overhead. A solution for this problem in classical computing comes in the form of so called crossbar…
Continuous-variable systems protected by bosonic quantum error-correcting codes have emerged as a promising platform for quantum information processing. To date, design of codewords has centered on optimizing the occupation of basis states…
Security of quantum key distribution (QKD) protocols relies solely on quantum physics laws, namely, on the impossibility to distinguish between non-orthogonal quantum states with absolute certainty. Due to this, a potential eavesdropper…
Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be…
Scaling up quantum computers to attain substantial speedups over classical computing requires fault tolerance. Conventionally, protocols for fault-tolerant quantum computation demand excessive space overheads by using many physical qubits…
Quantum synchronizable codes are quantum error-correcting codes designed to correct the effects of both quantum noise and block synchronization errors. While it is known that quantum synchronizable codes can be constructed from cyclic codes…
Surface and color codes are two forms of topological quantum error correction in two spatial dimensions with complementary properties. Surface codes have lower-depth error detection circuits and well-developed decoders to interpret and…