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Fault tolerant quantum error correction (QEC) networks are studied by a combination of numerical and approximate analytical treatments. The probability of failure of the recovery operation is calculated for a variety of CSS codes, including…
Superconducting quantum processor units (QPUs) are incapable of producing massive datasets for quantum error correction (QEC) because of hardware limitations. Thus, QEC decoders heavily depend on synthetic data from qubit error models.…
In the early years of fault-tolerant quantum computing (FTQC), it is expected that the available code distance and the number of magic states will be restricted due to the limited scalability of quantum devices and the insufficient…
Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited…
We suggest several techniques to improve the toric codes and the finite-rate generalized toric codes (quantum hypergraph-product codes) recently introduced by Tillich and Z\'emor. For the usual toric codes, we introduce the rotated lattices…
Bosonic codes, leveraging infinite-dimensional Hilbert spaces for redundancy, offer great potential for encoding quantum information. However, the realization of a practical continuous-variable bosonic code that can simultaneously correct…
In practical communication and computation systems, errors occur predominantly in adjacent positions rather than in a random manner. In this paper, we develop a stabilizer formalism for quantum burst error correction codes (QBECC) to combat…
Quantum Error Correction (QEC) is the cornerstone of practical Fault-Tolerant Quantum Computing (FTQC), but incurs enormous resource overheads. Circuits must decompose into Clifford+T gates, and the non-transversal T gates demand costly…
Topological quantum field theories (TQFT) encode quantum correlations in topological features of spaces. In this work, we leverage this feature to explore how information encoded in TQFTs can be stored and retrieved in the presence of local…
Quantum information processing at scale will require sufficiently stable and long-lived qubits, likely enabled by error-correction codes. Several recent superconducting-qubit experiments, however, reported observing intermittent…
Efficient and high-performance quantum error correction is essential for achieving fault-tolerant quantum computing. Low-depth random circuits offer a promising approach to identifying effective and practical encoding strategies. In this…
Quantum computers could solve problems beyond the reach of classical devices, but this potential depends on quantum error correction (QEC) to protect fragile quantum states from noise. A central challenge in QEC is decoding: inferring…
We consider hierarchically implemented quantum error correction (HI-QEC), in which the fidelities of logical qubits are differentially optimized to enhance the capabilities of quantum devices in scientific applications. By employing qubit…
It has been known that quantum error correction via concatenated codes can be done with exponentially small failure rate if the error rate for physical qubits is below a certain accuracy threshold. Other, unconcatenated codes with their own…
Quantum error correction is widely thought to be the key to fault-tolerant quantum computation. However, determining the most suited encoding for unknown error channels or specific laboratory setups is highly challenging. Here, we present a…
We analyze the effect of typical, unknown perturbations on the 2D toric code when acting as a quantum memory, incorporating the effects of error correction on read-out. By transforming the system into a 1D transverse Ising model undergoing…
Fault-tolerant (FT) computation by using quantum error correction (QEC) is essential for realizing large-scale quantum algorithms. Devices are expected to have enough qubits to demonstrate aspects of fault tolerance in the near future.…
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…
A quantum error correction (QEC) code uses $N_{\rm c}$ quantum bits to construct one "logical" quantum bits of better quality than the original "physical" ones. QEC theory predicts that the failure probability $p_L$ of logical qubits…
Designing quantum error correcting codes that promise a high error threshold, low resource overhead and efficient decoding algorithms is crucial to achieve large-scale fault-tolerant quantum computation. The concatenated quantum Hamming…