Related papers: Partial Self-Correction in Layer Codes
Quantum error correction (QEC) is essential for scalable quantum computing. However, it requires classical decoders that are fast and accurate enough to keep pace with quantum hardware. While quantum low-density parity-check codes have…
The most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilbert space. Recently this notion has led to a more general…
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…
The following open problems, which concern a fundamental limit on coding properties of quantum codes with realistic physical constraints, are analyzed and partially answered here: (a) the upper bound on code distances of quantum…
Quantum error correction is a critical component for scaling up quantum computing. Given a quantum code, an optimal decoder maps the measured code violations to the most likely error that occurred, but its cost scales exponentially with the…
We analyze several high dimensional generalizations of the toric code at nonzero temperature. We find that in large enough dimension, there can be a distinct separation between the critical temperature $T_c$, given by thermodynamic…
Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review we consider the formalism of qubit…
We propose and study a model of a quantum memory that features self-correcting properties and a lifetime growing arbitrarily with system size at non-zero temperature. This is achieved by locally coupling a 2D L x L toric code to a 3D bath…
Ongoing research and experiments have enabled quantum memory to realize the storage of qubits. On the other hand, interleaving techniques are used to deal with burst of errors. Effective interleaving techniques for combating burst of errors…
Low-depth random circuit codes possess many desirable properties for quantum error correction but have so far only been analyzed in the code capacity setting where it is assumed that encoding gates and syndrome measurements are noiseless.…
Standard approaches to quantum error correction (QEC) require active maintenance using measurements and classical processing. Passive QEC, by contrast, has so far been established only in unphysical spatial dimensions. Here, we give an…
Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this…
Quantum error correction offers a promising path for performing quantum computations with low errors. Although a fully fault-tolerant execution of a quantum algorithm remains unrealized, recent experimental developments, along with…
Arbitrarily long quantum computations require quantum memories that can be repeatedly measured without being corrupted. Here, we preserve the state of a quantum memory, notably with the additional use of flagged error events. All error…
We discuss energy barriers and their relationship to self-correcting quantum memories. We introduce the solid code, a 3-d version of Kitaev's surface code, and then combine several solid codes using a technique called welding. The resulting…
Quantum states are inherently fragile, making their storage a major concern for many practical applications and experimental tests of quantum mechanics. The field of quantum memories is concerned with how this storage may be achieved,…
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…
Quantum memory is a central component for quantum information processing devices, and will be required to provide high-fidelity storage of arbitrary states, long storage times and small access latencies. Despite growing interest in applying…
A new class of exact-repair regenerating codes is constructed by combining two layers of erasure correction codes together with combinatorial block designs, e.g., Steiner systems, balanced incomplete block designs and t-designs. The…
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…