Related papers: Quantum Error Correction via Codes over GF(4)
The surface code is a promising candidate for fault-tolerant quantum computation, achieving a high threshold error rate with nearest-neighbor gates in two spatial dimensions. Here, through a series of numerical simulations, we investigate…
In Part II we show that there exist quantum codes whose probability of undetected error falls exponentially with the length of the code and derive bounds on this exponent.The lower (existence) bound for stabilizer codes is proved by a…
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…
We investigate a novel class of quantum error correcting codes to correct errors on both qubits and higher-state quantum systems represented as qudits. These codes arise from an original graph-theoretic representation of sets of quantum…
We solve the fundamental quantum error correction problem for bi-unitary channels on two-qubit Hilbert space. By solving an algebraic compression problem, we construct qubit codes for such channels on arbitrary dimension Hilbert space, and…
Large-scale quantum computation will only be achieved if experimentally implementable quantum error correction procedures are devised that can tolerate experimentally achievable error rates. We describe a quantum error correction procedure…
Errors are inevitable during all kinds quantum informational tasks and quantum error-correcting codes (QECCs) are powerful tools to fight various quantum noises. For standard QECCs physical systems have the same number of energy levels.…
Due to the fragility of quantum mechanical effects, real quantum computers are plagued by frequent noise effects that cause errors during computations. Quantum error-correcting codes address this problem by providing means to identify and…
The theory of quantum error correction was established more than a decade ago as the primary tool for fighting decoherence in quantum information processing. Although great progress has already been made in this field, limited methods are…
The noise in physical qubits is fundamentally asymmetric: in most devices, phase errors are much more probable than bit flips. We propose a quantum error correcting code which takes advantage of this asymmetry and shows good performance at…
We identify optimal quantum error correction codes for situations that do not admit perfect correction. We provide analytic n-qubit results for standard cases with correlated errors on multiple qubits and demonstrate significant…
A quantum error correcting code is a subspace $\mathcal{C}$ such that allowed errors acting on any state in $\mathcal{C}$ can be corrected. A quantum code for which state recovery is only required up to a logical rotation within…
Recent progress in quantum computing has enabled systems with tens of reliable logical qubits, built from thousands of noisy physical qubits. However, many impactful applications demand quantum computations with millions of logical qubits,…
Several upper bounds on the size of quantum codes are derived using the linear programming approach. These bounds are strengthened for the linear quantum codes.
Quantum error correction protects quantum information against environmental noise. When using qubits, a measure of quality of a code is the maximum number of errors that it is able to correct. We show that a suitable notion of ``number of…
Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…
In this work we prove that the 5-qubit quantum error correcting code does not fix qubit independent errors, even assuming that the correction circuit does not introduce new errors. We say that a quantum code does not fix a quantum computing…
Tradeoffs between the information rate and fidelity of quantum error-correcting codes are discussed. Quantum channels to be considered are those subject to independent errors and modeled as tensor products of copies of a general completely…
Quantum computation and communication rely on the ability to manipulate quantum states robustly and with high fidelity. Thus, some form of error correction is needed to protect fragile quantum superposition states from corruption by…
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…