Related papers: The Subfield Metric and its Application to Quantum…
The surface code is a powerful quantum error correcting code that can be defined on a 2-D square lattice of qubits with only nearest neighbor interactions. Syndrome and data qubits form a checkerboard pattern. Information about errors is…
The homogeneous metric can be viewed as a natural extension of the Hamming metric to finite chain rings. It distinguishes between three types of elements: zero, non-zero elements in the socle, and elements outside the socle. Since the…
The realization of scalable fault-tolerant quantum computing is expected to hinge on quantum error-correcting codes. In the quest for more efficient quantum fault tolerance, a critical code parameter is the weight of measurements that…
Modular quantum computing architectures require error correction schemes that remain effective in the presense of noisy inter-processor operations. We introduce a distributed quantum error correction framework based on approximate codes to…
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…
We illustrate how computer-aided methods can be used to investigate the fundamental limits of the caching systems, which are significantly different from the conventional analytical approach usually seen in the information theory…
Contrary to the assumption that most quantum error-correcting codes (QECC) make, it is expected that phase errors are much more likely than bit errors in physical devices. By employing the entanglement-assisted stabilizer formalism, we…
Recently a framework for assisted quantum error correction was proposed in which a specific type of error is allowed to occur on auxiliary qubits, which is in contrast to standard entanglement assistance that requires noiseless auxiliary…
The relation between symmetry reduction before and after quantization of a field theory is discussed using a toy model: the axisymmetric Klein-Gordon field. We consider three possible notions of symmetry at the quantum level: invariance…
This paper presents encoding and decoding algorithms for several families of optimal rank metric codes whose codes are in restricted forms of symmetric, alternating and Hermitian matrices. First, we show the evaluation encoding is the right…
Multi-class classification is mandatory for real world problems and one of promising techniques for multi-class classification is Error Correcting Output Code. We propose a method for constructing the Error Correcting Output Code to obtain…
We present for the first time a general theory of error correction for permutation invariant (PI) codes. Using representation theory of the symmetric group we construct efficient algorithms that can correct any correctible error on any PI…
Necessary and sufficient criteria for metric subregularity (or calmness) of set-valued mappings between general metric or Banach spaces are treated in the framework of the theory of error bounds for a special family of extended real-valued…
Matrix-product codes over finite fields are an important class of long linear codes by combining several commensurate shorter linear codes with a defining matrix over finite fields. The construction of matrix-product codes with certain…
In the current paper the properties of a quantum field theory based on certain sets of Lorentz-violating coefficients in the nonminimal fermion sector of the Standard-Model Extension are analyzed. In particular, three families of…
Recent progress in quantum cryptography and quantum computers has given hope to their imminent practical realization. An essential element at the heart of the application of these quantum systems is a quantum error correction scheme. We…
We use entropy numbers in combination with the polynomial method to derive a new general lower bound for the n-th minimal error in the quantum setting of information-based complexity. As an application, we improve some lower bounds on…
Quantum error mitigation (QEM) is a class of promising techniques capable of reducing the computational error of variational quantum algorithms tailored for current noisy intermediate-scale quantum computers. The recently proposed…
Error control is significant to network coding, since when unchecked, errors greatly deteriorate the throughput gains of network coding and seriously undermine both reliability and security of data. Two families of codes, subspace and rank…
Quantum error-correcting codes protect fragile quantum information by encoding it redundantly, but identifying codes that perform well in practice with minimal overhead remains difficult due to the combinatorial search space and the high…