Related papers: A Hamming-Like Bound for Degenerate Stabilizer Cod…
We consider network coding for networks experiencing worst-case bit-flip errors, and argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network error-correcting…
Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The proposed weighted-Hamming metric is tailored to this setting and enables optimal decoding performance. We show that some…
In quantum coding theory, stabilizer codes are probably the most important class of quantum codes. They are regarded as the quantum analogue of the classical linear codes and the properties of stabilizer codes have been carefully studied in…
Variational algorithms may enable classically intractable simulations on near-future quantum computers. However, their potential is limited by hardware errors. It is therefore crucial to develop efficient ways to mitigate these errors.…
We consider Majorana fermion stabilizer codes with small number of modes and distance. We give an upper bound on the number of logical qubits for distance $4$ codes, and we construct Majorana fermion codes similar to the classical Hamming…
We perform an extended numerical search for practical fermion-to-qubit encodings with error correcting properties. Ideally, encodings should strike a balance between a number of the seemingly incompatible attributes, such as having a high…
Self-orthogonal $J$-affine variety codes have been successfully used to obtain quantum stabilizer codes with excellent parameters. In a previous paper we gave formulae for the dimension of this family of quantum codes, but no bound for the…
We introduce a notion of homogeneous topological order, which is obeyed by most, if not all, known examples of topological order including fracton phases on quantum spins (qudits). The notion is a condition on the ground state subspace,…
The relation between stabilizer codes and binary codes provided by Gottesman and Calderbank et al. is a celebrated result, as it allows the lifting of classical codes to quantum codes. An equivalent way to state this result is that the work…
We develop the theory of entanglement-assisted quantum error correcting (EAQEC) codes, a generalization of the stabilizer formalism to the setting in which the sender and receiver have access to pre-shared entanglement. Conventional…
Convolutional stabilizer codes promise to make quantum communication more reliable with attractive online encoding and decoding algorithms. This paper introduces a new approach to convolutional stabilizer codes based on direct limit…
The stabilizing properties of one-error correcting jump codes are explored under realistic non-ideal conditions. For this purpose the quantum algorithm of the tent-map is decomposed into a universal set of Hamiltonian quantum gates which…
We present general conditions for quantum error suppression for Hamiltonian-based quantum computation using subsystem codes. This involves encoding the Hamiltonian performing the computation using an error detecting subsystem code and the…
We apply quantum Construction X on quasi-cyclic codes with large Hermitian hulls over $\mathbb{F}_4$ and $\mathbb{F}_9$ to derive good qubit and qutrit stabilizer codes, respectively. In several occasions we obtain quantum codes with…
For every stabiliser $N$-qudit absolutely maximally entangled state, we present a method for determining the stabiliser generators and logical operators of a corresponding quantum error correction code. These codes encode $k$ qudits into…
We study a wave equation in one space dimension with a general diffusion coefficient which degenerates on part of the boundary. Degeneracy is measured by a real parameter $\mu_a>0$. We establish observability inequalities for weakly (when…
Quantum error correction allows to actively correct errors occurring in a quantum computation when the noise is weak enough. To make this error correction competitive information about the specific noise is required. Traditionally, this…
Quantum error-correction codes (QECCs) are a vital ingredient of quantum computation and communication systems. In that context it is highly desirable to design QECCs that can be represented by graphical models which possess a structure…
In this work, we explore a new approach to designing both algorithms and error detection codes for preparing approximate ground states of molecules. We propose a classical algorithm to find the optimal stabilizer state by using excitations…
We study variants of Shor's code that are adept at handling single-axis correlated idling errors, which are commonly observed in many quantum systems. By using the repetition code structure of the Shor's code basis states, we calculate the…