Related papers: Quotient Space Quantum Codes
In this paper, based on the nonbinary graph state, we present a systematic way of constructing good non-binary quantum codes, both additive and nonadditive, for systems with integer dimensions. With the help of computer search, which…
Stabilizer codes form an important class of quantum error correcting codes which have an elegant theory, efficient error detection, and many known examples. Constructing stabilizer codes of length $n$ is equivalent to constructing subspaces…
We report two analytical bounds for quantum error-correcting codes that do not have preexisting classical counterparts. Firstly the quantum Hamming and Singleton bounds are combined into a single tighter bound, and then the combined bound…
We address the task of verifying whether a quantum computer, designed to be protected by a specific stabilizer code, correctly encodes the corresponding logical qubits. To achieve this, we develop a general framework for subspace…
Many $q$-ary stabilizer quantum codes can be constructed from Hermitian self-orthogonal $q^2$-ary linear codes. This result can be generalized to $q^{2 m}$-ary linear codes, $m > 1$. We give a result for easily obtaining quantum codes from…
Quantum information is fragile and must be protected by a quantum error-correcting code for large-scale practical applications. Recently, highly efficient quantum codes have been discovered which require a high degree of spatial…
The codeword stabilized (CWS) quantum codes formalism presents a unifying approach to both additive and nonadditive quantum error-correcting codes (arXiv:0708.1021 [quant-ph]), but only for binary states. Here we generalize the CWS…
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…
We consider the characterization as well as the construction of quantum codes that allow to transmit both quantum and classical information, which we refer to as `hybrid codes'. We construct hybrid codes $[\![n,k{: }m,d]\!]_q$ with length…
In this paper we investigate the encoding of operator quantum error correcting codes i.e. subsystem codes. We show that encoding of subsystem codes can be reduced to encoding of a related stabilizer code making it possible to use all the…
Bosonic codes utilize the infinite-dimensional Hilbert space of harmonic oscillators to encode quantum information, offering a hardware-efficient approach to quantum error correction. Designing these codes requires precise geometric…
The challenge of quantum computing is to combine error resilience with universal computation. Diagonal gates such as the transversal $T$ gate play an important role in implementing a universal set of quantum operations. This paper…
This paper presents conditions for constructing permutation-invariant quantum codes for deletion errors and provides a method for constructing them. Our codes give the first example of quantum codes that can correct two or more deletion…
Quantum error correcting codes play the role of suppressing noise and decoherence in quantum systems by introducing redundancy. Some strategies can be used to improve the parameters of these codes. For example, entanglement can provide a…
There are well known necessary and sufficient conditions for a quantum code to correct a set of errors. We study weaker conditions under which a quantum code may correct errors with probabilities that may be less than one. We work with…
We show how entanglement-assisted codes can be constructed from arbitrary quantum codes by associating them with quantum codes for erasure channels. If a subset of physical qubits is correctable for an erasure error, then it naturally forms…
The increasing interest in using quantum error correcting codes in practical devices has heightened the need for designing quantum error correcting codes that can correct against specialized errors, such as that of amplitude damping errors…
The Measurement-based quantum computation provides an alternate model for quantum computation compared to the well-known gate-based model. It uses qubits prepared in a specific entangled state followed by single-qubit measurements. The…
Quantum error-correcting codes with good parameters can be constructed by evaluating polynomials at the roots of the polynomial trace. In this paper, we propose to evaluate polynomials at the roots of trace-depending polynomials (given by a…
It is conjectured that quantum computers are able to solve certain problems more quickly than any deterministic or probabilistic computer. A quantum computer exploits the rules of quantum mechanics to speed up computations. However, it is a…