Related papers: Quantum error-correcting codes from projective Ree…
In this paper, we study the construction of quantum codes by applying Steane-enlargement to codes from the Hermitian curve. We cover Steane-enlargement of both usual one-point Hermitian codes and of order bound improved Hermitian codes. In…
Error correcting codes with a universal set of transversal gates are a desideratum for quantum computing. Such codes, however, are ruled out by the Eastin-Knill theorem. Moreover, the theorem also rules out codes which are covariant with…
We introduce twisted unitary $t$-groups, a generalization of unitary $t$-groups under a twisting by an irreducible representation. We then apply representation theoretic methods to the Knill-Laflamme error correction conditions to show that…
We introduce the concept of generalized concatenated quantum codes. This generalized concatenation method provides a systematical way for constructing good quantum codes, both stabilizer codes and nonadditive codes. Using this method, we…
Covariant codes are quantum codes such that a symmetry transformation on the logical system could be realized by a symmetry transformation on the physical system, usually with limited capability of performing quantum error correction (an…
In this paper we show that there is a direct correspondence between quantum Boolean operations and certain forms of classical (non-quantum) logic known as Reed-Muller expansions. This allows us to readily convert Boolean circuits into their…
Quantum computers theoretically are able to solve certain problems more quickly than any deterministic or probabilistic computers. A quantum computer exploits the rules of quantum mechanics to speed up computations. However, one has to…
A universal set of quantum gates is constructed for the recently developed jump-error correcting quantum codes. These quantum codes are capable of correcting errors arising from the spontaneous decay of distinguishable qubits into…
A permutation-invariant quantum code on $N$ qudits is any subspace stabilized by the matrix representation of the symmetric group $S_N$ as permutation matrices that permute the underlying $N$ subsystems. When each subsystem is a complex…
Stacked quantum memory is an architecture in which multiple layers of qubits are stacked. Quantum rank-metric codes are effective for error correction in stacked quantum memories. However, the previously proposed quantum Gabidulin codes…
We investigate various aspects of operator quantum error-correcting codes or, as we prefer to call them, subsystem codes. We give various methods to derive subsystem codes from classical codes. We give a proof for the existence of subsystem…
Entanglement-assisted quantum error-correcting (EAQEC) codes are a subclass of quantum error-correcting codes which use entanglement as a resource. These codes can provide error correction capability higher than the codes derived from the…
One of the main problems in quantum information systems is the presence of errors due to noise, and for this reason quantum error-correcting codes (QECCs) play a key role. While most of the known codes are designed for correcting generic…
Connecting multiple smaller qubit modules by generating high-fidelity entangled states is a promising path for scaling quantum computing hardware. The performance of such a modular quantum computer is highly dependent on the quality and…
Fault-tolerant quantum computation is a technique that is necessary to build a scalable quantum computer from noisy physical building blocks. Key for the implementation of fault-tolerant computations is the ability to perform a universal…
A framework of monomial codes is considered, which includes linear codes generated by the evaluation of certain monomials. Polar and Reed-Muller codes are the two best-known representatives of such codes and can be considered as two extreme…
We study the performance of quantum error correction codes (QECCs) under the detection-induced coherent error due to the imperfectness of practical implementations of stabilizer measurements, after running a quantum circuit. Considering the…
Additive codes and some nonadditive codes use the single and multiple invariant subspaces of the stabilizer G, respectively, to construct quantum codes, so the selection of the invariant subspaces is a key problem. In this paper, I provide…
The Plotkin construction combines two codes to a code of doubled length. It can be applied recursively. The class of Reed-Muller (RM) codes is a particular example. Also, a special class of generalized concatenated codes (GCC) can be…
We discuss a method to construct quantum codes correcting amplitude damping errors via code concatenation. The inner codes are chosen as asymmetric Calderbank-Shor-Steane (CSS) codes. By concatenating with outer codes correcting symmetric…