Andrew Nemec
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View article: Structure theorem for quantum replacer codes
Structure theorem for quantum replacer codes Open
Quantum replacer codes are codes that can be protected from errors induced by a given set of quantum replacer channels, an important class of quantum channels that includes the erasures of subsets of qubits that arise in quantum error corr…
View article: Synchronizable hybrid subsystem codes
Synchronizable hybrid subsystem codes Open
Quantum synchronizable codes are quantum error correcting codes that can correct not only Pauli errors but also errors in block synchronization. The code can be constructed from two classical cyclic codes $\mathcal{C}$, $\mathcal{D}$ satis…
View article: SDP bounds on quantum codes
SDP bounds on quantum codes Open
This paper provides a semidefinite programming hierarchy based on state polynomial optimization to determine the existence of quantum codes with given parameters. The hierarchy is complete, in the sense that a $(\!(n, K, δ)\!)_2$ code exis…
View article: An infinite class of quantum codes derived from duadic constacyclic codes
An infinite class of quantum codes derived from duadic constacyclic codes Open
We present a family of quantum stabilizer codes using the structure of duadic constacyclic codes over $\mathbb{F}_4$. Within this family, quantum codes can possess varying dimensions, and their minimum distances are lower bounded by a squa…
View article: Robust Syndrome Extraction via BCH Encoding
Robust Syndrome Extraction via BCH Encoding Open
Quantum data-syndrome (QDS) codes are a class of quantum error-correcting codes that protect against errors both on the data qubits and on the syndrome itself via redundant measurement of stabilizer group elements. One way to define a QDS …
View article: A Hamming-Like Bound for Degenerate Stabilizer Codes
A Hamming-Like Bound for Degenerate Stabilizer Codes Open
The quantum Hamming bound was originally put forward as an upper bound on the parameters of nondegenerate quantum codes, but over the past few decades much work has been done to show that many degenerate quantum codes must also obey this b…
View article: Quantum Data-Syndrome Codes: Subsystem and Impure Code Constructions
Quantum Data-Syndrome Codes: Subsystem and Impure Code Constructions Open
Quantum error correction requires the use of error syndromes derived from measurements that may be unreliable. Recently, quantum data-syndrome (QDS) codes have been proposed as a possible approach to protect against both data and syndrome …
View article: Encoding classical information in gauge subsystems of quantum codes
Encoding classical information in gauge subsystems of quantum codes Open
In this paper, we show how to construct hybrid quantum-classical codes from subsystem codes by encoding the classical information into the gauge qudits using gauge fixing. Unlike previous work on hybrid codes, we allow for two separate min…
View article: A Combinatorial Interpretation for the Shor-Laflamme Weight Enumerators of CWS Codes
A Combinatorial Interpretation for the Shor-Laflamme Weight Enumerators of CWS Codes Open
We show that one of the Shor-Laflamme weight enumerators of a codeword stabilized quantum code may be interpreted as the distance enumerator of an associated classical code.
View article: Infinite Families of Quantum-Classical Hybrid Codes
Infinite Families of Quantum-Classical Hybrid Codes Open
Hybrid codes simultaneously encode both quantum and classical information into physical qubits. We give several general results about hybrid codes, most notably that the quantum codes comprising a genuine hybrid code must be impure and tha…
View article: Nonbinary Error-Detecting Hybrid Codes
Nonbinary Error-Detecting Hybrid Codes Open
Hybrid codes simultaneously encode both quantum and classical information, allowing for the transmission of both across a quan- tum channel. We construct a family of nonbinary error-detecting hybrid stabilizer codes that can detect one err…
View article: Hybrid Codes
Hybrid Codes Open
A hybrid code can simultaneously encode classical and quantum information\ninto quantum digits such that the information is protected against errors when\ntransmitted through a quantum channel. It is shown that a hybrid code has the\nremar…
View article: Families of Cyclic Codes over Finite Chain Rings
Families of Cyclic Codes over Finite Chain Rings Open
A major difficulty in quantum computation and communication is preventing and correcting errors in the quantum bits. Most of the research in this area has focused on stabilizer codes derived from self-orthogonal cyclic error-correcting cod…