Encoding classical information in gauge subsystems of quantum codes

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 minimum distances, one for the quantum information and one for the classical information. We give an explicit construction of hybrid codes from two classical linear codes using Bacon–Casaccino subsystem codes, as well as several new examples of good hybrid code.

New quantum codes from metacirculant graphs via self-dual additive $\mathbb{F}_4$-codes

<p style='text-indent:20px;'>We use symplectic self-dual additive codes over <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{F}_4 $\end{document}</tex-math></inline-formula> obtained from metacirculant graphs to construct, for the first time, <inline-formula><tex-math id="M2">\begin{document}$ \left[\kern-0.15em\left[ {\ell, 0, d} \right]\kern-0.15em\right] $\end{document}</tex-math></inline-formula> qubit codes with parameters <inline-formula><tex-math id="M3">\begin{document}$ (\ell,d) \in \{(78, 20), (90, 21), (91, 22), (93,21),(96,22)\} $\end{document}</tex-math></inline-formula>. Secondary constructions applied to the qubit codes result in many new qubit codes that perform better than the previous best-known.</p>

Theory of quasi-exact fault-tolerant quantum computing and valence-bond-solid codes

In this work, we develop the theory of quasi-exact fault-tolerant quantum (QEQ) computation, which uses qubits encoded into quasi-exact quantum error-correction codes (``quasi codes''). By definition, a quasi code is a parametric approximate code that can become exact by tuning its parameters. The model of QEQ computation lies in between the two well-known ones: the usual noisy quantum computation without error correction and the usual fault-tolerant quantum computation, but closer to the later. Many notions of exact quantum codes need to be adjusted for the quasi setting. Here we develop quasi error-correction theory using quantum instrument, the notions of quasi universality, quasi code distances, and quasi thresholds, etc. We find a wide class of quasi codes which are called valence-bond-solid codes, and we use them as concrete examples to demonstrate QEQ computation.

From Quantum Codes to Gravity: A Journey of Gravitizing Quantum Mechanics

In this note, I review a recent approach to quantum gravity that “gravitizes” quantum mechanics by emerging geometry and gravity from complex quantum states. Drawing further insights from tensor network toy models in AdS/CFT, I propose that approximate quantum error correction codes, when re-adapted into the aforementioned framework, also have promise in emerging gravity in near-flat geometries.

Error Probability Mitigation in Quantum Reading Using Classical Codes

A general framework describing the statistical discrimination of an ensemble of quantum channels is given by the name quantum reading. Several tools can be applied in quantum reading to reduce the error probability in distinguishing the ensemble of channels. Classical and quantum codes can be envisioned for this goal. The aim of this paper is to present a simple but fruitful protocol for this task using classical error-correcting codes. Three families of codes are considered: Reed–Solomon codes, BCH codes, and Reed–Muller codes. In conjunction with the use of codes, we also analyze the role of the receiver. In particular, heterodyne and Dolinar receivers are taken into consideration. The encoding and measurement schemes are connected by the probing step. As probes, we consider coherent states. In such a simple manner, interesting results are obtained. As we show, there is a threshold below which using codes surpass optimal and sophisticated schemes for any fixed rate and code. BCH codes in conjunction with Dolinar receiver turn out to be the optimal strategy for error mitigation in quantum reading.

Constacyclic codes over the ring Fq[u,v,w]/〈u2 − 1, v2 − 1,w3 − w, uv − vu,vw − wv,wu − uw〉

Let [Formula: see text] be the ring [Formula: see text], where [Formula: see text] for any odd prime [Formula: see text] and positive integer [Formula: see text]. In this paper, we study constacyclic codes over the ring [Formula: see text]. We define a Gray map by a matrix and decompose a constacyclic code over the ring [Formula: see text] as the direct sum of constacyclic codes over [Formula: see text], we also characterize self-dual constacyclic codes over the ring [Formula: see text] and give necessary and sufficient conditions for constacyclic codes to be dual-containing. As an application, we give a method to construct quantum codes from dual-containing constacyclic codes over the ring [Formula: see text].