Codeword Stabilized Codes from m-Uniform Graph States
Sowrabh Sudevan, Sourin Das, Thamadathil Aswanth, Nupur Patanker, Navin Kashyap

TL;DR
This paper introduces a method to construct quantum error-correcting codes using m-uniform graph states and classical codes, providing explicit examples and protocols for encoding and recovery.
Contribution
It presents a novel framework combining m-uniform graph states and classical codes to generate new quantum error-correcting codes within the CWS framework.
Findings
Constructed new families of QECCs with specific parameters.
Provided measurement-based encoding and recovery protocols.
Demonstrated the applicability of m-uniform states in QECC design.
Abstract
An m-uniform quantum state on n qubits is an entangled state in which every m-qubit subsystem is maximally mixed. Starting with an m-uniform state realized as the graph state associated with an m-regular graph, and a classical [n,k,d \ge m+1] binary linear code with certain additional properties, we show that pure [[n,k,m+1]]_2 quantum error-correcting codes (QECCs) can be constructed within the codeword stabilized (CWS) code framework. As illustrations, we construct pure [[2^{2r}-1,2^{2r}-2r-3,3]]_2 and [[(2^{4r}-1)^2, (2^{4r}-1)^2 - 32r-7, 5]]_2 QECCs. We also give measurement-based protocols for encoding into code states and for recovery of logical qubits from code states.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Data Storage Technologies · Radiation Effects in Electronics · Semiconductor materials and devices
