Codeword Stabilized Codes from m-Uniform Graph States
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866918157257539584 |
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| author | Sudevan, Sowrabh Das, Sourin Aswanth, Thamadathil Patanker, Nupur Kashyap, Navin |
| author_facet | Sudevan, Sowrabh Das, Sourin Aswanth, Thamadathil Patanker, Nupur Kashyap, Navin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06142 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Codeword Stabilized Codes from m-Uniform Graph States Sudevan, Sowrabh Das, Sourin Aswanth, Thamadathil Patanker, Nupur Kashyap, Navin Quantum Physics Information Theory 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. |
| title | Codeword Stabilized Codes from m-Uniform Graph States |
| topic | Quantum Physics Information Theory |
| url | https://arxiv.org/abs/2405.06142 |