Far from Perfect: Quantum Error Correction with (Hyperinvariant) Evenbly Codes
We introduce a new class of qubit codes that we call Evenbly codes, building on a previous proposal of hyperinvariant tensor networks. Its tensor network description consists of local, non-perfect tensors describing CSS codes interspersed with Hadamard gates, placed on a hyperbolic $\{p,q\}$ geometr...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2025-08-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2025-08-08-1826/pdf/ |
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| _version_ | 1849243054149468160 |
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| author | Matthew Steinberg Junyu Fan Robert J. Harris David Elkouss Sebastian Feld Alexander Jahn |
| author_facet | Matthew Steinberg Junyu Fan Robert J. Harris David Elkouss Sebastian Feld Alexander Jahn |
| author_sort | Matthew Steinberg |
| collection | DOAJ |
| description | We introduce a new class of qubit codes that we call Evenbly codes, building on a previous proposal of hyperinvariant tensor networks. Its tensor network description consists of local, non-perfect tensors describing CSS codes interspersed with Hadamard gates, placed on a hyperbolic $\{p,q\}$ geometry with even $q\geq 4$, yielding an infinitely large class of subsystem codes. We construct an example for a $\{5,4\}$ manifold and describe strategies of logical gauge fixing that lead to different rates $k/n$ and distances $d$, which we calculate analytically, finding distances which range from $d=2$ to $d \sim n^{2/3}$. Investigating threshold performance under erasure, depolarizing, and pure Pauli noise channels, we find that the code exhibits a depolarizing noise threshold of about 19.1% in the code-capacity model and 50% for pure Pauli and erasure channels under suitable gauges. We also test a constant-rate version with $k/n = 0.125$, finding excellent error resilience (about 40%) under the erasure channel. Recovery rates for these and other settings are studied both under an optimal decoder as well as a more efficient but non-optimal greedy decoder. We also consider generalizations beyond the CSS tensor construction, compute error rates and thresholds for other hyperbolic geometries, and discuss the relationship to holographic bulk/boundary dualities. Our work indicates that Evenbly codes may show promise for practical quantum computing applications. |
| format | Article |
| id | doaj-art-720dd67d28f84888be2a5beb474a9add |
| institution | Kabale University |
| issn | 2521-327X |
| language | English |
| publishDate | 2025-08-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-720dd67d28f84888be2a5beb474a9add2025-08-20T03:59:36ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2025-08-019182610.22331/q-2025-08-08-182610.22331/q-2025-08-08-1826Far from Perfect: Quantum Error Correction with (Hyperinvariant) Evenbly CodesMatthew SteinbergJunyu FanRobert J. HarrisDavid ElkoussSebastian FeldAlexander JahnWe introduce a new class of qubit codes that we call Evenbly codes, building on a previous proposal of hyperinvariant tensor networks. Its tensor network description consists of local, non-perfect tensors describing CSS codes interspersed with Hadamard gates, placed on a hyperbolic $\{p,q\}$ geometry with even $q\geq 4$, yielding an infinitely large class of subsystem codes. We construct an example for a $\{5,4\}$ manifold and describe strategies of logical gauge fixing that lead to different rates $k/n$ and distances $d$, which we calculate analytically, finding distances which range from $d=2$ to $d \sim n^{2/3}$. Investigating threshold performance under erasure, depolarizing, and pure Pauli noise channels, we find that the code exhibits a depolarizing noise threshold of about 19.1% in the code-capacity model and 50% for pure Pauli and erasure channels under suitable gauges. We also test a constant-rate version with $k/n = 0.125$, finding excellent error resilience (about 40%) under the erasure channel. Recovery rates for these and other settings are studied both under an optimal decoder as well as a more efficient but non-optimal greedy decoder. We also consider generalizations beyond the CSS tensor construction, compute error rates and thresholds for other hyperbolic geometries, and discuss the relationship to holographic bulk/boundary dualities. Our work indicates that Evenbly codes may show promise for practical quantum computing applications.https://quantum-journal.org/papers/q-2025-08-08-1826/pdf/ |
| spellingShingle | Matthew Steinberg Junyu Fan Robert J. Harris David Elkouss Sebastian Feld Alexander Jahn Far from Perfect: Quantum Error Correction with (Hyperinvariant) Evenbly Codes Quantum |
| title | Far from Perfect: Quantum Error Correction with (Hyperinvariant) Evenbly Codes |
| title_full | Far from Perfect: Quantum Error Correction with (Hyperinvariant) Evenbly Codes |
| title_fullStr | Far from Perfect: Quantum Error Correction with (Hyperinvariant) Evenbly Codes |
| title_full_unstemmed | Far from Perfect: Quantum Error Correction with (Hyperinvariant) Evenbly Codes |
| title_short | Far from Perfect: Quantum Error Correction with (Hyperinvariant) Evenbly Codes |
| title_sort | far from perfect quantum error correction with hyperinvariant evenbly codes |
| url | https://quantum-journal.org/papers/q-2025-08-08-1826/pdf/ |
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