Ising model formulation for highly accurate topological color codes decoding
Quantum error correction is an essential ingredient for reliable quantum computation for theoretically provable quantum speedup. Topological color codes, one of the quantum error correction codes, have an advantage against the surface codes in that all Clifford gates can be implemented transversally...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2024-01-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.6.013092 |
| _version_ | 1797210312619851776 |
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| author | Yugo Takada Yusaku Takeuchi Keisuke Fujii |
| author_facet | Yugo Takada Yusaku Takeuchi Keisuke Fujii |
| author_sort | Yugo Takada |
| collection | DOAJ |
| description | Quantum error correction is an essential ingredient for reliable quantum computation for theoretically provable quantum speedup. Topological color codes, one of the quantum error correction codes, have an advantage against the surface codes in that all Clifford gates can be implemented transversally. However, the hardness of decoding makes the color codes not suitable as the best candidate for experimentally feasible implementation of quantum error correction. Here we propose an Ising model formulation that enables highly accurate decoding of the color codes. In this formulation, we map stabilizer operators to classical spin variables to represent an error satisfying the syndrome. Then we construct an Ising Hamiltonian that counts the number of errors and formulate the decoding problem as an energy minimization problem of an Ising Hamiltonian, which is solved by simulated annealing. In numerical simulations on the (4.8.8) lattice, we find an error threshold of 10.36(5)% for bit-flip noise model, 18.47(5)% for depolarizing noise model, and 2.90(4)% for phenomenological noise model (bit-flip error is located on each of data and measurement qubits), all of which are higher than the thresholds of existing efficient decoding algorithms. Furthermore, we verify that the achieved logical error rates are almost optimal in the sense that they are almost the same as those obtained by exact optimizations by CPLEX with smaller decoding time in many cases. Since the decoding process has been a bottleneck for performance analysis, the proposed decoding method is useful for further exploration of the possibility of the topological color codes. |
| first_indexed | 2024-04-24T10:08:36Z |
| format | Article |
| id | doaj.art-711c816a0878486d8de9482a12ca2d8f |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:08:36Z |
| publishDate | 2024-01-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-711c816a0878486d8de9482a12ca2d8f2024-04-12T17:38:28ZengAmerican Physical SocietyPhysical Review Research2643-15642024-01-016101309210.1103/PhysRevResearch.6.013092Ising model formulation for highly accurate topological color codes decodingYugo TakadaYusaku TakeuchiKeisuke FujiiQuantum error correction is an essential ingredient for reliable quantum computation for theoretically provable quantum speedup. Topological color codes, one of the quantum error correction codes, have an advantage against the surface codes in that all Clifford gates can be implemented transversally. However, the hardness of decoding makes the color codes not suitable as the best candidate for experimentally feasible implementation of quantum error correction. Here we propose an Ising model formulation that enables highly accurate decoding of the color codes. In this formulation, we map stabilizer operators to classical spin variables to represent an error satisfying the syndrome. Then we construct an Ising Hamiltonian that counts the number of errors and formulate the decoding problem as an energy minimization problem of an Ising Hamiltonian, which is solved by simulated annealing. In numerical simulations on the (4.8.8) lattice, we find an error threshold of 10.36(5)% for bit-flip noise model, 18.47(5)% for depolarizing noise model, and 2.90(4)% for phenomenological noise model (bit-flip error is located on each of data and measurement qubits), all of which are higher than the thresholds of existing efficient decoding algorithms. Furthermore, we verify that the achieved logical error rates are almost optimal in the sense that they are almost the same as those obtained by exact optimizations by CPLEX with smaller decoding time in many cases. Since the decoding process has been a bottleneck for performance analysis, the proposed decoding method is useful for further exploration of the possibility of the topological color codes.http://doi.org/10.1103/PhysRevResearch.6.013092 |
| spellingShingle | Yugo Takada Yusaku Takeuchi Keisuke Fujii Ising model formulation for highly accurate topological color codes decoding Physical Review Research |
| title | Ising model formulation for highly accurate topological color codes decoding |
| title_full | Ising model formulation for highly accurate topological color codes decoding |
| title_fullStr | Ising model formulation for highly accurate topological color codes decoding |
| title_full_unstemmed | Ising model formulation for highly accurate topological color codes decoding |
| title_short | Ising model formulation for highly accurate topological color codes decoding |
| title_sort | ising model formulation for highly accurate topological color codes decoding |
| url | http://doi.org/10.1103/PhysRevResearch.6.013092 |
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