Quantum circuits for toric code and X-cube fracton model
We propose a systematic and efficient quantum circuit composed solely of Clifford gates for simulating the ground state of the surface code model. This approach yields the ground state of the toric code in $\lceil 2L+2+log_{2}(d)+\frac{L}{2d} \rceil$ time steps, where $L$ refers to the system size a...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2024-03-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2024-03-13-1276/pdf/ |
| _version_ | 1797263309710295040 |
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| author | Penghua Chen Bowen Yan Shawn X. Cui |
| author_facet | Penghua Chen Bowen Yan Shawn X. Cui |
| author_sort | Penghua Chen |
| collection | DOAJ |
| description | We propose a systematic and efficient quantum circuit composed solely of Clifford gates for simulating the ground state of the surface code model. This approach yields the ground state of the toric code in $\lceil 2L+2+log_{2}(d)+\frac{L}{2d} \rceil$ time steps, where $L$ refers to the system size and $d$ represents the maximum distance to constrain the application of the CNOT gates. Our algorithm reformulates the problem into a purely geometric one, facilitating its extension to attain the ground state of certain 3D topological phases, such as the 3D toric model in $3L+8$ steps and the X-cube fracton model in $12L+11$ steps. Furthermore, we introduce a gluing method involving measurements, enabling our technique to attain the ground state of the 2D toric code on an arbitrary planar lattice and paving the way to more intricate 3D topological phases. |
| first_indexed | 2024-04-25T00:10:58Z |
| format | Article |
| id | doaj.art-2613a04d31a24068aaa2b95b771c5403 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-04-25T00:10:58Z |
| publishDate | 2024-03-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-2613a04d31a24068aaa2b95b771c54032024-03-13T11:07:24ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2024-03-018127610.22331/q-2024-03-13-127610.22331/q-2024-03-13-1276Quantum circuits for toric code and X-cube fracton modelPenghua ChenBowen YanShawn X. CuiWe propose a systematic and efficient quantum circuit composed solely of Clifford gates for simulating the ground state of the surface code model. This approach yields the ground state of the toric code in $\lceil 2L+2+log_{2}(d)+\frac{L}{2d} \rceil$ time steps, where $L$ refers to the system size and $d$ represents the maximum distance to constrain the application of the CNOT gates. Our algorithm reformulates the problem into a purely geometric one, facilitating its extension to attain the ground state of certain 3D topological phases, such as the 3D toric model in $3L+8$ steps and the X-cube fracton model in $12L+11$ steps. Furthermore, we introduce a gluing method involving measurements, enabling our technique to attain the ground state of the 2D toric code on an arbitrary planar lattice and paving the way to more intricate 3D topological phases.https://quantum-journal.org/papers/q-2024-03-13-1276/pdf/ |
| spellingShingle | Penghua Chen Bowen Yan Shawn X. Cui Quantum circuits for toric code and X-cube fracton model Quantum |
| title | Quantum circuits for toric code and X-cube fracton model |
| title_full | Quantum circuits for toric code and X-cube fracton model |
| title_fullStr | Quantum circuits for toric code and X-cube fracton model |
| title_full_unstemmed | Quantum circuits for toric code and X-cube fracton model |
| title_short | Quantum circuits for toric code and X-cube fracton model |
| title_sort | quantum circuits for toric code and x cube fracton model |
| url | https://quantum-journal.org/papers/q-2024-03-13-1276/pdf/ |
| work_keys_str_mv | AT penghuachen quantumcircuitsfortoriccodeandxcubefractonmodel AT bowenyan quantumcircuitsfortoriccodeandxcubefractonmodel AT shawnxcui quantumcircuitsfortoriccodeandxcubefractonmodel |