Simulating noisy quantum circuits with matrix product density operators
Simulating quantum circuits with classical computers requires resources growing exponentially in terms of system size. Real quantum computer with noise, however, may be simulated polynomially with various methods considering different noise models. In this work, we simulate random quantum circuits i...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2021-04-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.3.023005 |
| _version_ | 1797211064761319424 |
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| author | Song Cheng Chenfeng Cao Chao Zhang Yongxiang Liu Shi-Yao Hou Pengxiang Xu Bei Zeng |
| author_facet | Song Cheng Chenfeng Cao Chao Zhang Yongxiang Liu Shi-Yao Hou Pengxiang Xu Bei Zeng |
| author_sort | Song Cheng |
| collection | DOAJ |
| description | Simulating quantum circuits with classical computers requires resources growing exponentially in terms of system size. Real quantum computer with noise, however, may be simulated polynomially with various methods considering different noise models. In this work, we simulate random quantum circuits in one dimension with matrix product density operators (MPDOs), for different noise models such as dephasing, depolarizing, and amplitude damping. We show that the method based on matrix product states (MPSs) fails to approximate the noisy output quantum states for any of the noise models considered, while the MPDO method approximates them well. Compared with the method of matrix product operators (MPOs), the MPDO method reflects a clear physical picture of noise (with inner indices taking care of the noise simulation) and quantum entanglement (with bond indices taking care of two-qubit gate simulation). Consequently, in case of weak system noise, the resource cost of the MPDO will be significantly less than that of the MPO due to a relatively small inner dimension needed for the simulation. In case of strong system noise, a relatively small bond dimension may be sufficient to simulate the noisy circuits, indicating a regime that the noise is large enough for an “easy” classical simulation, which is further supported by a comparison with the experimental results on an IBM cloud device. Moreover, we propose a more effective tensor updates scheme with optimal truncations for both the inner and the bond dimensions, performed after each layer of the circuit, which enjoys a canonical form of the MPDO for improving simulation accuracy. With truncated inner dimension to a maximum value κ and bond dimension to a maximum value χ, the cost of our simulation scales as ∼NDκ^{3}χ^{3}, for an N-qubit circuit with depth D. |
| first_indexed | 2024-04-24T10:20:33Z |
| format | Article |
| id | doaj.art-7f129542d3e940718f3950437de2f43d |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:20:33Z |
| publishDate | 2021-04-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-7f129542d3e940718f3950437de2f43d2024-04-12T17:08:49ZengAmerican Physical SocietyPhysical Review Research2643-15642021-04-013202300510.1103/PhysRevResearch.3.023005Simulating noisy quantum circuits with matrix product density operatorsSong ChengChenfeng CaoChao ZhangYongxiang LiuShi-Yao HouPengxiang XuBei ZengSimulating quantum circuits with classical computers requires resources growing exponentially in terms of system size. Real quantum computer with noise, however, may be simulated polynomially with various methods considering different noise models. In this work, we simulate random quantum circuits in one dimension with matrix product density operators (MPDOs), for different noise models such as dephasing, depolarizing, and amplitude damping. We show that the method based on matrix product states (MPSs) fails to approximate the noisy output quantum states for any of the noise models considered, while the MPDO method approximates them well. Compared with the method of matrix product operators (MPOs), the MPDO method reflects a clear physical picture of noise (with inner indices taking care of the noise simulation) and quantum entanglement (with bond indices taking care of two-qubit gate simulation). Consequently, in case of weak system noise, the resource cost of the MPDO will be significantly less than that of the MPO due to a relatively small inner dimension needed for the simulation. In case of strong system noise, a relatively small bond dimension may be sufficient to simulate the noisy circuits, indicating a regime that the noise is large enough for an “easy” classical simulation, which is further supported by a comparison with the experimental results on an IBM cloud device. Moreover, we propose a more effective tensor updates scheme with optimal truncations for both the inner and the bond dimensions, performed after each layer of the circuit, which enjoys a canonical form of the MPDO for improving simulation accuracy. With truncated inner dimension to a maximum value κ and bond dimension to a maximum value χ, the cost of our simulation scales as ∼NDκ^{3}χ^{3}, for an N-qubit circuit with depth D.http://doi.org/10.1103/PhysRevResearch.3.023005 |
| spellingShingle | Song Cheng Chenfeng Cao Chao Zhang Yongxiang Liu Shi-Yao Hou Pengxiang Xu Bei Zeng Simulating noisy quantum circuits with matrix product density operators Physical Review Research |
| title | Simulating noisy quantum circuits with matrix product density operators |
| title_full | Simulating noisy quantum circuits with matrix product density operators |
| title_fullStr | Simulating noisy quantum circuits with matrix product density operators |
| title_full_unstemmed | Simulating noisy quantum circuits with matrix product density operators |
| title_short | Simulating noisy quantum circuits with matrix product density operators |
| title_sort | simulating noisy quantum circuits with matrix product density operators |
| url | http://doi.org/10.1103/PhysRevResearch.3.023005 |
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