Effective temperature in approximate quantum many-body states
In the pursuit of numerically identifying ground states of quantum many-body systems, approximate quantum wave function ansatzes are commonly employed. This study focuses on the spectral decomposition of these approximate quantum many-body states into exact eigenstates of the target Hamiltonian, whi...
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| Language: | English |
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American Physical Society
2025-08-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/zpjv-bm5c |
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| author | Yu-Qin Chen Shi-Xin Zhang |
| author_facet | Yu-Qin Chen Shi-Xin Zhang |
| author_sort | Yu-Qin Chen |
| collection | DOAJ |
| description | In the pursuit of numerically identifying ground states of quantum many-body systems, approximate quantum wave function ansatzes are commonly employed. This study focuses on the spectral decomposition of these approximate quantum many-body states into exact eigenstates of the target Hamiltonian, which reflects the intricate physics at the interplay between quantum systems and numerical algorithms. Here, we examine various parametrized approximate quantum states constructed from neural networks, tensor networks, and quantum circuits, employing differentiable programming to numerically approximate ground states and imaginary-time evolved states. Our findings reveal a consistent exponential pattern in the energy eigenbasis decomposition contributions of approximate states across different ansatzes, optimization objectives, and quantum systems, characterized by remarkably small decay rates, i.e., high effective temperatures. This finding is counterintuitive for high-fidelity approximate ground states: While the total contribution from excited states can be made sufficiently small, the residual spectral weight does not decay rapidly with energy. This behavior is an intrinsic property of the variational ansatz, independent of the approximation’s overall accuracy. The effective temperature is related to ansatz expressiveness and accuracy and shows phase transition behaviors in learning imaginary-time evolved states. The universal picture and unique features suggest the significance and potential of the effective temperature metric in characterizing approximate quantum states. |
| format | Article |
| id | doaj-art-3fb1b7cfd0a8401fa15d2c3b0d95985f |
| institution | Kabale University |
| issn | 2643-1564 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj-art-3fb1b7cfd0a8401fa15d2c3b0d95985f2025-08-22T14:31:44ZengAmerican Physical SocietyPhysical Review Research2643-15642025-08-017303318510.1103/zpjv-bm5cEffective temperature in approximate quantum many-body statesYu-Qin ChenShi-Xin ZhangIn the pursuit of numerically identifying ground states of quantum many-body systems, approximate quantum wave function ansatzes are commonly employed. This study focuses on the spectral decomposition of these approximate quantum many-body states into exact eigenstates of the target Hamiltonian, which reflects the intricate physics at the interplay between quantum systems and numerical algorithms. Here, we examine various parametrized approximate quantum states constructed from neural networks, tensor networks, and quantum circuits, employing differentiable programming to numerically approximate ground states and imaginary-time evolved states. Our findings reveal a consistent exponential pattern in the energy eigenbasis decomposition contributions of approximate states across different ansatzes, optimization objectives, and quantum systems, characterized by remarkably small decay rates, i.e., high effective temperatures. This finding is counterintuitive for high-fidelity approximate ground states: While the total contribution from excited states can be made sufficiently small, the residual spectral weight does not decay rapidly with energy. This behavior is an intrinsic property of the variational ansatz, independent of the approximation’s overall accuracy. The effective temperature is related to ansatz expressiveness and accuracy and shows phase transition behaviors in learning imaginary-time evolved states. The universal picture and unique features suggest the significance and potential of the effective temperature metric in characterizing approximate quantum states.http://doi.org/10.1103/zpjv-bm5c |
| spellingShingle | Yu-Qin Chen Shi-Xin Zhang Effective temperature in approximate quantum many-body states Physical Review Research |
| title | Effective temperature in approximate quantum many-body states |
| title_full | Effective temperature in approximate quantum many-body states |
| title_fullStr | Effective temperature in approximate quantum many-body states |
| title_full_unstemmed | Effective temperature in approximate quantum many-body states |
| title_short | Effective temperature in approximate quantum many-body states |
| title_sort | effective temperature in approximate quantum many body states |
| url | http://doi.org/10.1103/zpjv-bm5c |
| work_keys_str_mv | AT yuqinchen effectivetemperatureinapproximatequantummanybodystates AT shixinzhang effectivetemperatureinapproximatequantummanybodystates |