Making Trotterization Adaptive and Energy-Self-Correcting for NISQ Devices and Beyond
Simulation of continuous-time evolution requires time discretization on both classical and quantum computers. A finer time step improves simulation precision but it inevitably leads to increased computational efforts. This is particularly costly for today’s noisy intermediate-scale quantum computers...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2023-08-01
|
| Series: | PRX Quantum |
| Online Access: | http://doi.org/10.1103/PRXQuantum.4.030319 |
| _version_ | 1797746657546207232 |
|---|---|
| author | Hongzheng Zhao Marin Bukov Markus Heyl Roderich Moessner |
| author_facet | Hongzheng Zhao Marin Bukov Markus Heyl Roderich Moessner |
| author_sort | Hongzheng Zhao |
| collection | DOAJ |
| description | Simulation of continuous-time evolution requires time discretization on both classical and quantum computers. A finer time step improves simulation precision but it inevitably leads to increased computational efforts. This is particularly costly for today’s noisy intermediate-scale quantum computers, where notable gate imperfections limit the circuit depth that can be executed at a given accuracy. Classical adaptive solvers are well developed to save numerical computation times. However, it remains an outstanding challenge to make optimal usage of the available quantum resources by means of adaptive time steps. Here, we introduce a quantum algorithm to solve this problem, providing a controlled solution of the quantum many-body dynamics of local observables. The key conceptual element of our algorithm is a feedback loop that self-corrects the simulation errors by adapting time steps, thereby significantly outperforming conventional Trotter schemes on a fundamental level and reducing the circuit depth. It even allows for a controlled asymptotic long-time error, where the usual Trotterized dynamics faces difficulties. Another key advantage of our quantum algorithm is that any desired conservation law can be included in the self-correcting feedback loop, which has a potentially wide range of applicability. We demonstrate the capabilities by enforcing gauge invariance, which is crucial for a faithful and long-sought-after quantum simulation of lattice gauge theories. Our algorithm can potentially be useful on a more general level whenever time discretization is involved also concerning, e.g., numerical approaches based on time-evolving block-decimation methods. |
| first_indexed | 2024-03-12T15:40:00Z |
| format | Article |
| id | doaj.art-3406c0928c9e4b3193469d33537dac6b |
| institution | Directory Open Access Journal |
| issn | 2691-3399 |
| language | English |
| last_indexed | 2024-03-12T15:40:00Z |
| publishDate | 2023-08-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | PRX Quantum |
| spelling | doaj.art-3406c0928c9e4b3193469d33537dac6b2023-08-09T16:00:03ZengAmerican Physical SocietyPRX Quantum2691-33992023-08-014303031910.1103/PRXQuantum.4.030319Making Trotterization Adaptive and Energy-Self-Correcting for NISQ Devices and BeyondHongzheng ZhaoMarin BukovMarkus HeylRoderich MoessnerSimulation of continuous-time evolution requires time discretization on both classical and quantum computers. A finer time step improves simulation precision but it inevitably leads to increased computational efforts. This is particularly costly for today’s noisy intermediate-scale quantum computers, where notable gate imperfections limit the circuit depth that can be executed at a given accuracy. Classical adaptive solvers are well developed to save numerical computation times. However, it remains an outstanding challenge to make optimal usage of the available quantum resources by means of adaptive time steps. Here, we introduce a quantum algorithm to solve this problem, providing a controlled solution of the quantum many-body dynamics of local observables. The key conceptual element of our algorithm is a feedback loop that self-corrects the simulation errors by adapting time steps, thereby significantly outperforming conventional Trotter schemes on a fundamental level and reducing the circuit depth. It even allows for a controlled asymptotic long-time error, where the usual Trotterized dynamics faces difficulties. Another key advantage of our quantum algorithm is that any desired conservation law can be included in the self-correcting feedback loop, which has a potentially wide range of applicability. We demonstrate the capabilities by enforcing gauge invariance, which is crucial for a faithful and long-sought-after quantum simulation of lattice gauge theories. Our algorithm can potentially be useful on a more general level whenever time discretization is involved also concerning, e.g., numerical approaches based on time-evolving block-decimation methods.http://doi.org/10.1103/PRXQuantum.4.030319 |
| spellingShingle | Hongzheng Zhao Marin Bukov Markus Heyl Roderich Moessner Making Trotterization Adaptive and Energy-Self-Correcting for NISQ Devices and Beyond PRX Quantum |
| title | Making Trotterization Adaptive and Energy-Self-Correcting for NISQ Devices and Beyond |
| title_full | Making Trotterization Adaptive and Energy-Self-Correcting for NISQ Devices and Beyond |
| title_fullStr | Making Trotterization Adaptive and Energy-Self-Correcting for NISQ Devices and Beyond |
| title_full_unstemmed | Making Trotterization Adaptive and Energy-Self-Correcting for NISQ Devices and Beyond |
| title_short | Making Trotterization Adaptive and Energy-Self-Correcting for NISQ Devices and Beyond |
| title_sort | making trotterization adaptive and energy self correcting for nisq devices and beyond |
| url | http://doi.org/10.1103/PRXQuantum.4.030319 |
| work_keys_str_mv | AT hongzhengzhao makingtrotterizationadaptiveandenergyselfcorrectingfornisqdevicesandbeyond AT marinbukov makingtrotterizationadaptiveandenergyselfcorrectingfornisqdevicesandbeyond AT markusheyl makingtrotterizationadaptiveandenergyselfcorrectingfornisqdevicesandbeyond AT roderichmoessner makingtrotterizationadaptiveandenergyselfcorrectingfornisqdevicesandbeyond |