Improved Accuracy for Trotter Simulations Using Chebyshev Interpolation
Quantum metrology allows for measuring properties of a quantum system at the optimal Heisenberg limit. However, when the relevant quantum states are prepared using digital Hamiltonian simulation, the accrued algorithmic errors will cause deviations from this fundamental limit. In this work, we show...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2024-02-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2024-02-26-1266/pdf/ |
| _version_ | 1827341011024609280 |
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| author | Gumaro Rendon Jacob Watkins Nathan Wiebe |
| author_facet | Gumaro Rendon Jacob Watkins Nathan Wiebe |
| author_sort | Gumaro Rendon |
| collection | DOAJ |
| description | Quantum metrology allows for measuring properties of a quantum system at the optimal Heisenberg limit. However, when the relevant quantum states are prepared using digital Hamiltonian simulation, the accrued algorithmic errors will cause deviations from this fundamental limit. In this work, we show how algorithmic errors due to Trotterized time evolution can be mitigated through the use of standard polynomial interpolation techniques. Our approach is to extrapolate to zero Trotter step size, akin to zero-noise extrapolation techniques for mitigating hardware errors. We perform a rigorous error analysis of the interpolation approach for estimating eigenvalues and time-evolved expectation values, and show that the Heisenberg limit is achieved up to polylogarithmic factors in the error. Our work suggests that accuracies approaching those of state-of-the-art simulation algorithms may be achieved using Trotter and classical resources alone for a number of relevant algorithmic tasks. |
| first_indexed | 2024-03-07T21:33:41Z |
| format | Article |
| id | doaj.art-726e08189f2f4d4898133528dba1075c |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-03-07T21:33:41Z |
| publishDate | 2024-02-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-726e08189f2f4d4898133528dba1075c2024-02-26T14:44:02ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2024-02-018126610.22331/q-2024-02-26-126610.22331/q-2024-02-26-1266Improved Accuracy for Trotter Simulations Using Chebyshev InterpolationGumaro RendonJacob WatkinsNathan WiebeQuantum metrology allows for measuring properties of a quantum system at the optimal Heisenberg limit. However, when the relevant quantum states are prepared using digital Hamiltonian simulation, the accrued algorithmic errors will cause deviations from this fundamental limit. In this work, we show how algorithmic errors due to Trotterized time evolution can be mitigated through the use of standard polynomial interpolation techniques. Our approach is to extrapolate to zero Trotter step size, akin to zero-noise extrapolation techniques for mitigating hardware errors. We perform a rigorous error analysis of the interpolation approach for estimating eigenvalues and time-evolved expectation values, and show that the Heisenberg limit is achieved up to polylogarithmic factors in the error. Our work suggests that accuracies approaching those of state-of-the-art simulation algorithms may be achieved using Trotter and classical resources alone for a number of relevant algorithmic tasks.https://quantum-journal.org/papers/q-2024-02-26-1266/pdf/ |
| spellingShingle | Gumaro Rendon Jacob Watkins Nathan Wiebe Improved Accuracy for Trotter Simulations Using Chebyshev Interpolation Quantum |
| title | Improved Accuracy for Trotter Simulations Using Chebyshev Interpolation |
| title_full | Improved Accuracy for Trotter Simulations Using Chebyshev Interpolation |
| title_fullStr | Improved Accuracy for Trotter Simulations Using Chebyshev Interpolation |
| title_full_unstemmed | Improved Accuracy for Trotter Simulations Using Chebyshev Interpolation |
| title_short | Improved Accuracy for Trotter Simulations Using Chebyshev Interpolation |
| title_sort | improved accuracy for trotter simulations using chebyshev interpolation |
| url | https://quantum-journal.org/papers/q-2024-02-26-1266/pdf/ |
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