Quantum Phase Estimation without Controlled Unitaries
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910678199042048 |
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| author | Clinton, Laura Cubitt, Toby S. Garcia-Patron, Raul Montanaro, Ashley Stanisic, Stasja Stroeks, Maarten |
| author_facet | Clinton, Laura Cubitt, Toby S. Garcia-Patron, Raul Montanaro, Ashley Stanisic, Stasja Stroeks, Maarten |
| contents | In this work we demonstrate the use of adapted classical phase retrieval algorithms to perform control-free quantum phase estimation. We eliminate the costly controlled time evolution and Hadamard test commonly required to access the complex time-series needed to reconstruct the spectrum. This significant reduction of the number of coherent controlled-operations lowers the circuit depth and considerably simplifies the implementation of statistical quantum phase estimation in near-term devices. This seemingly impossible task can be achieved by extending the problem that one wishes to solve to one with a larger set of input signals while exploiting natural constraints on the signal and/or the spectrum. We leverage well-established algorithms that are widely used in the context of classical signal processing, demonstrating two complementary methods to do this, vectorial phase retrieval and two-dimensional phase retrieval. We numerically investigate the feasibility of both approaches for estimating the spectrum of the Fermi-Hubbard model and discuss their resilience to inherent statistical noise. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_21517 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum Phase Estimation without Controlled Unitaries Clinton, Laura Cubitt, Toby S. Garcia-Patron, Raul Montanaro, Ashley Stanisic, Stasja Stroeks, Maarten Quantum Physics In this work we demonstrate the use of adapted classical phase retrieval algorithms to perform control-free quantum phase estimation. We eliminate the costly controlled time evolution and Hadamard test commonly required to access the complex time-series needed to reconstruct the spectrum. This significant reduction of the number of coherent controlled-operations lowers the circuit depth and considerably simplifies the implementation of statistical quantum phase estimation in near-term devices. This seemingly impossible task can be achieved by extending the problem that one wishes to solve to one with a larger set of input signals while exploiting natural constraints on the signal and/or the spectrum. We leverage well-established algorithms that are widely used in the context of classical signal processing, demonstrating two complementary methods to do this, vectorial phase retrieval and two-dimensional phase retrieval. We numerically investigate the feasibility of both approaches for estimating the spectrum of the Fermi-Hubbard model and discuss their resilience to inherent statistical noise. |
| title | Quantum Phase Estimation without Controlled Unitaries |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2410.21517 |