Qubit-optimal quantum phase estimation of block-encoded Hamiltonians
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916933869240320 |
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| author | Skelton, S. E. |
| author_facet | Skelton, S. E. |
| contents | Block-encodings have become one of the most common oracle assumptions in the circuit model. I present an algorithm that uses von Neumann's measurement procedure to measure a phase, using time evolution on a block-encoded Hamiltonian as a subroutine. This produces an extremely simple algorithm for quantum phase estimation, which can be performed with a pointer system of $\mathcal{O}(1)$ qubits.
I then use recent results for block-encoding implementations, showing that one can efficiently prepare QPE beginning from a linear combination of Pauli strings. Using this, I give the Clifford + T complexity bound for QPE with respect to model-relevant parameters of the Hamiltonian and the desired precision. In the process, I provide a very general error analysis for Clifford + T implementations of QSP, quantum eigenvalue transformation, or quantum singular value transformation circuits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_04246 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Qubit-optimal quantum phase estimation of block-encoded Hamiltonians Skelton, S. E. Quantum Physics Block-encodings have become one of the most common oracle assumptions in the circuit model. I present an algorithm that uses von Neumann's measurement procedure to measure a phase, using time evolution on a block-encoded Hamiltonian as a subroutine. This produces an extremely simple algorithm for quantum phase estimation, which can be performed with a pointer system of $\mathcal{O}(1)$ qubits. I then use recent results for block-encoding implementations, showing that one can efficiently prepare QPE beginning from a linear combination of Pauli strings. Using this, I give the Clifford + T complexity bound for QPE with respect to model-relevant parameters of the Hamiltonian and the desired precision. In the process, I provide a very general error analysis for Clifford + T implementations of QSP, quantum eigenvalue transformation, or quantum singular value transformation circuits. |
| title | Qubit-optimal quantum phase estimation of block-encoded Hamiltonians |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2509.04246 |