Hadamard Random Forest: Reconstructing real-valued quantum states with exponential reduction in measurement settings
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911139845111808 |
|---|---|
| author | Song, Zhixin Ren, Hang Lee, Melody Gard, Bryan Renaud, Nicolas Bryngelson, Spencer H. |
| author_facet | Song, Zhixin Ren, Hang Lee, Melody Gard, Bryan Renaud, Nicolas Bryngelson, Spencer H. |
| contents | Quantum tomography is a crucial tool for characterizing quantum states and devices and estimating nonlinear properties of the systems. Performing full quantum state tomography on an $N_\mathrm{q}$ qubit system requires an exponentially increasing overhead with $O(3^{N_\mathrm{q}})$ distinct Pauli measurement settings to resolve all complex phases and reconstruct the density matrix. However, many potential quantum computing applications, such as linear system solves, require only real-valued amplitudes. We introduce a readout method for real-valued quantum states that reduces measurement settings required for state vector reconstruction to $O(N_\mathrm{q})$; the post-processing cost remains exponential $Ω(2^{N_\mathrm{q}})$. This approach offers a substantial speedup over conventional tomography. We experimentally validate our method up to 10 qubits on the latest available IBM quantum processor and demonstrate that it accurately extracts key properties such as entanglement and magic. Our method also outperforms the standard SWAP test for state overlap estimation. This calculation resembles a numerical integration in certain cases and can be applied to extract nonlinear properties, which are important in application fields. We further implement the method to readout the solution from a quantum linear solver. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06455 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hadamard Random Forest: Reconstructing real-valued quantum states with exponential reduction in measurement settings Song, Zhixin Ren, Hang Lee, Melody Gard, Bryan Renaud, Nicolas Bryngelson, Spencer H. Quantum Physics Quantum tomography is a crucial tool for characterizing quantum states and devices and estimating nonlinear properties of the systems. Performing full quantum state tomography on an $N_\mathrm{q}$ qubit system requires an exponentially increasing overhead with $O(3^{N_\mathrm{q}})$ distinct Pauli measurement settings to resolve all complex phases and reconstruct the density matrix. However, many potential quantum computing applications, such as linear system solves, require only real-valued amplitudes. We introduce a readout method for real-valued quantum states that reduces measurement settings required for state vector reconstruction to $O(N_\mathrm{q})$; the post-processing cost remains exponential $Ω(2^{N_\mathrm{q}})$. This approach offers a substantial speedup over conventional tomography. We experimentally validate our method up to 10 qubits on the latest available IBM quantum processor and demonstrate that it accurately extracts key properties such as entanglement and magic. Our method also outperforms the standard SWAP test for state overlap estimation. This calculation resembles a numerical integration in certain cases and can be applied to extract nonlinear properties, which are important in application fields. We further implement the method to readout the solution from a quantum linear solver. |
| title | Hadamard Random Forest: Reconstructing real-valued quantum states with exponential reduction in measurement settings |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2505.06455 |