Hadamard random forest for reconstructing real valued pure quantum states
5 affiliations
- 1School of Physics, Georgia Institute of Technology
- 2Berkeley Center for Quantum Information and Computation
- 3School of Computational Science & Engineering, Georgia Institute of Technology
- 4CIPHER, Georgia Tech Research Institute
- 5Netherlands eScience Center
Abstract
Many potential quantum computing applications, such as linear system solvers, require efficient readout to preserve the algorithmic speedup, but only involve real amplitudes. Conventional tomography methods demand exponential resources for general complex-valued states. We introduce a readout method for real-valued pure quantum states based on amplitude superposition with Hadamard operations and a random forest algorithm for sign determination. Our method reduces the measurement settings required for state vector reconstruction to 𝒪(Nq) O ( N q ) for an N q qubit system; the post-processing cost remains exponential Ω (2Nq) Ω ( 2 N q ) . We experimentally validate our method on up to 10 qubits using the latest available IBM quantum processor and demonstrate that it accurately extracts key properties, such as magic. Our method also outperforms the standard SWAP test for state overlap estimation. This calculation resembles 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 read out the solution from a quantum linear solver.
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BibTeX
@article{song2026hadamard,
title = {{Hadamard random forest for reconstructing real valued pure quantum states}},
author = {Zhixin Song and Hang Ren and Melody Lee and Bryan Gard and Nicolas Renaud and Spencer H. Bryngelson},
journal = {Communications Physics},
year = {2026},
month = jul,
doi = {10.1038/s42005-026-02717-1},
url = {https://doi.org/10.1038/s42005-026-02717-1},
note = {CC BY},
}
RIS
TY - JOUR
TI - Hadamard random forest for reconstructing real valued pure quantum states
AU - Zhixin Song
AU - Hang Ren
AU - Melody Lee
AU - Bryan Gard
AU - Nicolas Renaud
AU - Spencer H. Bryngelson
PY - 2026
DA - 2026/07/01
JO - Communications Physics
DO - 10.1038/s42005-026-02717-1
UR - https://doi.org/10.1038/s42005-026-02717-1
AB - Many potential quantum computing applications, such as linear system solvers, require efficient readout to preserve the algorithmic speedup, but only involve real amplitudes. Conventional tomography methods demand exponential resources for general complex-valued states. We introduce a readout method for real-valued pure quantum states based on amplitude superposition with Hadamard operations and a random forest algorithm for sign determination. Our method reduces the measurement settings required for state vector reconstruction to 𝒪(N_q) O ( N q ) for an N q qubit system; the post-processing cost remains exponential Ω (2^N_q) Ω ( 2 N q ) . We experimentally validate our method on up to 10 qubits using the latest available IBM quantum processor and demonstrate that it accurately extracts key properties, such as magic. Our method also outperforms the standard SWAP test for state overlap estimation. This calculation resembles 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 read out the solution from a quantum linear solver.
SN - 2399-3650
ER -