arXiv:2602.15202v2 Announce Type: replace-cross Abstract: We present an algebraic algorithm for quantum state tomography that leverages measurements of certain observables to estimate structured entries of the underlying density matrix. Under low-rank assumptions, the remaining entries can be obtained solely using standard numerical linear algebra operations. The proposed algebraic matrix completion framework applies to a broad class of generic, low-rank mixed quantum states and, compared with state-of-the-art methods, is computationally efficient while providing deterministic recovery guarant
The paper provides a significant advancement in quantum state tomography, addressing a computational bottleneck in characterizing quantum states, which is crucial for the development and verification of quantum technologies.
This algebraic approach promises more efficient and reliable methods for quantum state verification, directly impacting the feasibility and scalability of quantum computing and sensing applications.
The ability to more efficiently characterize low-rank quantum states through algebraic methods rather than purely statistical ones reduces the computational burden and may accelerate quantum hardware development.
- · Quantum computing hardware developers
- · Quantum sensing researchers
- · Applied mathematicians in quantum information
- · National quantum initiatives
- · Researchers relying solely on older, computationally expensive tomography method
- · Classical supercomputing infrastructure for quantum state reconstruction
More accurate and faster verification of complex quantum states will accelerate the development cycle of quantum processors.
This could lead to a quicker identification and mitigation of errors in quantum systems, improving their stability and performance.
The enhanced ability to characterize quantum states may enable the design of more robust quantum algorithms and novel quantum materials.
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Read at arXiv cs.AI