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Ground-State Preparation Reached Its Query Bound
Two algorithms and a matching lower bound fixed the expected complexity when a gap threshold is known.
Summary
Two algorithms and a matching lower bound fixed the expected complexity when a gap threshold is known.
For a block-encoded Hamiltonian with a unique ground state and a known threshold inside the spectral gap, the authors give expected- and worst-case preparation algorithms. The expected version uses a constant-accuracy spectral filter, amplitude amplification and repeated high-accuracy checks; its Hamiltonian-query count is matched by a lower bound. The result settles the oracle-query scaling under the paper's access and overlap assumptions. It does not translate directly into wall-clock advantage on current quantum hardware.
Why it matters
Two algorithms and a matching lower bound fixed the expected complexity when a gap threshold is known.
Limits and context
- It does not translate directly into wall-clock advantage on current quantum hardware.
Key claims
Two algorithms and a matching lower bound fixed the expected complexity when a gap threshold is known.
Qualification: It does not translate directly into wall-clock advantage on current quantum hardware.
Evidence: source-2026-09-29-014
Sources
- arXiv preprint 2609.35668arXiv · primary research
Corrections
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