Sum of squares spectral amplification (SOSSA)
summary
Claims a practical cut to quantum chemistry phase estimation costs: compiled FeMoCo goes from “centuries” to hours by rewriting H in a sum of squares form and applying spectral amplification (the SOSSA procedure). Uses classical SDPs to find a shift β that certifies a low-energy sector, then block-encodes a square-root operator so phase estimation cost scales like √(λ·δ)/ε instead of λ/ε. Numerical runs report constant improvements ~5–10×; SYK analysis shows a √N asymptotic gain for degree-2 SOS, but degree-3 tightness inflates encoding cost and kills the win. Remaining bottleneck: coherent embedding and RDM readout (shot counts ∼N^8).
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chapters (8)
- 0:00Introduction and motivation
- 1:36State-of-the-art overview
- 10:30Background on modern algorithms
- 12:52Spectral amplification basics
- 20:58Sum-of-squares optimization
- 27:43The SOSSA algorithm structure
- 35:58SYK model analysis
- 45:50Quantum chemistry outlook
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