Quantum

Quantum-classical algorithm interpolation for spatial search

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Briefings

A new hybrid quantum-classical algorithm interpolates between classical and fully coherent quantum regimes to reduce spatial search dependence on classical hitting time. The study derives a parameterized family of algorithms where circuit depth scales as O(HT^gamma/2) and total query complexity balances setup, update, and checking costs. This approach trades circuit depth for total query complexity, offering a potential building block for other hybrid designs. The research was published on arXiv in October 2026.

Key points

• The study derives a parameterized family of hybrid quantum-classical spatial search algorithms that continuously interpolate between classical and fully coherent quantum regimes.
• For any gamma in [0,1], the algorithms use circuits of depth O(HT^gamma/2) and find a marked vertex with constant success probability at total cost O(HT^1-gamma*S + HT^1-gamma/2(U + C)).

Context and limitations

The research is presented as a preprint on arXiv and does not yet include experimental validation or results from near-term or early fault-tolerant quantum devices.

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