DQI resists classical simulation by locating high-probability outputs but is simulable at a low level of the polynomial hierarchy, constructively solves a MacWilliams-based coding bound, and corresponds to low-energy states of a quantum harmonic oscillator.
The state |ψ′ P ⟩ is supported on |s⟩ if and only if the decoder successfully infers some y where |y| ≤ ℓ
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On the Complexity of Decoded Quantum Interferometry
DQI resists classical simulation by locating high-probability outputs but is simulable at a low level of the polynomial hierarchy, constructively solves a MacWilliams-based coding bound, and corresponds to low-energy states of a quantum harmonic oscillator.