alisha-1000 commented on issue #456:
URL: https://github.com/apache/mahout/issues/456#issuecomment-3939390016

   Hi all,
   
   I’ve been reviewing this spike in the context of QDP’s current encoding and 
state-vector infrastructure. I’d like to clarify and align on the architectural 
role of quantum circuits in the kernel computation pipeline.
   
   In standard quantum kernel methods (e.g., Havlíček et al.), the core idea is:
   
   𝐾
   (
   𝑥
   ,
   𝑥
   ′
   )
   =
   ∣
   ⟨
   𝜙
   (
   𝑥
   )
   ∣
   𝜙
   (
   𝑥
   ′
   )
   ⟩
   ∣
   2
   K(x,x
   ′
   )=∣⟨ϕ(x)∣ϕ(x
   ′
   )⟩∣
   2
   
   where:
   
   A feature map circuit encodes classical data into a quantum state
   
   The kernel value is computed via overlap measurement (e.g., swap test or 
direct statevector inner product in simulation)
   
   Given QDP already supports:
   
   Data encoders (amplitude / angle / basis)
   
   Statevector simulation
   
   Zero-copy GPU pathways
   
   It seems the minimal viable quantum kernel pipeline could be:
   
   Encode input vector x → statevector ψ(x)
   
   Encode input vector x' → statevector ψ(x')
   
   Compute overlap via:
   
   Direct inner product (simulator mode)
   
   Swap test circuit (future hardware abstraction)
   
   Square magnitude for kernel value
   
   My main architectural question:
   
   Should Mahout:
   
   Treat kernel computation as a pure statevector-level primitive (fast GPU 
path), or
   
   Model it as a higher-level circuit abstraction with parameter binding and 
execution engine?
   
   The answer likely determines whether we prioritize:
   
   Parameterized gate infrastructure (#464–#469), or
   
   Optimized overlap primitives directly inside QDP.
   
   I’d be interested in aligning on this before contributing further design 
work.


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