Polynomial computational complexity of matrix elements of finite-rank-generated single-particle operators in products of finite bosonic states
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It is known that computing the permanent Per(1+A), where A is a finite-rank matrix requires a number of operations polynomial in the matrix size. I generalize this result to the expectation values ⟨Ψ| P(1+A) |Ψ⟩, where P() is the multiplicative extension of a single-particle operator and |Ψ⟩ is a product of a large number of identical finite bosonic states (i.e. bosonic states with a bounded number of bosons). I also improve an earlier polynomial estimate for the fermionic version of the same problem.
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