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I am aware that for a quadratic optimization problem, we are required to minimize $y$ where $y = x^t Q x$ where $x$ is a column vector of binary variables and $Q$ is a QUBO matrix. I have the following two questions in this regard:

  1. How do we calculate the offset value or the constant terms associated with the quadratic optimization problem?
  2. What is the relationship between the offset value obtained from the algorithm for the QUBO with its corresponding QAOA formulation?

Any help in this regard would be really appreciated! Thanks in advance!

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In this particular formulation of a QUBO, i.e. $x^T Q x$, the offset is always zero — there is no constant term. The offset is also completely irrelevant from the perspective of QAOA. Depending on your exact definition of the QAOA evolution operators, the offset may contribute a global phase, which is meaningless.

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