Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A complex projective $t$-design is a configuration of vectors which is ``evenly distributed'' on a sphere in the sense that sampling uniformly from it reproduces the moments of Haar measure up to order $2t$.  show that the set of all $n$-qubit stabilizer states forms a complex projective $3$-design in dimension $2^n$. Stabilizer states had previously only been known to constitute $2$-designs. The main technical ingredient is a general recursion formula for the so-called frame potential of stabilizer states. To establish it,  need to compute the number of stabilizer states with pre-described inner product with respect to a reference state. This, in turn, reduces to a counting problem in discrete symplectic vector spaces for which  find a simple formula.  sketch applications in quantum information and signal analysis.
['Richard Kueng', 'David J. Gross']
I am writing a research paper on a idea Qubit stabilizer states are complex projective 3-designs
[{"from": "human", "value": "I am writing a research paper on a idea Qubit stabilizer states are complex projective 3-designs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A complex projective $t$-design is a configuration of vectors which is ``evenly distributed'' on a sphere in the sense that sampling uniformly from it reproduces the moments of Haar measure up to order $2t$.  show that the set of all $n$-qubit stabilizer states forms a complex projective $3$-design in dimension $2^n$. Stabilizer states had previously only been known to constitute $2$-designs. The main technical ingredient is a general recursion formula for the so-called frame potential of stabilizer states. To establish it,  need to compute the number of stabilizer states with pre-described inner product with respect to a reference state. This, in turn, reduces to a counting problem in discrete symplectic vector spaces for which  find a simple formula.  sketch applications in quantum information and signal analysis."}]