What changes with exponentially many measurements?
Classify exponentially long STP protocols with polynomial quantum workspace and explicit classical controller-space bounds.
Discuss this questionAllow polynomially many active qubits and at most STP measurements generated by a succinct uniform controller. Specify controller space, workspace resets, fresh mixed-qubit supply, numerical precision, and bounded-error output. Compare logspace or finite-control variants with a polynomial-space controller, and give simulation upper bounds and complete problems for the resulting models.
Why this is interesting
An exponential list of operations is not a polynomial-size input. A succinct schedule and explicit classical memory bound are needed before long-depth STP has a meaningful complexity classification.
A place to start
Begin with a repeated fixed local schedule plus finite control, then add outcome-dependent branching. Identify whether memory in the state gives an advantage over the same classical controller.
Related work
These works provide context and established results. They need not be the origin of this exact formulation.
Discuss this question
Reading is public. Posting requires a GitHub account. You can also write to Kunal.