The Tree Evaluation Problem (TreeEval) is a computational problem originally proposed as a candidate to prove a separation between complexity classes P and L. Recently, this problem has gained significant attention after Cook and Mertz (STOC 2024) showed that TreeEval can be solved using $O(\log n\log\log n)$ bits of space. ... more >>>

Since the breakthrough superpolynomial multilinear formula lower bounds of Raz (Theory of Computing 2006), proving such lower bounds against multilinear algebraic branching programs (mABPs) has been a longstanding open problem in algebraic complexity theory. All known multilinear lower bounds rely on the min-partition rank method, and the best bounds against ... more >>>

We establish tight connections between entanglement entropy and the approximation error in Trotter–Suzuki product formulas for Hamiltonian simulation. Product formulas remain the workhorse of quantum simulation on near-term devices, yet standard error analyses yield worst-case bounds that can vastly overestimate the resources required for structured problems.

For systems governed by ... more >>>