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 >>>

Recently, together with Kulikov, Mihajlin, and Smirnova (STACS 2026), we gave conditional constructions of functions with large monotone circuit complexity, matrices with high rigidity, and $3$-dimensional tensors of strongly superlinear rank.
In this note, I strengthen the rigidity construction under the same assumption and, as a direct consequence, immediately obtain ... more >>>