We present efficient quantum circuits that implement high-dimensional unitary irreducible representations (irreps) of SU(n), where n>=2 is constant. For dimension N and error ?, the number of quantum gates in our circuits is polynomial in log(N) and log(1/?). Our construction relies on the Jordan-Schwinger representation, which allows us to realize ... more >>>

Guo, Saxena, and Sinhababu (TOC'18, CCC'18) defined a natural, approximative analog of the polynomial system satisfiability problem, which they called approximate polynomial satisfiability (APS). They proved algebraic and geometric properties of it and showed an NP-hardness lower bound and a PSPACE upper bound for it. They further established how the ... more >>>

The complexity of bilinear maps (equivalently, of $3$-mode tensors) has been studied extensively, most notably in the context of matrix multiplication. While circuit complexity and tensor rank coincide asymptotically for $3$-mode tensors, this correspondence breaks down for $d \geq 4$ modes. As a result, the complexity of $d$-mode tensors for ... more >>>