We obtain the first nontrivial time-space lower bound for quantum algorithms solving problems related to satisfiability. Our bound applies to MajSAT and MajMajSAT, which are complete problems for the first and second levels of the counting hierarchy, respectively. We prove that for every real $d$ and every positive real $\epsilon$ ... more >>>

We give two time- and space-efficient simulations of quantum computations with
intermediate measurements, one by classical randomized computations with
unbounded error and the other by quantum computations that use an arbitrary
fixed universal set of gates. Specifically, our simulations show that every
language solvable by a bounded-error quantum algorithm running ... more >>>

In a work by Raz (J. ACM and FOCS 16), it was proved that any algorithm for parity learning on $n$ bits requires either $\Omega(n^2)$ bits of classical memory or an exponential number (in~$n$) of random samples. A line of recent works continued that research direction and showed that for ... more >>>

We give the first explicit constant rate, constant relative distance, linear codes with an encoder that runs in time $n^{1 + o(1)}$ and space $\mathop{polylog}(n)$ provided random access to the message. Prior to this work, the only such codes were non-explicit, for instance repeat accumulate codes [DJM98] and the codes ... more >>>