We construct a classical oracle relative to which P= NP yet single-copy secure
pseudorandom quantum states exist. In the language of Impagliazzo's five worlds, this is a …

We present a distribution 𝓓 over inputs in {±1} 2 N, such that:(1) There exists a quantum
algorithm that makes one (quantum) query to the input, and runs in time O (log N), that …

This is a survey of unconditional pseudorandom generators (PRGs). A PRG uses a short,
truly random seed to generate a long," pseudorandom" sequence of bits. To be more …

Is randomness ever necessary for space-efficient computation? It is commonly conjectured
that L= BPL, meaning that halting decision algorithms can always be derandomized without …

We prove that the Impagliazzo-Nisan-Wigderson [Impagliazzo et al., 1994] pseudorandom
generator (PRG) fools ordered (read-once) permutation branching programs of unbounded …

We construct pseudorandom generators of seed length Õ (log (n)· log (1/є)) that є-fool
ordered read-once branching programs (ROBPs) of width 3 and length n. For unordered …

A weighted pseudorandom generator (WPRG) is a generalization of a pseudorandom
generator (PRG) in which, roughly speaking, probabilities are replaced with weights that are …

We prove that for every decision tree, the absolute values of the Fourier coefficients of given
order t≥ 1 sum to at most (cd/t) t/2 (1+ log n)(t− 1)/2, where n is the number of variables, d is …

We construct improved hitting set generators (HSGs) for ordered (read-once) regular
branching programs in two parameter regimes. First, we construct an explicit ε-HSG for …

The circuit class QAC 0 was introduced by Moore (1999) as a model for constant depth
quantum circuits where the gate set includes many-qubit Toffoli gates. Proving lower bounds …