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We give a non-adaptive algorithm that makes 2^{O(√klog(1/ε₂ − ε₁))} queries to a Boolean function f:{±1}ⁿ→{±1} and distinguishes between f being ε₁-close to some k-junta versus ε₂-far from every k-junta. At the heart of our algorithm is a local mean ...

The circuit class QAC⁰ 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 against such circuits is a longstanding challenge in quantum circuit ...

We study parity decision trees for Boolean functions. The motivation of our study is the log-rank conjecture for XOR functions and its connection to Fourier analysis and parity decision tree complexity. Our contributions are as follows: Let \(\(f : \mathbb ...\)