Lucas Gretta

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quant-ph2026

Shor's algorithm requires Fanout

Lucas Gretta, Malvika Raj Joshi

Shor's algorithm is a canonical quantum supremacy target whose core operation relies on the Quantum Fourier Transform (QFT). In this note, we resolve an open question of Fang, Fenn…

quant-ph2026

Polylogarithmic-Weight Dicke States in QAC $^{0}$ and Arbitrary Symmetric States in QAC $_{f}^{0}$

Lucas Gretta, Meghal Gupta, Malvika Raj Joshi

An $n$ -qubit Dicke state of weight $k$ , is the uniform superposition over all $n$ -bit strings of Hamming weight $k$ . Dicke states are central to quantum algorithms exhibiting speed…

quant-ph2026

Parity $\in /$ QAC0 $⟺$ QAC0 is Fourier-Concentrated

Lucas Gretta, Meghal Gupta, Malvika Raj Joshi

A major open problem in understanding shallow quantum circuits (QAC $^{0}$ ) is whether they can compute Parity. We show that this question is solely about the Fourier spectrum of QAC$…

Shor's algorithm requires Fanout

Polylogarithmic-Weight Dicke States in QAC0 and Arbitrary Symmetric States in QACf0​

Parity ∈/ QAC0 ⟺ QAC0 is Fourier-Concentrated

Polylogarithmic-Weight Dicke States in QAC $^{0}$ and Arbitrary Symmetric States in QAC $_{f}^{0}$

Parity $\in /$ QAC0 $⟺$ QAC0 is Fourier-Concentrated