Meghal Gupta

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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$…

quant-ph2026

Nearly Time-Optimal Pure State Tomography with Pauli Measurements

Sabee Grewal, Meghal Gupta, William He +2

We give an algorithm for pure state tomography with near-optimal copy and time complexity using only single-qubit measurements. Specifically, given $O (2^{n} / ε)$ copies of…

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

Parity ∈/ QAC0 ⟺ QAC0 is Fourier-Concentrated

Nearly Time-Optimal Pure State Tomography with Pauli Measurements

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

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