constant-depth circuits 1dicke states 1fanout gates 1qrams 1quantum state preparation 1symmetric states 1
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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 and Arbitrary Symmetric States in QAC
Lucas Gretta, Meghal Gupta, Malvika Raj Joshi
The paper shows that Dicke states with polylogarithmic weight can be prepared in constant-depth quantum circuits (QAC^0) using limited-width Toffoli and fanout gates, and extends t…
quant-ph2026
Parity QAC0 QAC0 is Fourier-Concentrated
Lucas Gretta, Meghal Gupta, Malvika Raj Joshi
A major open problem in understanding shallow quantum circuits (QAC) is whether they can compute Parity. We show that this question is solely about the Fourier spectrum of QAC$…