4 papers · 1 filter
QAC0 Can Prepare Every Logarithmic-Qubit State
Lucas Gretta, Meghal Gupta, Malvika Raj Joshi
is the class of constant-depth -ancilla circuits obtained by extending , the class of local circuits, to include nonlocal interac…
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…
Polylogarithmic-Weight Dicke States in QAC and Arbitrary Symmetric States in QAC
Lucas Gretta, Meghal Gupta, Malvika Raj Joshi
An -qubit Dicke state of weight , is the uniform superposition over all -bit strings of Hamming weight . Dicke states are central to quantum algorithms exhibiting speed…
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$…