6 papers
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$…
Constant-Depth Unitary Preparation of Dicke States
Malvika Raj Joshi, Francisca Vasconcelos
Dicke states serve as a critical resource in quantum metrology, communication, and computation. However, unitary preparation of Dicke states is limited to logarithmic depth in stan…
Improved Lower Bounds for QAC0
Malvika Raj Joshi, Avishay Tal, Francisca Vasconcelos +1
In this work, we prove the strongest known lower bounds for QAC, allowing polynomially many gates and ancillae. Our main results show that: (1) Depth-3 QAC circuits cannot…