Author

Lucas Gretta

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Preprint Sep 2026

QAC0 Can Prepare Every Logarithmic-Qubit State

$\mathsf{QAC}^0$ is the class of constant-depth $\mathrm{poly}(n)$-ancilla circuits obtained by extending $\mathsf{QNC}^0$, the class of local circuits, to include nonlocal interactions via arbitrary width Toffoli gates. It is believed to be weaker than its counterpart, $\mathsf{QNC}^0_f$, obtained by including arbitra...

Lucas Gretta, Meghal Gupta, M. Joshi · 2 citations · ⚡1

#machine learning Preprint Oct 2026

Read What Matters: Query-Adaptive Quantization for KV Caches

KV-cache entries are stored before their future queries are known, but each decoding query needs precision in different places. We study this mismatch using separate budgets for retained bits and bits fetched per query. ReadKV stores each key and value in a progressive code whose prefixes support different reconstructi...

Siddharth Bhandari, Lucas Gretta, K. Balasubramanian et al. · 0 citations

Preprint Aug 2026

Shor's algorithm requires Fanout

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, Fenner, Green, Homer and Zhang from 2006 by showing that approximating QFT in constant depth, for any $n$-qubit modulus, necessarily requires th...

Lucas Gretta, M. Joshi · 0 citations