Author

Andrew Lucas

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Preprint Oct 2026

Sample-efficient learning with Dense Associative Memories

We analytically study the evolution of the energy function of Dense Associative Memories (DenseAMs) as they train on randomly sampled codewords of random expander low-density parity-check codes (a.k.a. solutions of random XORSAT problems). We identify two distinct regimes and a transition between them, reminiscent of g...

Andrew Lucas, Dmitry Krotov · 0 citations

Preprint Aug 2026

Preparing approximate $N$-fold cat states with the phase space instruction set

The phase space instruction set is a continuous-variable universal gate set involving single-qubit rotations and qubit-dependent displacements on a single boson. Using these gates, we prove that a circuit depth $\mathrm{\Omega}(\varphi(N))$ is necessary to approximately prepare a large $N$-fold rotationally invariant S...

Shuyan Zhou, Andrew Lucas · 0 citations