Quantum Analog of Shannon's Lower Bound Theorem

Saugata Basu; Laxmi Parida

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arXiv · 2308.13091

Quantum Analog of Shannon's Lower Bound Theorem

Saugata Basu·Laxmi Parida

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Abstract

Shannon proved that almost all Boolean functions require a circuit of size $\Theta(2^n/n)$. We prove a quantum analog of this classical result. Unlike in the classical case the number of quantum circuits of any fixed size that we allow is uncountably infinite. Our main tool is a classical result in real algebraic geometry bounding the number of realizable sign conditions of any finite set of real polynomials in many variables.

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Saugata Basu, Laxmi Parida. 2023-08-24. Quantum Analog of Shannon's Lower Bound Theorem. https://arxiv.org/abs/2308.13091

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