Year: 2018
Type: preprint
Abstract: We show how to approximately represent a quantum state using the square root of the usual amount of classical memory. The classical representation of an $n$-qubit state $ψ$ consists of its inner products with $O(\sqrt{2^n})$ stabilizer states. A quantum state initially specified by its $2^n$ entries in the computational basis can be compressed to this form in time $O(2^n \mathrm{poly}(n))$, and, subsequently, the compressed description can be used to additively approximate the expectation value of an arbitrary observable. Our compression scheme directly gives a new protocol for the vector in subspace problem with randomized one-way communication complexity that matches (up to polylogarithmic factors) the optimal upper bound, due to Raz. We obtain an exponential improvement over Raz's protocol in terms of computational efficiency.
Source: arXiv (Cornell University)
Authors: Gosset, David, Smolin, John
Institution: University of Waterloo
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2783555413