Classical Simulation of Peaked Shallow Quantum Circuits
Sergey Bravyi, David Gosset, et al.
STOC 2024
Let |ψ〉 be an arbitrary stabilizer state distributed between three remote parties, such that each party holds several qubits. Let S be a stabilizer group of |ψ〉. We show that |ψ〉 can be converted by local unitaries into a collection of singlets, GHZ states, and local one-qubit states. The numbers of singlets and GHZs are determined by dimensions of certain subgroups of S. For an arbitrary number of parties m we find a formula for the maximal number of m-partite GHZ states that can be extracted from |ψ〉 by local unitaries. A connection with earlier introduced measures of multipartite correlations is made. An example of an undecomposable four-party stabilizer state with more than one qubit per party is given. These results are derived from a general theoretical framework that allows one to study interconversion of multipartite stabilizer states by local Clifford group operators. As a simple application, we study three-party entanglement in two-dimensional lattice models that can be exactly solved by the stabilizer formalism. © 2006 American Institute of Physics.
Sergey Bravyi, David Gosset, et al.
STOC 2024
Andrew Eddins, Youngseok Kim, et al.
APS March Meeting 2023
Sergey Bravyi, David Gosset
APS March Meeting 2021
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npj Quantum Information