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Center for Nonlinear Studies |
The properties of systems of identical bosons or fermions are generically difficult to obtain using classical computers. Quantum field theory suffers from the exponential growth in particle occupation space; alternatively one must calculate increasingly large permanents or determinants. In the fermionic case antisymmetrization appears superficially as entanglement, and indeed even non-interacting fermionic systems violate entanglement area laws. Yet non-interacting quantum systems are trivial to describe as products of single-particle states. An important question is: does quantum statistics alone provide any advantage over classical strategies for solving computational problems? To address this, I will discuss a mapping between free fermions and cluster states, maximally entangled states that are resources for universal measurement-based quantum computation. While from this perspective fermionic antisymmetry is equivalent to maximal entanglement, the resulting states can only be used to perform operations that are efficiently simulatable classically.
Host: Chris Ticknor