English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Fermionic Linear Optics (FLO) is a restricted model of quantum computationwhich in its original form is known to be efficiently classically simulable. Weshow that, when initialized with suitable input states, FLO circuits can beused to demonstrate quantum computational advantage with strong hardnessguarantees. Based on this, we propose a quantum advantage scheme which is afermionic analogue of Boson Sampling: Fermion Sampling with magic input states.  We consider in parallel two classes of circuits: particle-number conserving(passive) FLO and active FLO that preserves only fermionic parity and isclosely related to Matchgate circuits introduced by Valiant. Mathematically,these classes of circuits can be understood as fermionic representations of theLie groups $U(d)$ and $SO(2d)$. This observation allows us to prove our maintechnical results. We first show anticoncentration for probabilities in randomFLO circuits of both kind. Moreover, we prove robust average-case hardness ofcomputation of probabilities. To achieve this, we adapt theworst-to-average-case reduction based on Cayley transform, introduced recentlyby Movassagh, to representations of low-dimensional Lie groups. Taken together,these findings provide hardness guarantees comparable to the paradigm of RandomCircuit Sampling.  Importantly, our scheme has also a potential for experimental realization.Both passive and active FLO circuits are relevant for quantum chemistry andmany-body physics and have been already implemented in proof-of-principleexperiments with superconducting qubit architectures. Preparation of thedesired quantum input states can be obtained by a simple quantum circuit actingindependently on disjoint blocks of four qubits and using 3 entangling gatesper block. We also argue that due to the structured nature of FLO circuits,they can be efficiently certified.

Fermion Sampling: a robust quantum computational advantage scheme using fermionic linear optics and magic input states