Experimental demonstration of memory retrieval, spin-glass blackout, and paramagnetic phases in a photonic quantum simulator realizing a fully connected four-body Hopfield model via two-photon processes.
Permanents in linear optical networks
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We develop an abstract look at linear optical networks from the viewpoint of combinatorics and permanents. In particular we show that calculation of matrix elements of unitarily transformed photonic multi-mode states is intimately linked to the computation of permanents. An implication of this remarkable fact is that all calculations that are based on evaluating matrix elements are generically computationally hard. Moreover, quantum mechanics provides simpler derivations of certain matrix analysis results which we exemplify by showing that the permanent of any unitary matrix takes its values across the unit disk in the complex plane.
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UNVERDICTED 3representative citing papers
Derives a boson-fermion complementarity identity in linear interferometers that implies a previously unknown relation between |perm(A)|^2 and |det(A)|^2 for complex matrices, extending Muir's 19th-century identity.
A dual-valued phase shifter in linear optics creates variational cost landscapes with fewer local minima and outperforms prior linear-optical variational algorithms by mitigating barren plateaus.
citing papers explorer
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Observation of associative-memory retrieval and spin-glass phases on a photonic quantum simulator
Experimental demonstration of memory retrieval, spin-glass blackout, and paramagnetic phases in a photonic quantum simulator realizing a fully connected four-body Hopfield model via two-photon processes.
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Boson-fermion complementarity in a linear interferometer: An identity relating the determinant and permanent of a matrix
Derives a boson-fermion complementarity identity in linear interferometers that implies a previously unknown relation between |perm(A)|^2 and |det(A)|^2 for complex matrices, extending Muir's 19th-century identity.
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Mitigating the barren plateau problem in linear optics
A dual-valued phase shifter in linear optics creates variational cost landscapes with fewer local minima and outperforms prior linear-optical variational algorithms by mitigating barren plateaus.