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International Conference on Photonics, Optics and Laser Technology

Optics-inspired Computing

Bahram Jalali, Madhuri Suthar, Mohamad Asghari, Ata Mahjoubfar

Published Jan 1, 2017• 4 citations
Publisher
DOI
10.5220/0006271703400345

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Tensor network methods strike a middle ground between fully-fledged quantum computing and classical computing, as they take inspiration from quantum systems to significantly speed up certain classical operations. Their strength lies in their compressive power and the wide variety of efficient algorithms that operate within this compressed space. In this work, we focus on applying these methods to fundamental problems in image compression and processing and classical optics such as wave-front propagation and optical image formation, by using directly or indirectly parallels with quantum mechanics and computation. These quantum-inspired methods are expected to yield faster algorithms with applications ranging from astronomy and earth observation to microscopy and classical imaging more broadly.
The permanent is pivotal to both complexity theory and combinatorics. In quantum computing, the permanent appears in the expression of output amplitudes of linear optical computations, such as in the Boson Sampling model. Taking advantage of this connection, we give quantum-inspired proofs of many existing as well as new remarkable permanent identities. Most notably, we give a quantum-inspired proof of the MacMahon master theorem as well as proofs for new generalizations of this theorem. Previous proofs of this theorem used completely different ideas. Beyond their purely combinatorial applications, our results demonstrate the classical hardness of exact and approximate sampling of linear optical quantum computations with input cat states.