Quantum Path Computing
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Double slit interference experiment is fundamental for quantum mechanics (QM) presenting wave-particle duality as emphasized by Richard Feynman. Previous quantum computing (QC) architectures with simple interference set-ups utilizing generally the wave nature and superposition have cost of exponential increase in resources of time, space or energy. In this article, wave-particle duality, tensor product Hilbert space of particle trajectory histories and Feynman's path integral formalism are combined in a simple multi-plane interference set-up with a novel QC architecture denoted by quantum path computing (QPC). It is theoretically valid for all particles including electrons, photons, neutrons and molecules possessing path integral based modeling of QM in slit based interference architectures. QPC solves specific instances of simultaneous Diophantine approximation problem (NP-hard) as an important application. It combines exponentially large number of trajectories exploiting the particle nature while performing interference measurements exploiting the wave nature. QPC does not explicitly require exponential complexity of resources by combining tensor product space of path history inherently existing in physical set-up and path integrals naturally including histories. Hidden subgroup problem is solved as a fundamental QC tool in analogy with period finding algorithms utilizing quantum gates and multiple qubit entanglement while determining computational complexity of solving capability is an open issue. In addition, single plane interference systems analyzing exotic paths are extended to multi-plane set-up while simulations consider non-negligible effects of multiple exotic paths. Challenges are discussed for modeling complexity and experimental aspects including source energy and detection sensitivity.
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