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We perform a mathematical analysis of the classical computational complexity of two genuine quantum-mechanical problems, which are inspired in the calculation of the expected magnetizations and the entanglement between subsystems for a quantum spin system. These problems, which we respectively call SES and SESSP, are specified in terms of pure… (More)

In this paper the geometric entanglement (GE) of systems in one spatial dimension (1D) and in the thermodynamic limit is analyzed focusing on two aspects. First, we reexamine the calculation of the GE for translation-invariant matrix product states (MPSs) in the limit of infinite system size. We obtain a lower bound to the GE which collapses to an equality… (More)

- Akira Saitoh, A Kawaguchi, K Shimizu, Y Tokura, N Imoto, M C Bañuls +4 others
- 2015

There have been many studies on matrix-product-state (MPS) simulation of quantum computing for more than a decade [1, 2, 3, 4, 5, 6]. Although it is widely believed to be unlikely, it is still an open problem if a practical simulation of a powerful quantum algorithm like Shor's factoring algorithm is possible. This situation is owing to the fact that not… (More)

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