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arXiv · 1805.03385

Interactive Proofs with Polynomial-Time Quantum Prover for Computing the Order of Solvable Groups

François Le Gall·Tomoyuki Morimae·Harumichi Nishimura·Yuki Takeuchi
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Abstract

In this paper we consider what can be computed by a user interacting with a potentially malicious server, when the server performs polynomial-time quantum computation but the user can only perform polynomial-time classical (i.e., non-quantum) computation. Understanding the computational power of this model, which corresponds to polynomial-time quantum computation that can be efficiently verified classically, is a well-known open problem in quantum computing. Our result shows that computing the order of a solvable group, which is one of the most general problems for which quantum computing exhibits an exponential speed-up with respect to classical computing, can be realized in this model.

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François Le Gall, Tomoyuki Morimae, Harumichi Nishimura, Yuki Takeuchi. 2018-05-09. Interactive Proofs with Polynomial-Time Quantum Prover for Computing the Order of Solvable Groups. https://doi.org/10.4230/lipics.mfcs.2018.26

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