No-go Theorem for One-way Quantum Computing on Naturally Occurring Two-level Systems - Quantum PhysicsReport as inadecuate

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Abstract: One-way quantum computing achieves the full power of quantum computation byperforming single particle measurements on some many-body entangled state,known as the resource state. As single particle measurements are relativelyeasy to implement, the preparation of the resource state becomes a crucialtask. An appealing approach is simply to cool a strongly correlated quantummany-body system to its ground state. In addition to requiring the ground stateof the system to be universal for one-way quantum computing, we also want theHamiltonian to have non-degenerate ground state protected by a fixed energygap, to involve only two-body interactions, and to be frustration-free so thatmeasurements in the course of the computation leave the remaining particles inthe ground space. Recently, significant efforts have been made to the search ofresource states that appear naturally as ground states in spin lattice systems.The approach is proved to be successful in spin-5-2 and spin-3-2 systems. Yet,it remains an open question whether there could be such a natural resourcestate in a spin-1-2, i.e., qubit system. Here, we give a negative answer tothis question by proving that it is impossible for a genuinely entangled qubitstates to be a non-degenerate ground state of any two-body frustration-freeHamiltonian. What is more, we prove that every spin-1-2 frustration-freeHamiltonian with two-body interaction always has a ground state that is aproduct of single- or two-qubit states, a stronger result that is interestingindependent of the context of one-way quantum computing.

Author: Jianxin Chen, Xie Chen, Runyao Duan, Zhengfeng Ji, Bei Zeng


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