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arXiv · 2105.04649

Symmetry Protected Quantum Computation

Michael H. Freedman·Matthew B. Hastings·Modjtaba Shokrian Zini
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Abstract

We consider a model of quantum computation using qubits where it is possible to measure whether a given pair are in a singlet (total spin $0$) or triplet (total spin $1$) state. The physical motivation is that we can do these measurements in a way that is protected against revealing other information so long as all terms in the Hamiltonian are $SU(2)$-invariant. We conjecture that this model is equivalent to BQP. Towards this goal, we show: (1) this model is capable of universal quantum computation with polylogarithmic overhead if it is supplemented by single qubit $X$ and $Z$ gates. (2) Without any additional gates, it is at least as powerful as the weak model of "permutational quantum computation" of Jordan [14, 18]. (3) With postselection, the model is equivalent to PostBQP.

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Michael H. Freedman, Matthew B. Hastings, Modjtaba Shokrian Zini. 2021-05-10. Symmetry Protected Quantum Computation. https://doi.org/10.22331/q-2021-09-28-554

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