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Limitations on Transversal Computation through Quantum Homomorphic Encryption. (arXiv:1704.07798v1 [quant-ph])
来源于:arXiv
Transversality is a simple and effective method for implementing quantum
computation fault-tolerantly. However, no quantum error-correcting code (QECC)
can transversally implement a quantum universal gate set (Eastin and Knill,
Phys. Rev. Lett., 102, 110502). Since reversible classical computation is often
a dominating part of useful quantum computation, whether or not it can be
implemented transversally is an important open problem. We show that, other
than a small set of non-additive codes that we cannot rule out, no binary QECC
can transversally implement a classical reversible universal gate set. In
particular, no such QECC can implement the Toffoli gate transversally.
We prove our result by constructing an information theoretically secure (but
inefficient) quantum homomorphic encryption (ITS-QHE) scheme inspired by Ouyang
et al. (arXiv:1508.00938). Homomorphic encryption allows the implementation of
certain functions directly on encrypted data, i.e. homomorphically. Our scheme
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