1 transversality versus universality for additive quantum codes (706).

Content Provider	CiteSeerX
Author	Zeng, Bei Cross, Andrew Chuang, Isaac L.
Abstract	Abstract—Certain quantum codes allow logic operations to be performed on the encoded data, such that a multitude of errors introduced by faulty gates can be corrected. An important class of such operations are transversal, acting bitwise between corresponding qubits in each code block, thus allowing error propagation to be carefully limited. If any quantum operation could be implemented using a set of such gates, the set would be universal; codes with such a universal, transversal gate set have been widely desired for efficient fault-tolerant quantum computation. We study the structure of GF(4)-additive quantum codes and prove that no universal set of transversal logic operations exists for these codes. This result strongly supports the idea that additional primitive operations, based for example on quantum teleportation, are necessary to achieve universal faulttolerant computation on additive codes. I.
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Subject Keyword	Additive Quantum Code Transversality Versus Universality Error Propagation Logic Operation Important Class Code Block Efficient Fault-tolerant Quantum Computation Faulty Gate Universal Set Transversal Logic Operation Transversal Gate Additional Primitive Operation Abstract Certain Quantum Code Additive Code Universal Faulttolerant Computation Quantum Operation Quantum Teleportation
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