In a toy qubit model of quarks, baryons are fortuitous with exponential counting and super-exponential complexity while mesons are monotone with polynomial counting and power-law complexity.
Subsystem stabilizer codes cannot have a universal set of transversal gates for even one encoded qudit
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abstract
A long-standing open problem in fault-tolerant quantum computation has been to find a universal set of transversal gates. As three of us proved in arXiv: 0706.1382, such a set does not exist for binary stabilizer codes. Here we generalize our work to show that for subsystem stabilizer codes in $d$ dimensional Hilbert space, such a universal set of transversal gates cannot exist for even one encoded qudit, for any dimension $d$, prime or nonprime. This result strongly supports the idea that other primitives, such as quantum teleportation, are necessary for universal fault-tolerant quantum computation, and may be an important factor for fault tolerance noise thresholds.
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Fortuity and Complexity in a Simple Quark Model
In a toy qubit model of quarks, baryons are fortuitous with exponential counting and super-exponential complexity while mesons are monotone with polynomial counting and power-law complexity.