Complex instruction set computing architecture for performing accurate quantum $Z$ rotations with less magic
| Autor: | Landahl, Andrew J., Cesare, Chris |
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| Rok vydání: | 2013 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We present quantum protocols for executing arbitrarily accurate $\pi/2^k$ rotations of a qubit about its $Z$ axis. Reduced instruction set computing (\textsc{risc}) architectures typically restrict the instruction set to stabilizer operations and a single non-stabilizer operation, such as preparation of a "magic" state from which $T = Z(\pi/4)$ gates can be teleported. Although the overhead required to distill high-fidelity copies of this magic state is high, the subsequent quantum compiling overhead to realize $Z$ rotations in a \textsc{risc} architecture can be much greater. We develop a complex instruction set computing (\textsc{cisc}) architecture whose instruction set includes stabilizer operations and preparation of magic states from which $Z(\pi/2^k)$ gates can be teleported, for $2 \leq k \leq k_{\text{max}}$. This results in a substantial overall reduction in the number of gates required to achieve a desired gate accuracy for $Z$ rotations. The key to our construction is a family of shortened quantum Reed-Muller codes of length $2^{k+2}-1$, whose magic-state distillation threshold shrinks with $k$ but is greater than 0.85% for $k \leq 6$. Comment: 13 pages, 4 figures. Resource metric now non-Clifford states. Comparison now to Meier-Eastin-Knill distillation and (optimal) Selinger compiling. Minor tweaks made to concatenated teleportation analysis |
| Databáze: | arXiv |
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