Complex instruction set computing architecture for performing accurate quantum $Z$ rotations with less magic
Complex instruction set computing architecture for performing accurate quantum $Z$ rotations with less magic
复制标题
复杂的指令集计算架构，可以用更少的魔法执行精确的量子 $Z$ 旋转
DOI：
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发表时间：
2013
期刊：
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通讯作者：
C. Cesare
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作者：
A. Landahl;C. Cesare
我们提出了用于执行量子比特绕其\(Z\)轴进行任意精确的\(\pi/2^k\)旋转的量子协议。精简指令集计算（\(\text{RISC}\)）架构通常将指令集限制为稳定器操作以及单个非稳定器操作，例如制备一种“魔法”态，从该态可以远程传输\(T = Z(\pi/4)\)门。尽管提纯这种魔法态的高保真副本所需的开销很高，但在\(\text{RISC}\)架构中实现\(Z\)旋转的后续量子编译开销可能会更高。我们开发了一种复杂指令集计算（\(\text{CISC}\)）架构，其指令集包括稳定器操作以及制备魔法态，从这些魔法态可以远程传输\(Z(\pi/2^k)\)门，其中\(2\leq k\leq k_{\text{max}}\)。这导致实现\(Z\)旋转达到期望的门精度所需的门数量大幅减少。我们构造的关键是一族长度为\(2^{k + 2}-1\)的缩短量子里德 - 穆勒码，其魔法态提纯阈值随\(k\)减小，但当\(k\leq6\)时大于\(0.85\%\)。
We present quantum protocols for executing arbitrarily accurate $pi/2^k$ rotations of a qubit about its $Z$ axis. Reduced instruction set computing ( extsc{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 extsc{risc} architecture can be much greater. We develop a complex instruction set computing ( extsc{cisc}) architecture whose instruction set includes stabilizer operations and preparation of magic states from which $Z(pi/2^k)$ gates can be teleported, for $2 leq k leq k_{ ext{max}}$. 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 $k leq 6$.