In ensemble (or bulk) quantum computation, all computations are performed on an ensemble of computers rather than on a single computer. Measurements of qubits in an individual computer cannot be performed; instead, only expectation values (over the complete ensemble of computers) can be measured. As a result of this limitation on the model of computation, many algorithms cannot be processed directly on such computers, and must be modified, as the common strategy of delaying the measurements usually does not resolve this ensemble-measurement problem. Here we present several new strategies for resolving this problem. Based on these strategies we provide new versions of some of the most important quantum algorithms, versions that are suitable for implementing on ensemble quantum computers, e.g., on liquid NMR quantum computers. These algorithms are Shor’s factorization algorithm, Grover’s search algorithm (with several marked items), and an algorithm for quantum fault-tolerant computation. The first two algorithms are simply modified using a randomizing and a sorting strategies. For the last algorithm, we develop a classical-quantum hybrid strategy for removing measurements. We use it to present a novel quantum fault-tolerant scheme. More explicitly, we present schemes for fault-tolerant measurement-free implementation of Toffoli and \(\sigma_{z}^{1/4},\) as these operations cannot be implemented “bitwise”, and their standard fault-tolerant implementations require measurement.

中文翻译：

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集合量子计算机上的算法。


在整体（或批量）量子计算中，所有计算都是在计算机整体上而不是在单个计算机上执行。无法在单个计算机中进行量子位的测量；相反，只能测量期望值（在整个计算机集合上）。由于计算模型的这种限制，许多算法不能直接在此类计算机上处​​理，并且必须进行修改，因为延迟测量的常见策略通常不能解决这种集成测量问题。在这里，我们提出了解决这个问题的几种新策略。基于这些策略，我们提供了一些最重要的量子算法的新版本，这些版本适合在集合量子计算机上实现，例如在液体核磁共振量子计算机上。这些算法是 Shor 的因式分解算法、Grover 的搜索算法（带有多个标记项）和量子容错计算算法。前两种算法只需使用随机化和排序策略进行修改。对于最后一种算法，我们开发了一种经典量子混合策略来删除测量。我们用它来提出一种新颖的量子容错方案。更明确地，我们提出了 Toffoli 和\(\sigma_{z}^{1/4},\)的容错无测量实现方案，因为这些操作无法“按位”实现，并且它们的标准容错实现需要测量。