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中国科学通报：英文版

Review on the study of entanglement in quantum computation speedup

Ding, ShengChao, Jin, Zhi

Published Jan 1, 2007• 2 citations
OpenAlex

Abstract

量纠纷在量计算加速起的作用广泛地被争论了，相信那量计算“如果纠纷是不在的，在古典计算上的 s 加速是不可能的，当其它宣称纠纷的存在不是为一些量算法的一个必要条件时。这篇论文系统地讨论这个问题。与古典资源模仿量计算被分析，在已知的算法的纠纷被考察。纠纷的存在是处于纯状态或伪 pure 状态量计算加速的一个必要然而并非足够的条件，这被结束。有混合状态的盒子仍然保持开。进一步从介绍结果研究量计算愿望利益。

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Review on the study of entanglement in quantum computation speedup

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量纠纷在量计算加速起的作用广泛地被争论了，相信那量计算“如果纠纷是不在的，在古典计算上的 s 加速是不可能的，当其它宣称纠纷的存在不是为一些量算法的一个必要条件时。这篇论文系统地讨论这个问题。与古典资源模仿量计算被分析，在已知的算法的纠纷被考察。纠纷的存在是处于纯状态或伪 pure 状态量计算加速的一个必要然而并非足够的条件，这被结束。有混合状态的盒子仍然保持开。进一步从介绍结果研究量计算愿望利益。
In a quantum computation with pure states, the generation of large amounts of entanglement is known to be necessary for a speedup with respect to classical computations. However, examples of quantum computations with mixed states are known, such as the deterministic computation with one quantum qubit (DQC1) model [Knill and Laflamme, Phys. Rev. Lett. 81, 5672 (1998)], in which entanglement is at most marginally present, and yet a computational speedup is believed to occur. Correlations, and not entanglement, have been identified as a necessary ingredient for mixed-state quantum computation speedups. Here we show that correlations, as measured through the operator Schmidt rank, are indeed present in large amounts in the DQC1 circuit. This provides evidence for the preclusion of efficient classical simulation of DQC1 by means of a whole class of classical simulation algorithms, thereby reinforcing the conjecture that DQC1 leads to a genuine quantum computational speedup.
It is often argued that entanglement is at the root of the speedup for quantum compared to classical computation, and that one needs a sufficient amount of entanglement for this speedup to be manifest. In measurement-based quantum computing, the need for a highly entangled initial state is particularly obvious. Defying this intuition, we show that quantum states can be too entangled to be useful for the purpose of computation, in that high values of the geometric measure of entanglement preclude states from offering a universal quantum computational speedup. We prove that this phenomenon occurs for a dramatic majority of all states: the fraction of useful n-qubit pure states is less than exp(-n;{2}). This work highlights a new aspect of the role entanglement plays for quantum computational speedups.
We present a classical protocol to efficiently simulate any pure-state quantum computation that involves only a restricted amount of entanglement. More generally, we show how to classically simulate pure-state quantum computations on n qubits by using computational resources that grow linearly in n and exponentially in the amount of entanglement in the quantum computer. Our results imply that a necessary condition for an exponential computational speedup (with respect to classical computations) is that the amount of entanglement increases with the size n of the computation, and provide an explicit lower bound on the required growth.