FABLE: Fast Approximate Quantum Circuits for Block-Encodings
FABLE: Fast Approximate Quantum Circuits for Block-Encodings
复制标题
FABLE：用于块编码的快速近似量子电路
DOI：
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发表时间：
2022
期刊：
影响因子：
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通讯作者：
R. Beeumen
中科院分区：
文献类型：
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作者：
Daan Camps;R. Beeumen
矩阵的块编码已经成为量子奇异值变换衍生的量子算法的基本元素。这包括从量子线性系统问题到量子行走、哈密顿模拟和量子机器学习的各种算法。这些算法中的许多算法在黑盒矩阵Oracle查询方面实现了最佳复杂度，但到目前为止，计算矩阵块编码的量子电路实现的问题尚未得到充分重视。在本文中，我们提出了FABLE，一种方法来产生近似量子电路块编码的矩阵在一个快速的方式。FABLE电路具有简单的结构，并且直接用单量子位和双量子位门来表示。对于小型和结构化矩阵，它们在NISQ时代是可行的，并且可以轻松生成多达15个量子位问题的电路参数。此外，我们表明，FABLE电路可以被压缩和稀疏化。我们提供了一个压缩定理，涉及到压缩阈值的块编码的错误。我们基准我们的方法海森堡和哈伯德哈密顿算子，拉普拉斯算子，以说明它们可以实现降低门的复杂性没有近似误差。
Block-encodings of matrices have become an essential element of quantum algorithms derived from the quantum singular value transformation. This includes a variety of algorithms ranging from the quantum linear systems problem to quantum walk, Hamiltonian simulation, and quantum machine learning. Many of these algorithms achieve optimal complexity in terms of black box matrix oracle queries, but so far the problem of computing quantum circuit implementations for block-encodings of matrices has been under-appreciated. In this paper we propose FABLE, a method to generate approximate quantum circuits for block-encodings of matrices in a fast manner. FABLE circuits have a simple structure and are directly formulated in terms of one- and two-qubit gates. For small and structured matrices they are feasible in the NISQ era, and the circuit parameters can be easily generated for problems up to fifteen qubits. Furthermore, we show that FABLE circuits can be compressed and sparsified. We provide a compression theorem that relates the compression threshold to the error on the block-encoding. We benchmark our method for Heisenberg and Hubbard Hamiltonians, and Laplacian operators to illustrate that they can be implemented with a reduced gate complexity without approximation error.
影响因子：
6.7
作者：
McClean, Jarrod R.;Rubin, Nicholas C.;Babbush, Ryan
通讯作者：
Babbush, Ryan