Variational Power of Quantum Circuit Tensor Networks
Variational Power of Quantum Circuit Tensor Networks
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DOI：
10.1103/physrevx.12.011047
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发表时间：
2022-03-11
影响因子：
12.5
通讯作者：
Chan, Garnet Kin-Lic
中科院分区：
文献类型：
--
作者：
Haghshenas, Reza;Gray, Johnnie;Chan, Garnet Kin-Lic
在物理多体基态表象中，我们刻画了量子电路张量网络的变分幂。这种张量网络是通过用局域量子电路取代标准张量网络中的稠密块幺正和等距来形成的。我们探索了量子电路矩阵乘积态和量子电路多尺度纠缠重正化Annomalization，并引入了一种自适应方法来优化所得到的电路，使其具有超过10（4）个参数。我们对标准张量网络，以及其他常见的电路架构，为1D和2D海森堡和1D费米-哈伯德模型的表现力进行基准测试。我们发现量子电路张量网络在这些问题上比其他量子电路更有表现力，它们甚至可以比标准张量网络更紧凑。外推到电路的深度，它不再可以模拟经典，这表明在物理基态的表示量子表现力的优势区域。
We characterize the variational power of quantum circuit tensor networks in the representation of physical many-body ground states. Such tensor networks are formed by replacing the dense block unitaries and isometries in standard tensor networks by local quantum circuits. We explore both quantum circuit matrix product states and the quantum circuit multiscale entanglement renormalization Ansatz, and introduce an adaptive method to optimize the resulting circuits to high fidelity with more than 10(4) parameters. We benchmark their expressiveness against standard tensor networks, as well as other common circuit architectures, for the 1D and 2D Heisenberg and 1D Fermi-Hubbard models. We find quantum circuit tensor networks to be substantially more expressive than other quantum circuits for these problems, and that they can even be more compact than standard tensor networks. Extrapolating to circuit depths which can no longer be emulated classically, this suggests a region of advantage in quantum expressiveness in the representation of physical ground states.