Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
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DOI：
10.1038/s41567-019-0704-4
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发表时间：
2020-02-01
期刊：
影响因子：
19.6
通讯作者：
Chan, Garnet Kin-Lic
中科院分区：
文献类型：
--
作者：
Motta, Mario;Sun, Chong;Chan, Garnet Kin-Lic
在量子计算机上精确计算哈密顿基态、激发态和热态将影响物理和计算机科学中的许多问题，从量子模拟到机器学习。鉴于构建大规模量子计算机所面临的挑战，这些任务应该以资源有效的方式进行。在这方面，现有的技术的基础上相位估计或变分算法显示潜在的缺点;相位估计需要深的电路与附属，这是很难可靠地执行没有纠错，而变分算法，而灵活的电路深度，需要额外的高维经典优化。在这里，我们介绍了量子虚时间演化和量子Lanczos算法，这是类似的经典算法寻找基态和激发态。与经典算法相比，它们每次迭代所需的空间和时间呈指数级减少，并且可以在没有深度电路和辅助电路或高维优化的情况下实现。我们还讨论了量子虚时间演化作为一个子程序，通过模拟最小纠缠的典型热态产生吉布斯平均。最后，我们通过使用精确的经典仿真的实现以及通过Rigetti量子虚拟机和白杨-1量子处理单元上的原型电路来展示这些算法的潜力。量子虚时间演化和Lanczos算法提供了一种在量子计算机上计算目标哈密顿量的基态或激发态的资源有效的方法。这为近期噪声器件的量子模拟提供了希望。
The accurate computation of Hamiltonian ground, excited and thermal states on quantum computers stands to impact many problems in the physical and computer sciences, from quantum simulation to machine learning. Given the challenges posed in constructing large-scale quantum computers, these tasks should be carried out in a resource-efficient way. In this regard, existing techniques based on phase estimation or variational algorithms display potential disadvantages; phase estimation requires deep circuits with ancillae, that are hard to execute reliably without error correction, while variational algorithms, while flexible with respect to circuit depth, entail additional high-dimensional classical optimization. Here, we introduce the quantum imaginary time evolution and quantum Lanczos algorithms, which are analogues of classical algorithms for finding ground and excited states. Compared with their classical counterparts, they require exponentially less space and time per iteration, and can be implemented without deep circuits and ancillae, or high-dimensional optimization. We furthermore discuss quantum imaginary time evolution as a subroutine to generate Gibbs averages through an analogue of minimally entangled typical thermal states. Finally, we demonstrate the potential of these algorithms via an implementation using exact classical emulation as well as through prototype circuits on the Rigetti quantum virtual machine and Aspen-1 quantum processing unit.The quantum imaginary time evolution and Lanczos algorithms offer a resource-efficient way to compute ground or excited states of target Hamiltonians on quantum computers. This offers promise for quantum simulation on near-term noisy devices.