Algorithms for Quantum Simulation at Finite Energies
Algorithms for Quantum Simulation at Finite Energies
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DOI：
10.1103/prxquantum.2.020321
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发表时间：
2020-06
期刊：
影响因子：
9.7
通讯作者：
Sirui Lu;M. Bañuls;I. Cirac
中科院分区：
文献类型：
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作者：
Sirui Lu;M. Bañuls;I. Cirac
我们考虑使用量子算法来计算多体问题的有限能量区间内可观测量的期望值。它基于过滤算子，类似于量子相位估计，可以投射出该区间之外的能量。然而，它不是对物理状态执行此操作，而是通过执行干涉测量来恢复物理值，而不需要准备过滤状态。我们表明，计算时间与量子位的数量、规定方差的倒数和逆误差呈多项式缩放。在实践中，该算法不需要长时间的进化，而是需要大量的测量才能获得合理的结果。然后，我们提出一种混合经典量子算法来计算接近微规范和规范系综期望值的其他量。他们利用经典的蒙特卡罗技术，其中采样算法使用量子计算机作为资源。所有算法都可以与小型量子计算机和模拟量子模拟器一起使用，只要它们可以执行干涉测量。我们还表明，最后一项任务可以大大简化，但代价是执行更多测量。
We consider a quantum algorithm to compute expectation values of observables in a finite energy interval for many-body problems. It is based on a filtering operator, similar to quantum phase estimation, which projects out energies outside that interval. However, instead of performing this operation on a physical state, it recovers the physical values by performing interferometric measurements without the need to prepare the filtered state. We show that the computational time scales polynomially with the number of qubits, the inverse of the prescribed variance, and the inverse error. In practice, the algorithm does not require the evolution for long times, but instead a significant number of measurements in order to obtain sensible results. We then propose a hybrid classical-quantum algorithm to compute other quantities which approach the expectation values for the microcanonical and canonical ensembles. They utilize classical Monte Carlo techniques, where the sampling algorithms use the quantum computer as a resource. All algorithms can be used with small quantum computers and analog quantum simulators, as long as they can perform the interferometric measurements. We also show that this last task can be greatly simplified at the expense of performing more measurements.