论文标题
概率假想时间进化方法的加速与量子振幅相结合
Acceleration of probabilistic imaginary-time evolution method combined with quantum amplitude amplification
论文作者
论文摘要
提出了一种概率假想时间演化（PITE）方法作为在量子计算机上获得基态的非不同方法。在这种形式主义中，随着假想时间的进行，获得所有作用于初始状态的所有假想时间进化算子的成功概率降低。为了减轻不良性质，我们提出了与量子振幅扩增（QAA）方法结合使用的量子电路。我们通过引入前放大操作员来减少与QAA组合电路中的电路深度。我们成功地证明了Pite和QAA的组合有效地起作用，并报告了实现量子加速度的情况。此外，我们发现，通过优化馅饼的参数，我们可以减少QAA操作的数量，并且可以实现确定性的假想时间演化（确定性ITE），从而避免了pite的概率性质。我们将确定性ITE程序应用于多个虚构的步骤，并讨论了电路的计算成本。最后，例如，我们证明了斑点电路的数值结果与QAA结合在第一和第二量化的汉密尔顿人中。
A probabilistic imaginary-time evolution (PITE) method was proposed as a nonvariational method to obtain a ground state on a quantum computer. In this formalism, the success probability of obtaining all imaginary-time evolution operators acting on the initial state decreases as the imaginary time proceeds. To alleviate the undesirable nature, we propose quantum circuits for PITE combined with the quantum amplitude amplification (QAA) method. We reduce the circuit depth in the combined circuit with QAA by introducing a pre-amplification operator. We successfully demonstrated that the combination of PITE and QAA works efficiently and reported a case in which the quantum acceleration is achieved. Additionally, we have found that by optimizing a parameter of PITE, we can reduce the number of QAA operations and that deterministic imaginary-time evolution (deterministic ITE) can be achieved which avoids the probabilistic nature of PITE. We applied the deterministic ITE procedure to multiple imaginary-time steps and discussed the computational cost for the circuits. Finally, as an example, we demonstrate the numerical results of the PITE circuit combined with QAA in the first- and second-quantized Hamiltonians.
