自下而上的量子模拟：重比特的情况
Quantum simulation from the bottom up: the case of rebits
摘要：
通常，量子力学被认为是一种线性理论，其幺正演化由薛定谔方程控制。虽然这在技术上是正确的，并且对物理学家有用，但就计算而言，这是一个不幸的狭隘观点。正如经典计算机可以模拟经典态的高度非线性函数一样，更一般的量子计算机也可以模拟量子态的非线性演化。我们详细介绍了量子计算机上的非线性模拟，展示了如何使用酉实振幅量子计算机（总共由$n+1$量子比特组成）模拟整个$\mathbb{R}$ -酉演化（在$n$量子比特上）。这些算子可以表示为线性算子和反线性算子的和，并且为量子算法设计者的工具箱添加了一组有趣的新的非线性量子门。此外，通过利用Clifford算子可以模拟非Clifford（实际上，非线性）算子的事实，可以有效地经典模拟这些非线性演化的子组，称为$\mathbb{R}$ -Clifford。这种使用物理操作符来模拟非物理操作符的观点，我们称之为自下而上的模拟，我们给出了一些例子来说明其更广泛的含义。
英文摘要：
Typically, quantum mechanics is thought of as a linear theory with unitary evolution governed by the Schrödinger equation. While this is technically true and useful for a physicist, with regards to computation it is an unfortunately narrow point of view. Just as a classical computer can simulate highly nonlinear functions of classical states, so too can the more general quantum computer simulate nonlinear evolutions of quantum states. We detail one particular simulation of nonlinearity on a quantum computer, showing how the entire class of $\mathbb{R}$-unitary evolutions (on $n$ qubits) can be simulated using a unitary, real-amplitude quantum computer (consisting of $n+1$ qubits in total). These operators can be represented as the sum of a linear and antilinear operator, and add an intriguing new set of nonlinear quantum gates to the toolbox of the quantum algorithm designer. Furthermore, a subgroup of these nonlinear evolutions, called the $\mathbb{R}$-Cliffords, can be efficiently classically simulated, by making use of the fact that Clifford operators can simulate non-Clifford (in fact, non-linear) operators. This perspective of using the physical operators that we have to simulate non-physical ones that we do not is what we call bottom-up simulation, and we give some examples of its broader implications.
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