The time evolution operator plays a crucial role in the precise computation of chemical experiments on quantum computers and holds immense promise for advancing the fields of physical and computer sciences, with applications spanning quantum simulation and machine learning. However, the construction of large-scale quantum computers poses significant challenges, prompting the need for innovative and resource-efficient strategies. Traditional methods like phase estimation or variational algorithms come with certain limitations such as the use of classical optimization or complex quantum circuitry. One successful method is the Trotterization technique used for quantum simulation, specifically in atomic structure problems with a gate complexity of approximately O(n^2) for an n-qubit realization. In this work, we have proposed a new encoding method, namely quantum approximate time evolution (QATE) for the quantum implementation of the kinetic energy operator as a diagonal unitary operator considering the first quantization level. The theoretical foundations of our approach are discussed, and experimental results are obtained on an IBM quantum machine. Our proposed method offers gate complexity in sub-quadratic polynomial with qubit size $n$ which is an improvement over previous work. Further, the fidelity improvement for the time evolution of the Gaussian wave packet has also been demonstrated.
Approximate Quantum Error Correction with 1D Log-Depth Circuits
Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院量子信息中心）；Yau Mathematical Sciences Center, Tsinghua University（清华大学丘成桐数学科学中心）
Approximate quantum error correction theory of non-isometric codes
Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS)（上海数学与交叉学科研究院）；Joint Center for Quantum Information and Computer Science, University of Maryland（马里兰大学量子信息与计算机科学联合中心）；Yau Mathematical Sciences Center, Tsinghua University（清华大学丘成桐数学科学中心）
All-optical generation of states for "Encoding a qubit in an oscillator"
离散和连续系统都可以用来编码量子信息。大多数量子计算方案提出在二能级系统中编码量子比特，例如二能级原子或电子自旋。另一些则利用无限维系统，如谐振子。在“Encoding a qubit in an oscillator”[Phys. Rev. A 64 012310（2001）]中，Gottesman、Kitaev和Preskill（GKP）结合了这些方法，提出了一种容错量子计算方案，其中qubit被编码在振荡器的连续位置和动量自由度中。该方案的一个优点是它可以通过使用相对简单的线性光学器件、压缩和零差检测来执行。然而，我们缺乏一个实用的方法来准备初始GKP状态。在这里，我们提出了一个近似的GKP状态的产生，使用叠加的光学相干态（有时称为“薛定谔猫态”），压缩，线性光学器件，和零差检测。
Quantum Encoding of Structured Data with Matrix Product States
Centre for Quantum Information, Simulation and Algorithms, School of Physics, Mathematics and Computing, The University of Western Australia（西澳大利亚大学物理、数学与计算学院量子信息、模拟与算法中心）
Institute of Mathematical Sciences（马哈拉施特拉数学科学研究所）；QCAR Group, The Institute of Mathematical Sciences (IMSc)（量子计算与应用研究组，马哈拉施特拉数学科学研究所）；Pecslab Research（Pecslab 研究）；Homi Bhabha National Institute（霍米·巴巴国家研究所）
Quantum Calculation of Classical Kinetic Equations: A Novel Approach for Numerical Analysis of 6D Boltzmann-Maxwell Equations in Collisionless Plasmas Using Quantum Computing
