The Quantum Approximate Optimization Algorithm (QAOA) represents a significant opportunity for practical quantum computing applications, particularly in the era before error correction is fully realized. This algorithm is especially relevant for addressing constraint satisfaction problems (CSPs), which are critical in various fields such as supply chain management, energy distribution, and financial modeling. In our study, we conduct a numerical comparison of three different strategies for incorporating linear constraints into QAOA: transforming them into an unconstrained format, introducing penalty dephasing, and utilizing the quantum Zeno effect. We assess the efficiency and effectiveness of these methods using the knapsack problem as a case study. Our findings provide insights into the potential applicability of different encoding methods for various use cases.
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-valid-state HOBO encoding for constrained combinatorial optimization on NISQ devices
Tokyo University of Agriculture and Technology（东京农工大学）；The Institute of Medical Science, The University of Tokyo（东京大学医学科学研究所）；The University of Tokyo（东京大学）
Thermodynamic significance of QUBO encoding on quantum annealers
University of Massachusetts, Boston（马萨诸塞大学波士顿分校）；University of Maryland, Baltimore County（马里兰大学巴尔的摩县分校）；Quantum Science Institute, University of Maryland, Baltimore County（马里兰大学巴尔的摩县分校量子科学研究所）；Universität Tübingen（蒂宾根大学）；Forschungszentrum Jülich（于利希研究中心）；Polish Academy of Sciences（波兰科学院）
Fully quantum algorithmic framework for partial differential equation-constrained optimization
Toyota Central R&D Labs., Inc.（丰田中央研究所）；Quantum Computing Center, Keio University（庆应义塾大学量子计算中心）；Mitsubishi UFJ Financial Group, Inc.（三菱UFJ金融集团）；MUFG Bank, Ltd.（三菱UFJ银行）；Graduate School of Science and Technology, Keio University（庆应义塾大学理工学研究科）；Advanced Material Engineering Division, Toyota Motor Corporation（丰田汽车公司先进材料工程部）；Department of Applied Physics and Physico-Informatics, Keio University（庆应义塾大学应用物理与物理信息学系）
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）
Quantum data encoding as a distinct abstraction layer in the design of quantum circuits
IBM Quantum, IBM Research（IBM量子，IBM研究院）；Dipartimento di Fisica, Politecnico di Milano（米兰理工大学物理系）；Istituto di Fotonica e Nanotecnologie, Consiglio Nazionale delle Ricerche（国家研究委员会光子和纳米技术研究所）
