Motivated by recent progress of quantum technologies, we study a discretized quantum adiabatic process for a one-dimensional free fermion system described by a variational wave function, i.e., a parametrized quantum circuit. The wave function is composed of $M$ layers of two elementary sets of time-evolution operators, each set being decomposed into commutable local operators. The evolution time of each time-evolution operator is treated as a variational parameter so as to minimize the expectation value of the energy. We show that the exact ground state is reached by applying the layers of time-evolution operators as many as a quarter of the system size. This is the minimum number $M_B$ of layers set by the limit of speed, i.e., the Lieb-Robinson bound, for propagating quantum entanglement via the local time-evolution operators. Quantities such as the energy $E$ and the entanglement entropy $S$ of the optimized variational wave function with $M < M_B$ are independent of the system size $L$ but fall into some universal functions of $M$. The development of the entanglement in these ansatz is further manifested in the progressive propagation of single-particle orbitals in the variational wave function. We also find that the optimized variational parameters show a systematic structure that provides the optimum scheduling function in the quantum adiabatic process. We also investigate the imaginary-time evolution of this variational wave function, where the causality relation is absent due to the non-unitarity of the imaginary-time evolution operators, thus the norm of the wave function being no longer conserved. We find that the convergence to the exact ground state is exponentially fast, despite that the system is at the critical point, suggesting that implementation of the non-unitary imaginary-time evolution in a quantum circuit is highly promising to further shallow the circuit depth.
A probabilistic imaginary-time evolution quantum algorithm for advection-diffusion equation: Explicit gate-level implementation and comparisons to quantum linear system algorithms
Adiabatic Approximation in the Density Matrix Approach: Non-Degenerate Systems
利用密度矩阵方法研究了耦合到弱耗散介质中的量子系统的绝热极限。量子模型的能谱被假定为非简并的。在没有耗散的情况下，M. V. Berry以前得到的周期哈密顿算子的几何相位在本方法中被恢复。我们确定的必要条件所满足的系数的线性展开的非酉部分的Liouvillian为了虚相位所获得的元素的密度矩阵，由于耗散效应，是几何的。所得结果与模型无关。我们将它们应用到热力学平衡下自旋1/2耦合到库的模型中。
University of Waterloo（滑铁卢大学）；Perimeter Institute for Theoretical Physics（理论物理珀金斯研究所）；Institute for Quantum Computing, University of Waterloo（滑铁卢大学量子计算研究所）
Imaginary Hamiltonian variational ansatz for combinatorial optimization problems
Peking University（北京大学）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）；Center for High Energy Physics, Peking University（北京大学高能物理中心）；Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS), RIKEN（理化学研究所跨学科理论与数学科学项目（iTHEMS））；Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器）；Computation-Based Science and Technology Research Center, The Cyprus Institute（塞浦路斯研究所计算科学与技术研究中心）；Institut für Physik, Humboldt-Universität zu Berlin（柏林洪堡大学物理研究所）
Warm Starts, Cold States: Exploiting Adiabaticity for Variational Ground-States
Institute of Physics, Ecole Polytechnique F\' e d\' e rale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland；Centre for Quantum Science；Engineering, Ecole Polytechnique F\' e d\' e rale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland；Barcelona Supercomputing Center, Plaça Eusebi G\"uell, 1-3, 08034 Barcelona, Spain；Institute for Theoretical Physics, ETH Zürich, 8093, Zürich, Switzerland
Approximate Reduced Lindblad Dynamics via Algebraic and Adiabatic Methods
University of Padova（帕多瓦大学）；Laboratoire de Physique de l’Ecole Normale Supérieure, Mines Paris-PSL, Inria, ENS-PSL, Université PSL, CNRS, Sorbonne Université（巴黎高等师范学校物理实验室，巴黎矿业综合理工学院-巴黎文理研究大学，法国国家信息与自动化研究所，巴黎文理研究大学高等师范学校-巴黎文理研究大学，法国国家科学研究中心，索邦大学）；Ghent University（根特大学）；Dartmouth College（达特茅斯学院）；Padua Quantum Technologies Research Center, University of Padova（帕多瓦大学帕多瓦量子技术研究中心）
Gate Based Implementation of the Laplacian with BRGC Code for Universal Quantum Computers
我们研究了基于门的实现的二进制反射格雷码（BRGC）和二进制码的酉时间演化算子由于拉普拉斯离散的格与周期性边界条件。我们发现，由此产生的Trotter错误是独立的系统大小为一个固定的晶格间距通过贝克-坎贝尔-豪斯多夫公式。然后，我们提出了我们的算法来构建BRGC量子电路。对于绝热演化时间$t$与此电路，和谱范数误差$ε$，我们发现电路成本（门的数量）和所需的深度是$\mc{O}(t^2 n A D /ε)$与$n-3$辅助量子位的系统与$2^n$格点每维$D$和粒子数$A$ ;改进二进制位置编码，需要指数数量的$n$ -本地运营商。此外，在$[T,V]$限制$Δt$的合理假设下，其中$T$是动能，$V$是非平凡的势，拉普拉斯算子的QFT（量子傅里叶变换）实现的成本缩放为具有深度$\mc{O}\left(n\right)$的$\mc{O}\left(n^2\right)$，而BRGC缩放为$\mc{O}\left(n\right)$，从而为BRGC实现提供优势。
