Real time evolution for ultracompact Hamiltonian eigenstates on quantum hardware
Katherine Klymko, Carlos Mejuto-Zaera, Stephen J. Cotton, Filip Wudarski, Miroslav Urbanek, Diptarka Hait, Martin Head-Gordon, K. Birgitta Whaley, Jonathan Mous… 展开作者
Katherine Klymko, Carlos Mejuto-Zaera, Stephen J. Cotton, Filip Wudarski, Miroslav Urbanek, Diptarka Hait, Martin Head-Gordon, K. Birgitta Whaley, Jonathan Moussa, Nathan Wiebe, Wibe A. de Jong, Norm M. Tubman
In this work we present a detailed analysis of variational quantum phase estimation (VQPE), a method based on real-time evolution for ground and excited state estimation on near-term hardware. We derive the theoretical ground on which the approach stands, and demonstrate that it provides one of the most compact variational expansions to date for solving strongly correlated Hamiltonians. At the center of VQPE lies a set of equations, with a simple geometrical interpretation, which provides conditions for the time evolution grid in order to decouple eigenstates out of the set of time evolved expansion states, and connects the method to the classical filter diagonalization algorithm. Further, we introduce what we call the unitary formulation of VQPE, in which the number of matrix elements that need to be measured scales linearly with the number of expansion states, and we provide an analysis of the effects of noise which substantially improves previous considerations. The unitary formulation allows for a direct comparison to iterative phase estimation. Our results mark VQPE as both a natural and highly efficient quantum algorithm for ground and excited state calculations of general many-body systems. We demonstrate a hardware implementation of VQPE for the transverse field Ising model. Further, we illustrate its power on a paradigmatic example of strong correlation (Cr2 in the SVP basis set), and show that it is possible to reach chemical accuracy with as few as ~50 timesteps.
A penalty-free quantum algorithm to find energy eigenstates
National University of Singapore（新加坡国立大学）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；Department of Physics, National University of Singapore（新加坡国立大学物理系）
Digital Simulation of Non-Hermitian Knotted Bands on Quantum Hardware
National University of Singapore（新加坡国立大学）；A*STAR Quantum Innovation Centre (Q.InC), Agency for Science, Technology and Research (A*STAR)（科技研究局量子创新中心）；School of Physical and Mathematical Sciences, Nanyang Technological University（南洋理工大学物理与数学科学学院）；Bioinformatics Institute, Agency for Science, Technology and Research (A*STAR)（科技研究局生物信息学研究所）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）
Quantum Spectral Authentication: Entity Authentication and Key Derivation from a Hidden Eigenstate of a Public Unitary Challenge
University of Technology Sydney（悉尼科技大学）；Centre for Quantum Software and Information, University of Technology Sydney（悉尼科技大学量子软件与信息中心）；Data61, CSIRO（CSIRO数据六一分部）；Institute of Computer Science, Polish Academy of Sciences（波兰科学院计算机科学研究所）
Imaginary Time Spectral Transforms for Excited State Preparation
IBM Quantum, IBM Research Europe（IBM量子，IBM欧洲研究院）；University of Southampton（南安普顿大学）；The Hartree Centre, STFC（哈特里中心，STFC）；Yusuf Hamied Department of Chemistry, University of Cambridge（剑桥大学尤素夫·哈米德化学系）；Clarendon Laboratory, University of Oxford（牛津大学克拉伦登实验室）；SUPA, School of Physics and Astronomy, University of Edinburgh（爱丁堡大学物理与天文学学院，SUPA）
Quantum Computing and Error Mitigation with Deep Learning for Frenkel Excitons
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；IBM Research Almaden Lab（IBM阿尔马登研究中心）；Materials Research Laboratory, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校材料研究实验室）；National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校国家超级计算应用中心）
Optimizing Unitary Coupled Cluster Wave Functions on Quantum Hardware: Error Bound and Resource-Efficient Optimizer
Eviden Quantum Lab（Eviden量子实验室）；Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；École Polytechnique, I.P. Paris（巴黎理工学院高等师范学校）；MajuLab, CNRS–UCA-SU-NUS-NTU International Joint Research Laboratory（MajuLab，CNRS-南法大学-苏黎世联邦理工学院-新加坡国立大学-南洋理工大学国际联合研究实验室）
迄今为止，量子硬件上的小分子量子化学计算仅在通用门量子计算机上得到证明，而不是量子退火机。后一种设备仅限于找到伊辛哈密顿量的最低本征态，而电子哈密顿量不能映射到伊辛形式，而伊辛哈密顿量不会随着系统的大小呈指数增长[J. Phys. Chem. B 122，3384（2018）]。在这里，我们提出了一种新的混合离散-连续优化算法，该算法使用量子退火器来求解问题的离散部分，从而找到量子比特耦合簇（QCC）方法的最低本征态。QCC方法是一种在量子比特空间中构造电子波函数的潜在精确方法。因此，我们的方法允许使用量子退火系统地改进量子化学计算。我们通过计算LiH、H $_2$ O和C $_6$ H $_6$分子的QCC基态电子态来说明我们的方法的能力。C $_6$ H $_6$计算涉及36个量子比特，是迄今为止在量子退火机（D-Wave 2000 Q系统）上进行的最大量子化学计算。我们的发现为量子退火机在高通量材料发现中的应用开辟了新的视角。
Applications of the Quantum Phase Difference Estimation Algorithm to the Excitation Energies in Spin Systems on a NISQ Device
TCG Centres for Research and Education in Science and Technology（TCG科学技术研究中心与教育学院）；Indian Institute of Technology Tirupati（蒂鲁帕提印度理工学院）；Keio University（庆应义塾大学）；Tokyo Institute of Technology（东京工业大学）
Hamiltonian-reconstruction distance as a success metric for the Variational Quantum Eigensolver
School of Applied and Engineering Physics, Cornell University（康奈尔大学应用工程物理学院）；Laboratory of Atomic and Solid State Physics, Cornell University（康奈尔大学原子与固态物理实验室）；Kavli Institute at Cornell for Nanoscale Science, Cornell University（康奈尔大学卡弗里纳米科学研究所）
