Posted Content•
Accessing ground state and excited states energies in many-body system after symmetry restoration using quantum computers
TL;DR: In this article, the authors explore the possibility to perform symmetry restoration with the variation after projection technique on a quantum computer followed by additional post-processing and develop configuration interaction techniques based on many-body trial states pre-optimized on the quantum computer.
Abstract: We explore the possibility to perform symmetry restoration with the variation after projection technique on a quantum computer followed by additional post-processing. The final goal is to develop configuration interaction techniques based on many-body trial states pre-optimized on a quantum computer. We show how the projection method used for symmetry restoration can prepare optimized states that could then be employed as initial states for quantum or hybrid quantum-classical algorithms. We use the quantum phase estimation and quantum Krylov approaches for the post-processing. The latter method combined with the quantum variation after projection (Q-VAP) leads to very fast convergence towards the ground-state energy. The possibility to access excited states energies is also discussed. Illustrations of the different techniques are made using the pairing hamiltonian.
References
More filters
TL;DR: In this article, the essential aspects of coupled-cluster theory are explained and illustrated with informative numerical results, showing that the theory offers the most accurate results among the practical ab initio electronic-structure theories applicable to moderate-sized molecules.
Abstract: Today, coupled-cluster theory offers the most accurate results among the practical ab initio electronic-structure theories applicable to moderate-sized molecules. Though it was originally proposed for problems in physics, it has seen its greatest development in chemistry, enabling an extensive range of applications to molecular structure, excited states, properties, and all kinds of spectroscopy. In this review, the essential aspects of the theory are explained and illustrated with informative numerical results.
2,667 citations
Book•
31 Aug 2009TL;DR: In this paper, the authors present a simple, clear, unified approach to describe the mathematical tools and diagrammatic techniques employed in many-body perturbation theory and Coupled-Cluster theories.
Abstract: Written by two leading experts in the field, this book explores the 'many-body' methods that have become the dominant approach in determining molecular structure, properties and interactions. With a tight focus on the highly popular Many-Body Perturbation Theory (MBPT) and Coupled-Cluster theories (CC), the authors present a simple, clear, unified approach to describe the mathematical tools and diagrammatic techniques employed. Using this book the reader will be able to understand, derive and confidently implement relevant algebraic equations for current and even new multi-reference CC methods. Hundreds of diagrams throughout the book enhance reader understanding through visualization of computational procedures and extensive referencing allows further exploration of this evolving area. With an extensive bibliography and detailed index, this book will be suitable for graduates and researchers within quantum chemistry, chemical physics and atomic, molecular and solid-state physics.
609 citations
TL;DR: In this paper, the authors apply the self-consistent Green's functions to nuclei and nuclear matter to determine one and two-nucleon removal probabilities in nuclei since the corresponding amplitudes are directly related to the imaginary parts of the single particle and twoparticle propagators.
409 citations
TL;DR: The In-Medium Similarity Renormalization Group (IM-SRG) as mentioned in this paper employs a continuous unitary transformation of the manybody Hamiltonian to decouple the ground state from all excitations, thereby solving the many-body problem.
230 citations
TL;DR: In this article, the authors introduce the quantum imaginary time evolution and quantum Lanczos algorithms, which are analogues of classical algorithms for finding ground and excited states, and demonstrate the potential of these algorithms via an implementation using exact classical emulation as well as prototype circuits on the Rigetti quantum virtual machine and Aspen-1 quantum processing unit.
Abstract: The accurate computation of Hamiltonian ground, excited and thermal states on quantum computers stands to impact many problems in the physical and computer sciences, from quantum simulation to machine learning. Given the challenges posed in constructing large-scale quantum computers, these tasks should be carried out in a resource-efficient way. In this regard, existing techniques based on phase estimation or variational algorithms display potential disadvantages; phase estimation requires deep circuits with ancillae, that are hard to execute reliably without error correction, while variational algorithms, while flexible with respect to circuit depth, entail additional high-dimensional classical optimization. Here, we introduce the quantum imaginary time evolution and quantum Lanczos algorithms, which are analogues of classical algorithms for finding ground and excited states. Compared with their classical counterparts, they require exponentially less space and time per iteration, and can be implemented without deep circuits and ancillae, or high-dimensional optimization. We furthermore discuss quantum imaginary time evolution as a subroutine to generate Gibbs averages through an analogue of minimally entangled typical thermal states. Finally, we demonstrate the potential of these algorithms via an implementation using exact classical emulation as well as through prototype circuits on the Rigetti quantum virtual machine and Aspen-1 quantum processing unit. The quantum imaginary time evolution and Lanczos algorithms offer a resource-efficient way to compute ground or excited states of target Hamiltonians on quantum computers. This offers promise for quantum simulation on near-term noisy devices.
158 citations