Related papers: Classical mechanics technique for quantum linear r…
An iterative algorithm is presented for solving the RPA equations of linear response. The method optimally computes the energy-weighted moments of the strength function, allowing one to match the computational effort to the intrinsic…
The method of quantum Lanczos recursion is extended to solve for multiple excitations on the quantum computer. While quantum Lanczos recursion is in principle capable of obtaining excitations, the extension to a block Lanczos routine can…
Random Phase Approximation (RPA) is the theory most commonly used to describe the excitations of many-body systems. In this article, the secular equations of the theory are obtained by using three different approaches: the equation of…
This paper describes a method to do ab initio molecular dynamics in electronically excited systems within the random phase approximation (RPA). Using a dynamical variational treatment of the RPA frequency, which corresponds to the…
A state-preserving quantum counting algorithm is used to obtain coefficients of a Lanczos recursion from a single ground state wavefunction on the quantum computer. This is used to compute the continued fraction representation of an…
The random-phase approximation (RPA) as an approach for computing the electronic correlation energy is reviewed. After a brief account of its basic concept and historical development, the paper is devoted to the theoretical formulations of…
This work introduces a method for determining the energy spectrum of lattice quantum chromodynamics (LQCD) by applying the Lanczos algorithm to the transfer matrix and using a bootstrap generalization of the Cullum-Willoughby method to…
Extracting molecular properties from a wave function can be done through the linear response (LR) formalism or, equivalently, the equation of motion (EOM) formalism. For a simple model system, He in a 6-31G basis, it is here shown that…
We simulate the excited states of the Lipkin model using the recently proposed Quantum Equation of Motion (qEOM) method. The qEOM generalizes the EOM on classical computers and gives access to collective excitations based on quasi-boson…
In statistical mechanics, it is well known that finite-state classical lattice models can be recast as quantum models, with distinct classical configurations identified with orthogonal basis states. This mapping makes classical statistical…
The quantum-classical correspondence between local minima on the classical energy landscape and excited eigenstates in the energy spectrum is studied within the context of many-body quantum spin systems. In mean-field approximations of a…
In the past decade quantum algorithms have been found which outperform the best classical solutions known for certain classical problems as well as the best classical methods known for simulation of certain quantum systems. This suggests…
We review the Random Batch Methods (RBM) for interacting particle systems consisting of $N$-particles, with $N$ being large. The computational cost of such systems is of $O(N^2)$, which is prohibitively expensive. The RBM methods use small…
Ground state preparation is a central application of quantum algorithms for electronic structure. We introduce the classical reservoir approach, a low cost variational ansatz tailored to near-term hardware, requiring only nearest-neighbor…
We present a real-space method for computing the random phase approximation (RPA) correlation energy within Kohn-Sham density functional theory, leveraging the low-rank nature of the frequency-dependent density response operator. In…
Variational algorithms have particular relevance for near-term quantum computers but require non-trivial parameter optimisations. Here we propose Analytic Descent: Given that the energy landscape must have a certain simple form in the local…
The characterization of quantum critical phenomena is pivotal for the understanding and harnessing of quantum many-body physics. However, their complexity makes the inference of such fundamental processes difficult. Thus, efficient and…
A probabilistic interpretation of one-particle relativistic quantum mechanics is proposed. Quantum Action Principle formulated earlier is used for to make the dynamics of the Minkowsky time variable of a particle to be classical. After…
Response functions are key observables for probing the structure and dynamics of many-body systems. We introduce and demonstrate a quantum-classical framework for computing response functions of general many-fermion systems that also…
Physical learning machines, be they classical or quantum, are necessarily dissipative systems. The rate of energy dissipation decreases as the learning error rate decreases linking thermodynamic efficiency and learning efficiency. In the…