We present explicit expressions for the central piece of a variational method developed by Shi et al. which extends variational wave functions that are efficiently computable on classical computers beyond mean-field to generalized Gaussian states [1]. In particular, we derive iterative analytical expressions for the evaluation of expectation values of products of fermionic creation and annihilation operators in a Grassmann variable-free representation. Using this result we find a closed expression for the energy functional and its gradient of a general fermionic quantum many-body Hamiltonian. We present a simple gradient-descent-based algorithm that can be used as an optimization subroutine in combination with imaginary time evolution, which by construction guarantees a monotonic decrease of the energy in each iteration step. Due to the simplicity of the quantum circuit implementing the variational state Ansatz, the results of the algorithms discussed here and in [1] could serve as an improved, beyond mean-field initial state in quantum computation.
[1] Tao Shi, Eugene Demler, and J. Ignacio Cirac. Variational study of fermionic and bosonic systems with non-gaussian states: Theory and applications. Annals of Physics, 390: 245-302, 2018.

The authors introduce a class of quantum states for variational studies that exhibits entanglement while still admitting efficient computation of expectation values.

We systematically investigate the ground-state properties of self-bound droplets of quasi-two-dimensional binary Bose gases using Gaussian state theory, including quantum phases, radial size, energy, density profiles, and atom number distribution. We map out the phase diagram and determine all phase boundaries via both numerical and nearly analytical methods. We also find a virial relation connecting various contributions to total energy. In particular, we find two easily accessible signatures f...

The authors develop a variational non-Gaussian diagonalization method as an solver for strongly correlated electron-electron and electron-phonon systems, and explore the phase diagram of the two-dimensional Hubbard-Holstein model.

#1Yuqi Wang(CAS: Chinese Academy of Sciences)H-Index: 1

#2Longfei Guo(CAS: Chinese Academy of Sciences)H-Index: 1

Last. Tao Shi(CAS: Chinese Academy of Sciences)H-Index: 25

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The authors propose a Gaussian-based theory to study dipolar droplets that reveals the onset of liquid-gas phase transition as well as showing the emergence of a self-bound gas-phase dominated by the squeezed condensate.

We present a systematic geometric framework to study closed quantum systems based on suitably chosen variational families. For the purpose of (A) real time evolution, (B) excitation spectra, (C) spectral functions and (D) imaginary time evolution, we show how the geometric approach highlights the necessity to distinguish between two classes of manifolds: Kahler and non-Kahler. Traditional variational methods typically require the variational family to be a Kahler manifold, where multiplication b...

#1Ruijin Liu(RUC: Renmin University of China)H-Index: 1

#2Yue-Ran Shi(RUC: Renmin University of China)H-Index: 2

Last. Wei Zhang(RUC: Renmin University of China)H-Index: 17

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We study the Fermi polaron problem of one mobile spin-up impurity immersed atop the bath consisting of spin-down fermions in one- and two-dimensional square lattices. We solve this problem by applying a variational approach with non-Gaussian states after separating the impurity and the background by the Lee-Low-Pines transformation. The ground state for a fixed total momentum can be obtained via imaginary time evolution for the variational parameters. For the one-dimensional case, the variationa...

Last. Brendan Gimby(UM: University of Michigan)H-Index: 2

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Quantum simulation of chemistry and materials is predicted to be an important application for both near-term and fault-tolerant quantum devices. However, at present, developing and studying algorithms for these problems can be difficult due to the prohibitive amount of domain knowledge required in both the area of chemistry and quantum algorithms. To help bridge this gap and open the field to more researchers, we have developed the OpenFermion software package (www.openfermion.org). OpenFermion ...

As the search continues for useful applications of noisy intermediate scale quantum devices, variational simulations of fermionic systems remain one of the most promising directions. Here, we perform a series of quantum simulations of chemistry which involve twice the number of qubits and more than ten times the number of gates as the largest prior experiments. We model the binding energy of {\rm H}_6 {\rm H}_8 {\rm H}_{10}and {\rm H}_{12}chains as well as the isomerization of diazen...

We consider dynamics of a Rydberg impurity in a cloud of ultracold bosonic atoms in which the Rydberg electron can undergo spin-changing collisions with surrounding atoms. This system realizes a new type of the quantum impurity problem that compounds essential features of the Kondo model, the Bose polaron, and the central spin model. To capture the interplay of the Rydberg-electron spin dynamics and the orbital motion of atoms, we employ a new variational method that combines an impurity-decoupl...

#1Yuto Ashida(UTokyo: University of Tokyo)H-Index: 20

#2Tao Shi(CAS: Chinese Academy of Sciences)H-Index: 25

Last. Eugene Demler(MPG: Max Planck Society)H-Index: 101

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We develop an efficient variational approach to studying dynamics of a localized quantum spin coupled to a bath of mobile spinful bosons. We use parity symmetry to decouple the impurity spin from the environment via a canonical transformation and reduce the problem to a model of the interacting bosonic bath. We describe coherent time evolution of the latter using bosonic Gaussian states as a variational ansatz. We provide full analytical expressions for equations describing variational time evol...

The most efficient known quantum circuits for preparing unitary coupled cluster states and applying Trotter steps of the arbitrary basis electronic structure Hamiltonian involve interleaved sequences of fermionic Gaussian circuits and Ising interaction type circuits. These circuits arise from factorizing the two-body operators generating those unitaries as a sum of squared one-body operators that are simulated using product formulas. We introduce a numerical algorithm for performing this factori...