Related papers: Efficient impurity-bath trial states from superpos…
The coherent superposition of non-orthogonal fermionic Gaussian states has been shown to be an efficient approximation to the ground states of quantum impurity problems [Bravyi and Gosset,Comm. Math. Phys.,356 451 (2017)]. We present a…
A new efficient numerical algorithm for interacting fermion systems is proposed and examined in detail. The ground state is expressed approximately by a linear combination of numerically chosen basis states in a truncated Hilbert space. Two…
We give a quasi-polynomial time classical algorithm for estimating the ground state energy and for computing low energy states of quantum impurity models. Such models describe a bath of free fermions coupled to a small interacting subsystem…
The study of ground-state properties of the Fermi-Hubbard model is a long-lasting task in the research of strongly correlated systems. Owing to the exponentially growing complexity of the system, a quantitative analysis usually demands high…
We propose a general framework for finding the ground state of many-body fermionic systems by using feed-forward neural networks. The anticommutation relation for fermions is usually implemented to a variational wave function by the Slater…
This paper introduces an innovative approach for representing Gaussian fermionic states, pivotal in quantum spin systems and fermionic models, within a range of alternative quantum bases. We focus on transitioning these states from the…
A variational upper bound on the ground state energy $E_{\rm gs}$ of a quantum system, $E_{\rm gs} \leqslant \langle \Psi|H| \Psi \rangle$, is well-known (here $H$ is the Hamiltonian of the system and $\Psi$ is an arbitrary wave function).…
We discuss classical algorithms for approximating the largest eigenvalue of quantum spin and fermionic Hamiltonians based on semidefinite programming relaxation methods. First, we consider traceless $2$-local Hamiltonians $H$ describing a…
Out-of-equilibrium fermionic quantum impurity models (QIM), describing a small interacting system coupled to a continuous fermionic bath, play an important role in condensed matter physics. Solving such models is a computationally demanding…
We consider Gaussian states of fermionic systems and study the action of the partial transposition on the density matrix. It is shown that, with a suitable choice of basis, these states are transformed into a linear combination of two…
By means of a trial wave function, the multi-D$_1$ ansatz, extensive variational calculations with more than ten thousand parameters have been carried out to study quantum phase transitions in the ground states of a two-impurity system…
We provide a detailed formulation of the recently proposed variational approach [Y. Ashida et al., Phys. Rev. Lett. 121, 026805 (2018)] to study ground-state properties and out-of-equilibrium dynamics for generic quantum spin-impurity…
Variational quantum circuits characterise the state of a quantum system through the use of parameters that are optimised using classical optimisation procedures that typically rely on gradient information. The circuit-execution complexity…
We present a new variational method for investigating the ground state and out of equilibrium dynamics of quantum many-body bosonic and fermionic systems. Our approach is based on constructing variational wavefunctions which extend Gaussian…
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…
We propose a qubit efficient scheme to study ground state properties of quantum many-body systems on near-term noisy intermediate scale quantum computers. One can obtain a tensor network representation of the ground state using a number of…
Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state energy in a systematic fashion, scales…
Simulating strongly correlated fermionic systems is notoriously hard on classical computers. An alternative approach, as proposed by Feynman, is to use a quantum computer. Here, we discuss quantum simulation of strongly correlated fermionic…
Computing Gaussian ground states via variational optimization is challenging because the covariance matrices must satisfy the uncertainty principle, rendering constrained or Riemannian optimization costly, delicate, and thus difficult to…
Variational quantum algorithms aim at harnessing the power of noisy intermediate-scale quantum computers, by using a classical optimizer to train a parameterized quantum circuit to solve tractable quantum problems. The variational quantum…