Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2103.15445 · Physical review. B./Physical review. B

Gutzwiller wave function on a digital quantum computer

Bruno Murta, Joaquín Fernández-Rossier

Published Jun 21, 2021• 14 citations
arXivHTMLPDF

Abstract

The determination of the ground state of quantum many-body systems via digital quantum computers rests upon the initialization of a sufficiently educated guess. This requirement becomes more stringent the greater the system. Preparing physically motivated Ans\"atze on quantum hardware is therefore important to achieve a quantum advantage in the simulation of correlated electrons. In this spirit, we introduce the Gutzwiller wave function (GWF) within the context of the digital quantum simulation of the Fermi-Hubbard model. We present a quantum routine to initialize the GWF that comprises two parts. In the first, the noninteracting state associated with the $U=0$ limit of the model is prepared. In the second, the nonunitary Gutzwiller operator that selectively removes states with doubly occupied sites from the wave function is performed by adding to every lattice site an ancilla qubit, the measurement of which in the $|0\ensuremath{\rangle}$ state confirms the operator was applied. Due to its nondeterministic nature, we estimate the success rate of the algorithm in generating the GWF as a function of the lattice size and the interaction strength $U/t$. The scaling of the quantum circuit metrics and its integration in general quantum simulation algorithms are also discussed.

DOI
10.1103/physrevb.103.l241113

Related papers

Preparing the Gutzwiller wave function for attractive SU(3) fermions on a quantum computer

Han Xu, Kazuhiro Seki, Seiji Yunoki

We implement the Gutzwiller wave function for attractive SU(3) fermion systems on a quantum computer using a quantum-classical hybrid scheme based on the discrete Hubbard-Stratonovich transformation. In this approach, the nonunitary Gutzwiller operator is decomposed into a linear combination of unitaries constructed from two-qubit fermionic Givens-rotation gates, whose rotation angles are dictated by the auxiliary fields. We develop and reformulate two complementary methods to perform the sum over these auxiliary fields. In the first method, the Gutzwiller wave function is probabilistically prepared on the register qubits by projectively postselecting the desired state via measurements of ancilla qubits. We analyze the success rate both analytically and numerically as a function of the Gutzwiller variational parameter g for the Fermi-sea and BCS-like trial states at half filling. The success rate is found to decay exponentially for small | g | , but remains finite in the | g | → ∞ limit, with increasing | g | . In the second method, we employ importance sampling to address the Gutzwiller variational problem, where the central objective is to estimate the expectation values of observables. We demonstrate the proposed scheme by calculating the energy and triple occupancy of the attractive SU(3) Hubbard model in the framework of digital quantum simulation. Moreover, we present experimental results obtained on a trapped-ion quantum computer for the two-site attractive SU(3) Hubbard model, showing good agreement with exact values within statistical errors.

arXiv:2504.18149•Physical Review Research•Jul 28, 2025•0 citations

From Heisenberg to Hubbard: An initial state for the shallow quantum simulation of correlated electrons

Bruno Murta, Joaquín Fernández-Rossier

The widespread use of the noninteracting ground state as the initial state for the digital quantum simulation of the Fermi-Hubbard model is largely due to the scarcity of alternative easy-to-prepare approximations to the exact ground state in the literature. Exploiting the fact that the spin-$\frac{1}{2}$ Heisenberg model is the effective low-energy theory of the Fermi-Hubbard model at half-filling in the strongly interacting limit, here we propose a three-step deterministic quantum routine to prepare an educated guess of the ground state of the Fermi-Hubbard model through a shallow circuit suitable for near-term quantum hardware. First, the ground state of the Heisenberg model is initialized via a hybrid variational method using an ansatz that explores only the correct symmetry subspace. Second, a general method is devised to convert a multi-spin-$\frac{1}{2}$ wave function into its fermionic version. Third, taking inspiration from the Baeriswyl ansatz, a constant-depth single-parameter layer that adds doublon-holon pairs is applied to this fermionic state. Numerical simulations on chains and ladders with up to 12 sites confirm the improvement over the noninteracting ground state of the overlap with the exact ground state for the intermediate values of the interaction strength at which quantum simulation is found to be most relevant. More broadly, the general scheme to convert a multi-spin-$\frac{1}{2}$ state into a half-filled fermionic state may bridge the gap between quantum spin models and lattice models of correlated fermions in the realm of digital quantum simulation.

arXiv:2310.16775•Physical review. B./Physical review. B•Jan 16, 2024•4 citations

Gutzwiller wave function on a quantum computer using a discrete Hubbard-Stratonovich transformation

Kazuhiro Seki, Yuichi Otsuka, Seiji Yunoki

We propose a quantum-classical hybrid scheme for implementing the nonunitary Gutzwiller factor using a discrete Hubbard-Stratonovich transformation, which allows us to express the Gutzwiller factor as a linear combination of unitary operators involving only single-qubit rotations, at the cost of the sum over the auxiliary fields. To perform the sum over the auxiliary fields, we introduce two approaches that have complementary features. The first approach employs a linear-combination-of-unitaries circuit, which enables one to probabilistically prepare the Gutzwiller wave function on a quantum computer, while the second approach uses importance sampling to estimate observables stochastically, similar to a quantum Monte Carlo method in classical computation. The proposed scheme is demonstrated with numerical simulations for the half-filled Fermi-Hubbard model. Furthermore, we perform quantum simulations using a real quantum device, demonstrating that the proposed scheme can reproduce the exact ground-state energy of the two-site Fermi-Hubbard model within error bars.

arXiv:2201.11381•Physical review. B./Physical review. B•Apr 13, 2022•14 citations

An efficient random-sampling method for calculating double occupancy of Gutzwiller wave function in single-band 1D and 2D lattices

Feng Zhang, Zhuo Ye, Yongxin Yao +2 more

We report a random-sampling method for computing the expectation value of physical quantities based on the Gutzwiler variational wave function. As the first application, we calculated the double occupancy, which is a critical quantity for understanding the correlation effects in many-body systems, for single-band 1D and 2D lattices. We demonstrated that the random-sampling scheme is more efficient than an existing Metropolis Monte-Carlo algorithm. For the 1D Hubbard model with only nearest-neighbour hopping, our results are almost identical to the exact analytic solution. We have also studied systems to which analytic solutions are not available, including the 1D lattices with next-nearest-neighbour hopping and 2D lattices. In addition, constraints on real-space configurations can be easily implemented in the current scheme to further improve the Gutzwiller wave function. As an example, we calculated the double occupancy for 1D Hubbard model by applying the constraint that all double-occupied sites are paired with an empty site. With enhanced correlation between double-occupied and empty sites, the constraint results in much improved ground-state energy for 1D Hubbard model with strong on-site repulsion.

Molecular Physics•Aug 28, 2020•3 citations

Correlated-basis-function method for fermions on a lattice: The one-dimensional Hubbard model

X. Q. Wang, Stefano Fantoni, Erio Tosatti +2 more

We introduce a new lattice version of the correlated-basis-function approach for the study of strongly interacting electrons. As a first application we have chosen the one-dimensional Hubbard model. For this system, we have implemented different types of correlations: namely, (a) Gutzwiller; (b) Jastrow; (c) nearest-neighbor spin-spin; (d) excitonic (e-d); and (f) pairing (BCS). The resulting energies, momentum distribution, and other quantities are compared with exact results (when available) and are discussed, both from the methodological and physical point of view. The most important correlations that are needed to obtain good ground-state energies are found to be Gutzwiller (reduced double occupancy) plus e-d correlations (between empty and doubly occupied sites), in agreement with other studies.

Physical review. B, Condensed matter•Jun 1, 1990•16 citations

Programmable digital quantum simulation of 2D Fermi-Hubbard dynamics using 72 superconducting qubits

Faisal Alam, Jan Lukas Bosse, Ieva Čepaitė +41 more

Simulating the time-dynamics of quantum many-body systems was the original use of quantum computers proposed by Feynman, motivated by the critical role of quantum interactions between electrons in the properties of materials and molecules. Accurately simulating such systems remains one of the most promising applications of general-purpose digital quantum computers, in which all the parameters of the model can be programmed and any desired physical quantity output. However, performing such simulations on today's quantum computers at a scale beyond the reach of classical methods requires advances in the efficiency of simulation algorithms and error mitigation techniques. Here we demonstrate programmable digital quantum simulation of the dynamics of the 2D Fermi-Hubbard model -- one of the best-known simplified models of electrons in crystalline solids -- at a scale beyond exact classical state-vector simulation. We implement simulations of this model on lattice sizes up to ${6\times 6}$ using 72 qubits on Google's Willow quantum processor, across a range of physical parameters, including different on-site electron-electron interaction strengths and magnetic flux values, and study phenomena including formation of magnetic polarons (charge carriers surrounded by local magnetic polarisation), dynamical symmetry-breaking in stripe-ordered states, attraction of charge carriers on an entangled background state known as a valence bond solid, and the approach to equilibrium through thermalisation. We validate our results against exact calculations in parameter regimes where these are feasible, and compare them to approximate classical simulations performed using tensor network and operator propagation methods. Our results demonstrate that meaningful programmable digital quantum simulation of many-body interacting electron models is now feasible on state-of-the-art quantum hardware.

arXiv:2510.26845•Oct 30, 2025•0 citations
The determination of the ground state of quantum many-body systems via digital quantum computers rests upon the initialization of a sufficiently educated guess. This requirement becomes more stringent the greater the system. Preparing physically motivated Ans"atze on quantum hardware is therefore important to achieve a quantum advantage in the simulation of correlated electrons. In this spirit, we introduce the Gutzwiller wave function (GWF) within the context of the digital quantum simulation of the Fermi-Hubbard model. We present a quantum routine to initialize the GWF that comprises two parts. In the first, the noninteracting state associated with the U=0U=0U=0 limit of the model is prepared. In the second, the nonunitary Gutzwiller operator that selectively removes states with doubly occupied sites from the wave function is performed by adding to every lattice site an ancilla qubit, the measurement of which in the ∣0\ensuremath⟩|0\ensuremath{\rangle}∣0\ensuremath⟩ state confirms the operator was applied. Due to its nondeterministic nature, we estimate the success rate of the algorithm in generating the GWF as a function of the lattice size and the interaction strength U/tU/tU/t. The scaling of the quantum circuit metrics and its integration in general quantum simulation algorithms are also discussed.
We implement the Gutzwiller wave function for attractive SU(3) fermion systems on a quantum computer using a quantum-classical hybrid scheme based on the discrete Hubbard-Stratonovich transformation. In this approach, the nonunitary Gutzwiller operator is decomposed into a linear combination of unitaries constructed from two-qubit fermionic Givens-rotation gates, whose rotation angles are dictated by the auxiliary fields. We develop and reformulate two complementary methods to perform the sum over these auxiliary fields. In the first method, the Gutzwiller wave function is probabilistically prepared on the register qubits by projectively postselecting the desired state via measurements of ancilla qubits. We analyze the success rate both analytically and numerically as a function of the Gutzwiller variational parameter g for the Fermi-sea and BCS-like trial states at half filling. The success rate is found to decay exponentially for small | g | , but remains finite in the | g | → ∞ limit, with increasing | g | . In the second method, we employ importance sampling to address the Gutzwiller variational problem, where the central objective is to estimate the expectation values of observables. We demonstrate the proposed scheme by calculating the energy and triple occupancy of the attractive SU(3) Hubbard model in the framework of digital quantum simulation. Moreover, we present experimental results obtained on a trapped-ion quantum computer for the two-site attractive SU(3) Hubbard model, showing good agreement with exact values within statistical errors.
The widespread use of the noninteracting ground state as the initial state for the digital quantum simulation of the Fermi-Hubbard model is largely due to the scarcity of alternative easy-to-prepare approximations to the exact ground state in the literature. Exploiting the fact that the spin-12\frac{1}{2}21​ Heisenberg model is the effective low-energy theory of the Fermi-Hubbard model at half-filling in the strongly interacting limit, here we propose a three-step deterministic quantum routine to prepare an educated guess of the ground state of the Fermi-Hubbard model through a shallow circuit suitable for near-term quantum hardware. First, the ground state of the Heisenberg model is initialized via a hybrid variational method using an ansatz that explores only the correct symmetry subspace. Second, a general method is devised to convert a multi-spin-12\frac{1}{2}21​ wave function into its fermionic version. Third, taking inspiration from the Baeriswyl ansatz, a constant-depth single-parameter layer that adds doublon-holon pairs is applied to this fermionic state. Numerical simulations on chains and ladders with up to 12 sites confirm the improvement over the noninteracting ground state of the overlap with the exact ground state for the intermediate values of the interaction strength at which quantum simulation is found to be most relevant. More broadly, the general scheme to convert a multi-spin-12\frac{1}{2}21​ state into a half-filled fermionic state may bridge the gap between quantum spin models and lattice models of correlated fermions in the realm of digital quantum simulation.
We propose a quantum-classical hybrid scheme for implementing the nonunitary Gutzwiller factor using a discrete Hubbard-Stratonovich transformation, which allows us to express the Gutzwiller factor as a linear combination of unitary operators involving only single-qubit rotations, at the cost of the sum over the auxiliary fields. To perform the sum over the auxiliary fields, we introduce two approaches that have complementary features. The first approach employs a linear-combination-of-unitaries circuit, which enables one to probabilistically prepare the Gutzwiller wave function on a quantum computer, while the second approach uses importance sampling to estimate observables stochastically, similar to a quantum Monte Carlo method in classical computation. The proposed scheme is demonstrated with numerical simulations for the half-filled Fermi-Hubbard model. Furthermore, we perform quantum simulations using a real quantum device, demonstrating that the proposed scheme can reproduce the exact ground-state energy of the two-site Fermi-Hubbard model within error bars.
We report a random-sampling method for computing the expectation value of physical quantities based on the Gutzwiler variational wave function. As the first application, we calculated the double occupancy, which is a critical quantity for understanding the correlation effects in many-body systems, for single-band 1D and 2D lattices. We demonstrated that the random-sampling scheme is more efficient than an existing Metropolis Monte-Carlo algorithm. For the 1D Hubbard model with only nearest-neighbour hopping, our results are almost identical to the exact analytic solution. We have also studied systems to which analytic solutions are not available, including the 1D lattices with next-nearest-neighbour hopping and 2D lattices. In addition, constraints on real-space configurations can be easily implemented in the current scheme to further improve the Gutzwiller wave function. As an example, we calculated the double occupancy for 1D Hubbard model by applying the constraint that all double-occupied sites are paired with an empty site. With enhanced correlation between double-occupied and empty sites, the constraint results in much improved ground-state energy for 1D Hubbard model with strong on-site repulsion.
We introduce a new lattice version of the correlated-basis-function approach for the study of strongly interacting electrons. As a first application we have chosen the one-dimensional Hubbard model. For this system, we have implemented different types of correlations: namely, (a) Gutzwiller; (b) Jastrow; (c) nearest-neighbor spin-spin; (d) excitonic (e-d); and (f) pairing (BCS). The resulting energies, momentum distribution, and other quantities are compared with exact results (when available) and are discussed, both from the methodological and physical point of view. The most important correlations that are needed to obtain good ground-state energies are found to be Gutzwiller (reduced double occupancy) plus e-d correlations (between empty and doubly occupied sites), in agreement with other studies.
Simulating the time-dynamics of quantum many-body systems was the original use of quantum computers proposed by Feynman, motivated by the critical role of quantum interactions between electrons in the properties of materials and molecules. Accurately simulating such systems remains one of the most promising applications of general-purpose digital quantum computers, in which all the parameters of the model can be programmed and any desired physical quantity output. However, performing such simulations on today's quantum computers at a scale beyond the reach of classical methods requires advances in the efficiency of simulation algorithms and error mitigation techniques. Here we demonstrate programmable digital quantum simulation of the dynamics of the 2D Fermi-Hubbard model -- one of the best-known simplified models of electrons in crystalline solids -- at a scale beyond exact classical state-vector simulation. We implement simulations of this model on lattice sizes up to 6×6{6\times 6}6×6 using 72 qubits on Google's Willow quantum processor, across a range of physical parameters, including different on-site electron-electron interaction strengths and magnetic flux values, and study phenomena including formation of magnetic polarons (charge carriers surrounded by local magnetic polarisation), dynamical symmetry-breaking in stripe-ordered states, attraction of charge carriers on an entangled background state known as a valence bond solid, and the approach to equilibrium through thermalisation. We validate our results against exact calculations in parameter regimes where these are feasible, and compare them to approximate classical simulations performed using tensor network and operator propagation methods. Our results demonstrate that meaningful programmable digital quantum simulation of many-body interacting electron models is now feasible on state-of-the-art quantum hardware.