# Strategies for solving the Fermi-Hubbard model on near-term quantum computers

@article{Cade2019StrategiesFS, title={Strategies for solving the Fermi-Hubbard model on near-term quantum computers}, author={Chris Cade and Lana Mineh and Ashley Montanaro and Stasja Stanisic}, journal={arXiv: Quantum Physics}, year={2019} }

The Fermi-Hubbard model is of fundamental importance in condensed-matter physics, yet is extremely challenging to solve numerically. Finding the ground state of the Hubbard model using variational methods has been predicted to be one of the first applications of near-term quantum computers. Here we carry out a detailed analysis and optimisation of the complexity of variational quantum algorithms for finding the ground state of the Hubbard model, including costs associated with mapping to a real…

## 77 Citations

### Compressed variational quantum eigensolver for the Fermi-Hubbard model.

- Physics
- 2020

The Fermi-Hubbard model is a plausible target to be solved by a quantum computer using the variational quantum eigensolver algorithm. However, problem sizes beyond the reach of classical exact…

### Resource Estimation for Quantum Variational Simulations of the Hubbard Model

- Physics
- 2019

This Article outlines the details about the gate sequence, the measurement scheme and the relevant error mitigation techniques for the implementation of the Hubbard VQE on a NISQ platform, and performs resource estimation on Hubbard VZE using silicon spin qubits as an example platform.

### Simulating a ring-like Hubbard system with a quantum computer

- Physics, Computer SciencePhysical Review Research
- 2022

This work studies a four-site Hubbard ring that exhibits a transition from a product state to an intrinsically interacting ground state as hopping amplitudes are changed, and solves for the ground state energy with high quantitative accuracy using a variational quantum algorithm executed on an IBM quantum computer.

### Quantum-optimal-control-inspired ansatz for variational quantum algorithms

- Mathematics
- 2020

A central component of variational quantum algorithms (VQA) is the state-preparation circuit, also known as ansatz or variational form. This circuit is most commonly designed to respect the…

### Exploring entanglement and optimization within the Hamiltonian Variational Ansatz

- PhysicsArXiv
- 2020

This paper focuses on a special family of quantum circuits called the Hamiltonian Variational Ansatz (HVA), which takes inspiration from the quantum approximation optimization algorithm and adiabatic quantum computation and exhibits favorable structural properties and numerically observes that the optimization landscape of HVA becomes almost trap free when the ansatz is over-parameterized.

### Early fault-tolerant simulations of the Hubbard model

- Computer ScienceQuantum Science and Technology
- 2021

There is a potentially useful application for fault-tolerant quantum computers using around one million Toffoli gates using the split-operator FFFT method, and plaquette Trotterization is introduced that works on any size lattice and improved error bound analysis is applied to show competitive resource costs.

### Nearly tight Trotterization of correlated electrons

- Physics
- 2020

We consider simulating quantum systems on digital quantum computers. We show that the performance of quantum simulation can be improved by simultaneously exploiting the commutativity of Hamiltonian,…

### Error mitigation by training with fermionic linear optics

- Physics
- 2021

Noisy intermediate-scale quantum (NISQ) computers could solve quantum-mechanical simulation problems that are beyond the capabilities of classical computers. However, NISQ devices experience…

### Nearly tight Trotterization of interacting electrons

- PhysicsQuantum
- 2021

It suffices to use O gates to simulate electronic structure in the plane-wave basis with $n$ spin orbitals and $\eta$ electrons up to a negligible factor, improving the best previous result in second quantization while outperforming the first-quantized simulation when $n=\mathcal{O}\left(\eta^2\right)$.

### Variational Quantum Algorithms

- Physics, Computer ScienceNature Reviews Physics
- 2021

An overview of the field of Variational Quantum Algorithms is presented and strategies to overcome their challenges as well as the exciting prospects for using them as a means to obtain quantum advantage are discussed.

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