Solving strongly correlated electron models on a quantum computer

Abstract

One of the main applications of future quantum computers will be the simulation of quantum models. While the evolution of a quantum state under a Hamiltonian is straightforward (if sometimes expensive), using quantum computers to determine the ground state phase diagram of a quantum model and the properties of its phases is more involved. Using the Hubbard model as a prototypical example, we here show all the steps necessary to determine its phase diagram and ground state properties on a quantum computer. In particular, we discuss strategies for efficiently determining and preparing the ground state of the Hubbard model starting from various mean-field states with broken symmetry. We present an efficient procedure to prepare arbitrary Slater determinants as initial states and present the complete set of quantum circuits needed to evolve from these to the ground state of the Hubbard model. We show that, using efficient nesting of the various terms each time step in the evolution can be performed with just $\mathcal{O}(N)$ gates and $\mathcal{O}(\log N)$ circuit depth. We give explicit circuits to measure arbitrary local observables and static and dynamic correlation functions, both in the time and frequency domain. We further present efficient non-destructive approaches to measurement that avoid the need to re-prepare the ground state after each measurement and that quadratically reduce the measurement error.

25 pages, 14 figures

References in corpus (6)

• Theory of Intertwined Orders in High Temperature Superconductors
• The power of quantum systems on a line
• Chemical Basis of Trotter-Suzuki Errors in Quantum Chemistry Simulation
• Adiabatic approximation with exponential accuracy for many-body systems and quantum computation
• Adiabatic Preparation of Topological Order
• d-wave resonating valence bond states of fermionic atoms in optical lattices

Cited by in corpus (204)

• Quantum Computing in the NISQ era and beyond
• Quantum computational chemistry
• Quantum Chemistry in the Age of Quantum Computing
• The Variational Quantum Eigensolver: a review of methods and best practices
• Elucidating Reaction Mechanisms on Quantum Computers
• Hartree-Fock on a superconducting qubit quantum computer
• Toward the first quantum simulation with quantum speedup
• A Theory of Trotter Error
• Quantum Simulation of Electronic Structure with Linear Depth and Connectivity
• The Hubbard model: A computational perspective
• Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity
• A Race Track Trapped-Ion Quantum Processor
• Quantum Simulation for High Energy Physics
• Quantum computing enhanced computational catalysis
• Quantum Computer Systems for Scientific Discovery
• Hybrid quantum-classical approach to correlated materials
• Tapering off qubits to simulate fermionic Hamiltonians
• A perspective on the current state-of-the-art of quantum computing for drug discovery applications
• Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
• A Software Methodology for Compiling Quantum Programs
• Low rank representations for quantum simulation of electronic structure
• Improved Fault-Tolerant Quantum Simulation of Condensed-Phase Correlated Electrons via Trotterization
• Quantum algorithms to simulate many-body physics of correlated fermions
• Fermionic partial tomography via classical shadows
• Resource-efficient digital quantum simulation of $d$-level systems for photonic, vibrational, and spin-$s$ Hamiltonians
• Variational Quantum Eigensolver with Fewer Qubits
• Quantum Algorithms for Simulating the Lattice Schwinger Model
• Electron-Phonon Systems on a Universal Quantum Computer
• Exact Ising model simulation on a quantum computer
• Drug design on quantum computers
• Adaptive Variational Quantum Dynamics Simulations
• qHiPSTER: The Quantum High Performance Software Testing Environment
• Measuring the Renyi entropy of a two-site Fermi-Hubbard model on a trapped ion quantum computer
• Quantum Algorithm for Spectral Measurement with Lower Gate Count
• Observing ground-state properties of the Fermi-Hubbard model using a scalable algorithm on a quantum computer
• Many-body physics in the NISQ era: quantum programming a discrete time crystal
• A Jastrow-type decomposition in quantum chemistry for low-depth quantum circuits
• Quantum Power Method by a Superposition of Time-Evolved States
• Quantum Computing for Neutrino-nucleus Scattering
• Calculating energy derivatives for quantum chemistry on a quantum computer
• Operator Locality in Quantum Simulation of Fermionic Models
• Observation of separated dynamics of charge and spin in the Fermi-Hubbard model
• Digital quantum computation of fermion-boson interacting systems
• Exponentially More Precise Quantum Simulation of Fermions in the Configuration Interaction Representation
• Calculation of the Green's function on near-term quantum computers
• Quantum-optimal-control-inspired ansatz for variational quantum algorithms
• Complexity of quantum impurity problems
• Simulating Quantum Materials with Digital Quantum Computers
• Local spin operators for fermion simulations
• Entanglement spectroscopy on a quantum computer
• Quantum Filter Diagonalization with Double-Factorized Hamiltonians
• NISQ Computers: A Path to Quantum Supremacy
• Toward scalable simulations of Lattice Gauge Theories on quantum computers
• Optimal fermion-to-qubit mapping via ternary trees with applications to reduced quantum states learning
• Time-dependent unbounded Hamiltonian simulation with vector norm scaling
• Time-marching based quantum solvers for time-dependent linear differential equations
• Quantum codes for quantum simulation of Fermions on a square lattice of qubits
• Nearly tight Trotterization of interacting electrons
• Majorana loop stabilizer codes for error correction of fermionic quantum simulations
• Resource Estimation for Quantum Variational Simulations of the Hubbard Model
• Quantum Hamiltonian-Based Models and the Variational Quantum Thermalizer Algorithm
• Non-equilibrium quantum impurity problems via matrix-product states in the temporal domain
• Quantum inverse iteration algorithm for programmable quantum simulators
• Optimizing quantum phase estimation for the simulation of Hamiltonian eigenstates
• Generalization despite overfitting in quantum machine learning models
• Robust quantum compilation and circuit optimisation via energy minimisation
• Simulating key properties of lithium-ion batteries with a fault-tolerant quantum computer
• Near- and long-term quantum algorithmic approaches for vibrational spectroscopy
• General quantum algorithms for Hamiltonian simulation with applications to a non-Abelian lattice gauge theory
• Hamiltonian simulation with random inputs
• Boundaries of quantum supremacy via random circuit sampling
• Dynamical mean field theory algorithm and experiment on quantum computers
• Quantum-classical simulation of two-site dynamical mean-field theory on noisy quantum hardware
• Hybridized Methods for Quantum Simulation in the Interaction Picture
• Floquet quantum simulation with superconducting qubits
• Non-unitary operations for ground-state calculations in near term quantum computers
• Autonomous tuning and charge state detection of gate defined quantum dots
• Qubit-efficient encoding scheme for quantum simulations of electronic structure
• Non-linear quantum-classical scheme to simulate non-equilibrium strongly correlated fermionic many-body dynamics
• A variational quantum eigensolver for dynamic correlation functions
• Construction of Green's functions on a quantum computer: applications to molecular systems
• Control of Fano resonances and slow light using Bose-Einstein condensates in a nanocavity
• Time-dependent Hamiltonian Simulation of Highly Oscillatory Dynamics and Superconvergence for Schrödinger Equation
• Spin-projection for quantum computation: A low-depth approach to strong correlation
• An efficient magic state approach to small angle rotations
• Preparing Bethe Ansatz Eigenstates on a Quantum Computer
• Algebraic Bethe Circuits
• Quantum gates and architecture for the quantum simulation of the Fermi-Hubbard model
• Effective calculation of the Green's function in the time domain on near-term quantum processors
• A method to efficiently simulate the thermodynamical properties of the Fermi-Hubbard model on a quantum computer
• Hybrid quantum-classical algorithm for computing imaginary-time correlation functions
• An Alternative Approach to Quantum Imaginary Time Evolution
• Improved algorithms of quantum imaginary time evolution for ground and excited states of molecular systems
• QVECTOR: an algorithm for device-tailored quantum error correction
• Resource estimate for quantum many-body ground-state preparation on a quantum computer
• Creating and manipulating a Laughlin-type $\nu =1/3$ fractional quantum Hall state on a quantum computer with linear depth circuits
• Bethe states on a quantum computer: success probability and correlation functions
• Qubit-Efficient Randomized Quantum Algorithms for Linear Algebra
• Group-theoretic error mitigation enabled by classical shadows and symmetries
• Towards the Practical Application of Near-Term Quantum Computers in Quantum Chemistry Simulations: A Problem Decomposition Approach
• Charge and spin response functions on a quantum computer: applications to molecules
• Using Differential Evolution to avoid local minima in Variational Quantum Algorithms
• Adaptive construction of shallower quantum circuits with quantum spin projection for fermionic systems
• Minimal Effective Gibbs Ansatz (MEGA): A simple protocol for extracting an accurate thermal representation for quantum simulation
• Hardware-efficient fermionic simulation with a cavity-QED system
• Simulating strongly interacting Hubbard chains with the Variational Hamiltonian Ansatz on a quantum computer
• Exploiting fermion number in factorized decompositions of the electronic structure Hamiltonian
• The advantage of quantum control in many-body Hamiltonian learning
• Fermionic Quantum Approximate Optimization Algorithm
• Spatial, spin, and charge symmetry projections for a Fermi-Hubbard model on a quantum computer
• Berry Phase Estimation in Gate-Based Adiabatic Quantum Simulation
• Nuclear scattering via quantum computing
• Non-Equilibrium Dynamics of a Dissipative Two-Site Hubbard Model Simulated on IBM Quantum Computers
• Gutzwiller wave function on a digital quantum computer
• A stochastic quantum Krylov protocol with double factorized Hamiltonians
• Efficient Quantum Analytic Nuclear Gradients with Double Factorization
• Gutzwiller wave function on a quantum computer using a discrete Hubbard-Stratonovich transformation
• Measurement-Based Time Evolution for Quantum Simulation of Fermionic Systems
• Discovering optimal fermion-qubit mappings through algorithmic enumeration
• Excitations and spectra from equilibrium real-time Green's functions
• Deterministic Bethe state preparation
• Efficient and precise quantum simulation of ultra-relativistic quark-nucleus scattering
• Digital-analog quantum simulation of fermionic models
• Simulating a ring-like Hubbard system with a quantum computer
• Classical and Quantum Algorithms for Tensor Principal Component Analysis
• A Quantum Computing Implementation of Nuclear-Electronic Orbital (NEO) Theory: Towards an Exact pre-Born-Oppenheimer Formulation of Molecular Quantum Systems
• Compilation of a simple chemistry application to quantum error correction primitives
• Trotter error with commutator scaling for the Fermi-Hubbard model
• Fermionic wave packet scattering: a quantum computing approach
• State preparation of AGP on a quantum computer without number projection
• Quantum algorithm for linear non-unitary dynamics with near-optimal dependence on all parameters
• Self-Consistent Determination of Single-Impurity Anderson Model Using Hybrid Quantum-Classical Approach on a Spin Quantum Simulator
• Solving reaction dynamics with quantum computing algorithms
• Fast digital methods for adiabatic state preparation
• TFermion: A non-Clifford gate cost assessment library of quantum phase estimation algorithms for quantum chemistry
• Multi-nucleon structure and dynamics via quantum computing
• Analysis of Superfast Encoding Performance for Electronic Structure Simulations
• Computation of Green's function by local variational quantum compilation
• A Hybrid Quantum-Classical Method for Electron-Phonon Systems
• Implementing Jastrow--Gutzwiller operators on a quantum computer using the cascaded variational quantum eigensolver algorithm
• Graph Optimization Perspective for Low-Depth Trotter-Suzuki Decomposition
• Digital quantum simulation of the BCS model with a central-spin-like quantum processor
• On connectivity-dependent resource requirements for digital quantum simulation of $d$-level particles
• Convergence and Quantum Advantage of Trotterized MERA for Strongly-Correlated Systems
• Entanglement-assisted phase estimation algorithm for calculating dynamical response functions
• Local, Expressive, Quantum-Number-Preserving VQE Ansatze for Fermionic Systems
• Exploiting anticommutation in Hamiltonian simulation
• Calculating the Green's function of two-site Fermionic Hubbard model in a photonic system
• Many-Body Physics in Small Systems: Observing the Onset and Saturation of Correlation in Linear Atomic Chains
• Super-resolution of Green's functions on noisy quantum computers
• Adaptive variational quantum dynamics simulations with compressed circuits and fewer measurements
• Estimating Bethe roots with VQE
• Roadmap for quantum simulation of the fractional quantum Hall effect
• Adaptive variational quantum computing approaches for Green's functions and nonlinear susceptibilities
• Shallow quantum circuits for efficient preparation of Slater determinants and correlated states on a quantum computer
• Partition Function Estimation: Quantum and Quantum-Inspired Algorithms
• Improved resource-tunable near-term quantum algorithms for transition probabilities, with applications in physics and variational quantum linear algebra
• Exploring Ground States of Fermi-Hubbard Model on Honeycomb Lattices with Counterdiabaticity
• Quantum Simulation of the First-Quantized Pauli-Fierz Hamiltonian
• Compressing Hamiltonians with ab initio downfolding for simulating strongly-correlated materials on quantum computers
• Simulating Non-Markovian Dynamics in Multidimensional Electronic Spectroscopy via Quantum Algorithm
• Bethe Ansatz, Quantum Circuits, and the F-basis
• Resource-optimized fault-tolerant simulation of the Fermi-Hubbard model and high-temperature superconductor models
• Trotterization is substantially efficient for low-energy states
• Estimating the error of an analog quantum simulator by additional measurements
• From Heisenberg to Hubbard: An initial state for the shallow quantum simulation of correlated electrons
• Variational Quantum Simulation of Valence-Bond Solids
• Going Beyond Gadgets: The Importance of Scalability for Analogue Quantum Simulators
• Quantum phase estimation based filtering: performance analysis and application to low-energy spectral calculation
• Fidelity-based distance bounds for $N$-qubit approximate quantum error correction
• Imaginary Hamiltonian variational ansatz for combinatorial optimization problems
• Quantum simulation by qubitization without Toffoli gates
• Efficient Quantum Cooling Algorithm for Fermionic Systems
• General, efficient, and robust Hamiltonian engineering
• Recipes for the Digital Quantum Simulation of Lattice Spin Systems
• Reducing Circuit Depth in Quantum State Preparation for Quantum Simulation Using Measurements and Feedforward
• Classical Benchmarks for Variational Quantum Eigensolver Simulations of the Hubbard Model
• Quantum Iterative Methods for Solving Differential Equations with Application to Computational Fluid Dynamics
• Sparse-Hamiltonian approach to the time evolution of molecules on quantum computers
• Systematic many-fermion Hamiltonian input scheme and spectral calculations on quantum computers
• Digital Quantum Simulation of the Kitaev Quantum Spin Liquid
• Analyzing the spectral density of a perturbed analog quantum simulator using Keldysh formalism
• Recursive relations and quantum eigensolver algorithms within modified Schrieffer--Wolff transformations for the Hubbard dimer
• Learning Density Functionals from Noisy Quantum Data
• Pathfinding Quantum Simulations of Neutrinoless Double-Beta Decay
• Digital Quantum Simulation of Scalar Yukawa Coupling
• Algorithm for initializing a generalized fermionic Gaussian state on a quantum computer
• Extracting the spin excitation spectrum of a fermionic system using a quantum processor
• Solving the Hubbard model using density matrix embedding theory and the variational quantum eigensolver
• Quantum Algorithm for Green's Functions Measurements in the Fermi-Hubbard Model
• Digital-Analog Simulations of Schrödinger Cat States in the Dicke-Ising Model
• Characterizing maximally many-body entangled fermionic states by using $M$-body density matrix
• Hybrid quantum gap estimation algorithm using a filtered time series
• Maximal Entanglement: Applications in Quantum Information and Particle Physics
• Quantum Utility in Simulating the Real-time Dynamics of the Fermi-Hubbard Model using Superconducting Quantum Computers
• On sampling determinantal and Pfaffian point processes on a quantum computer
• Preparation of the single-spinon wave function on a quantum computer
• Quantum speed-up for solving the one-dimensional Hubbard model using quantum annealing
• Chemistry beyond the Hartree-Fock limit via quantum computed moments
• Majorana string simulation of nonequilibrium dynamics in two-dimensional lattice fermion systems
• Preparing the Gutzwiller wave function for attractive SU(3) fermions on a quantum computer
• Quantum adiabaticity in many-body systems and almost-orthogonality in complementary subspace
• Noise-resilient and resource-efficient hybrid algorithm for robust quantum gap estimation
• Entanglement swapping for partially entangled qudits and the role of quantum complementarity