Quantum Algorithms for Fermionic Simulations

Abstract

We investigate the simulation of fermionic systems on a quantum computer. We show in detail how quantum computers avoid the dynamical sign problem present in classical simulations of these systems, therefore reducing a problem believed to be of exponential complexity into one of polynomial complexity. The key to our demonstration is the spin-particle connection (or generalized Jordan-Wigner transformation) that allows exact algebraic invertible mappings of operators with different statistical properties. We give an explicit implementation of a simple problem using a quantum computer based on standard qubits.

38 pages, 2 psfigure

Cited by in corpus (203)

• A variational eigenvalue solver on a quantum processor
• Quantum Simulation
• Quantum computational chemistry
• Quantum Chemistry in the Age of Quantum Computing
• Simulated Quantum Computation of Molecular Energies
• The Variational Quantum Eigensolver: a review of methods and best practices
• Quantum information processing with superconducting circuits: a review
• Noise-Induced Barren Plateaus in Variational Quantum Algorithms
• Towards Quantum Chemistry on a Quantum Computer
• Efficient variational quantum simulator incorporating active error minimisation
• Toward the first quantum simulation with quantum speedup
• The Bravyi-Kitaev transformation for quantum computation of electronic structure
• Simulation of Electronic Structure Hamiltonians Using Quantum Computers
• Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation
• Quantum-Classical Computation of Schwinger Model Dynamics using Quantum Computers
• Quantum Simulation of Electronic Structure with Linear Depth and Connectivity
• Simulating Physical Phenomena by Quantum Networks
• Simulating chemistry using quantum computers
• Classical simulation of noninteracting-fermion quantum circuits
• Quantum Metropolis Sampling
• Quantum Computation of Electronic Transitions using a Variational Quantum Eigensolver
• Gate count estimates for performing quantum chemistry on small quantum computers
• Solving strongly correlated electron models on a quantum computer
• Efficient Symmetry-Preserving State Preparation Circuits for the Variational Quantum Eigensolver Algorithm
• From transistor to trapped-ion computers for quantum chemistry
• Simulating lattice gauge theories on a quantum computer
• Unbiasing Fermionic Quantum Monte Carlo with a Quantum Computer
• Optimal Quantum Measurements of Expectation Values of Observables
• Chemical Basis of Trotter-Suzuki Errors in Quantum Chemistry Simulation
• Emerging quantum computing algorithms for quantum chemistry
• Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
• Digitization of Scalar Fields for Quantum Computing
• Improved Fault-Tolerant Quantum Simulation of Condensed-Phase Correlated Electrons via Trotterization
• Quantum algorithms to simulate many-body physics of correlated fermions
• General Methods for Digital Quantum Simulation of Gauge Theories
• Variational Quantum Eigensolver with Fewer Qubits
• Quantum simulation of a lattice Schwinger model in a chain of trapped ions
• A Quantum-Quantum Metropolis Algorithm
• Improved Techniques for Preparing Eigenstates of Fermionic Hamiltonians
• Application of fermionic marginal constraints to hybrid quantum algorithms
• Quantum computers as universal quantum simulators: state-of-art and perspectives
• Algebraic Approach to Interacting Quantum Systems
• Electron-Phonon Systems on a Universal Quantum Computer
• Exact Ising model simulation on a quantum computer
• Using Quantum Computers for Quantum Simulation
• An efficient quantum algorithm for the time evolution of parameterized circuits
• Quantum Computation of Finite-Temperature Static and Dynamical Properties of Spin Systems Using Quantum Imaginary Time Evolution
• Quantum algorithm for simulating the dynamics of an open quantum system
• Polynomial-Time Simulation of Pairing Models on a Quantum Computer
• Linear Response on a Quantum Computer
• Parton Physics on a Quantum Computer
• Calculating energy derivatives for quantum chemistry on a quantum computer
• Variational Quantum Boltzmann Machines
• Quantum Critical Points and the Sign Problem
• Bravyi-Kitaev Superfast simulation of fermions on a quantum computer
• Quantum Simulation of Chemistry with Sublinear Scaling in Basis Size
• Digital quantum computation of fermion-boson interacting systems
• Fermionic quantum processing with programmable neutral atom arrays
• Adiabatic state preparation study of methylene
• Deeply inelastic scattering structure functions on a hybrid quantum computer
• A measurement-based variational quantum eigensolver
• Quantum-optimal-control-inspired ansatz for variational quantum algorithms
• Minimally-Entangled State Preparation of Localized Wavefunctions on Quantum Computers
• Solving Nuclear Structure Problems with the Adaptive Variational Quantum Algorithm
• Computational Complexity in Electronic Structure
• Fock Parafermions and Self-Dual Representations of the Braid Group
• Quantum computing applied to calculations of molecular energies: CH2 benchmark
• Nearly tight Trotterization of interacting electrons
• Decomposition of Unitary Matrices for Finding Quantum Circuits: Application to Molecular Hamiltonians
• Quantum Hamiltonian-Based Models and the Variational Quantum Thermalizer Algorithm
• Majorana loop stabilizer codes for error correction of fermionic quantum simulations
• Quantum computation of magnon spectra
• Non-equilibrium quantum impurity problems via matrix-product states in the temporal domain
• Impact of qubit connectivity on quantum algorithm performance
• Simulation of interaction-induced chiral topological dynamics on a digital quantum computer
• Optimizing qubit resources for quantum chemistry simulations in second quantization on a quantum computer
• Correlating AGP on a quantum computer
• Simulating key properties of lithium-ion batteries with a fault-tolerant quantum computer
• Error-Mitigated Simulation of Quantum Many-Body Scars on Quantum Computers with Pulse-Level Control
• Benchmarking neural networks for quantum computation
• Introduction to Quantum Algorithms for Physics and Chemistry
• Quantum simulation of gauge theory via orbifold lattice
• Initial state preparation for quantum chemistry on quantum computers
• Efficient quantum algorithm for preparing molecular-system-like states on a quantum computer
• Quantum computation of molecular response properties
• Stabilizing multiple topological fermions on a quantum computer
• Free fermions behind the disguise
• Quantum Machine Learning in Drug Discovery: Applications in Academia and Pharmaceutical Industries
• An efficient adaptive variational quantum solver of the Schrodinger equation based on reduced density matrices
• Quantum Simulation of Resonant Transitions for Solving the Eigen-problem of an Effective Water Hamiltonian
• Variational Quantum Algorithms for Dimensionality Reduction and Classification
• Control of Quantum Systems
• Quantum Simulation of Nuclear Inelastic Scattering
• Lattice Renormalization of Quantum Simulations
• Quantum simulations of excited states with active-space downfolded Hamiltonians
• Gutzwiller Hybrid Quantum-Classical Computing Approach for Correlated Materials
• Quantum simulation of interacting high-dimensional systems: the influence of noise
• Dynamical critical scaling and effective thermalization in quantum quenches: the role of the initial state
• Accelerating lattice quantum field theory calculations via interpolator optimization using NISQ-era quantum computing
• Towards Dynamic Simulations of Materials on Quantum Computers
• Testing integrability with a single bit of quantum information
• A Trotter-Suzuki approximation for Lie groups with applications to Hamiltonian simulation
• Quantum Computation for Periodic Solids in Second Quantization
• Digital quantum simulators in a scalable architecture of hybrid spin-photon qubits
• Strategies for the Determination of the Running Coupling of $(2+1)$-dimensional QED with Quantum Computing
• Causal Fermions in Discrete Spacetime
• Quantum Annealing-Based Software Components: An Experimental Case Study with SAT Solving
• On the Quantum Computational Complexity of the Ising Spin Glass Partition Function and of Knot Invariants
• Enhancing quantum utility: simulating large-scale quantum spin chains on superconducting quantum computers
• Quantum Computation of Reactions on Surfaces Using Local Embedding
• Preparing Valence-Bond-Solid states on noisy intermediate-scale quantum computers
• The Fermionic Quantum Emulator
• Hybrid Oscillator-Qubit Quantum Processors: Instruction Set Architectures, Abstract Machine Models, and Applications
• Quantum computation of the Anderson transition in presence of imperfections
• Error-resilient Monte Carlo quantum simulation of imaginary time
• When is a Quantum Cellular Automaton (QCA) a Quantum Lattice Gas Automaton (QLGA)?
• Quantum simulations of one dimensional quantum systems
• Dual Exponential Coupled Cluster Theory: Unitary Adaptation, Implementation in the Variational Quantum Eigensolver Framework and Pilot Applications
• Spin-free quantum computational simulations and symmetry adapted states
• Lower bounds for the fidelity of entangled state preparation
• The Complexity of the Consistency and N-representability Problems for Quantum States
• A generic map from non-Lindblad to Lindblad master equations
• Minimal Effective Gibbs Ansatz (MEGA): A simple protocol for extracting an accurate thermal representation for quantum simulation
• Introduction to Quantum Information Processing
• Engineered Open Systems and Quantum Simulations with Atoms and Ions
• Short-depth circuits for efficient expectation value estimation
• Tailoring Term Truncations for Electronic Structure Calculations Using a Linear Combination of Unitaries
• Fault-tolerant fermionic quantum computation based on color code
• Quantum algorithms for scientific computing
• Classical Ising model test for quantum circuits
• Quantum-assisted Monte Carlo algorithms for fermions
• Optimizing the information extracted by a single qubit measurement
• Quantum Simulations of Chemistry in First Quantization with any Basis Set
• Simulating ${\mathbb{Z}}_2$ Lattice Gauge Theory with the Variational Quantum Thermalizer
• Generalized Zeno effect and entanglement dynamics induced by fermion counting
• Quantum Computation of Hydrogen Bond Dynamics and Vibrational Spectra
• Dynamical mean-field theory for the Hubbard-Holstein model on a quantum device
• Discovering optimal fermion-qubit mappings through algorithmic enumeration
• Measurement-Based Time Evolution for Quantum Simulation of Fermionic Systems
• Quantum computation algorithm for many-body studies
• Excitations and spectra from equilibrium real-time Green's functions
• Optimal quantum circuit cuts with application to clustered Hamiltonian simulation
• Quantum Computational Method of Finding the Ground State Energy and Expectation Values
• Digital-analog quantum simulation of fermionic models
• Strategies for quantum-optimized construction of interpolating operators in classical simulations of lattice quantum field theories
• Quantum Computation of the Massive Thirring Model
• Fast quantum algorithms for traversing paths of eigenstates
• Beyond MP2 initialization for unitary coupled cluster quantum circuits
• Computing real time correlation functions on a hybrid classical/quantum computer
• From Ansätze to Z-gates: a NASA View of Quantum Computing
• Adaptive projected variational quantum dynamics
• Excited-state molecular dynamics simulation based on variational quantum algorithms
• Distributed Quantum Computing with QMPI
• Pauli Decomposition via the Fast Walsh-Hadamard Transform
• A Hybrid Quantum-Classical Method for Electron-Phonon Systems
• Simulation of linear non-Hermitian boundary-value problems with quantum singular value transformation
• Analysis of Superfast Encoding Performance for Electronic Structure Simulations
• Solving reaction dynamics with quantum computing algorithms
• Ultrafast Hybrid Fermion-to-Qubit mapping
• Operator Space Entangling Power of Quantum Dynamics and Local Operator Entanglement Growth in Dual-Unitary Circuits
• Calculation of core-excited and core-ionized states using variational quantum deflation method and applications to photocatalyst modelling
• Digital quantum simulation of the BCS model with a central-spin-like quantum processor
• Quantum simulation of fermionic systems using hybrid digital-analog quantum computing approach
• Quantum Computation of Electronic Structure with Projector Augmented-Wave Method and Plane Wave Basis Set
• Quantum circuit for measuring an operator's generalized expectation values and its applications to non-Hermitian winding numbers
• Dynamical localization simulated on actual quantum hardware
• Parity-dependent state transfer for direct entanglement generation
• A Comprehensive Cross-Model Framework for Benchmarking the Performance of Quantum Hamiltonian Simulations
• Effects of Noise, Correlations and errors in the preparation of initial states in Quantum Simulations
• Quantum Cellular Automata from Lattice Field Theories
• A Method to Calculate Correlation for Density Functional Theory on a Quantum Processor
• Quantum computing and information extraction for a dynamical quantum system
• Reconstructing Thermal Quantum Quench Dynamics from Pure States
• Problem-tailored Simulation of Energy Transport on Noisy Quantum Computers
• Roadmap for quantum simulation of the fractional quantum Hall effect
• Quantum Simulation of Simple Many-Body Dynamics
• Shallow quantum circuits for efficient preparation of Slater determinants and correlated states on a quantum computer
• Efficient state initialization by a quantum spectral filtering algorithm
• Cascaded variational quantum eigensolver algorithm
• Optimize quantum simulation using a force-gradient integrator
• Triply-heavy/strange baryons with Cornell potential on a quantum computer
• Variational Quantum Simulation of Valence-Bond Solids
• Reducing Circuit Depth in Quantum State Preparation for Quantum Simulation Using Measurements and Feedforward
• Nonlinear Spectroscopy via Generalized Quantum Phase Estimation
• Sparse-Hamiltonian approach to the time evolution of molecules on quantum computers
• Parallelization techniques for quantum simulation of fermionic systems
• Dirac particle dynamics of a superconducting circuit
• Quantum nuclear dynamics on a distributed set of ion-trap quantum computing systems
• Quantum simulation of quantum mechanical system with spatial noncommutativity
• Toward extracting scattering phase shift from integrated correlation functions on quantum computers
• Discontinuous Galerkin discretization for quantum simulation of chemistry
• Quantum error mitigation for parametric circuits
• Algorithm for initializing a generalized fermionic Gaussian state on a quantum computer
• Quantum Simulation of Neutrino Oscillation and Dirac Particle Dynamics in Curved Space-time
• Quantum Utility in Simulating the Real-time Dynamics of the Fermi-Hubbard Model using Superconducting Quantum Computers
• Characterizing maximally many-body entangled fermionic states by using $M$-body density matrix
• The Representation of Numbers in Quantum Mechanics
• Maximal Entanglement: Applications in Quantum Information and Particle Physics
• Effective non-local parity-dependent couplings in qubit chains
• Mapping quantum chemical dynamics problems onto spin-lattice simulators
• Preparing the Gutzwiller wave function for attractive SU(3) fermions on a quantum computer
• Quantum operation of fermionic systems and process tomography using Majorana fermion gates
• On sampling determinantal and Pfaffian point processes on a quantum computer