Quantum computation of molecular response properties
arXiv:2001.03406 · doi:10.1103/PhysRevResearch.2.033324
Abstract
Accurately predicting response properties of molecules such as the dynamic polarizability and hyperpolarizability using quantum mechanics has been a long-standing challenge with widespread applications in material and drug design. Classical simulation techniques in quantum chemistry are hampered by the exponential growth of the many-electron Hilbert space as the system size increases. In this work, we propose an algorithm for computing linear and nonlinear molecular response properties on quantum computers, by first reformulating the target property into a symmetric expression more suitable for quantum computation via introducing a set of auxiliary quantum states, and then determining these auxiliary states via solving the corresponding linear systems of equations on quantum computers. On one hand, we prove that using the quantum linear system algorithm [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)] as a subroutine the proposed algorithm scales only polynomially in the system size instead of the dimension of the exponentially large Hilbert space, and hence achieves an exponential speedup over existing classical algorithms. On the other hand, we introduce a variational hybrid quantum-classical variant of the proposed algorithm, which is more practical for near-term quantum devices.
arXiv comment7 pages
References in corpus (42)
- Quantum Computing in the NISQ era and beyond
- A variational eigenvalue solver on a quantum processor
- Quantum algorithm for solving linear systems of equations
- Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
- Quantum Simulation
- The theory of variational hybrid quantum-classical algorithms
- Quantum computational chemistry
- Quantum Chemistry in the Age of Quantum Computing
- Simulated Quantum Computation of Molecular Energies
- Error mitigation for short-depth quantum circuits
- Resonant Inelastic X-ray Scattering Studies of Elementary Excitations
- Quantum fingerprinting
- Fermionic quantum computation
- Extending the computational reach of a noisy superconducting quantum processor
- A quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors
- Scalable Quantum Simulation of Molecular Energies
- Towards Quantum Chemistry on a Quantum Computer
- Simulating Hamiltonian dynamics with a truncated Taylor series
- Simulation of Many-Body Fermi Systems on a Universal Quantum Computer
- Towards Practical Quantum Variational Algorithms
- Efficient variational quantum simulator incorporating active error minimisation
- Quantum algorithm for systems of linear equations with exponentially improved dependence on precision
- The Bravyi-Kitaev transformation for quantum computation of electronic structure
- Quantum chemistry calculations on a trapped-ion quantum simulator
- Simulating Physical Phenomena by Quantum Networks
- Quantum Algorithms for Fermionic Simulations
- Quantum Implementation of Unitary Coupled Cluster for Simulating Molecular Electronic Structure
- Preconditioned quantum linear system algorithm
- Error-mitigated digital quantum simulation
- The SWAP test and the Hong-Ou-Mandel effect are equivalent
- Quantum algorithms for systems of linear equations inspired by adiabatic quantum computing
- Experimental Quantum Computing to Solve Systems of Linear Equations
- Quantum Simulation of Helium Hydride in a Solid-State Spin Register
- Quantum hardware simulating four-dimensional inelastic neutron scattering
- Experimental realization of quantum algorithm for solving linear systems of equations
- Solving systems of linear equations on a quantum computer
- Calculating energy derivatives for quantum chemistry on a quantum computer
- Solving Systems of Linear Equations with a Superconducting Quantum Processor
- Quantum Algorithm for Molecular Properties and Geometry Optimization
- Precise measurement of quantum observables with neural-network estimators
- Quantum computation of magnon spectra
- Charge and spin response functions on a quantum computer: applications to molecules
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- The Variational Quantum Eigensolver: a review of methods and best practices
- Biology and medicine in the landscape of quantum advantages
- Fast inversion, preconditioned quantum linear system solvers, and fast evaluation of matrix functions
- Near- and long-term quantum algorithmic approaches for vibrational spectroscopy
- Variational Quantum Computation of Molecular Linear Response Properties on a Superconducting Quantum Processor
- A variational quantum eigensolver for dynamic correlation functions
- Which options exist for NISQ-friendly linear response formulations?
- Quantum Equation of Motion with Orbital Optimization for Computing Molecular Properties in Near-Term Quantum Computing
- Fermionic Simulators for Enhanced Scalability of Variational Quantum Simulation
- Understanding and mitigating noise in molecular quantum linear response for spectroscopic properties on quantum computers
- Entanglement-assisted phase estimation algorithm for calculating dynamical response functions
- Improved resource-tunable near-term quantum algorithms for transition probabilities, with applications in physics and variational quantum linear algebra
- Simulating Non-Markovian Dynamics in Multidimensional Electronic Spectroscopy via Quantum Algorithm
- Near-term quantum algorithm for computing molecular and materials properties based on recursive variational series methods
- Simulating optically-active spin defects with a quantum computer
- Optimizing Quantum Chemistry Simulations with a Hybrid Quantization Scheme
- Moments-based quantum computation of the electric dipole moment of molecular systems