An efficient adaptive variational quantum solver of the Schrodinger equation based on reduced density matrices

Abstract

Recently, an adaptive variational algorithm termed Adaptive Derivative-Assembled Pseudo-Trotter ansatz Variational Quantum Eigensolver (ADAPT-VQE) has been proposed by Grimsley et al. (Nat. Commun. 10, 3007) while the number of measurements required to perform this algorithm scales O(N^8). In this work, we present an efficient adaptive variational quantum solver of the Schrodinger equation based on ADAPT-VQE together with the reduced density matrix reconstruction approach, which reduces the number of measurements from O(N^8) to O(N^4). This new algorithm is quite suitable for quantum simulations of chemical systems on near-term noisy intermediate-scale hardware due to low circuit complexity and reduced measurement. Numerical benchmark calculations for small molecules demonstrate that this new algorithm provides an accurate description of the ground-state potential energy curves. In addition, we generalize this new algorithm for excited states with the variational quantum deflation approach and achieve the same accuracy as ground-state simulations.

arXiv comment27 pages and 5 figures

References in corpus (39)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Quantum Computing in the NISQ era and beyond
• A variational eigenvalue solver on a quantum processor
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• 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
• Evaluating analytic gradients on quantum hardware
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Fermionic quantum computation
• Scalable Quantum Simulation of Molecular Energies
• Hartree-Fock on a superconducting qubit quantum computer
• Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States
• Simulation of Electronic Structure Hamiltonians Using Quantum Computers
• Variational Quantum Computation of Excited States
• Robust determination of molecular spectra on a quantum processor
• Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation
• Quantum chemistry calculations on a trapped-ion quantum simulator
• qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansatze on a quantum processor
• Quantum Algorithms for Fermionic Simulations
• Quantum Implementation of Unitary Coupled Cluster for Simulating Molecular Electronic Structure
• Measurement Optimization in the Variational Quantum Eigensolver Using a Minimum Clique Cover
• Variational quantum algorithms for discovering Hamiltonian spectra
• Efficient and Noise Resilient Measurements for Quantum Chemistry on Near-Term Quantum Computers
• Witnessing eigenstates for quantum simulation of Hamiltonian spectra
• Efficient quantum measurement of Pauli operators in the presence of finite sampling error
• Is the Trotterized UCCSD Ansatz chemically well-defined?
• Measurement reduction in variational quantum algorithms
• Quantum Solver of Contracted Eigenvalue Equations for Scalable Molecular Simulations on Quantum Computing Devices
• Excitonic optical spectrum of semiconductors obtained by time-dependent density-functional theory with the exact-exchange kernel
• Quantum Algorithm for Obtaining the Energy Spectrum of Molecular Systems
• Nearly Optimal Measurement Scheduling for Partial Tomography of Quantum States
• Ground-state properties of the hydrogen chain: insulator-to-metal transition, dimerization, and magnetic phases
• Second-order Green's function perturbation theory for periodic systems
• A Feasible Approach for Automatically Differentiable Unitary Coupled-Cluster on Quantum Computers
• Exploring connections between statistical mechanics and Green's functions for realistic systems. Temperature dependent electronic entropy and internal energy from a self-consistent second-order Green's function
• Exact Two-body Expansion of the Many-particle Wave Function
• Unveiling the Finite Temperature Physics of Hydrogen Chains via Auxiliary Field Quantum Monte Carlo

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• Reducing the Resources Required by ADAPT-VQE Using Coupled Exchange Operators and Improved Subroutines
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• Classical Pre-optimization Approach for ADAPT-VQE: Maximizing the Potential of High-Performance Computing Resources to Improve Quantum Simulation of Chemical Applications
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