Dissipative ground state preparation in ab initio electronic structure theory

Abstract

Dissipative engineering is a powerful tool for quantum state preparation, and has drawn significant attention in quantum algorithms and quantum many-body physics in recent years. In this work, we introduce a novel approach using the Lindblad dynamics to efficiently prepare the ground state for general ab initio electronic structure problems on quantum computers, without variational parameters. These problems often involve Hamiltonians that lack geometric locality or sparsity structures, which we address by proposing two generic types of jump operators for the Lindblad dynamics. Type-I jump operators break the particle number symmetry and should be simulated in the Fock space. Type-II jump operators preserves the particle number symmetry and can be simulated more efficiently in the full configuration interaction space. For both types of jump operators, we prove that in a simplified Hartree-Fock framework, the spectral gap of our Lindbladian is lower bounded by a universal constant. For physical observables such as energy and reduced density matrices, the convergence rate of our Lindblad dynamics with Type-I jump operators remains universal, while the convergence rate with Type-II jump operators only depends on coarse grained information such as the number of orbitals and the number of electrons. To validate our approach, we employ a Monte Carlo trajectory-based algorithm for simulating the Lindblad dynamics for full ab initio Hamiltonians, demonstrating its effectiveness on molecular systems amenable to exact wavefunction treatment.

25 pages, 10 figures, 2 tables

References in corpus (42)

• Variational Quantum Algorithms
• Adiabatic Quantum Computing
• Simulated Quantum Computation of Molecular Energies
• Preparation of Entangled States by Quantum Markov Processes
• Concepts and methods in the theory of open quantum systems
• Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
• Variational ansatz-based quantum simulation of imaginary time evolution
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation
• Quantum Monte Carlo method using phase-free random walks with Slater determinants
• Is there evidence for exponential quantum advantage in quantum chemistry?
• Unbiasing Fermionic Quantum Monte Carlo with a Quantum Computer
• Relaxation times of dissipative many-body quantum systems
• Heisenberg-limited ground state energy estimation for early fault-tolerant quantum computers
• Quantum phase estimation of multiple eigenvalues for small-scale (noisy) experiments
• Near-optimal ground state preparation
• Quantum State Preparation with Optimal Circuit Depth: Implementations and Applications
• Exact solution of Markovian master equations for quadratic fermi systems: thermal baths, open XY spin chains, and non-equilibrium phase transition
• On thermalization in Kitaev's 2D model
• Dissipative Dynamics and Phase Transitions in Fermionic Systems
• Measurement as a shortcut to long-range entangled quantum matter
• Quantum logarithmic Sobolev inequalities and rapid mixing
• The ${\chi }^2$-divergence and Mixing times of quantum Markov processes
• Completely positive master equation for arbitrary driving and small level spacing
• A randomized quantum algorithm for statistical phase estimation
• Fast inversion, preconditioned quantum linear system solvers, and fast evaluation of matrix functions
• Even shorter quantum circuit for phase estimation on early fault-tolerant quantum computers with applications to ground-state energy estimation
• Solving quasi-free and quadratic Lindblad master equations for open fermionic and bosonic systems
• Single-ancilla ground state preparation via Lindbladians
• Nearly tight Trotterization of interacting electrons
• Hypercontractivity of quasi-free quantum semigroups
• Thermal State Preparation via Rounding Promises
• Rapid thermalization of spin chain commuting Hamiltonians
• Heisenberg-limited quantum phase estimation of multiple eigenvalues with few control qubits
• Rapid initial state preparation for the quantum simulation of strongly correlated molecules
• Stochastic Wave-Function Unravelling of the Generalized Lindblad Master Equation
• On the complexity of implementing Trotter steps
• Dissipative preparation and stabilization of many-body quantum states in a superconducting qutrit array
• Efficient quantum Gibbs samplers with Kubo--Martin--Schwinger detailed balance condition
• Symmetry-protected dissipative preparation of matrix product states
• Entropy decay for Davies semigroups of a one dimensional quantum lattice
• Quantum-jump vs stochastic Schrödinger dynamics for Gaussian states with quadratic Hamiltonians and linear Lindbladians