Adaptive Variational Quantum Imaginary Time Evolution Approach for Ground State Preparation

Abstract

An adaptive variational quantum imaginary time evolution (AVQITE) approach is introduced that yields efficient representations of ground states for interacting Hamiltonians on near-term quantum computers. It is based on McLachlan's variational principle applied to imaginary time evolution of variational wave functions. The variational parameters evolve deterministically according to equations of motions that minimize the difference to the exact imaginary time evolution, which is quantified by the McLachlan distance. Rather than working with a fixed variational ansatz, where the McLachlan distance is constrained by the quality of the ansatz, the AVQITE method iteratively expands the ansatz along the dynamical path to keep the McLachlan distance below a chosen threshold. This ensures the state is able to follow the quantum imaginary time evolution path in the system Hilbert space rather than in a restricted variational manifold set by a predefined fixed ansatz. AVQITE is used to prepare ground states of H${}_4$, H${}_2$O and BeH${}_2$ molecules, where it yields compact variational ansätze and ground state energies within chemical accuracy. Polynomial scaling of circuit depth with system size is demonstrated through a set of AVQITE calculations of quantum spin models. Finally, it is shown that quantum Lanczos calculations can also be naturally performed alongside AVQITE without additional quantum resource costs.

16 pages, 4 figures

References in corpus (40)

• A variational eigenvalue solver on a quantum processor
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Barren plateaus in quantum neural network training landscapes
• The theory of variational hybrid quantum-classical algorithms
• Quantum computational chemistry
• Quantum Circuit Learning
• 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
• Towards Practical Quantum Variational Algorithms
• Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
• The Bravyi-Kitaev transformation for quantum computation of electronic structure
• Density matrix embedding: A simple alternative to dynamical mean-field theory
• Variational ansatz-based quantum simulation of imaginary time evolution
• Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States
• Quantum Natural Gradient
• Variational Quantum Computation of Excited States
• Theory of variational quantum simulation
• Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation
• qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansatze on a quantum processor
• An initialization strategy for addressing barren plateaus in parametrized quantum circuits
• Quantum algorithms for electronic structure calculations: particle/hole Hamiltonian and optimized wavefunction expansions
• Density matrix embedding: A strong-coupling quantum embedding theory
• Quantum embedding theories
• Hybrid Quantum-Classical Approach to Quantum Optimal Control
• Exploring entanglement and optimization within the Hamiltonian Variational Ansatz
• Witnessing eigenstates for quantum simulation of Hamiltonian spectra
• Estimating the gradient and higher-order derivatives on quantum hardware
• Efficient variational simulation of non-trivial quantum states
• Methodology for replacing indirect measurements with direct measurements
• Adaptive Variational Quantum Dynamics Simulations
• Quantum Power Method by a Superposition of Time-Evolved States
• Calculation of the Green's function on near-term quantum computers
• Efficient step-merged quantum imaginary time evolution algorithm for quantum chemistry
• Slave Boson Theory of Orbital Differentiation with Crystal Field Effects: Application to UO${}_2$
• Gutzwiller Hybrid Quantum-Classical Computing Approach for Correlated Materials
• Making Trotters Sprint: A Variational Imaginary Time Ansatz for Quantum Many-body Systems
• Rotationally invariant slave-boson and density matrix embedding theory: A unified framework and a comparative study on the 1D and 2D Hubbard Model

Cited by in corpus (53)

• The Variational Quantum Eigensolver: a review of methods and best practices
• Performance comparison of optimization methods on variational quantum algorithms
• Overlap-ADAPT-VQE: Practical Quantum Chemistry on Quantum Computers via Overlap-Guided Compact Ansätze
• Toward Quantum Computing Phase Diagrams of Gauge Theories with Thermal Pure Quantum States
• Unitary Selective Coupled-Cluster Method
• Hybrid quantum-classical algorithm for computing imaginary-time correlation functions
• Improved algorithms of quantum imaginary time evolution for ground and excited states of molecular systems
• Quantum imaginary time evolution steered by reinforcement learning
• Avoiding symmetry roadblocks and minimizing the measurement overhead of adaptive variational quantum eigensolvers
• Benchmarking variational quantum eigensolvers for the square-octagon-lattice Kitaev model
• Nearly-optimal state preparation for quantum simulations of lattice gauge theories
• Adaptive variational simulation for open quantum systems
• Preparing quantum many-body scar states on quantum computers
• Quantum algorithms for grid-based variational time evolution
• Adaptive variational quantum minimally entangled typical thermal states for finite temperature simulations
• Comparative study of adaptive variational quantum eigensolvers for multi-orbital impurity models
• Adaptive construction of shallower quantum circuits with quantum spin projection for fermionic systems
• Quantum Simulations of SO(5) Many-Fermion Systems using Qudits
• Reducing the Resources Required by ADAPT-VQE Using Coupled Exchange Operators and Improved Subroutines
• Variational quantum iterative power algorithms for global optimization
• Real-time chiral dynamics at finite temperature from quantum simulation
• Variational quantum algorithm for generalized eigenvalue problems and its application to the finite element method
• Quantum subspace expansion in the presence of hardware noise
• Quantum Computed Green's Functions using a Cumulant Expansion of the Lanczos Method
• Towards Efficient Quantum Computing for Quantum Chemistry: Reducing Circuit Complexity with Transcorrelated and Adaptive Ansatz Techniques
• Improved iterative quantum algorithm for ground-state preparation
• Accelerating quantum imaginary-time evolution with random measurements
• Two-dimensional coherent spectrum of high-spin models via a quantum computing approach
• Double-bracket quantum algorithms for quantum imaginary-time evolution
• Coupled cluster method tailored with quantum computing
• Greedy Gradient-free Adaptive Variational Quantum Algorithms on a Noisy Intermediate Scale Quantum Computer
• Quantum Dynamics Simulation of the Advection-Diffusion Equation
• Quantum Simulation of non-Abelian Lattice Gauge Theories: a variational approach to ${\mathbb{D}}_8$
• Adaptive variational quantum dynamics simulations with compressed circuits and fewer measurements
• Adaptive variational ground state preparation for spin-1 models on qubit-based architectures
• Problem-tailored Simulation of Energy Transport on Noisy Quantum Computers
• Adaptive variational quantum computing approaches for Green's functions and nonlinear susceptibilities
• Exact block encoding of imaginary time evolution with universal quantum neural networks
• Quantum simulation of the phase transition of the massive Thirring model
• Exploiting subspace constraints and ab initio variational methods for quantum chemistry
• Classical Benchmarks for Variational Quantum Eigensolver Simulations of the Hubbard Model
• Comparative study on compact quantum circuits of hybrid quantum-classical algorithms for quantum impurity models
• Performance and scaling analysis of variational quantum simulation
• Adaptive Quantum Generative Training using an Unbounded Loss Function
• Efficient Berry Phase Calculation via Adaptive Variational Quantum Computing Approach
• Role of Riemannian geometry in double-bracket quantum imaginary-time evolution
• Robust preparation of ground state phases under noisy imaginary time evolution
• Quantum simulation of massive Thirring and Gross--Neveu models for arbitrary number of flavors
• Nonperturbative signatures of fractons in the twisted multiflavor Schwinger Model
• Double-bracket quantum algorithms for high-fidelity ground state preparation
• Hybrid Real-Imaginary Time Evolution for Low-Depth Hamiltonian Simulation in Quantum Optimization
• Linear Foundation Model for Quantum Embedding: Data-Driven Compression of the Ghost Gutzwiller Variational Space
• Quantum Algorithms for State Preparation and Data Classification based on Stabilizer Codes