Variational quantum computing for quantum simulation: principles, implementations, and challenges

Abstract

This work presents a comprehensive overview of variational quantum computing and their key role in advancing quantum simulation. This work explores the simulation of quantum systems and sets itself apart from approaches centered on classical data processing, by focusing on the critical role of quantum data in Variational Quantum Algorithms (VQA) and Quantum Machine Learning (QML). We systematically delineate the foundational principles of variational quantum computing, establish their motivational and challenges context within the noisy intermediate-scale quantum (NISQ) era, and critically examine their application across a range of prototypical quantum simulation problems. Operating within a hybrid quantum-classical framework, these algorithms represent a promising yet problem-dependent pathway whose practicality remains contingent on trainability and scalability under noise and barren-plateau constraints.This review serves to complement and extend existing literature by synthesizing the most recent advancements in the field and providing a focused perspective on the persistent challenges and emerging opportunities that define the current landscape of variational quantum computing for quantum simulation.

20 pages, 5 figures, 9 example boxes

References in corpus (99)

• Quantum Computing in the NISQ era and beyond
• Quantum Machine Learning
• A variational eigenvalue solver on a quantum processor
• Quantum algorithm for solving linear systems of equations
• Variational Quantum Algorithms
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Quantum Simulation
• Barren plateaus in quantum neural network training landscapes
• The theory of variational hybrid quantum-classical algorithms
• Noisy intermediate-scale quantum (NISQ) algorithms
• Quantum Circuit Learning
• Quantum Chemistry in the Age of Quantum Computing
• Quantum Convolutional Neural Networks
• Simulated Quantum Computation of Molecular Energies
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Evaluating analytic gradients on quantum hardware
• The Variational Quantum Eigensolver: a review of methods and best practices
• Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms
• Scalable Quantum Simulation of Molecular Energies
• Challenges and Opportunities in Quantum Machine Learning
• Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
• The quest for a Quantum Neural Network
• A short introduction to the Lindblad Master Equation
• Connecting ansatz expressibility to gradient magnitudes and barren plateaus
• Self-Verifying Variational Quantum Simulation of the Lattice Schwinger Model
• Quantum Computation as Geometry
• Toward the first quantum simulation with quantum speedup
• Variational ansatz-based quantum simulation of imaginary time evolution
• Quantum advantage in learning from experiments
• Variational Quantum Computation of Excited States
• Theory of variational quantum simulation
• Generalized Unitary Coupled Cluster Wavefunctions for Quantum Computation
• Training variational quantum algorithms is NP-hard
• Polynomial-time quantum algorithm for the simulation of chemical dynamics
• Quantum Implementation of Unitary Coupled Cluster for Simulating Molecular Electronic Structure
• Variational quantum simulation of general processes
• Variational Fast Forwarding for Quantum Simulation Beyond the Coherence Time
• Exploring entanglement and optimization within the Hamiltonian Variational Ansatz
• Effect of barren plateaus on gradient-free optimization
• Beyond Barren Plateaus: Quantum Variational Algorithms Are Swamped With Traps
• Diagnosing Barren Plateaus with Tools from Quantum Optimal Control
• Optimal Quantum Measurements of Expectation Values of Observables
• Quantum circuits for strongly correlated quantum systems
• Quantum Simulation of Generic Many-Body Open System Dynamics Using Classical Noise
• Quantum Machine Learning for Chemistry and Physics
• Digital quantum simulation of open quantum systems using quantum imaginary time evolution
• Reachability Deficits in Quantum Approximate Optimization
• A Lie Algebraic Theory of Barren Plateaus for Deep Parameterized Quantum Circuits
• Quantum Machine Learning for Electronic Structure Calculations
• Variational Thermal Quantum Simulation via Thermofield Double States
• Quantum Simulating Nature's Fundamental Fields
• Higher Order Derivatives of Quantum Neural Networks with Barren Plateaus
• Quantum localization bounds Trotter errors in digital quantum simulation
• Beyond-classical computation in quantum simulation
• An efficient quantum algorithm for the time evolution of parameterized circuits
• On barren plateaus and cost function locality in variational quantum algorithms
• Quantum Machine Learning in High Energy Physics
• Universal Variational Quantum Computation
• A Comparison of Various Classical Optimizers for a Variational Quantum Linear Solver
• Simulation of Many-Body Hamiltonians using Perturbation Theory with Bounded-Strength Interactions
• Quantum simulation of the single-particle Schrodinger equation
• Optimal quantum circuits for general phase estimation
• Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks
• Controllability of open quantum systems with Kraus-map dynamics
• Application of Quantum Machine Learning using the Quantum Kernel Algorithm on High Energy Physics Analysis at the LHC
• Quantum-optimal-control-inspired ansatz for variational quantum algorithms
• Implementation of quantum imaginary-time evolution method on NISQ devices: Nonlocal approximation
• Does provable absence of barren plateaus imply classical simulability?
• On the practical usefulness of the Hardware Efficient Ansatz
• Hamiltonian variational ansatz without barren plateaus
• Variational preparation of finite-temperature states on a quantum computer
• The Adjoint Is All You Need: Characterizing Barren Plateaus in Quantum Ansätze
• Variational Consistent Histories as a Hybrid Algorithm for Quantum Foundations
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition
• Benchmarking of Different Optimizers in the Variational Quantum Algorithms for Applications in Quantum Chemistry
• Limitations in quantum computing from resource constraints
• Progress toward favorable landscapes in quantum combinatorial optimization
• Quantum approximate optimization via learning-based adaptive optimization
• Absence of barren plateaus in finite local-depth circuits with long-range entanglement
• Quantum simulation of thermodynamics in an integrated quantum photonic processor
• Trainability Enhancement of Parameterized Quantum Circuits via Reduced-Domain Parameter Initialization
• Dynamical simulation via quantum machine learning with provable generalization
• A Neural-Network Variational Quantum Algorithm for Many-Body Dynamics
• Non-trivial symmetries in quantum landscapes and their resilience to quantum noise
• A semi-agnostic ansatz with variable structure for quantum machine learning
• Quantum neural networks to simulate many-body quantum systems
• Hardware-efficient quantum algorithm for the simulation of open-system dynamics and thermalisation
• Variational Gibbs State Preparation on NISQ devices
• Adaptive variational simulation for open quantum systems
• Quantum Convolutional Neural Networks with Interaction Layers for Classification of Classical Data
• Lie-algebraic classical simulations for quantum computing
• Fault-tolerant quantum algorithms for quantum molecular systems: A survey
• Calculating the ground state energy of benzene under spatial deformations with noisy quantum computing
• Variational quantum algorithm for ergotropy estimation in quantum many-body batteries
• Extending the Variational Quantum Eigensolver to Finite Temperatures
• Mitigating Quantum Errors via Truncated Neumann Series
• Variational-quantum-eigensolver-inspired optimization for spin-chain work extraction
• Simulating thermodynamic properties of dinuclear metal complexes using Variational Quantum Algorithms