Accelerated variational algorithms for digital quantum simulation of many-body ground states

Abstract

One of the key applications for the emerging quantum simulators is to emulate the ground state of many-body systems, as it is of great interest in various fields from condensed matter physics to material science. Traditionally, in an analog sense, adiabatic evolution has been proposed to slowly evolve a simple Hamiltonian, initialized in its ground state, to the Hamiltonian of interest such that the final state becomes the desired ground state. Recently, variational methods have also been proposed and realized in quantum simulators for emulating the ground state of many-body systems. Here, we first provide a quantitative comparison between the adiabatic and variational methods with respect to required quantum resources on digital quantum simulators, namely the depth of the circuit and the number of two-qubit quantum gates. Our results show that the variational methods are less demanding with respect to these resources. However, they need to be hybridized with a classical optimization which can converge slowly. Therefore, as the second result of the paper, we provide two different approaches for speeding the convergence of the classical optimizer by taking a good initial guess for the parameters of the variational circuit. We show that these approaches are applicable to a wide range of Hamiltonian and provide significant improvement in the optimization procedure.

15 pages, 10 figures

References in corpus (67)

• Adam: A Method for Stochastic Optimization
• A variational eigenvalue solver on a quantum processor
• The density-matrix renormalization group
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Quantum Simulation
• Probing many-body dynamics on a 51-atom quantum simulator
• The theory of variational hybrid quantum-classical algorithms
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• Machine learning phases of matter
• Integrated Photonic Quantum Technologies
• Quantum Communication Through an Unmodulated Spin Chain
• Error mitigation for short-depth quantum circuits
• Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
• Extending the computational reach of a noisy superconducting quantum processor
• Scalable Quantum Simulation of Molecular Energies
• Towards Practical Quantum Variational Algorithms
• Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
• Quantum optimization using variational algorithms on near-term quantum devices
• Efficient variational quantum simulator incorporating active error minimisation
• Discovering Phase Transitions with Unsupervised Learning
• Universal digital quantum simulation with trapped ions
• Self-Verifying Variational Quantum Simulation of the Lattice Schwinger Model
• Variational ansatz-based quantum simulation of imaginary time evolution
• Practical Quantum Error Mitigation for Near-Future Applications
• Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States
• Quantum dynamics of a single, mobile spin impurity
• Spectral signatures of many-body localization with interacting photons
• Simulation of Electronic Structure Hamiltonians Using Quantum Computers
• Digitized adiabatic quantum computing with a superconducting circuit
• Variational Quantum Computation of Excited States
• Microscopic observation of magnon bound states and their dynamics
• Robust determination of molecular spectra on a quantum processor
• Theory of variational quantum simulation
• Optimal Quantum Circuits for General Two-Qubit Gates
• Quantum chemistry calculations on a trapped-ion quantum simulator
• Quantum algorithms for electronic structure calculations: particle/hole Hamiltonian and optimized wavefunction expansions
• Quantum simulation of a Fermi-Hubbard model using a semiconductor quantum dot array
• Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems
• Entanglement Entropy dynamics in Heisenberg chains
• Quantum Implementation of Unitary Coupled Cluster for Simulating Molecular Electronic Structure
• Emulating many-body localization with a superconducting quantum processor
• Variational quantum algorithms for discovering Hamiltonian spectra
• Digital quantum simulation of spin models with circuit quantum electrodynamics
• Low-cost error mitigation by symmetry verification
• Machine Learning Phases of Strongly Correlated Fermions
• Probing Slow Relaxation and Many-Body Localization in Two-Dimensional Quasi-Periodic Systems
• Finding Exponential Product Formulas of Higher Orders
• Mitigation of readout noise in near-term quantum devices by classical post-processing based on detector tomography
• One-Dimensional Magnetism
• Machine Learning Assisted Many-Body Entanglement Measurement
• Digital Quantum Simulation of Spin Systems in Superconducting Circuits
• Negativity as the Entanglement Measure to Probe the Kondo Regime in the Spin-Chain Kondo Model
• Quantum Simulation of the Hubbard Model with Dopant Atoms in Silicon
• State transfer in static and dynamic spin chains with disorder
• Quantum Impurity Entanglement
• Scaling of variational quantum circuit depth for condensed matter systems
• Solving Quantum Ground-State Problems with Nuclear Magnetic Resonance
• Information Transferring Ability of the Different Phases of a finite XXZ Spin Chain
• Adiabatic many-body state preparation and information transfer in quantum dot arrays
• Impurity Entanglement Entropy and the Kondo Screening Cloud
• Quantum Computing with Acceptor Spins in Silicon
• Spin State Transfer in Laterally Coupled Quantum Dot Chains with Disorders
• Accelerated variational algorithms for digital quantum simulation of many-body ground states
• A diagrammatic approach to variational quantum ansatz construction
• Variational quantum Gibbs state preparation with a truncated Taylor series
• Error Mitigation in Quantum Computers subject to Spatially Correlated Noise

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• Fermionic Simulators for Enhanced Scalability of Variational Quantum Simulation
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• Quantum simulation costs for Suzuki-Trotter decomposition of quantum many-body lattice models
• Entanglement-informed Construction of Variational Quantum Circuits
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