Classically optimized Hamiltonian simulation

Abstract

Hamiltonian simulation is a promising application for quantum computers to achieve a quantum advantage. We present classical algorithms based on tensor network methods to optimize quantum circuits for this task. We show that, compared to Trotter product formulas, the classically optimized circuits can be orders of magnitude more accurate and significantly extend the total simulation time.

13 pages, 16 figures, 2 tables

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• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
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Cited by in corpus (52)

• NISQ Computers: A Path to Quantum Supremacy
• Towards adiabatic quantum computing using compressed quantum circuits
• Hamiltonian variational ansatz without barren plateaus
• Optimised Trotter Decompositions for Classical and Quantum Computing
• Realization of quantum signal processing on a noisy quantum computer
• Quantum computing for chemistry and physics applications from a Monte Carlo perspective
• Nonlinear dynamics as a ground-state solution on quantum computers
• Measuring the Loschmidt amplitude for finite-energy properties of the Fermi-Hubbard model on an ion-trap quantum computer
• Variational Quantum Time Evolution without the Quantum Geometric Tensor
• Classification of dynamical Lie algebras for translation-invariant 2-local spin systems in one dimension
• Efficient Large-Scale Many-Body Quantum Dynamics via Local-Information Time Evolution
• Hamiltonian simulation for hyperbolic partial differential equations by scalable quantum circuits
• Krylov complexity and Trotter transitions in unitary circuit dynamics
• Quantum algorithms for scientific computing
• Scalable Quantum Simulations of Scattering in Scalar Field Theory on 120 Qubits
• Combining Matrix Product States and Noisy Quantum Computers for Quantum Simulation
• Assessment of various Hamiltonian partitionings for the electronic structure problem on a quantum computer using the Trotter approximation
• Quantum algorithm for partial differential equations of non-conservative systems with spatially varying parameters
• Problem specific classical optimization of Hamiltonian simulation
• Continuous Hamiltonian dynamics on digital quantum computers without discretization error
• Adaptive Trotterization for time-dependent Hamiltonian quantum dynamics using piecewise conservation laws
• QFactor: A Domain-Specific Optimizer for Quantum Circuit Instantiation
• Time Evolution of Uniform Sequential Circuits
• Trotter error with commutator scaling for the Fermi-Hubbard model
• Riemannian quantum circuit optimization for Hamiltonian simulation
• Adaptive projected variational quantum dynamics
• Efficient and practical Hamiltonian simulation from time-dependent product formulas
• Sequential optimal selection of a single-qubit gate and its relation to barren plateau in parameterized quantum circuits
• Efficient Quantum Circuit Compilation for Near-Term Quantum Advantage
• Approximate Quantum Compiling for Quantum Simulation: A Tensor Network based approach
• Scalable simulation of non-equilibrium quantum dynamics via classically optimised unitary circuits
• Tensor-based quantum phase difference estimation for large-scale demonstration
• Quantum Tensor Product Decomposition from Choi State Tomography
• Riemannian quantum circuit optimization based on matrix product operators
• Quantum circuit compilation with quantum computers
• Quantum simulation costs for Suzuki-Trotter decomposition of quantum many-body lattice models
• Quantum error mitigation in the regime of high noise using deep neural network: Trotterized dynamics
• Deep Circuit Compression for Quantum Dynamics via Tensor Networks
• Cost of Emulating a Small Quantum Annealing Problem in the Circuit-Model
• Simplifying the simulation of local Hamiltonian dynamics
• Optimal compression of constrained quantum time evolution
• Preparation Circuits for Matrix Product States by Classical Variational Disentanglement
• A recipe for local simulation of strongly-correlated fermionic matter on quantum computers: the 2D Fermi-Hubbard model
• Correcting and extending Trotterized quantum many-body dynamics
• Describing Trotterized Time Evolutions on Noisy Quantum Computers via Static Effective Lindbladians
• Trotter error time scaling separation via commutant decomposition
• Enhancing Scalability of Quantum Eigenvalue Transformation of Unitary Matrices for Ground State Preparation through Adaptive Finer Filtering
• Digit quantum simulation of a fermion field in an expanding universe
• Fluctuation-guided adaptive random compiler for Hamiltonian simulation
• Tensor-based phase difference estimation on time series analysis
• A quantum eigenvalue solver based on tensor networks
• Time evolution of controlled many-body quantum systems with matrix product operators