Low-depth Hamiltonian Simulation by Adaptive Product Formula

Abstract

Various Hamiltonian simulation algorithms have been proposed to efficiently study the dynamics of quantum systems on a quantum computer. The existing algorithms generally approximate the time evolution operators, which may need a deep quantum circuit that is beyond the capability of near-term noisy quantum devices. Here, focusing on the time evolution of a fixed input quantum state, we propose an adaptive approach to construct a low-depth time evolution circuit. By introducing a measurable quantifier that characterizes the simulation error, we use an adaptive strategy to learn the shallow quantum circuit that minimizes that error. We numerically test the adaptive method with electronic Hamiltonians of the ${\mathrm{H}}_2\mathrm{O}$ and ${\mathrm{H}}_4$ molecules, and the transverse field Ising model with random coefficients. Compared to the first-order Suzuki-Trotter product formula, our method can significantly reduce the circuit depth (specifically the number of two-qubit gates) by around two orders while maintaining the simulation accuracy. We show applications of the method in simulating many-body dynamics and solving energy spectra with the quantum Krylov algorithm. Our work sheds light on practical Hamiltonian simulation with noisy-intermediate-scale-quantum devices.

arXiv comment23 pages, 2 figures

References in corpus (55)

• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Variational Quantum Algorithms
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Quantum Simulation
• A Quantum Engineer's Guide to Superconducting Qubits
• Noisy intermediate-scale quantum (NISQ) algorithms
• Quantum computational chemistry
• Adiabatic Quantum Computing
• Superconducting Qubits: Current State of Play
• Simulated Quantum Computation of Molecular Energies
• Error mitigation for short-depth quantum circuits
• Microwave photonics with superconducting quantum circuits
• Predicting Many Properties of a Quantum System from Very Few Measurements
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Fermionic quantum computation
• Extending the computational reach of a noisy superconducting quantum processor
• Hamiltonian Simulation by Qubitization
• Optimal Hamiltonian Simulation by Quantum Signal Processing
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
• Efficient variational quantum simulator incorporating active error minimisation
• Quantum Simulators: Architectures and Opportunities
• Toward the first quantum simulation with quantum speedup
• Variational ansatz-based quantum simulation of imaginary time evolution
• Practical Quantum Error Mitigation for Near-Future Applications
• Hybrid quantum-classical algorithms and quantum error mitigation
• Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States
• A Theory of Trotter Error
• Theory of variational quantum simulation
• Quantum Simulation of Electronic Structure with Linear Depth and Connectivity
• qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansatze on a quantum processor
• Cloud Quantum Computing of an Atomic Nucleus
• A random compiler for fast Hamiltonian simulation
• Mitigating measurement errors in multi-qubit experiments
• Qulacs: a fast and versatile quantum circuit simulator for research purpose
• Measurement Optimization in the Variational Quantum Eigensolver Using a Minimum Clique Cover
• Learning-based quantum error mitigation
• Variational quantum simulation of general processes
• Adiabatic Quantum Simulation of Quantum Chemistry
• Nearly optimal lattice simulation by product formulas
• Faster quantum simulation by randomization
• Quantum localization bounds Trotter errors in digital quantum simulation
• Decoding quantum errors with subspace expansions
• Adaptive Variational Quantum Dynamics Simulations
• Quantum Computation of Finite-Temperature Static and Dynamical Properties of Spin Systems Using Quantum Imaginary Time Evolution
• Dynamics of quantum information
• Time-dependent Hamiltonian simulation with $L^1$-norm scaling
• Nearly Optimal Measurement Scheduling for Partial Tomography of Quantum States
• Mitigating realistic noise in practical noisy intermediate-scale quantum devices
• Quantum simulation with hybrid tensor networks
• Experimental quantum state measurement with classical shadows
• Concentration for random product formulas
• Quantum inverse iteration algorithm for programmable quantum simulators
• Perturbative quantum simulation

Cited by in corpus (12)

• Barren Plateaus in Variational Quantum Computing
• Quantum Computing for High-Energy Physics: State of the Art and Challenges. Summary of the QC4HEP Working Group
• Error Bounds for Variational Quantum Time Evolution
• Fault-tolerant quantum algorithms for quantum molecular systems: A survey
• Adaptive Trotterization for time-dependent Hamiltonian quantum dynamics using piecewise conservation laws
• Qsun: an open-source platform towards practical quantum machine learning applications
• Measuring Trotter error and its application to precision-guaranteed Hamiltonian simulations
• Practical limitations of quantum data propagation on noisy quantum processors
• Multi-set variational quantum dynamics algorithm for simulating nonadiabatic dynamics on quantum computers
• Divergence-free algorithms for solving nonlinear differential equations on quantum computers
• Optical Quantum Computing
• Single-Period Floquet Control of Bosonic Codes with Quantum Lattice Gates