Quantum dynamics simulations beyond the coherence time on NISQ hardware by variational Trotter compression

Abstract

We demonstrate a post-quench dynamics simulation of a Heisenberg model on present-day IBM quantum hardware that extends beyond the coherence time of the device. This is achieved using a hybrid quantum-classical algorithm that propagates a state using Trotter evolution and then performs a classical optimization that effectively compresses the time-evolved state into a variational form. When iterated, this procedure enables simulations to arbitrary times with an error controlled by the compression fidelity and a fixed Trotter step size. We show how to measure the required cost function, the overlap between the time-evolved and variational states, on present-day hardware, making use of several error mitigation methods. In addition to carrying out simulations on real hardware, we investigate the performance and scaling behavior of the algorithm with noiseless and noisy classical simulations. We find the main bottleneck in going to larger system sizes to be the difficulty of carrying out the optimization of the noisy cost function.

arXiv comment11 pages, 9 figures

References in corpus (41)

• Quantum Computing in the NISQ era and beyond
• The density-matrix renormalization group in the age of matrix product states
• Variational Quantum Algorithms
• Noisy intermediate-scale quantum (NISQ) algorithms
• Error mitigation for short-depth quantum circuits
• Quantum fingerprinting
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Optimal Hamiltonian Simulation by Quantum Signal Processing
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Towards Practical Quantum Variational Algorithms
• Efficient quantum algorithms for simulating sparse Hamiltonians
• Efficient variational quantum simulator incorporating active error minimisation
• Toward the first quantum simulation with quantum speedup
• Hybrid quantum-classical algorithms and quantum error mitigation
• A Theory of Trotter Error
• Theory of variational quantum simulation
• Optimal Quantum Circuits for General Two-Qubit Gates
• qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansatze on a quantum processor
• Simulating quantum many-body dynamics on a current digital quantum computer
• Variational Fast Forwarding for Quantum Simulation Beyond the Coherence Time
• Exploring entanglement and optimization within the Hamiltonian Variational Ansatz
• Structure optimization for parameterized quantum circuits
• Real- and imaginary-time evolution with compressed quantum circuits
• The SWAP test and the Hong-Ou-Mandel effect are equivalent
• Sequential minimal optimization for quantum-classical hybrid algorithms
• Nearly optimal lattice simulation by product formulas
• Hardware-efficient variational quantum algorithms for time evolution
• Is efficiency of classical simulations of quantum dynamics related to integrability?
• Exponential Error Suppression for Near-Term Quantum Devices
• Exact Ising model simulation on a quantum computer
• Adaptive Variational Quantum Dynamics Simulations
• Parallel Quantum Simulation of Large Systems on Small Quantum Computers
• An efficient quantum algorithm for the time evolution of parameterized circuits
• Fast-forwarding of Hamiltonians and Exponentially Precise Measurements
• Unified approach to data-driven quantum error mitigation
• Multi-exponential Error Extrapolation and Combining Error Mitigation Techniques for NISQ Applications
• Quasiprobability decompositions with reduced sampling overhead
• Reinforcement Learning for Digital Quantum Simulation
• Algebraic Compression of Quantum Circuits for Hamiltonian Evolution
• Destructive Error Interference in Product-Formula Lattice Simulation
• Constant-Depth Circuits for Dynamic Simulations of Materials on Quantum Computers

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• Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer
• Quantum time dynamics of 1D-Heisenberg models employing the Yang-Baxter equation for circuit compression
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• Lie-algebraic classical simulations for quantum computing
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• Qutrit Circuits and Algebraic Relations: A Pathway to Efficient Spin-1 Hamiltonian Simulation
• Adaptive projected variational quantum dynamics
• Tsallis relative $\alpha$ entropy of coherence dynamics in Grover's search algorithm
• Digital quantum simulation of non-perturbative dynamics of open systems with orthogonal polynomials
• Two-dimensional coherent spectrum of high-spin models via a quantum computing approach
• Adaptive variational quantum dynamics simulations with compressed circuits and fewer measurements
• Problem-tailored Simulation of Energy Transport on Noisy Quantum Computers
• Adaptive variational ground state preparation for spin-1 models on qubit-based architectures
• Exploring quantum ergodicity of unitary evolution through the Krylov approach
• Compressed quantum error mitigation
• Accelerating two-dimensional electronic spectroscopy simulations with a probe qubit protocol
• Deep Circuit Compression for Quantum Dynamics via Tensor Networks
• Optimal compression of constrained quantum time evolution
• Systematic many-fermion Hamiltonian input scheme and spectral calculations on quantum computers
• Fast-forwardability of Qubit-mapped Fermion models based on Cartan decomposition