Digital quantum simulation of non-perturbative dynamics of open systems with orthogonal polynomials

Abstract

Classical non-perturbative simulations of open quantum systems' dynamics face several scalability problems, namely, exponential scaling of the computational effort as a function of either the time length of the simulation or the size of the open system. In this work, we propose the use of the Time Evolving Density operator with Orthogonal Polynomials Algorithm (TEDOPA) on a quantum computer, which we term as Quantum TEDOPA (Q-TEDOPA), to simulate non-perturbative dynamics of open quantum systems linearly coupled to a bosonic environment (continuous phonon bath). By performing a change of basis of the Hamiltonian, the TEDOPA yields a chain of harmonic oscillators with only local nearest-neighbour interactions, making this algorithm suitable for implementation on quantum devices with limited qubit connectivity such as superconducting quantum processors. We analyse in detail the implementation of the TEDOPA on a quantum device and show that exponential scalings of computational resources can potentially be avoided for time-evolution simulations of the systems considered in this work. We applied the proposed method to the simulation of the exciton transport between two light-harvesting molecules in the regime of moderate coupling strength to a non-Markovian harmonic oscillator environment on an IBMQ device. Applications of the Q-TEDOPA span problems which can not be solved by perturbation techniques belonging to different areas, such as the dynamics of quantum biological systems and strongly correlated condensed matter systems.

References in corpus (61)

• The density-matrix renormalization group in the age of matrix product states
• Quantum Simulation
• Area laws for the entanglement entropy - a review
• Long-lived quantum coherence in photosynthetic complexes at physiological temperature
• Hamiltonian Simulation by Qubitization
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Efficient variational quantum simulator incorporating active error minimisation
• Toward the first quantum simulation with quantum speedup
• Noise tailoring for scalable quantum computation via randomized compiling
• Hybrid quantum-classical algorithms and quantum error mitigation
• Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
• A Theory of Trotter Error
• Efficient simulation of strong system-environment interactions
• Quantum Approximate Optimization of Non-Planar Graph Problems on a Planar Superconducting Processor
• Theory of variational quantum simulation
• Origin of Long Lived Coherences in Light-Harvesting Complexes
• DBG2OLC: Efficient Assembly of Large Genomes Using Long Erroneous Reads of the Third Generation Sequencing Technologies
• IBM Q Experience as a versatile experimental testbed for simulating open quantum systems
• Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials
• Probabilistic error cancellation with sparse Pauli-Lindblad models on noisy quantum processors
• Hybrid quantum-classical approach to correlated materials
• Variational quantum simulation of general processes
• Variational Fast Forwarding for Quantum Simulation Beyond the Coherence Time
• Digital zero noise extrapolation for quantum error mitigation
• Efficient simulation of finite-temperature open quantum systems
• Higher Order Decompositions of Ordered Operator Exponentials
• Digital quantum simulation of open quantum systems using quantum imaginary time evolution
• Resource-efficient digital quantum simulation of $d$-level systems for photonic, vibrational, and spin-$s$ Hamiltonians
• Quantum Simulation of Open Quantum Systems Using a Unitary Decomposition of Operators
• Mitiq: A software package for error mitigation on noisy quantum computers
• Mappings of open quantum systems onto chain representations and Markovian embeddings
• Tensor network simulation of non-Markovian dynamics in organic polaritons
• Simulating open quantum dynamics with time-dependent variational matrix product states: Towards microscopic correlation of environment dynamics and reduced system evolution
• An efficient quantum algorithm for the time evolution of parameterized circuits
• Bloch-Redfield equations for modeling light-harvesting complexes
• Digital quantum computation of fermion-boson interacting systems
• Observation of separated dynamics of charge and spin in the Fermi-Hubbard model
• Hamiltonian simulation in the low-energy subspace
• Faster Digital Quantum Simulation by Symmetry Protection
• Multi-exponential Error Extrapolation and Combining Error Mitigation Techniques for NISQ Applications
• A general quantum algorithm for open quantum dynamics demonstrated with the Fenna-Matthews-Olson complex
• Capturing Non-Markovian Dynamics on Near-Term Quantum Computers
• Concentration for random product formulas
• Simulating Bosonic Baths with Error Bars
• Variational Hamiltonian Diagonalization for Dynamical Quantum Simulation
• Open systems with error bounds: spin boson model with spectral density variations
• Dynamical mean field theory algorithm and experiment on quantum computers
• Computationally Efficient Zero Noise Extrapolation for Quantum Gate Error Mitigation
• Quantum dynamics simulations beyond the coherence time on NISQ hardware by variational Trotter compression
• Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer
• Hardware-efficient quantum algorithm for the simulation of open-system dynamics and thermalisation
• Efficient Quantum Algorithms for Simulating Lindblad Evolution
• Fingerprint and universal Markovian closure of structured bosonic environments
• Variational Quantum Simulation of Ultrastrong Light-Matter Coupling
• Excitation dynamics in chain-mapped environments
• Optical response of laser-driven charge-transfer complex described by Holstein-Hubbard model coupled to heat baths: Hierarchical equations of motion approach
• Non-Equilibrium Dynamics of a Dissipative Two-Site Hubbard Model Simulated on IBM Quantum Computers
• Long-Time Error-Mitigating Simulation of Open Quantum Systems on Near Term Quantum Computers
• Interplay of vibration- and environment-assisted energy transfer
• Simulation of non-radiative energy transfer in photosynthetic systems using a quantum computer
• Influence of non-adiabatic effects on linear absorption spectra in the condensed phase: Methylene blue

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