Towards Quantum Simulation of Non-Markovian Open Quantum Dynamics: A Universal and Compact Theory

Abstract

Non-Markovianity, the intricate dependence of an open quantum system on its temporal evolution history, holds tremendous implications across various scientific disciplines. However, accurately characterizing the complex non-Markovian effects has posed a formidable challenge for numerical simulations. While quantum computing technologies show promise, a universal theory enabling practical quantum algorithm implementation has been elusive. We address this gap by introducing the dissipaton-embedded quantum master equation in second quantization (DQME-SQ). This exact and compact theory offers two key advantages: representability by quantum circuits and universal applicability to any Gaussian environment. We demonstrate these capabilities through digital quantum simulations of non-Markovian dissipative dynamics in both bosonic and fermionic environments. The DQME-SQ framework opens a new horizon for the efficient exploration of complex open quantum systems by leveraging the rapidly advancing quantum computing technologies.

Typo correction, addition of detailed analysis of complexity and error

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Cited by in corpus (7)

• Role of Quantum Coherence in Kinetic Uncertainty Relations
• Simulating Non-Markovian Quantum Dynamics on NISQ Computers Using the Hierarchical Equations of Motion
• Input-Output Hierarchical Equations Of Motion
• Nonlinear response theory for lossy superconducting quantum circuits
• Multi-set variational quantum dynamics algorithm for simulating nonadiabatic dynamics on quantum computers
• Extended Non-Markovian Stochastic Schrödinger Equation with Complex Frequency Modes for General Basis Functions
• Exact description of fermionic reservoirs via purified damped ancillary fermions