Researchers from George Mason University have developed a quantum algorithm to simulate nonMarkovian quantum dynamics in open quantum systems. Based on Feynman’s path integral formulation of the multispin-boson Hamiltonian, the algorithm applies to many condensed-phase quantum dynamics. It fully utilizes the quantum computer’s ability to create superposition and entanglement states and represent sizeable Hilbert space. The algorithm also simplifies numerical convergence. The simulation results show that the memory requirement on a quantum machine is significantly reduced compared to a classical computer, suggesting potential for simulating complex nonMarkovian quantum dynamics.
Quantum Algorithm for Simulating NonMarkovian Quantum Dynamics
Peter L Walters and Fei Wang from the Department of Chemistry and Biochemistry and Quantum Science and Engineering Center at George Mason University have developed a path integral-based quantum algorithm. This algorithm is designed to simulate nonMarkovian quantum dynamics in open quantum systems. The research, published in Physical Review Research, focuses on a quantum system linearly coupled to its harmonic bath.
Open Quantum System Dynamics
Open quantum system dynamics has been a growing area of interest in recent years. The theory of open quantum systems provides a versatile tool to study quantum systems interacting with their external environment. This has led to the emergence of various interesting physics, including nonequilibrium phase transitions, topological and entangled state preparation by reservoir engineering, information backflow, and direct emulation of open quantum systems on quantum devices.
Quantum Algorithm Development
The development of quantum algorithms for simulating open quantum system dynamics has been a focus in recent years. However, most of the literature has been focused on Markovian dynamics. The algorithm developed by Walters and Wang is for nonMarkovian evolution, which is still in the nascent stage of development. The algorithm is based on Feynman’s path integral formulation of the multispin-boson Hamiltonian.
Advantages of the New Algorithm
The new algorithm has several merits. Firstly, it is generally applicable to simulating many condensed phase quantum dynamics. Secondly, all the path sums are done on the quantum machine, fully taking advantage of the quantum computer to create superposition and entanglement states and its natural ability to represent exponentially large Hilbert space. Lastly, the nonMarkovianity is directly related to the time span of correlation function in the influence functional, making the numerical convergence straightforward.
Simulation Results and Future Work
The simulation results were presented with a comparison between classical and quantum computing. The memory requirement has exponential reduction on the quantum machine, whereas the runtime complexity stays roughly the same as for the classical computer. This points to the possibility of using this algorithm to simulate multilevel and multisite nonMarkovian quantum dynamics beyond classical computers’ reach. The researchers plan to continue their work in this area.
In the article titled “Path integral quantum algorithm for simulating non-Markovian quantum dynamics in open quantum systems”, authors Patrick Walters and F. Wang present their research on a new quantum algorithm. The article was published in the Physical Review Research journal on February 1, 2024. The research focuses on the simulation of non-Markovian quantum dynamics in open quantum systems using a path integral quantum algorithm.
