Lindbladian Simulation with Logarithmic Precision Scaling via Two Ancillas

Area of Science:

• Quantum Computing
• Quantum Information Science
• Computational Chemistry

Background:

• Simulating open quantum systems is crucial for quantum chemistry and error correction.
• Existing methods for simulating Lindbladian dynamics face challenges with experimental feasibility and circuit depth.
• Nonunitary operations inherent in open systems pose significant computational hurdles.

Purpose of the Study:

• To develop a novel framework for efficient and accurate simulation of Lindbladian dynamics in open quantum systems.
• To overcome the limitations of existing methods regarding ancilla usage and circuit depth.
• To provide a scalable solution for near-term quantum hardware.

Main Methods:

• Introduction of the linear combinations of superoperators framework.
• Utilizing simple gates and Trotter decompositions for error compensation.
• Extension of the method to handle time-dependent Lindbladians.

Main Results:

• Achieved exponential reduction in circuit depth with respect to simulation precision using only two ancillas.
• Demonstrated logarithmic depth in precision for time-dependent Lindbladians.
• Numerical simulations confirmed significant performance advantages over existing approaches.

Conclusions:

• The proposed framework offers a practical and scalable method for simulating open quantum systems.
• The approach significantly reduces the complexity and resource requirements for quantum simulations.
• This work paves the way for advanced applications in quantum chemistry and error correction on current quantum devices.