Practical Unitary Simulator for Non-Markovian Complex Processes.

Area of Science:

• Quantum computing
• Computational science
• Statistical modeling

Background:

• Stochastic processes are fundamental in quantitative sciences but challenging to simulate.
• Classical simulations often require significant memory and can suffer from information loss.
• Existing quantum models have limitations in memory or operational requirements.

Purpose of the Study:

• To propose a novel unitary quantum simulator for discrete-time stochastic processes.
• To reduce internal memory requirements compared to classical analogues.
• To enable efficient and information-preserving simulation of stochastic processes.

Main Methods:

• Development of a unitary quantum simulator architecture.
• Utilizing a small, finite-dimensional Hilbert space for the quantum simulator.
• Stepwise construction methodology for broad applicability to various stochastic processes.

Main Results:

• The proposed quantum simulator requires less internal memory than any classical analogue.
• Memory requirements are on par with the best previous quantum models.
• The simulator operates unitarily, preventing unnecessary information loss.

Conclusions:

• The quantum simulator offers a more efficient and accurate method for simulating stochastic processes.
• The design facilitates experimental implementation on current quantum computation platforms.
• This work advances the simulation capabilities for complex stochastic systems.