Open Quantum System Simulation via Heisenberg Formulation
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current simulation methods for open quantum systems, particularly those using the Schrödinger picture, face significant computational challenges when dealing with composite systems, as the size of the density matrix grows exponentially with the number of quantum entities, making simulations of even two or three quantum entities computationally demanding or impractical.
Innovation Solution
The proposed method employs the Heisenberg formulation, focusing on local calculations within decoherence-free spaces and using a trace-preserving and completely-positive linear Kraus map formulation to simulate open quantum systems, avoiding the full Hilbert space tensor product calculations that are computationally infeasible. This involves splitting the Lindblad master equation into local nominal dynamics and perturbation portions, with the processor calculating invariant operators and approximating the time evolution of the density operator.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If the Schrödinger picture simulation method is used with sufficient truncature to capture the physics of the Lindblad master equation, then the simulation accuracy is improved, but the computational time and resources become prohibitively large for composite systems with multiple quantum entities
Solution Approach 1:
The patent segments the global simulation problem into local problems by separating the evolution of each quantum entity's density matrix from the others. Instead of computing the full composite density matrix evolution, each quantum entity's density matrix is evolved independently using local Lindblad master equations, dramatically reducing computational complexity while maintaining accuracy for composite systems
Solution Approach 2:
The patent extracts and eliminates the unnecessary tensor product calculations that dominate computational cost in traditional Schrödinger picture simulations. By directly computing local density matrix evolutions without forming the full composite density matrix, the method removes the exponential scaling bottleneck while preserving the essential physics of composite quantum systems
2Measurement precision
If the truncature parameter N is increased to capture the dynamics of higher energy states, then the simulation precision is improved, but the size of the density matrix and computational complexity increase exponentially
Solution Approach 1:
The patent segments the computational problem by treating each quantum entity's density matrix evolution independently rather than as part of a large composite system. This segmentation allows using moderate truncature values for each local density matrix while avoiding the exponential complexity that would result from using high truncature on the full composite system
Solution Approach 2:
The patent applies partial action by computing only the necessary local density matrix evolutions required to capture the essential physics, rather than performing exhaustive calculations on the full composite system. This partial computation approach achieves sufficient precision without the excessive computational complexity of complete simulations
Data Source
AI summary
A device simulates an open quantum system including one or more quantum entities, each quantum entity being stabilized around a decoherence-free space. The corresponding simulation method is based on an original asymptotic development adapted to the so-called Heisenberg formulation of quantum mechanics and based on invariant operators of the local and nominal dynamics associated with each of the quantum entities. A computer-implemented simulates an open quantum system including a plurality of quantum entities including: one or more first quantum entities each being stabilized around a decoherence-free space, and a one or more second entities wherein each second quantum entity has an unstabilized component during a time period T such that a respective decoherence-free space cannot be defined for each second quantum entity during time 0<t<T.