Optimization Apparatus Imaginary Time Propagation Noise
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Solution Overview
Problem
Quantum annealing methods face challenges in efficiently finding the ground state of Ising models due to prolonged computation times caused by the need to avoid first-order quantum phase transitions, which require slow reduction of the transverse field, and often result in suboptimal solutions or failure to reach the ground state.
Innovation Solution
The introduction of an imaginary time propagation method combined with noise addition to the Ising model simulation, allowing for real-time and imaginary-time propagation processes to efficiently find the ground state by disrupting symmetry and increasing the probability of reaching the optimal solution.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the transverse field is reduced slowly to avoid first-order quantum phase transitions, then the reliability of finding the ground state is improved, but the computation time increases significantly
Solution Approach 1:
The patent applies imaginary time propagation to skip the problematic real-time evolution through the first-order quantum phase transition region. By transforming to imaginary time, the system can rapidly pass through the critical region where the energy gap closes, avoiding the need for slow adiabatic evolution while still reaching the ground state with high probability. This resolves the contradiction by allowing fast computation without sacrificing reliability.
Solution Approach 2:
The patent changes the time parameter from real time to imaginary time in the propagation process. This parameter transformation allows the system to bypass the limitations of real-time quantum annealing, where slow evolution is required to maintain ground state occupancy. In imaginary time, the propagation naturally favors the ground state while allowing rapid evolution, thus improving both speed and reliability.
2Productivity
If the transverse field is reduced quickly to shorten computation time, then the productivity is improved, but the system fails to reach the ground state and settles in excited states
Solution Approach 1:
By using imaginary time propagation, the method can rapidly evolve the system through the entire parameter space including the critical region, achieving fast computation while maintaining accuracy. The imaginary time evolution naturally suppresses excited state populations and drives the system toward the ground state, unlike real-time evolution which requires slow passage through critical regions.
Solution Approach 2:
The patent replaces the physical quantum annealing process (real-time evolution) with an equivalent imaginary-time propagation method. This substitution allows the use of computational techniques that are not constrained by the adiabatic theorem, enabling fast convergence to the ground state without the need for slow parameter changes.
3Reliability
If noise is added to the Ising model simulation, then the ability to disrupt symmetry and reach ground state is improved, but the complexity of the simulation process increases
Solution Approach 1:
The patent introduces noise as an intermediary element in the imaginary time propagation process. This noise serves to disrupt symmetries that could trap the system in excited states or metastable configurations, while the imaginary time evolution ensures that the noise ultimately drives the system toward the ground state. The noise acts as a mediator that facilitates convergence without requiring complex control mechanisms.
Data Source
AI summary
An optimization apparatus finds the ground state of an Ising model that represents a target problem by running a simulation of state changes of the Ising model that occur upon reduction in a magnetic field applied to the Ising model. In doing so, the optimization apparatus adds a value corresponding to noise to some of coefficients used in the simulation. Then, the optimization apparatus performs a first process of real time propagation of reducing strength of the magnetic field as time in the simulation progresses and a second process of reducing energy of the Ising model based on an imaginary time propagation method.