Adaptive Annealing Schedule for Quantum Phase Transition in Ising Model

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Solution Overview

Problem

Quantum annealing methods face challenges in efficiently searching for the ground state of Ising models due to prolonged calculation times caused by first-order quantum phase transitions, where the energy gap between the ground and excited states becomes smaller, leading to increased computational complexity.

Innovation Solution

Implementing a non-transitory computer-readable storage medium with a solution search program that adjusts the annealing schedule before and after a quantum phase transition occurs, reducing the magnetic field strength according to different schedules and incorporating a nonlinear external magnetic field to prevent transitions to excited states, thereby reducing calculation amounts and improving solution search efficiency.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If a standard quantum annealing method is used to search for the ground state of the Ising model, then the solution can be obtained through adiabatic transition, but the calculation time is prolonged when the energy gap between ground state and excited state becomes small

Engineering Contradiction:

Improveprobability of obtaining ground stateVSAvoidcalculation time

Core Design Contradiction:

ReliabilityVSLoss of time

Solution Approach 1:

The patent applies dynamics by making the annealing schedule adaptive rather than static. The schedule dynamically adjusts the magnetic field reduction rate based on the detected quantum phase transition point. Before the transition point, the magnetic field is reduced at a first rate; after detecting the transition point (through energy gap monitoring or other indicators), the rate changes to a second rate, optimizing both accuracy and speed.

Inventive Principle:

Principle #15Dynamics

Solution Approach 2:

The patent changes the parameter of magnetic field strength according to a two-stage annealing schedule. The key innovation is changing the rate parameter of magnetic field reduction based on the system state. By monitoring the energy gap or other phase transition indicators, the system switches between different reduction rates, effectively adapting to the changing energy landscape during quantum annealing.

Inventive Principle:

Principle #35Parameter changes

2Productivity

If the magnetic field is reduced rapidly to shorten calculation time, then productivity improves, but the system may transition to excited states instead of reaching the ground state

Engineering Contradiction:

Improvesolution search speedVSAvoidaccuracy of ground state solution

Core Design Contradiction:

ProductivityVSReliability

Solution Approach 1:

The patent applies preliminary action by detecting the quantum phase transition point before completing the full annealing process. By monitoring indicators such as energy gap changes during the annealing process, the system identifies the transition point in advance and adjusts the magnetic field reduction rate accordingly, ensuring the system remains in or near the ground state while optimizing the overall calculation time.

Inventive Principle:

Principle #10Preliminary action

3Reliability

If a slow adiabatic transition is used to ensure ground state accuracy, then solution reliability improves, but the calculation time increases significantly

Engineering Contradiction:

Improveground state solution accuracyVSAvoidcalculation efficiency

Core Design Contradiction:

ReliabilityVSProductivity

Solution Approach 1:

The patent applies segmentation by dividing the quantum annealing process into two distinct stages based on the quantum phase transition point. The first stage (before transition) uses a slower magnetic field reduction rate to maintain accuracy, while the second stage (after transition) uses a faster rate to improve efficiency. This segmentation allows the system to optimize for accuracy when needed and for speed when safe.

Inventive Principle:

Principle #1Segmentation

Applied Scientific Principles

This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.

Function Achieved in This Case

This approach reduces the calculation time and increases the probability of obtaining the ground state by optimizing the annealing schedule and introducing a nonlinear external magnetic field, enhancing the efficiency of quantum annealing in solving combinatorial optimization problems.

Implementation Method 1

a quantum phase transition occurs in the Ising model

Methodology Applied

Scientific EffectQuantum phase transition: Phase Change

Implementation Method 2

By weakening the magnetic field so as not to excite to an excited state from here, it is possible to sufficiently slowly transition to a Hamiltonian of an optimization problem to be obtained

Methodology Applied

Scientific EffectAdiabatic transition:

Data Source

PatentUS20230351236A1Storage medium, solution search method, and information processing device

Publication Date: 2023.11.02 FUJITSU LTD

AI summary

A non-transitory computer-readable storage medium storing a solution search program that causes at least one computer to execute a process, the process includes reducing, when searching for a ground state of the Ising model that represents a problem by obtaining a state change of the Ising model, a strength of a magnetic field applied to the Ising model according to a first annealing schedule from an initial state of the Ising model; and reducing, after a quantum phase transition occurs in the Ising model, the strength of the magnetic field according to a second annealing schedule.