Quantum Nonlinear Oscillator Annealing for Combinatorial Optimization

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Solution Overview

Problem

Current quantum annealing methods for solving combinatorial optimization problems require lengthy execution times, especially when first-order phase transitions occur, leading to exponential increases in required time with problem size.

Innovation Solution

A calculation device and method utilizing quantum nonlinear oscillators coupled by first and second couplers, with a control unit adjusting control parameters and coupling strengths over time to avoid first-order phase transitions, enabling non-stoquastic quantum annealing and reducing the minimum energy gap, thereby shortening execution time.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Loss of time

If quantum annealing is executed using conventional methods, then the quantum state evolves according to standard quantum mechanics, but the execution time becomes excessively long due to first-order phase transitions

Engineering Contradiction:

Improveexecution timeVSAvoidsolution accuracy

Core Design Contradiction:

Loss of timeVSReliability

Solution Approach 1:

The patent modifies the quantum annealing Hamiltonian by introducing a non-stoquastic term with parameter γ (gamma) that changes the nature of phase transitions. By adjusting the parameter γ in the Hamiltonian H(s) = H₀(s) + γH₁(s), the system transforms first-order phase transitions into second-order phase transitions, thereby reducing execution time while maintaining solution accuracy through controlled parameter evolution

Inventive Principle:

Principle #35Parameter changes

2Measurement precision

If the coupling strength between quantum nonlinear oscillators is increased to improve solution quality, then the minimum energy gap decreases, but the execution time increases exponentially

Engineering Contradiction:

Improvesolution qualityVSAvoidexecution time

Core Design Contradiction:

Measurement precisionVSDuration of action of moving object

Solution Approach 1:

The patent employs dynamic control of coupling strengths through time-dependent functions f(s) and g(s) that modulate the interaction between oscillators. The coupling term γg(s)(a_i†a_j + a_i a_j†) allows the system to adapt coupling strength during annealing, maintaining strong coupling when needed for solution quality while reducing it during critical phases to avoid exponential time increases

Inventive Principle:

Principle #15Dynamics

3Loss of time

If quantum nonlinear oscillators are used to enable non-stoquastic quantum annealing, then first-order phase transitions can be avoided, but the device complexity increases due to additional couplers and control mechanisms

Engineering Contradiction:

Improveexecution timeVSAvoidsystem structure

Core Design Contradiction:

Loss of timeVSDevice complexity

Solution Approach 1:

The patent designs the second coupler to serve multiple functions: it provides non-stoquastic coupling to prevent first-order phase transitions, enables dynamic control of energy gaps, and facilitates adaptive parameter adjustment throughout the annealing process. This multi-functionality reduces the need for separate dedicated components for each control aspect

Inventive Principle:

Principle #6Universality (Multi-functionality)

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 execution time of quantum annealing by potentially transforming first-order phase transitions into second-order phase transitions, decreasing the time required to solve combinatorial optimization problems from exponential to power function growth.

Implementation Method 1

Quantum annealing using quantum mechanical phenomena has been proposed as one method of solving combinatorial optimization problems

Methodology Applied

Scientific EffectQuantum mechanical phenomena:

Implementation Method 2

a first coupler that couples the quantum nonlinear oscillators to one another at a coupling strength corresponding to a combinatorial optimization problem

Methodology Applied

Scientific EffectQuantum coupling:

Implementation Method 3

a second coupler that couples the quantum nonlinear oscillators to one another separately from the first coupler

Methodology Applied

Scientific EffectQuantum coupling:

Implementation Method 4

a control means that, in response to a passage of time, controls the control parameter value of the quantum nonlinear oscillators and the coupling strength between the quantum nonlinear oscillators by the second coupler

Methodology Applied

Scientific EffectQuantum annealing: Annealing

Implementation Method 5

a measurement device that measures the quantum state represented by the quantum nonlinear oscillators

Methodology Applied

Scientific EffectQuantum state measurement:

Data Source

PatentUS20240242105A1Calculation device, calculation method and recording medium

Publication Date: 2024.07.18 NEC CORP

AI summary

A calculation device includes: a plurality of quantum nonlinear oscillators that change a quantum state from one quantum state to one of two quantum states, which differ from the one quantum state, or to a combined state of the two quantum states, according to a change in a control parameter value; a first coupler that couples the quantum nonlinear oscillators to one another at a coupling strength corresponding to a combinatorial optimization problem; a second coupler that couples the quantum nonlinear oscillators to one another separately from the first coupler; a controller that, in response to a passage of time, controls the control parameter value of the quantum nonlinear oscillators and the coupling strength between the quantum nonlinear oscillators by the second coupler; and a measurement device that measures the quantum state represented by the quantum nonlinear oscillators.