Alternate Annealing Scheme for Higher-Order Combinatorial Optimization
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Solution Overview
Problem
Quantum annealing machines can only handle combinatorial optimization problems represented in a second-order form, limiting their ability to solve equations with third- or higher-order terms of variables.
Innovation Solution
A combinatorial optimization problem processing apparatus that employs an alternate optimization algorithm using both annealing and non-annealing schemes to solve functions with third- or higher-order terms, involving a first optimization processing for variable q and a second optimization processing for variable X, with conditions set to maximize the partition function.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If quantum annealing machine uses interaction between adjacent quantum bits, then it can process combinatorial optimization problems at high speed, but it can handle only problems represented in second-order form
Solution Approach 1:
The patent introduces an auxiliary variable as an intermediary to transform the problem representation. By adding this intermediate variable, the system can represent higher-order interactions (third-order and above) using only pairwise interactions between quantum bits, thereby maintaining compatibility with the quantum annealing hardware while expanding the range of solvable problems
Solution Approach 2:
The patent changes the parameter representation of the optimization problem by transforming higher-order terms into equivalent second-order formulations through parameter substitution. This allows the problem to be expressed in a form that matches the quantum annealing machine's operational constraints while preserving the original problem's solution space
2Adaptability or versatility
If alternate optimization algorithm is used to solve higher-order problems, then solution capability is improved, but computational complexity increases
Solution Approach 1:
The patent segments the optimization problem into two separate sub-problems: one involving the original variables and another involving the auxiliary variable. By dividing the complex higher-order optimization into smaller, more manageable second-order sub-problems that can be solved alternately, the overall computational complexity is reduced while maintaining the ability to solve higher-order problems
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
Enables the acquisition of solutions for combinatorial optimization problems represented by functions with third- or higher-order terms, leveraging quantum annealing to find local maximum values of the partition function.
Implementation Method 1
an annealing unit configured to acquire, using an annealing scheme, a candidate for a first solution in an alternate optimization algorithm
Data Source
AI summary
A combinatorial optimization problem processing apparatus includes an annealing unit that acquires, using an annealing scheme, a candidate for a first solution that is a variable q satisfying a first condition regarding a partition function whose Hamiltonian is a function representing a combination optimization problem that is an analysis target and the function includes third- or higher-order terms of a variable q, the Hamiltonian being represented by an integral representation using a variable X, the Hamiltonian being represented by a sum of a first equation that includes only second- or lower-order terms of the variable q and a second equation that does not include the variable q, in an alternate optimization algorithm in which first optimization processing for acquiring the first solution and second optimization processing for acquiring a second solution that is a variable X satisfying a second condition regarding the partition function are repeated until an end condition is satisfied, a calculation unit that acquires the second solution, and a solution candidate acquisition unit that acquires a candidate for the immediately preceding first solution when the end condition is satisfied, as a candidate for a solution of the combinatorial optimization problem.