Parity Encoding for Quantum Annealing Optimization
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Solution Overview
Problem
Current quantum annealing hardware faces inefficiencies in solving parity encoded optimization problems due to rigid layout topologies and limitations in simulating higher-order interaction terms, requiring significant overhead and manual mapping processes, which restricts direct hardware usage and increases computational complexity.
Innovation Solution
A method that transforms parity encoded optimization problems by replacing higher-order terms with unconstrained parity variables, allowing the encoding of optimization problems directly onto existing quantum annealing hardware topologies, reducing computational overhead and enabling efficient mapping and solution on the hardware itself.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If minor-embedding is used to map problems to native topology, then the problem can be solved on quantum annealing hardware, but the number of variables increases significantly and performance is affected
Solution Approach 1:
The patent segments the problem mapping process into two distinct approaches: (1) native mapping for quadratic problems that directly use the hardware topology, and (2) parity encoding for higher-order problems that use algebraic transformations. This segmentation allows each type of problem to be handled with the most appropriate method, avoiding the variable overhead of minor-embedding for problems that don't require it.
Solution Approach 2:
The patent introduces parity-encoded variables as intermediaries that represent groups of original variables. Instead of directly mapping each original variable to hardware qubits (which causes variable overhead), the parity-encoded variables serve as mediators that can be efficiently mapped to the hardware topology while preserving the problem structure.
2Adaptability or versatility
If higher-order interaction terms are simulated using additional variables, then the optimization problem can be solved, but significant overhead in the form of additional variables is introduced
Solution Approach 1:
The patent changes the parameter representation of higher-order interactions by transforming them into quadratic forms using parity encoding. Instead of representing a k-body interaction directly (which would require many variables), the interaction is rewritten in terms of parity-encoded variables that reduce the dimensional overhead while maintaining the interaction's computational effect.
Solution Approach 2:
The patent creates a transformed copy of the optimization problem using parity-encoded variables. This copied version of the problem has the same solution space and optimal solutions as the original, but with reduced variable overhead when mapped to hardware. The copying process involves algebraic transformations that preserve the problem's essential structure.
3Adaptability or versatility
If manual mapping is performed for each new problem, then the problem can be solved on hardware, but the process is time consuming and computationally difficult
Solution Approach 1:
The patent creates a universal mapping framework based on parity encoding that can handle multiple types of optimization problems (quadratic and higher-order) through a single systematic approach. This universal method eliminates the need for problem-specific manual mapping, as the same parity encoding transformations can be applied across different problem types, significantly reducing the time and computational effort required for each new problem.
Data Source
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AI summary
A method (100) for solving parity encoded optimization problems having high-order interaction terms on quantum annealing hardware (10) is proposed, wherein an optimization problem is encoded in a function f of terms of quantized variables s, wherein a parity encoded function f' is obtained from the function f by replacing the quantized variables s and products of the quantized variables s with constrained parity variables s' and by adding additional terms of higher than quadratic order in the constrained parity variables s' representing constraints on the constrained parity variables s', wherein a transformed function f" is obtained by introducing unconstrained parity variables y by replacing terms of higher than quadratic order in the constrained parity variables s' with terms of at most quadratic order in the constrained parity variables s' and in the unconstrained parity variables y.