Quantum Processor Embedding via Automorphism Chain Strength Reduction
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Solution Overview
Problem
Existing quantum processors are limited by their architecture and connectivity, which restricts the type, size, and complexity of problems that can be solved, as direct mapping techniques often require significant pre-processing and reduce the scope of solvable problems.
Innovation Solution
The method involves embedding a problem graph into the hardware graph of a quantum processor using automorphisms and modifying the embedding to achieve lower chain strengths, allowing for broader problem-solving capabilities by adjusting coupling strengths and using a hybrid computing system to refine the embedding and ensure chain integrity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If direct mapping techniques are used to map problems to quantum processors, then the mapping process is simple, but the problem scope is limited and requires significant pre-processing
Solution Approach 1:
The patent introduces an intermediary embedding layer that maps problem graph nodes to chains of hardware qubits. This intermediary structure allows flexible problem representation while adapting to the fixed hardware topology, resolving the contradiction between simple mapping and broad problem scope.
Solution Approach 2:
The patent changes the mapping parameters by allowing multiple hardware qubits to represent a single problem variable through chains, and by adjusting coupling strength parameters to handle higher-order interactions. This enables versatile problem representation while maintaining manageable mapping complexity.
2Adaptability or versatility
If higher-order interactions are broken down into pair-wise terms for QUBO formulation, then the problem can be mapped to pairwise-connected quantum processors, but significant pre-processing is required and the computational complexity increases
Solution Approach 1:
The patent segments higher-order interactions into effective pair-wise couplings by introducing auxiliary qubits and coupling chains. This segmentation allows the quantum processor to handle complex interactions through a combination of simpler pairwise terms, reducing pre-processing requirements.
Solution Approach 2:
The patent adds an auxiliary dimension by introducing extra qubits and coupling chains to represent higher-order interactions. This dimensional extension allows the system to encode complex problem structures without requiring complex pre-processing of the original problem formulation.
3Reliability
If multiple qubits are used to represent the same variable in chain embeddings, then chain integrity can be maintained, but the scope of problems that can be solved is reduced
Solution Approach 1:
The patent makes the embedding dynamic by allowing the choice of chain lengths and configurations to be adjusted based on the specific problem being solved. This dynamic adaptation enables the system to maintain chain integrity when needed while maximizing problem scope by using shorter chains when appropriate.
Data Source
AI summary
Generate an automorphism of the problem graph, determine an embedding of the automorphism to the hardware graph and modify the embedding of the problem graph into the hardware graph to correspond to the embedding of the automorphism to the hardware graph. Determine an upper-bound on the required chain strength. Calibrate and record properties of the component of a quantum processor with a digital processor, query the digital processor for a range of properties. Generate a bit mask and change the sign of the bias of individual qubits according to the bit mask before submitting a problem to a quantum processor, apply the same bit mask to the bit result. Generate a second set of parameters of a quantum processor from a first set of parameters via a genetic algorithm.