Quantum Processor Problem Compilation Using Ancilla Variables
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Solution Overview
Problem
Quantum computers face limitations in solving k-local optimization problems due to constraints on the number of variables and precision of coupling coefficients, leading to issues when converting problems to 2-local forms using ancilla variables.
Innovation Solution
A method is developed to transform k-local optimization problems into modified specifications using ancilla variables, optimizing their selection through procedures like Integer Linear Programming and greedy algorithms to limit the number of variables and precision required, enabling solution on quantum processors with limited hardware capacity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If ancilla variables are introduced to transform k-local problems to 2-local form, then the problem can be solved on quantum hardware with coupling constraints, but the total number of variables exceeds hardware capacity
Solution Approach 1:
The patent segments the transformation process into multiple passes, where each pass handles a subset of k-local terms and introduces only the necessary ancilla variables for that subset. This incremental approach prevents the total variable count from exceeding hardware capacity while still transforming the entire k-local problem to 2-local form.
Solution Approach 2:
The patent applies partial transformation by selecting and transforming only certain k-local terms in each pass rather than transforming all terms simultaneously. This partial action allows the system to make progress on solving k-local problems while keeping the number of introduced ancilla variables within hardware limits.
2Adaptability or versatility
If ancilla variables are introduced to transform k-local problems to 2-local form, then the problem can be solved on quantum hardware with coupling constraints, but the required precision of coupling coefficients exceeds available precision
Solution Approach 1:
The patent segments the transformation into passes that group k-local terms by their coefficient magnitudes. Each pass handles terms with similar precision requirements, introducing ancilla variables that maintain coupling coefficients within the available precision range. This prevents the accumulation of precision requirements that would otherwise exceed hardware capabilities.
Solution Approach 2:
The patent changes the parameters of the transformation process by adjusting which terms are transformed in each pass and how ancilla variables are assigned. This dynamic parameter adjustment ensures that coupling coefficients remain within the precision constraints of the quantum hardware while still achieving the goal of solving k-local problems.
3Ease of manufacture
If random selection of variable pairs is used to form ancilla variables, then the transformation can be implemented simply, but the total number of variables and precision requirements exceed quantum computer capacity
Solution Approach 1:
The patent makes the selection of variable pairs dynamic rather than random or static. The selection adapts based on the current state of the transformation, the remaining k-local terms to be processed, and the hardware capacity constraints. This dynamic selection optimizes the number of ancilla variables introduced while maintaining implementation feasibility.
Solution Approach 2:
The patent incorporates feedback mechanisms where the selection of ancilla variables and the transformation process are adjusted based on monitoring the total variable count and precision requirements. This feedback ensures that the transformation remains within quantum computer capacity while still achieving the goal of solving k-local problems.
Data Source
AI summary
Solution of a problem of determining values of a set of N problem variables xi makes use of a quantum processor that has a limited number of hardware elements for representing quantum bits and/or limitations on coupling between quantum bits. A method includes accepting a specification of the problem that includes a specification of a set of terms where each term corresponds to a product of at least three variables and is associated with a non-zero coefficient. A set of ancilla variables, each ancilla variable corresponding to a pair of problem variables, is determined by applying an optimization procedure to the specification of the set of the terms. The accepted problem specification is then transformed according to the determined ancilla variables to form a modified problem specification for use in configuring the quantum processor and solution of problem.