Quantum Circuit Optimization via Local SWAP Gate Insertion
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Solution Overview
Problem
Existing quantum circuit optimization methods are inefficient for large numbers of qubits and gates, as they either take too long to find a globally optimal solution or become unusable due to exponential complexity, especially when physical locality constraints are imposed by infrastructure.
Innovation Solution
A method that uses a token exchange algorithm and precalculated shortest paths to iteratively optimize quantum circuits by inserting SWAP gates, minimizing the additional cost while ensuring functional equivalence and locality, employing a heuristic approach to determine relevant permutations and accumulate costs across a sequence of gates.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If SWAP gates are inserted to make quantum gates local, then the circuit can be deployed on physical infrastructures with locality constraints, but the gate transit time and overall circuit cost increase
Solution Approach 1:
The patent pre-calculates shortest paths between all pairs of qubits before optimizing the quantum circuit. This preliminary computation of distance metrics enables efficient determination of SWAP gate requirements without repeated calculations during circuit optimization, reducing overall computational time while ensuring locality constraints are met
Solution Approach 2:
The patent applies a heuristic approach that processes a limited sequence of quantum gates (e.g., 3-5 gates) at a time rather than attempting to optimize the entire circuit globally. This partial action approach finds sufficiently good solutions in polynomial time without requiring exhaustive search of all possible SWAP gate configurations, balancing solution quality with computational feasibility
2Manufacturing precision
If global optimization methods are used to find the optimal circuit configuration, then the best solution is found, but the computational time becomes exponential and unusable for large circuits
Solution Approach 1:
The patent segments the quantum circuit optimization problem into smaller, manageable units by processing sequences of 3-5 quantum gates at a time. This segmentation transforms the exponential global optimization problem into a series of polynomial-time local optimizations, making the overall process computationally feasible while maintaining acceptable solution quality
Solution Approach 2:
The patent changes the optimization parameter from seeking globally optimal solutions to finding locally optimal solutions within small gate sequences. This parameter change from global to local optimization reduces computational complexity from exponential to polynomial time, enabling practical optimization of large-scale quantum circuits
Data Source
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Figure 5a~5d
AI summary
The invention relates to a method for optimizing a quantum circuit composed of an ordered series of quantum gates applied to an initial arrangement of qubit values, consisting of inserting a set of local SWAP gates, so that all the gates in the circuit are local, comprising steps consisting of: - for each gate in the series, if it is not local, inserting a set of local SWAP gates, - determining (S4) the set of permutations, each consisting of a succession of inversions of qubit values along the shortest paths between the qubit positions associated with the gate, and, - choosing (S5) from the set of permutations, a permutation minimizing a cost representing the number of inversions needed to make the gates of a sequence within the series local, of substantially smaller size;- restore (S7) the initial arrangement by establishing a spanning tree of a graph representing the arrangement of the qubits of the circuit, and by performing swaps of qubit values along paths of the tree.;