Qubit Routing Optimization via Doubly Stochastic Matrices
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Solution Overview
Problem
Current qubit routing techniques in quantum computing face challenges in efficiently mapping logical qubits to physical qubits while adhering to hardware connectivity constraints, leading to increased circuit depth and error rates.
Innovation Solution
The use of doubly stochastic matrices in a swap mapper to determine optimal qubit routing by minimizing constraint violations and circuit depth, thereby improving the efficiency and accuracy of quantum circuit design.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional qubit routing techniques are used to map logical qubits to physical qubits, then the mapping can be achieved, but the circuit depth increases and error rates increase due to hardware connectivity constraints
Solution Approach 1:
The patent changes the mathematical representation from traditional routing methods to doubly stochastic matrices, allowing continuous optimization of qubit permutations. This parameter transformation enables finding optimal routing paths that minimize circuit depth while satisfying hardware connectivity constraints, thereby reducing both circuit depth and error rates simultaneously
Solution Approach 2:
The patent introduces dynamic optimization by using gradient descent methods to iteratively adjust the doubly stochastic matrices. This dynamic approach allows the routing solution to adapt and converge to optimal configurations, minimizing circuit depth and constraint violations rather than relying on static routing tables
2Ease of operation
If SWAP gates are introduced to satisfy connectivity constraints, then the routing can be achieved, but the solver time increases from minutes to hours
Solution Approach 1:
The patent replaces traditional combinatorial optimization methods with a continuous mathematical optimization approach using doubly stochastic matrices and gradient descent. This substitution transforms the discrete, computationally intensive SWAP gate insertion problem into a continuous optimization problem that converges much faster, reducing solver time from hours to minutes while maintaining routing feasibility
Solution Approach 2:
By changing the problem formulation from discrete permutation search to continuous matrix optimization, the patent achieves faster convergence. The doubly stochastic matrix parameters can be optimized using efficient gradient-based methods, dramatically reducing the computational time required to find feasible routing solutions
Data Source
AI summary
A method for building a quantum computing circuit optimizes qubit routing in the circuit. A computer processor receives a plurality of qubits and an initial input circuit layer. Layers of quantum sub-circuits are extracted from the initial input circuit layer. Adjacency matrices are built for the layers of quantum sub-circuits. A cost function is determined for the extracted layers, based on the number of constraints violations determined by the doubly stochastic matrices. In addition, a final quantum circuit topology is selected based on the cost function of the extracted layers.