Superconducting Quantum Circuit Tiling for Fast Eigenmode Simulation
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Solution Overview
Problem
Existing methods for determining physical parameters of superconducting quantum circuits are computationally expensive and limited in the number of eigenmodes that can be simulated, particularly for larger and more complex circuits, using finite-element solvers and other tools that are not tailored for quantum circuits.
Innovation Solution
A computer-implemented method that tiles a superconducting quantum circuit blueprint into elements with no self-resonance frequencies, calculates scattering parameters, and uses a holomorphic non-linear eigenvalue solver to determine mode frequencies and amplitudes, allowing parallel processing and accurate eigenmode determination.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If large finite-element Maxwell solvers are used to simulate superconducting quantum circuits, then simulation accuracy is improved, but computation time and computational cost increase significantly
Solution Approach 1:
The patent divides the quantum circuit blueprint into multiple non-overlapping elements, each representing a portion of the circuit. Each element is characterized independently by computing its scattering parameters, and then all elements are assembled into a global scattering matrix. This segmentation allows parallel computation of individual element parameters and significantly reduces the computational burden compared to simulating the entire circuit with a single large finite-element solver.
2Measurement precision
If large finite-element Maxwell solvers are used to simulate superconducting quantum circuits, then simulation accuracy is improved, but the number of eigenmodes that can be simulated is limited
Solution Approach 1:
The patent transforms the eigenmode simulation problem from solving a large system of differential equations directly to finding eigenvalues of a matrix constructed from scattering parameters. By using the scattering matrix formulation and solving the characteristic equation det(I - S) = 0, the method can efficiently compute a large number of eigenmodes without the severe limitations imposed by finite-element solvers on the number of extractable eigenmodes.
3Adaptability or versatility
If conventional simulation tools are used for superconducting quantum circuits, then general-purpose simulation capability is maintained, but computational efficiency and speed are reduced
Solution Approach 1:
The patent replaces the traditional finite-element method (a continuous field-solving approach) with a discrete scattering parameter-based matrix formulation. Instead of solving Maxwell's equations continuously across the entire circuit geometry, the method uses scattering parameters characterizing each circuit element and assembles them into a global matrix system. This substitution of the simulation methodology enables efficient parallel computation and dramatically improves computational efficiency while maintaining accuracy.
Data Source
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AI summary
A computer-implemented method for determining physical parameters of a superconducting quantum circuit comprises the following operations: a) obtaining a superconducting quantum circuit blueprint comprising a representation of a physical arrangement of a superconducting metal and a dielectric substrate for forming a 2D or 3D superconducting quantum circuit and a frequency range in the microwave domain, b) tiling (500) said superconducting quantum circuit blueprint into elements having at least one port for receiving or emitting electromagnetic microwaves, each of said elements being defined as a closed region of said representation and being such that it showcases no self-resonance frequency in said frequency range, and such that each element comprises a port connected to a port of another element, the elements thereby defining a closed network and a corresponding network matrix based on the connections between the ports of respective elements, c) obtaining (510) scattering parameters for each of said elements, said scattering parameters defining the relationships between all output radiation and all input radiation for each port of each of said elements in the form of a scattering matrix in which the scattering parameters are expressed as a complex function of frequency that is holomorphic in a complex domain, d) determining (530) mode frequencies and corresponding mode amplitude vectors for a superconducting quantum circuit fabricated using the superconducting quantum circuit blueprint by using a holomorphic non-linear eigenvalue solver to solve the equation (FS(ω) - I)a = 0 where F is the network matrix, S is a block diagonal matrix comprising all of the scattering matrices of operation c), I is the identity matrix, ω is a complex frequency in the domain where matrix S is holomorphic, and a is a mode amplitude vector.