Modeling superconducting quantum circuit systems

A non-transitory computer-readable medium storing computer-executable instructions which, when executed by one or more processors, cause the one or more processors to perform operations comprising:

• generating a graph representing a quantum circuit system, wherein the graph includes vertices and edges, the edges representing circuit elements of the quantum circuit system and the vertices representing physical connections between the circuit elements of the quantum circuit system;
• assigning, to the graph, inverse inductances, conductances, capacitances, and junction inverse inductances to respective edges of the graph based on a lumped-element approximation of the quantum circuit system;
• determining a coordinate system based on the graph;
• generating a matrix representation of the system based on the coordinate system;
• determining a Hamiltonian for the quantum circuit system using the matrix representation;
• and
• simulating the quantum circuit system based on the Hamiltonian;
• wherein the matrix representation is specific to a plurality of sub-circuits within the quantum circuit system, the sub-circuits being identified at specific ports.

A computer system comprising:

• memory that stores computer-executable instructions;
• and
• one or more processors configured to access the memory, wherein the one or more processors are configured to execute the computer-executable instructions to:
• generate a graph representing a quantum circuit system, wherein the graph includes vertices and edges, the edges representing circuit elements of the quantum circuit system and the vertices representing physical connections between the circuit elements of the quantum circuit system;
• assign, to the graph, inverse inductances, conductances, capacitances, and junction inverse inductances to respective edges of the graph based on a lumped-element approximation of the quantum circuit system;
• determine a coordinate system based on the graph;
• generate a matrix representation of the system based on the coordinate system;
• determine a Hamiltonian for the quantum circuit system using the matrix representation;
• and
• simulate the quantum circuit system based on the Hamiltonian;
• wherein the matrix representation is specific to a plurality of sub-circuits within the quantum circuit system, the sub-circuits being identified at specific ports.

A non-transitory computer-readable medium storing computer-executable instructions which, when executed by one or more processors, cause the one or more processors to perform operations comprising:

• generating a graph representing a quantum circuit system, wherein the graph includes vertices and edges, the edges representing circuit elements of the quantum circuit system and the vertices representing physical connections between the circuit elements of the quantum circuit system;
• assigning, to the graph, inverse inductances, conductances, capacitances, and junction inverse inductances to respective edges of the graph based on a lumped-element approximation of the quantum circuit system;
• providing a system of equations of motion representing current in the quantum circuit system;
• generating a spanning tree based on the graph;
• generating a matrix representation of the system of equations of motion based on the spanning tree;
• and
• simulating the quantum circuit system based on the matrix representation;
• wherein the quantum circuit system is comprised of a plurality of modular units with a cascading construction.

A computer system comprising:

• memory that stores computer-executable instructions;
• and
• one or more processors configured to access the memory, wherein the one or more processors are configured to execute the computer-executable instructions to:
• generate a graph representing a quantum circuit system, wherein the graph includes vertices and edges, the edges representing circuit elements of the quantum circuit system and the vertices representing physical connections between the circuit elements of the quantum circuit system;
• assign inverse inductances, conductances, capacitances, and junction inverse inductances to respective edges of the graph based on a lumped-element approximation of the quantum circuit system;
• provide a system of equations of motion representing current in the quantum circuit system;
• generate a spanning tree based on the graph;
• generate a matrix representation of the system of equations of motion based on the spanning tree;
• and
• simulate the quantum circuit system based on the matrix representation;
• wherein the quantum circuit system is comprised of a plurality of modular units with a cascading construction.

A computer-implemented simulation method comprising:

• generating a graph representing a quantum circuit system, wherein the graph includes vertices and edges, the edges representing circuit elements of the quantum circuit system and the vertices representing physical connections between the circuit elements of the quantum circuit system;
• assigning, to the graph, inverse inductances, conductances, capacitances, and junction inverse inductances to respective edges of the graph based on a lumped-element approximation of the quantum circuit system;
• determining a coordinate system based on the graph;
• generating a matrix representation of the system based on the coordinate system;
• determining a Hamiltonian for the quantum circuit system using the matrix representation;
• and
• simulating the quantum circuit system based on the Hamiltonian;
• wherein the matrix representation is specific to a plurality of sub-circuits within the quantum circuit system, the sub-circuits being identified at specific ports.