SYSTEMS AND METHODS FOR SIMULATION OF QUANTUM CIRCUITS USING EXTRACTED HAMILTONIANS
A method for optimizing a quantum circuit is disclosured. The method comprises acquiring a representation of a quantum circuit comprising one or more qubits, transforming, by linear transformation, first Hamiltonian corresponding to the quantum circuit to generate modes, generating a third Hamiltonian by removing the free modes from a second Hamiltonian in which free modes are decoupled from non-free the second Hamiltonian, simulating a behavior of the quantum circuit using the third Hamiltonian, and adjusting a design of the quantum circuit based on the simulated behavior of the quantum circuit.
1 . A method for optimizing a quantum circuit, comprising:
acquiring a representation of a quantum circuit comprising one or more qubits;
transforming, using a linear transformation matrix, a first Hamiltonian corresponding to the quantum circuit to generate a second Hamiltonian in which free modes are decoupled from non-free modes;
generating a third Hamiltonian by removing the free modes from the second Hamiltonian;
simulating a behavior of the quantum circuit using the third Hamiltonian; and
adjusting a design of the quantum circuit based on the simulated behavior of the quantum circuit.
2 . The method of claim 1 , wherein transforming the first Hamiltonian to generate the second Hamiltonian comprises:
transforming an inverse of a charge coupling matrix of the first Hamiltonian to an inverse of a transformed charge coupling matrix such that the transformed charge coupling matrix in the second Hamiltonian is block diagonalized into a free mode sector and a non-free mode sector.
3 . The method of claim 2 , wherein transforming the first Hamiltonian to generate the second Hamiltonian further comprises:
transforming a charge operator of the first Hamiltonian using the linear transformation matrix.
4 . The method of claim 2 , wherein transforming the first Hamiltonian to generate the second Hamiltonian further comprises:
transforming a flux operator of the first Hamiltonian such that a canonical commutation relation of the first Hamiltonian is preserved in the second Hamiltonian.
5 . The method of claim 1 , further comprises performing Gaussian elimination on an effective capacitance matrix of the first Hamiltonian using the linear transformation matrix.
6 . The method of claim 1 , wherein simulating the behavior of the quantum circuit using the third Hamiltonian comprises:
obtaining discrete energy eigenvalues of the quantum circuit by diagonalizing the third Hamiltonian.
7 . The method of claim 1 , wherein the behavior of the quantum circuit comprises a frequency of a qubit among the one or more qubits.
8 . An apparatus for optimizing a quantum circuit, comprising:
a memory for storing a set of instructions; and
at least one processor configured to execute the set of instructions to cause the apparatus to perform operations including:
acquiring a representation of a quantum circuit comprising one or more qubits;
transforming, using a linear transformation matrix, a first Hamiltonian corresponding to the quantum circuit to generate a second Hamiltonian in which free modes are decoupled from non-free modes;
generating a third Hamiltonian by removing the free modes from the second Hamiltonian;
simulating a behavior of the quantum circuit using the third Hamiltonian; and
adjusting a design of the quantum circuit based on the simulated behavior of the quantum circuit.
9 . The apparatus of claim 8 , wherein transforming the first Hamiltonian to generate the second Hamiltonian includes:
transforming an inverse of a charge coupling matrix of the first Hamiltonian to an inverse of a transformed charge coupling matrix such that the transformed charge coupling matrix in the second Hamiltonian is block diagonalized into a free mode sector and a non-free mode sector.
10 . The apparatus of claim 9 , wherein in transforming the first Hamiltonian to generate the second Hamiltonian further includes:
transforming a charge operator of the first Hamiltonian using the linear transformation matrix.
11 . The apparatus of claim 9 , wherein in transforming the first Hamiltonian to generate the second Hamiltonian further includes:
transforming a flux operator of the first Hamiltonian such that a canonical commutation relation of the first Hamiltonian is preserved in the second Hamiltonian.
12 . The apparatus of claim 8 , wherein the linear transformation matrix is configured to perform Gaussian elimination on an effective capacitance matrix of the first Hamiltonian.
13 . The apparatus of claim 8 , wherein simulating the behavior of the quantum circuit using the third Hamiltonian further comprises:
obtaining discrete energy eigenvalues of the quantum circuit by diagonalizing the third Hamiltonian.
14 . The apparatus of claim 7 wherein the behavior of the quantum circuit comprises a frequency of a qubit among the one or more qubits.
15 . A non-transitory computer readable medium that stores a set of instructions that is executable by at least one processor of a computing device to perform a method for optimizing a quantum circuit, the method comprising:
acquiring a representation of a quantum circuit comprising one or more qubits;
transforming, using a linear transformation matrix, a first Hamiltonian corresponding to the quantum circuit to generate a second Hamiltonian in which free modes are decoupled from non-free modes;
generating a third Hamiltonian by removing the free modes from the second Hamiltonian;
simulating a behavior of the quantum circuit using the third Hamiltonian; and
adjusting a design of the quantum circuit based on the simulated behavior of the quantum circuit.
16 . The computer readable medium of claim 15 , wherein in transforming the first Hamiltonian to generate the second Hamiltonian further comprises:
transforming an inverse of a charge coupling matrix of the first Hamiltonian to an inverse of a transformed charge coupling matrix such that the transformed charge coupling matrix in the second Hamiltonian is block diagonalized into a free mode sector and a non-free mode sector.
17 . The computer readable medium of claim 16 , wherein in transforming the first Hamiltonian to generate the second Hamiltonian further comprises:
transforming a charge operator of the first Hamiltonian using the linear transformation matrix.
18 . The computer readable medium of claim 16 , wherein in transforming the first Hamiltonian to generate the second Hamiltonian further comprises:
transforming a flux operator of the first Hamiltonian such that a canonical commutation relation of the first Hamiltonian is preserved in the second Hamiltonian.
19 . The computer readable medium of claim 15 , wherein generating the third Hamiltonian further comprises:
perform Gaussian elimination on an effective capacitance matrix of the first Hamiltonian using the linear transformation matrix.
20 . The computer readable medium of claim 15 , wherein in simulating the behavior of the quantum circuit using the third Hamiltonian further comprises:
obtaining discrete energy eigenvalues of the quantum circuit by diagonalizing the third Hamiltonian.
21 . The computer readable medium of claim 15 , wherein the behavior of the quantum circuit comprises a frequency of a qubit among the one or more qubits.