DEVICE FOR IMPLEMENTATION OF A TWO-QUBIT CZ GATE BETWEEN SUPERCONDUCTING QUBITS BASED ON HIGH KINETIC INDUCTANCE Russian patent published in 2023 - IPC G06N10/40 

FIELD: quantum computing.

SUBSTANCE: invention is related to a device for implementation of two-qubit CZ gate between superconducting qubits based on high kinetic inductance. The device contains two computational superconducting qubits based on high kinetic inductance, capacitively coupled by means of an intermediate coupling qubit based on high kinetic inductance, each of the two computational qubits, as well as the intermediate coupling qubit, have a Hamiltonian operator equivalent to the Hamiltonian operator of the fluxonium qubit, and the equivalent electrical circuits of each of two computational qubits, as well as an intermediate linking qubit, include a Josephson tunnel junction, which ensures nonlinearity, and is shunted by a kinetic inductor and capacitance to ground. The Josephson contact and the kinetic inductor form a closed circuit, in which the magnetic flux control line is galvanically built-in, with a mutual inductance with the qubit circuit and shorted to ground, while the four computational states of the two-qubit system correspond to the cases when either both computational qubits are in their ground states, either one of the two computational qubits is in its ground state and the other computational qubit is in its first excited state, and vice versa, or both computational qubits are in their first excited states. The first electrode of the intermediate linking qubit is capacitively coupled to the first electrode of the first computational qubit and the first electrode of the second computational qubit in such a way that the capacitive couplings with the first and second computational qubits based on the kinetic inductance are symmetrical, and the frequencies of the first and second computational qubits based on the kinetic inductance at the point of magnetic flux degeneracy, when the magnetic flux in the circuit of each of the computational qubits is equal in absolute value to half of the magnetic flux quantum, are less than the anharmonicity of the first and second computational qubits. The operating point of the intermediate linking qubit, at which the two-qubit gate CZ (controlled Z) is executed on the computational qubits, corresponds to the zero value of the external magnetic flux in the circuit of the intermediate linking qubit, and the frequency of the main transition of the intermediate linking qubit depends on the states of the first and second computational qubits. The minimum value of the main transition frequency of the intermediate linking qubit is reached when the first and second computing qubits are in their ground states, the maximum value of the main transition frequency of the intermediate linking qubit is reached when the first and second computing qubits are in their first excited states, and in cases where one of the two computational qubits is in the ground state, and the other computational qubit is in the first excited state at that moment, and vice versa, the values of the main transition frequency of the intermediate linking qubit lie between the maximum and minimum values and are equal to each other if the frequencies of the computational qubits are also equal with each other, while the two-qubit gate CZ is executed by applying a microwave pulse to the galvanically coupled flow control line of the intermediate linking qubit with a frequency equal to half the sum of the minimum value of the main transition frequency of the intermediate coupling element and a value equal to the average value of the frequencies of the main transition of the intermediate computing qubit, when one of the two computational qubits is in the ground state, and the other computational qubit is in the first excited state at this moment, and vice versa, and the duration of the corresponding time during which the intermediate linking qubit once switches from its ground state to the first excited state and back, if at least one or simultaneously both computational qubits were in their ground states, and will go from its ground state to the first excited state and back twice if both computational qubits were simultaneously in their first excited states. On each of the three computational states of a two-qubit system, when at least one or simultaneously both computational qubits are in their ground states, a phase will increment, the value of which is equal to the number pi, and on the state of a two-qubit system, when both computational qubits are simultaneously in their first excited states , a phase equal to twice the number pi will increment, so the interaction between the first and second computational qubits eventually induces an effective relative phase shift equal to pi on the computational state of the two-qubit system when both computational qubits are in their first excited states, but this does not cause a swap of excitation between the two computational qubits.

EFFECT: implementation of a two-qubit gate CZ, which does not require the restructuring of the external magnetic flux in the closed circuit of the coupling element.

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