Superconducting quantum circuit apparatus having coupler including at least one Josephson junction

1 . A superconducting quantum circuit apparatus comprising:

first through fourth qubits; and

a coupler arranged in a region surrounded by a ground plane, the coupler disposed spaced apart from the ground plane, wherein

the coupler includes:

a first electrode and a second electrode arranged opposed to each other; and

a nonlinear element including at least one Josephson junction bridged between the first electrode and the second electrode,

the first electrode including

first and second opposing portions extended toward the first and second qubits, respectively, ends of the first and second opposing portions being opposed to ends of coupler connection portions of the first and second qubits, for capacitive coupling therewith, respectively,

the second electrode including

third and fourth opposing portions extended toward third and fourth qubit, respectively, ends of the third and fourth opposing portions being opposed to ends of coupler connection portions of the third and fourth qubits, for capacitive coupling therewith, respectively, wherein

the ends of the first and second opposing portions and the ends of the third and fourth opposing portions are disposed within the region surrounded by the ground plane, wherein the first through fourth qubits each include a resonator including:

a loop circuit including a first superconducting line; a first Josephson junction; a second superconducting line; and a second Josephson junction connected in a loop, and

a capacitor connected in parallel to the loop circuit.

2 . The superconducting quantum circuit apparatus according to claim 1 , wherein the coupler connection portions of the first and second qubits have parts along respective longitudinal directions, inclusive of the ends thereof, protruding into the region surrounded by the ground plane, and

the coupler connection portions of the third and fourth qubits have parts along respective longitudinal directions, inclusive of the ends thereof, protruding into the region surrounded by the ground plane.

3 . The superconducting quantum circuit apparatus according to claim 1 , comprising:

the ground plane provided, via a gap, on each of both sides of the coupler connection portions of each one of the first through fourth qubits, along a longitudinal direction thereof; and

an air bridge striding over at least one coupler connection portion among the coupler connection portions of the first through fourth qubits to connect the ground plane on the both sides of the at least one coupler connection portion.

4 . The superconducting quantum circuit apparatus according to claim 1 , wherein the first and second electrodes of the coupler each include an edge spaced apart from an opposing edge of the ground plane surrounding the region by a distance equivalent of an order of a size of each of the first and second electrodes.

5 . The superconducting quantum circuit apparatus according to claim 4 , wherein the distance is in a range from one fifth to five times the size of each of the first and second electrodes.

6 . The superconducting quantum circuit apparatus according to claim 1 , wherein the coupler connection portions of the first and second qubits have the ends thereof, located at a position on a boundary or not reaching but close to the boundary, of the region surrounded by the ground plane, and

the coupler connection portions of the third and fourth qubits have the ends located at a position on a boundary or not reaching but close the boundary, of the region surrounded by the ground plane.

7 . The superconducting quantum circuit apparatus according to claim 1 , wherein, in each of the first through fourth qubits, the second superconducting line of the loop circuit is connected to ground,

the first superconducting line of the loop circuit is connected to a first end of the coupler connection portion,

the coupler connection portions of the first and second qubits have second ends for capacitively coupling with the ends of the first and second opposing portions of the coupler, respectively, and

the coupler connection portions of the third and fourth qubits have second ends for capacitively coupling with the ends of the third and fourth opposing portions of the coupler, respectively.

8 . The superconducting quantum circuit apparatus according to claim 1 , wherein the nonlinear element of the coupler includes

a loop circuit including;

first and second superconducting lines configuring a loop; and

a first Josephson junctions connecting one ends of the first and second superconducting lines; and

a second Josephson junctions connecting other ends of the first and second superconducting lines.

9 . The superconducting quantum circuit apparatus according to claim 1 , wherein a strength of four-body interaction includes a term C g +C+C s /2,

where C is a capacitance value of a capacitive coupling between the coupler and each of the first through fourth qubits,

C g is a capacitance value between the first and second electrodes of the coupler, and Cs is a floating capacitance value between ground and each of the first and second electrodes of the coupler, wherein

contribution of C s to the strength of four-body interaction is reduced with reduction of C s .

10 . The superconducting quantum circuit apparatus according to claim 1 , wherein the first through fourth qubits are configured as Josephson parametric oscillators and the coupler constitute a unit structure in a quantum computer.

11 . The superconducting quantum circuit apparatus according to claim 10 , comprising:

a plurality of the unit structures, wherein the quantum computer is configured such that at least one qubit among the first through fourth qubits included in one unit structure is shared by one or a plurality of other unit structures.

12 . A superconducting quantum circuit apparatus comprising:

first through fourth qubits; and

a coupler arranged in a region surrounded by a ground plane, the coupler disposed spaced apart from the ground plane, wherein

the coupler includes:

a first electrode and a second electrode arranged opposed to each other; and

a nonlinear element including at least one Josephson junction bridged between the first electrode and the second electrode,

the first electrode including

first and second opposing portions extended toward the first and second qubits, respectively, ends of the first and second opposing portions being opposed to ends of coupler connection portions of the first and second qubits, for capacitive coupling therewith, respectively,

the second electrode including

third and fourth opposing portions extended toward third and fourth qubit, respectively, ends of the third and fourth opposing portions being opposed to ends of coupler connection portions of the third and fourth qubits, for capacitive coupling therewith, respectively, wherein

the ends of the first and second opposing portions and the ends of the third and fourth opposing portions are disposed within the region surrounded by the ground plane, wherein at least one coupler connection portion among the coupler connection portions of the first through fourth qubits includes

a first section including the end and a second section contiguous with the first section along a longitudinal direction of the coupler connection portion, the first section having a first width, the second section having a second width that expands from the first width to be more than the first width,

the first section of the coupler connection portion is provided with the ground plane on each of both sides thereof, via a gap, wherein

the superconducting quantum circuit apparatus includes

an air bridge wiring striding over the first section of the coupler connection portion to connect the ground plane on the both sides thereof.