Scalable quantum error correction architecture using dual-function Transmon couplers in a fluxonium qubit array

1 . A system for quantum error correction, the system comprising:

a plurality of fluxonium qubits arranged as data qubits for storing quantum information;

a plurality of transmon qubits arranged as ancilla qubits,

wherein the plurality of fluxonium qubits and the plurality of transmon qubits are arranged in a grid implementing a rotated surface code, the plurality of transmon qubits positioned at vertex locations of the grid, and

wherein, for each respective transmon qubit of the plurality of transmon qubits:

the respective transmon qubit is positioned between a respective first fluxonium qubit of the plurality of fluxonium qubits and a respective second fluxonium qubit of the plurality of fluxonium qubits,

the respective transmon qubit comprises a respective tunable coupling element connected between the respective first fluxonium qubit and the respective second fluxonium qubit, and

the respective tunable coupling element is connected to a respective coupling control circuit that (1) controls a coupling strength between the respective first fluxonium qubit and the respective second fluxonium qubit and (2) increases an impedance state of the respective tunable coupling element during an idle period between the respective first fluxonium qubit and the respective second fluxonium qubit to isolate the plurality of fluxonium qubits from residual interactions during the idle period.

2 . The system of claim 1 , wherein the respective coupling control circuit comprises a flux bias line applying a magnetic flux to the respective tunable coupling element to switch the respective tunable coupling element to a high-impedance state during the idle period.

3 . The system of claim 1 , further comprising a control processor connected to the respective coupling control circuit, the control processor executing stored control instructions to adjust activation timing of the respective tunable coupling element based on prior measurement outcomes obtained from the respective transmon qubit.

4 . A system for quantum error correction, the system comprising:

a plurality of fluxonium qubits arranged as data qubits;

a plurality of transmon qubits arranged as ancilla qubits,

wherein the plurality of fluxonium qubits and the plurality of transmon qubits are arranged in a grid implementing a rotated surface code, the plurality of transmon qubits positioned at vertex locations of the grid, and

wherein, for a first transmon qubit of the plurality of transmon qubits:

the first transmon qubit is positioned between a first fluxonium qubit of the plurality of fluxonium qubits and a second fluxonium qubit of the plurality of fluxonium qubits,

the first transmon qubit comprises a readout resonator and a tunable coupling element connected between the first fluxonium qubit and the second fluxonium qubit, and

the tunable coupling element is connected to a coupling control circuit that (1) controls a coupling strength between the first fluxonium qubit and the second fluxonium qubit and (2) increases an impedance state of the tunable coupling element during an idle period between the first fluxonium qubit and the second fluxonium qubit.

5 . The system of claim 4 , wherein the plurality of fluxonium qubits and the plurality of transmon qubits are arranged in a linear chain implementing a repetition code, wherein each respective transmon qubit of the plurality of transmon qubits is positioned between respective fluxonium qubit pairs and comprises both a respective tunable coupling element and a respective readout resonator for syndrome extraction.

6 . The system of claim 4 , further comprising a control processor connected to the coupling control circuit, the control processor executing stored control instructions to adjust activation timing of the tunable coupling element based on prior measurement outcomes obtained from the first transmon qubit.

7 . The system of claim 4 , wherein the tunable coupling element comprises a resonator having a first port connected to the first fluxonium qubit and a second port connected to the second fluxonium qubit.

8 . The system of claim 4 , wherein the coupling control circuit comprises a flux bias line magnetically coupled to the tunable coupling element, and wherein the flux bias line causes a magnetic flux increase that increases the impedance state of the tunable coupling element during the idle period.

9 . The system of claim 4 , wherein the first fluxonium qubit, the first transmon qubit, and the second fluxonium qubit share a common substrate.

10 . The system of claim 4 , further comprising a second transmon qubit that is positioned between the second fluxonium qubit and a third fluxonium qubit of the plurality of fluxonium qubits, wherein the second transmon qubit comprises a readout wherein the second transmon qubit comprises a second tunable coupling element that is connected to a second coupling control circuit that (1) controls a coupling strength between the second fluxonium qubit and the third fluxonium qubit and (2) increases an impedance state of the second tunable coupling element during an idle period between the second fluxonium qubit and the third fluxonium qubit.

11 . A system for quantum error correction, the system comprising:

a plurality of fluxonium qubits arranged as data qubits;

a plurality of transmon qubits arranged as ancilla qubits,

wherein, for a first transmon qubit of the plurality of transmon qubits:

the first transmon qubit is positioned between a first fluxonium qubit of the plurality of fluxonium qubits and a second fluxonium qubit of the plurality of fluxonium qubits,

the first transmon qubit comprises a readout resonator and a tunable coupling element connected between the first fluxonium qubit and the second fluxonium gubit, and

the tunable coupling element is connected to a coupling control circuit that (1) controls a coupling strength between the first fluxonium qubit and the second fluxonium qubit and (2) increases an impedance state of the tunable coupling element during an idle period between the first fluxonium qubit and the second fluxonium qubit,

wherein the plurality of fluxonium qubits comprise high-inductance elements formed using nanowire arrays or superinductors, and the plurality of transmon qubits comprise multi-junction elements, wherein the plurality of fluxonium qubits and the plurality of transmon qubits are co-fabricated on a common substrate using a multi-layer aluminum deposition process with controlled oxidation to define Josephson junctions for both qubit types in a single lithography mask set.

12 . A method for operating a quantum error correction system, the method comprising:

adjusting, by a coupling control circuit connected to a tunable coupling element of a first transmon qubit of a plurality of transmon qubits arranged as ancilla qubits, a coupling strength between a first fluxonium qubit and a second fluxonium qubit during a quantum error correction cycle, wherein a plurality of fluxonium qubits arranged as data qubits comprises the first fluxonium qubit and the second fluxonium qubit,

wherein the plurality of fluxonium qubits and the plurality of transmon qubits are operated according to a rotated surface code error correction cycle, wherein the plurality of transmon qubits are positioned at vertex locations of a two-dimensional lattice;

in response to an idle period between the first fluxonium qubit and the second fluxonium qubit, increasing an impedance state of the tunable coupling element;

measuring a state of the first transmon qubit by transmitting a readout signal to a dedicated readout resonator coupled to the first transmon qubit and detecting the response of the dedicated readout resonator in a predetermined basis to obtain syndrome information; and

applying correction operations to one or more qubits of the plurality of fluxonium qubits based on the syndrome information.

13 . The method of claim 12 , wherein measuring the first transmon qubit comprises adjusting a measurement timing or measurement basis based on additional syndrome information that is previously obtained from the plurality of transmon qubits.

14 . The method of claim 12 , wherein adjusting the coupling strength comprises tuning a resonator element disposed between the first fluxonium qubit and the second fluxonium qubit, the resonator element having a first port connected to the first fluxonium qubit and a second port connected to the second fluxonium qubit through the tunable coupling element of the first transmon qubit.

15 . The method of claim 12 , wherein adjusting the coupling strength comprises supplying a flux bias signal via the coupling control circuit to vary an effective inductance of the tunable coupling element.

16 . The method of claim 12 , further comprising:

deactivating the tunable coupling elements between non-target fluxonium qubit pairs; and

executing a quantum gate operation on a target fluxonium qubit pair in a chain arrangement after the deactivating of the tunable coupling elements.

17 . A method for operating a quantum error correction system, the method comprising:

adjusting, by a coupling control circuit connected to a tunable coupling element of a first transmon qubit of a plurality of transmon qubits arranged as ancilla qubits, a coupling strength between a first fluxonium qubit and a second fluxonium qubit during a quantum error correction cycle, wherein a plurality of fluxonium qubits arranged as data qubits comprises the first fluxonium qubit and the second fluxonium qubit;

prior to an idle period between the first fluxonium qubit and the second fluxonium qubit, precharging the tunable coupling element to an increased impedance state to reduce crosstalk between the first fluxonium qubit and the second fluxonium qubit;

in response to the idle period between the first fluxonium qubit and the second fluxonium qubit, increasing an impedance state of the tunable coupling element;

measuring a state of the first transmon qubit by transmitting a readout signal to a dedicated readout resonator coupled to the first transmon qubit and detecting the response of the dedicated readout resonator in a predetermined basis to obtain syndrome information;

applying correction operations to one or more qubits of the plurality of fluxonium qubits based on the syndrome information.

18 . A method for operating a quantum error correction system, the method comprising:

adjusting, by a coupling control circuit connected to a tunable coupling element of a first transmon qubit of a plurality of transmon qubits arranged as ancilla qubits, a coupling strength between a first fluxonium qubit and a second fluxonium qubit during a quantum error correction cycle, wherein a plurality of fluxonium qubits arranged as data qubits comprises the first fluxonium qubit and the second fluxonium qubit;

in response to an idle period between the first fluxonium qubit and the second fluxonium qubit, increasing an impedance state of the tunable coupling element;

measuring a state of the first transmon qubit by transmitting a readout signal to a dedicated readout resonator coupled to the first transmon qubit and detecting the response of the dedicated readout resonator in a predetermined basis to obtain syndrome information,

wherein the predetermined basis is an X-basis, and

wherein obtaining the syndrome information comprises:

initializing the first transmon qubit in the X-basis;

performing an entangling controlled-NOT gate operation by transmitting control pulses to the first fluxonium qubit and the first transmon qubit through the coupling control circuit; and

measuring the first transmon qubit in the X-basis to obtain the syndrome information; and

applying correction operations to one or more qubits of the plurality of fluxonium qubits based on the syndrome information.