Superconducting interposer for transmitting quantum information for quantum error correction

Abstract

A system for transmitting quantum information for quantum error correction includes: an ancilla qubit chip including a plurality of ancilla qubits, and a data qubit chip spaced apart from the ancilla qubit chip and including a plurality of data qubits. The system includes an interposer coupled to the ancilla qubit chip and the data qubit chip, the interposer including a dielectric material and a plurality of superconducting structures formed in the dielectric material. The superconducting structures enable quantum information to be transmitted for quantum error correction between the plurality of data qubits on the data qubit chip and the plurality of ancilla qubits on the ancilla qubit chip via virtual photons.

Description

Background Art

[0001] Embodiments of the present invention for which protection is currently claimed relate to systems and methods for quantum error correction, and more particularly, to a superconducting interposer for transmitting quantum information for quantum error correction.

[0002] As the number of qubits on a given quantum processor increases, it becomes necessary to move quantum information between qubits fabricated on separate chips, particularly quantum information for applications such as quantum error correction. The prior art uses planar structures (such as bus resonators) to transmit quantum information between qubits. Summary of the Invention

[0003] According to an embodiment of the present invention, a system for transmitting quantum information for quantum error correction includes: an ancilla qubit chip including a plurality of ancilla qubits, and a data qubit chip spaced apart from the ancilla qubit chip and including a plurality of data qubits. The system includes an interposer coupled to the ancilla qubit chip and the data qubit chip, the interposer including a dielectric material and a plurality of superconducting structures formed in the dielectric material. The superconducting structures enable quantum information to be transmitted for quantum error correction between the plurality of data qubits on the data qubit chip and the plurality of ancilla qubits on the ancilla qubit chip via virtual photons.

[0004] According to an embodiment of the present invention, a method of transmitting quantum information for quantum error correction includes providing a plurality of ancilla qubits, and providing a plurality of data qubits spaced apart from the plurality of ancilla qubits. The method includes mapping errors from the plurality of data qubits to the plurality of ancilla qubits via virtual photons in a superconducting microwave transmission line, and measuring the plurality of ancilla qubits to detect errors. The method includes performing quantum error correction based on the detected errors.

[0005] According to an embodiment of the present invention, a quantum computer includes a refrigeration system under vacuum, the refrigeration system including a sealed container. The system includes an ancilla qubit chip housed within a refrigerated vacuum environment defined by the containment container, the ancilla qubit chip including a plurality of ancilla qubits. The system includes a data qubit chip housed within a refrigerated vacuum environment defined by the sealed container. The data qubit chip is spaced apart from the ancilla qubit chip and includes a plurality of data qubits. The system includes an interposer housed within a refrigerated vacuum environment defined by the sealed container. The interposer is coupled to the ancilla qubit chip and the data qubit chip and includes a dielectric material and a plurality of superconducting structures formed in the dielectric material. A superconducting resonator including the superconducting structures formed in the interposer enables quantum information to be transmitted for quantum error correction between the plurality of data qubits on the data qubit chip and the plurality of ancilla qubits on the ancilla qubit chip via virtual photons. Brief Description of the Drawings

[0006] Figure 1 Schematic diagram of a system for transmitting quantum information for quantum error correction according to an embodiment of the present invention.

[0007] Figure 2A Schematic diagram of a top view of an ancilla qubit chip according to an embodiment of the present invention.

[0008] Figure 2B Schematic diagram of a top view of an interposer according to an embodiment of the present invention.

[0009] Figure 2C Schematic diagram of a top view of a data qubit chip according to an embodiment of the present invention.

[0010] Figure 2D According to an embodiment of the present invention, coupled to Figure 2A Ancilla chip and Figure 2C Of the data chip Figure 2B Schematic diagram of a top view of the interposer.

[0011] Figure 3 Schematic diagram of an ancilla qubit chip according to an embodiment of the present invention, the ancilla qubit chip including an ancilla qubit and an ancilla measurement resonator configured to measure the ancilla qubit.

[0012] Figure 4 Schematic diagram of a data qubit chip according to an embodiment of the present invention, the data qubit chip including a data qubit and a data measurement resonator configured to measure the data qubit.

[0013] Figure 5 According to an embodiment of the present invention, coupled to the data qubit chip through an interposer Figure 4 Of the Figure 3 Schematic diagram of an ancilla qubit chip.

[0014] Figure 6 Schematic diagram of an ancilla qubit chip and a data qubit chip coupled to the same surface of the interposer.

[0015] Figure 7 Schematic diagram of a system for transmitting quantum information for quantum error correction according to an embodiment of the present invention.

[0016] Figure 8 Flowchart showing a method for transmitting quantum information for quantum error correction according to an embodiment of the present invention.

[0017] Figure 9 Schematic diagram of a quantum computer according to an embodiment of the present invention. Detailed Description

[0018] Figure 1Schematic diagram of a system 100 for transmitting quantum information for quantum error correction according to an embodiment of the present invention. The system 100 includes an ancilla qubit chip 102, which includes a plurality of ancilla qubits 104, 106, 108. The system 100 includes a data qubit chip 110 spaced apart from the ancilla qubit chip 102. The data qubit chip 110 includes a plurality of data qubits 112, 114, 116. The system 100 includes an interpolator 118 coupled to the ancilla qubit chip 102 and the data qubit chip 110. The interpolator 118 includes a dielectric material 120 and a plurality of superconducting structures 122, 124, 126 formed in the dielectric material 120. The superconducting structures 122, 124, 126 enable the transmission of quantum information for quantum error correction between the plurality of data qubits 112, 114, 116 on the data qubit chip 110 and the plurality of ancilla qubits 104, 106, 108 on the ancilla qubit chip 102 via virtual photons.

[0019] As Figure 1 shown, the interpolator 118 according to an embodiment of the present invention includes a first surface 128 and a second surface 130 opposite to the first surface 128. The ancilla qubit chip 102 is coupled to the first surface 128 of the interpolator 118, and the data qubit chip 110 is coupled to the second surface 130 of the interpolator 118.

[0020] According to an embodiment of the present invention, each of the plurality of superconducting structures extends from a data qubit among the plurality of data qubits to an ancilla qubit among the plurality of ancilla qubits. For example, in Figure 1 , the superconducting structure 122 extends from the data qubit 112 to the ancilla qubit 104. According to an embodiment of the present invention, the data qubit 112 has a first frequency, the ancilla qubit 104 has a second frequency, and a superconducting resonator including the superconducting structure 122, solder bumps 132 and 138, and right-angle capacitor couplers on the chips 102 and 110 has a third frequency. The superconducting structure 122 formed in the interpolator allows the transmission of quantum information because it forms part of the superconducting resonator. The superconducting resonator may also include solder bumps 132 and 138 and structures on the ancilla and data qubit chips electrically coupled to the solder bumps 132 and 138. The structures on the ancilla and data qubit chips may be coplanar waveguide transmission lines, as in the figure, although embodiments of the present invention are not limited to coplanar waveguide transmission lines. In some embodiments, the superconducting structure 122 itself may form the superconducting resonator.

[0021] The frequency of the superconducting resonator (referred to herein as the third frequency) is sufficiently detuned from the first and second frequencies to prevent actual photon transfer between the data qubit and the ancilla qubit. Instead, quantum information is transferred from the data qubit 112 and the ancilla qubit 104 via virtual photon transfer. Virtual photon transfer ensures that the quantum information stored in the data qubit 112 is protected from the electromagnetic Purcell effect. Virtual photon transfer also protects the quantum information from dielectric losses of the insulating material forming the interpolant 118.

[0022] According to an embodiment of the present invention, the ancilla qubit chip is bonded to the interpolant. In Figure 1 , the ancilla qubit chip 102 is bonded to the interpolant 118 using a plurality of solder bumps 132, 134, 136. The solder bumps couple the ancilla qubits 104, 106, 108 to the superconducting structures 122, 124, 126. As Figure 1 shown, the solder bumps can be electrically coupled to the superconducting structures 122, 124, 126 and capacitively coupled to the ancilla qubits 104, 106, 108. Embodiments of the present invention are not limited to Figure 1 the specific number of ancilla qubits, data qubits, and superconducting structures and solder bumps shown.

[0023] According to an embodiment of the present invention, the data qubit chip is bonded to the interpolant. In Figure 1 , the data qubit chip 110 is bonded to the interpolant 118 using a plurality of solder bumps 138, 140, 142. As Figure 1 shown, the solder bumps can be electrically coupled to the superconducting structures 122, 124, 126 and capacitively coupled to the data qubits 112, 114, 116. The solder bumps can be formed of a superconducting material, but embodiments of the present invention are not limited to solder bumps formed of a superconducting material. An example material for the solder bumps is indium. The system 100 according to an embodiment of the present invention can include a plurality of ancilla qubit chips and data qubit chips. The ancilla qubit chips and the data qubit chips can be bonded to a single interpolant or to a plurality of interpolants.

[0024] Figure 2A is a schematic top view of an ancilla qubit chip 200 according to an embodiment of the present invention. The ancilla qubit 200 includes three ancilla qubits 202, 204, 206. However, the ancilla qubit chip according to other embodiments of the present invention is not limited to any specific number of ancilla qubits. In other embodiments, there can be more than three or less than three ancilla qubits.

[0025] Figure 2BIt is a schematic top view of the interpolant 208. The interpolant includes a plurality of superconducting structures 210, 212, 214, 216. For example, the superconducting structure can be a superconducting via hole. The superconducting via hole can be part of a superconducting transmission line resonator formed partially or completely within the interpolant. The superconducting structure can be formed of one or more of, for example, niobium, aluminum, tin, electroplated rhenium, or indium. Although Figure 2B the illustrated embodiment shows an example of four superconducting structures 210, 212, 214, 216, other embodiments can have fewer than four or more than four superconducting structures.

[0026] Figure 2C It is a schematic top view of the data qubit chip 218. The data qubit chip 218 includes two data qubits 220, 222. Other embodiments of the data qubit chip can have more or fewer than two data qubits.

[0027] Figure 2D It is a schematic top view of the interpolant coupled to the auxiliary chip and the data chip. The auxiliary qubits 202, 204, 206 and the data qubits 220, 222 are connected to each other through the superconducting structures 210, 212, 214, 216.

[0028] Embodiments of the present invention enable the transmission of quantum information for quantum error correction. Quantum error correction often requires a large number of data qubits and auxiliary qubits to be coupled to each other. The data qubit is a qubit with a relatively long relaxation and coherence time, while the auxiliary qubit can be a qubit with a relatively short relaxation and coherence time. The quantum information is distributed over a set of data qubits. The data qubits are coupled to the auxiliary qubits such that errors in the quantum information are mapped from the data qubits to the auxiliary qubits. The auxiliary qubits can be measured to detect and / or correct the errors.

[0029] Quantum error correction algorithms such as, but not limited to, the Surface Code, the Shor Code, and the Steane Code, require frequent measurements of the auxiliary qubits. These measurements provide information about the data qubits to which the auxiliary qubits are coupled and also stabilize the data qubits. The frequency of the measurements requires fast measurements, and fast measurements require a strong coupling between the measurement resonator coupled to the auxiliary qubit and the environment. Although the strong coupling enables fast measurement of the auxiliary qubits, it also makes the auxiliary qubits more vulnerable to environmental noise and increases the spontaneous decay rate of the auxiliary qubits through the Purcell effect. If a strong coupling is applied to the data qubits, this strong coupling will shorten the lifetime of the quantum states in the data qubits.

[0030] Embodiments of the present invention enable strong coupling between the ancillary qubits and the environment, while reducing the coupling between the data qubits and the environment. The ancillary qubits are physically separated from the data qubits and are coupled to the data qubits through superconducting structures formed in the interposer.

[0031] This physical separation also allows the use of different materials and processes to form the data qubit chip and the ancillary qubit chip. Although both chips can include multiple qubits, the quality requirements for the data qubits and the ancillary qubits can be very different. The requirements for the ancillary qubits can be based on the frequencies at which they are measured. According to some embodiments, the ancillary qubit measurement period can be about 1 μs, so the ancillary qubits can have a coherence time greater than 1 μs, such as about a few microseconds. The material requirements for such qubits are not as strict as those for manufacturing higher-quality qubits, such as data qubits. Further, fabrication methods capable of changing the frequencies of the ancillary qubits (such as lithography) can be used to form and modify the ancillary qubit chip. The ancillary qubit chip can also be formed such that the ancillary qubits are tunable qubits. Although having tunable qubits can assist in system control, the process of forming tunable qubits may require breaking the ground plane of the microwave resonators coupled to these qubits. Due to flux noise sensitivity and the introduction of spurious microwave modes, this may be undesirable for data qubits but may be acceptable for ancillary qubits that allow shorter coherence times.

[0032] According to embodiments of the present invention, the interposer includes a dielectric material, such as a printed circuit board, an organic laminate, a silicon chip, a ceramic, a glass-reinforced epoxy laminate material such as FR-4, a hard glue, or a polyether ether ketone (PEEK).

[0033] According to embodiments of the present invention, the ancillary qubit chip includes an ancillary measurement resonator coupled to the plurality of ancillary qubits. The ancillary measurement resonator is configured to measure the plurality of ancillary qubits. For example, the ancillary measurement resonator can be a superconducting microwave coplanar waveguide resonator. Figure 3 is a schematic diagram of an ancillary qubit chip 300, which includes ancillary qubits 302 and an ancillary measurement resonator 304 configured to measure the ancillary qubits 302. The ancillary measurement resonator 304 can capacitively couple the ancillary qubits 302 to the measurement and control instrument. Figure 3 A capacitor 306 is shown, which capacitively couples the ancillary measurement resonator 304 and the ancillary qubits 302 to a port 308 having a measurement and control instrument.

[0034] According to embodiments of the present invention, the data qubit chip includes a data measurement resonator coupled to the plurality of data qubits. The data measurement resonator can be, for example, a superconducting microwave resonator.Figure 4 Schematic diagram of a data qubit chip 400 including data qubits 402 and a data measurement resonator 404 configured to measure the data qubits 402. Figure 4 A capacitor 406 is shown that capacitively couples the data measurement resonator 404 and the data qubits 402 to a port 408 for a measurement and control instrument.

[0035] Figure 5 is Figure 3 Schematic diagram of an auxiliary qubit chip 300 coupled to the Figure 4 data qubit chip 400 through an interposer. As Figure 5 shown, a capacitor 500 coupling the auxiliary qubits 502 and the auxiliary measurement resonator 504 to the measurement and control instrument is much larger than a capacitor 506 coupling the data qubits 508 and the data measurement resonator 510 to the measurement and control instrument. The strong coupling between the auxiliary measurement resonator 504 and the readout electronics enables fast measurement of the auxiliary qubits 502. This is useful for quantum error correction that may require a measurement period on the order of 1 μs per 1. In contrast, the data measurement resonator 510 is weakly coupled to the measurement electronics because the data qubits 508 can be read only when the quantum algorithm is complete, rather than being read every 1 μs. The weak coupling can be compensated for with a longer measurement time. The weak coupling between the data qubits 508 and the measurement electronics helps maintain the coherence of the data qubits 508. The data qubits 508 can have, for example, a relaxation and coherence time greater than 75 μs. The data qubits 508 can have, for example, a relaxation and coherence time on the order of 100 μs.

[0036] As Figure 1 an alternative to the configuration shown, the auxiliary qubit chip and the data qubit chip can be coupled to the same surface of the interposer. Figure 6 Schematic diagram of an auxiliary qubit chip 600 and a data qubit chip 602 coupled to the same surface 604 of an interposer 606.

[0037] According to an embodiment of the present invention, for each of a plurality of data qubits, a superconducting structure enables transmission of quantum information between the data qubit and at least two of a plurality of auxiliary qubits. Similarly, for each of a plurality of auxiliary qubits, a superconducting structure can enable transmission of quantum information between the auxiliary qubit and at least two of a plurality of data qubits. Quantum information can be mapped from at least two data qubits to an auxiliary qubit to allow measurement of the eigenstate of the data qubit without destroying the quantum information.

[0038] Figure 7Schematic diagram of a system 700 for transmitting quantum information for quantum error correction according to an embodiment of the present invention. Ancillary qubits 702 on an ancillary qubit chip 704 are coupled to two superconducting structures 706, 708. The superconducting structures enable the transmission of quantum information between the ancillary qubits 702 and two data qubits 710, 712. Another superconducting structure 714 enables the transmission of quantum information between the data qubit 712 and a second ancillary qubit 716. Although Figure 7 only two qubits coupled to two other qubits are shown, each qubit on the ancillary chip and the data chip can be coupled to two or more qubits on another chip via superconducting structures. For example, a quantum error correction code such as a surface code may require each data qubit to be coupled to multiple ancillary qubits, and each ancillary qubit to be coupled to multiple data qubits. In the example of a surface code, CNOT gates can be used to map errors from the data qubits to the ancillary qubits via virtual photons exchanged through the superconducting structures. For example, in a surface code, the measurement of the ancillary qubits can give the parity check of the data qubits. Since the parity check is an eigenvalue of the Bell state, the measurement of the ancillary qubits stabilizes the quantum information in these data qubits. Although surface codes are discussed herein, embodiments of the present invention are not limited to surface codes. Other quantum error correction algorithms can be used.

[0039] Figure 8 Flowchart showing a method 800 for transmitting quantum information for quantum error correction according to an embodiment of the present invention. Method 800 includes providing a plurality of ancillary qubits (802), and providing a plurality of data qubits spaced apart from the plurality of ancillary qubits (804). Method 800 includes mapping errors from the plurality of data qubits to the plurality of ancillary qubits via virtual photons in superconducting microwave transmission lines (806). Method 800 further includes measuring the plurality of ancillary qubits to detect errors (808), and performing quantum error correction based on the detected errors (810).

[0040] According to an embodiment of the present invention, measuring the plurality of ancillary qubits 808 gives the parity check of the plurality of data qubits.

[0041] Figure 9Schematic diagram of a quantum computer 900 according to an embodiment of the present invention. The quantum computer 900 includes a refrigeration system under vacuum, and the refrigeration system includes a sealed container 902. The quantum computer 900 includes an auxiliary qubit chip 904, and the auxiliary qubit chip 904 is accommodated in the refrigerated vacuum environment defined by the sealed container 902. The auxiliary qubit chip 904 includes a plurality of auxiliary qubits 906, 908, 910. The quantum computer 900 includes a data qubit chip 912, and the data qubit chip is accommodated in the refrigerated vacuum environment defined by the sealed container 902. The data qubit chip 912 is spaced apart from the auxiliary qubit chip 904 and includes a plurality of data qubits 914, 916, 918. The quantum computer 900 includes an interposer 920, and the interposer is accommodated in the refrigerated vacuum environment defined by the accommodating container 902. The interposer 920 is coupled to the auxiliary qubit chip 904 and the data qubit chip 912 and includes a dielectric material 922 and a plurality of superconducting structures 924, 926, 928 formed in the dielectric material 922. The superconducting structures 924, 926, 928 enable quantum information to be transmitted between the plurality of data qubits 914, 916, 918 on the data qubit chip 912 and the plurality of auxiliary qubits 906, 908, 910 on the auxiliary qubit chip 904 by virtual photons for quantum error correction.

[0042] The quantum computer according to an embodiment of the present invention may include a plurality of auxiliary qubit chips, data qubit chips, and interposers. Further, the embodiments of the present invention are not limited to Figure 9 the specific numbers of the auxiliary qubits, data qubits, superconducting structures, and solder bumps shown in

[0043] Embodiments of the present invention can use a dielectric interposer with a partially embedded microwave transmission line bus resonator to transmit quantum information. The quantum information is transmitted by virtual photons in the resonator. The use of virtual photons ensures that quantum information is not lost due to the electromagnetic Purcell effect or dielectric losses of the material. By dividing the qubit chips into those including data qubits (long-lived, high-quality qubits) and those including auxiliary qubits (which require fast measurement and control and are thus more vulnerable to the effects of lossy channels), superconducting interposers can be used to map errors onto the auxiliary qubits.

[0044] The description of the various embodiments of the present invention has been presented for purposes of illustration, but the description is not intended to be exhaustive or limited to the disclosed embodiments. Many modifications and variations will be apparent to a person of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terms used herein have been chosen to best explain the principles of the embodiments, practical application, or technical improvement of the technology found in the marketplace, or to enable a person of ordinary skill in the art to understand the embodiments disclosed herein.

Claims

1. A system for transmitting quantum information for quantum error correction, comprising: an ancilla qubit chip including a plurality of ancilla qubits; a data qubit chip spaced apart from the ancilla qubit chip, the data qubit chip including a plurality of data qubits; and an interposer coupled to the ancilla qubit chip and the data qubit chip, the interposer including a dielectric material and a plurality of superconducting structures formed in the dielectric material, wherein the data qubits have a first frequency, the ancilla qubits have a second frequency, and a superconducting resonator including the superconducting structures formed in the interposer has a third frequency, wherein the third frequency is sufficiently detuned from the first frequency and the second frequency to prevent actual photon transmission between the data qubits and the ancilla qubits, and wherein the superconducting structures enable transmission of quantum information for quantum error correction between the plurality of data qubits on the data qubit chip and the plurality of ancilla qubits on the ancilla qubit chip via virtual photons.

2. The system for transmitting quantum information for quantum error correction according to claim 1, wherein, the ancilla qubit chip further includes an ancilla measurement resonator coupled to the plurality of ancilla qubits, the ancilla measurement resonator being configured for measurement of the plurality of ancilla qubits.

3. The system for transmitting quantum information for quantum error correction according to claim 2, wherein, the data qubit chip further includes a data measurement resonator coupled to the plurality of data qubits, the data measurement resonator being configured for measurement of the plurality of data qubits.

4. The system for transmitting quantum information for quantum error correction according to claim 3, wherein, the coupling of the ancilla measurement resonator to the measurement electronics is stronger than the coupling of the data measurement resonator to the measurement electronics.

5. The system for transmitting quantum information for quantum error correction according to claim 1, wherein, the interposer includes a first surface and a second surface opposite the first surface, and wherein the ancilla qubit chip is coupled to the first surface of the interposer, and the data qubit chip is coupled to the second surface of the interposer.

6. The system for transmitting quantum information for quantum error correction according to claim 1, wherein, the ancilla qubit chip and the data qubit chip are coupled to the same surface of the interposer.

7. The system for transmitting quantum information for quantum error correction according to claim 1, wherein, each of the plurality of superconducting structures extends from a data qubit among the plurality of data qubits to an ancilla qubit among the plurality of ancilla qubits.

8. The system for transmitting quantum information for quantum error correction according to claim 1, wherein, for each data qubit among the plurality of data qubits, the superconducting structures enable transmission of quantum information between the data qubit and at least two ancilla qubits among the plurality of ancilla qubits.

9. The system for transmitting quantum information for quantum error correction according to claim 1, wherein, for each of the plurality of ancillary qubits, the superconducting structure enables transmission of quantum information between the one ancillary qubit and at least two of the plurality of data qubits.

10. The system for transmitting quantum information for quantum error correction according to claim 1, wherein, the ancillary qubit chip is bonded to the interposer.

11. The system for transmitting quantum information for quantum error correction according to claim 1, wherein, the data qubit chip is bonded to the interposer.

12. The system for transmitting quantum information for quantum error correction according to claim 1, wherein, the plurality of ancillary qubits includes a plurality of frequency-tunable ancillary qubits.

13. The system for transmitting quantum information for quantum error correction according to claim 1, wherein, each of the ancillary qubits has a relaxation time and a coherence time greater than 1 μs.

14. The system for transmitting quantum information for quantum error correction according to claim 1, wherein, each of the data qubits has a relaxation time and a coherence time greater than or equal to 75 μs.

15. A method for transmitting quantum information for quantum error correction, comprising: providing a plurality of ancillary qubits, the ancillary qubits in the plurality of ancillary qubits having a second frequency; providing a plurality of data qubits spaced apart from the plurality of ancillary qubits, the data qubits in the plurality of data qubits having a first frequency; mapping errors from the plurality of data qubits to the plurality of ancillary qubits; measuring the plurality of ancillary qubits to detect the errors; and performing quantum error correction based on the detected errors, wherein the mapping errors include an exchange of virtual photons between the data qubits and the ancillary qubits through a superconducting microwave transmission line having a third frequency detuned from the first frequency and the second frequency.

16. The method for transmitting quantum information for quantum error correction according to claim 15, wherein, the measuring of the plurality of ancillary qubits gives a parity check of the plurality of data qubits.

17. A quantum computer, comprising: a refrigeration system under vacuum, which includes a sealed container; an ancillary qubit chip accommodated in the refrigerated vacuum environment defined by the sealed container, the ancillary qubit chip including a plurality of ancillary qubits; a data qubit chip accommodated in the refrigerated vacuum environment defined by the sealed container, the data qubit chip being spaced apart from the ancillary qubit chip and including a plurality of data qubits; and an interposer accommodated in the refrigerated vacuum environment defined by the sealed container, the interposer being coupled to the ancillary qubit chip and the data qubit chip and including a dielectric material and a plurality of superconducting structures formed in the dielectric material, wherein the data qubits have a first frequency, the ancillary qubits have a second frequency, and a superconducting resonator including the superconducting structures formed in the interposer has a third frequency, wherein the third frequency is sufficiently detuned from the first frequency and the second frequency to prevent actual photon transfer between the data qubit and the ancilla qubit, and wherein the superconducting resonator including the superconducting structure formed in the interposer enables transfer of quantum information between the plurality of data qubits on the data qubit chip and the plurality of ancilla qubits on the ancilla qubit chip via virtual photons for quantum error correction.

18. The quantum computer according to claim 17, wherein, each of the plurality of superconducting structures extends from a data qubit among the plurality of data qubits to an ancilla qubit among the plurality of ancilla qubits.

19. The quantum computer according to claim 17, wherein, each of the plurality of superconducting structures extends from at least one data qubit among the plurality of data qubits to at least one ancilla qubit among the plurality of ancilla qubits.

20. The quantum computer according to claim 17, wherein the relaxation time and the coherence time of each data qubit among the plurality of data qubits are greater than the relaxation time and the coherence time of each ancilla qubit among the plurality of ancilla qubits.

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