Multimode resonators for cavity-induced phase gates

Abstract

Techniques are provided for qubit coupling structures that enable RIP gates. For example, one or more embodiments described herein may comprise an apparatus that may include a coupling structure coupled to a first qubit and a second qubit. The coupling structure may have multiple coupling paths. One of the multiple coupling paths may be a resonator. Also, the first qubit may be coupled to a first end of the resonator, and the second qubit may be coupled to a point along the length of the resonator.

Description

[Technical Field]

[0001] The present disclosure relates to multi-mode resonators for enabling resonator-induced phase ("RIP") gates, and more particularly to qubit-coupling structures that include multiple coupling paths that can collectively suppress qubit-coupling interactions while the RIP gate is not in operation. [Background technology]

[0002] Qubits are coupled within quantum computers to perform various quantum processing operations. Traditionally, qubits are each coupled to a common resonator bus, and the qubits' frequencies are significantly detuned from the bus's frequency. For example, two coupled qubits can be capacitively coupled to each end of a length of coplanar waveguide, thereby forming a full microwave gate for the coupled qubits. For example, the coplanar waveguide can provide interaction between the qubits, such that the frequency of each qubit can depend on the state of the other, and exciting the waveguide with a microwave tone can alter the degree of frequency change.

[0003] When the qubits are fixed-frequency superconducting qubits (e.g., transmons), a RIP gate can be formed by applying a non-resonant tone to the resonator bus. The signal at the resonator, and therefore the Stark shift experienced by the qubit, depends on the coupling state of the qubits. To achieve significant RIP entanglement rates, a qubit coupling structure that allows for large qubit frequency shifts is desired. However, in conventional coupling structures, increasing the amount of qubit frequency shift allowed for a RIP gate also increases the amount of unwanted quantum entanglement between qubits during times when RIP is not active. Summary of the Invention

[0004] The following presents a summary to provide a basic understanding of one or more embodiments of the present invention. This summary is not intended to identify key or critical elements, nor is it intended to delineate the scope of particular embodiments or claims. Its sole purpose is to present concepts in a simplified form as a prelude to the more detailed description that is presented later. In one or more embodiments described herein, an apparatus, device, and / or system relating to a qubit-coupling structure that can enable one or more RIP gates is described.

[0005] According to an embodiment, an apparatus is provided. The apparatus may include a coupling structure coupled to a first qubit and a second qubit. The coupling structure may have multiple coupling paths. Additionally, one of the multiple coupling paths may be a resonator. The first qubit may be coupled to a first end of the resonator, and the second qubit may be coupled to a point along the length of the resonator. An advantage of such an apparatus may be that the difference between the zero qubit-qubit coupling frequency and the resonance frequency may be controlled based on the placement of the second qubit along the resonator length.

[0006] In some examples, the coupling path may establish a resonator-induced phase gate between the first qubit and the second qubit, thereby allowing the coupling structure to beneficially operate as a RIP quantum logic gate. In other words, the coupling path may enable a resonator-induced phase gate to be performed between the first qubit and the second qubit. Thus, the coupling structure may beneficially be used to perform a RIP quantum logic gate.

[0007] According to an embodiment, an apparatus is provided. The apparatus may include a coupling structure coupled to a first qubit and a second qubit. The coupling structure may have multiple coupling paths. One of the multiple coupling paths may be a resonator having a transmission line branch. An advantage of such an apparatus may be that the resonator may exhibit multiple resonant modes.

[0008] In some examples, multiple coupling paths can collectively suppress coupling interactions between the first qubit and the second qubit. An advantage of such a device can be the reduction of unwanted quantum entanglement between the first qubit and the second qubit.

[0009] According to an embodiment, an apparatus is provided. The apparatus may include a quarter-wave superconducting waveguide capacitively coupled to a first qubit and a second qubit. The quarter-wave superconducting waveguide may have multiple impedances. An advantage of such an apparatus may be the formation of a multi-mode resonator coupled to the first qubit and the second qubit.

[0010] In some examples, the apparatus may further include a resonator-induced phase gate that may drive the quarter-wave superconducting waveguide in a first resonator mode of the plurality of resonator modes. The resonator-induced phase gate may thereby promote a coupling interaction between the first qubit and the second qubit. An advantage of such an apparatus may be that qubit-qubit coupling may be suppressed when the RIP gate is not operating.

[0011] According to an embodiment, an apparatus is provided. The apparatus may include a quarter-wave superconducting waveguide coupled to a first qubit and a second qubit. The quarter-wave superconducting waveguide may have multiple impedances. Additionally, the apparatus may include a half-wave superconducting waveguide capacitively coupled to the first qubit and the second qubit. An advantage of such an apparatus may be a coupling structure that can enable a RIP gate for high qubit fidelity.

[0012] In some examples, the device may further comprise a superconducting ground connection that may be coupled to the quarter wavelength superconducting waveguide to electrically ground. An advantage of such a device may be the enablement of multiple interfering resonant modes.

[0013] According to an embodiment, an apparatus is provided. The apparatus may include a quarter-wave superconducting waveguide coupled to a first qubit and a second qubit. The quarter-wave superconducting waveguide may have multiple impedances. Additionally, the apparatus may include direct capacitive coupling between the first qubit and the second qubit. An advantage of such an apparatus may be multiple coupling paths between the first qubit and the second qubit.

[0014] In some examples, the quarter-wave superconducting waveguide may have a first segment between the first qubit and the capacitor and a second segment between the capacitor and the second qubit. The device may also include a superconducting ground connection coupled to the first segment and electrically groundable. An advantage of such a device may be a multimode resonator that can enable a RIP gate, where the even and odd resonant modes may exhibit different shapes. [Brief explanation of the drawings]

[0015] [Figure 1] FIG. 1 is a diagram of an exemplary, non-limiting first resonator bus topology for enabling a RIP gate between a first qubit and a second qubit, in accordance with one or more embodiments described herein. [Figure 2] FIG. 1 is a diagram of an exemplary, non-limiting first microwave circuit that may illustrate a first resonator bus topology according to one or more embodiments described herein. [Figure 3A] FIG. 10 is an exemplary, non-limiting graph that may illustrate changes in qubit-qubit coupling that may be realized by a first microwave circuit according to one or more embodiments described herein. [Figure 3B] FIG. 10 is an exemplary, non-limiting graph that may illustrate changes in qubit-qubit coupling that may be realized by a first microwave circuit according to one or more embodiments described herein. [Figure 4]FIG. 10 is a diagram of an exemplary, non-limiting second resonator bus topology for enabling a RIP gate between a first qubit and a second qubit, in accordance with one or more embodiments described herein. [Figure 5] FIG. 1 is a diagram of an exemplary, non-limiting second microwave circuit that may illustrate a second resonator bus topology according to one or more embodiments described herein. [Figure 6A] FIG. 10 is an exemplary, non-limiting graph that may illustrate changes in qubit-qubit coupling that may be realized by a second microwave circuit according to one or more embodiments described herein. [Figure 6B] FIG. 10 is an exemplary, non-limiting graph that may illustrate changes in qubit-qubit coupling that may be realized by a second microwave circuit according to one or more embodiments described herein. [Figure 7] FIG. 10 is a diagram of an exemplary, non-limiting third resonator bus topology for enabling a RIP gate between a first qubit and a second qubit, in accordance with one or more embodiments described herein. [Figure 8] FIG. 10 is a diagram of an exemplary, non-limiting third microwave circuit that may illustrate a third resonator bus topology according to one or more embodiments described herein. [Figure 9] FIG. 10 is a diagram of an exemplary, non-limiting fourth resonator bus topology for enabling a RIP gate between a first qubit and a second qubit, in accordance with one or more embodiments described herein. [Figure 10] FIG. 10 is a diagram of an exemplary, non-limiting fourth microwave circuit that may illustrate a first resonator bus topology according to one or more embodiments described herein. [Figure 11] FIG. 10 is an exemplary, non-limiting graph that may illustrate changes in qubit-qubit coupling that may be realized by a fourth microwave circuit according to one or more embodiments described herein. DETAILED DESCRIPTION OF THE INVENTION

[0016] The following detailed description is for illustrative purposes only and is not intended to limit the embodiments or the application and / or uses of the embodiments, nor is it intended to defer to any express or implied information presented in the preceding Background or Summary or Detailed Description sections.

[0017] One or more embodiments are now described with reference to the drawings, wherein like reference numerals are used to refer to like elements throughout. In the following detailed description, for purposes of explanation, numerous specific details are set forth in order to provide a more thorough understanding of one or more embodiments. It will be apparent, however, that in various instances, one or more embodiments may be practiced without these specific details.

[0018] While there are problems with other implementations of qubit-coupling structures for RIP gates, the present disclosure can be implemented to create solutions to one or more of those problems through degenerate multimode resonators that enable RIP gates. Various embodiments described herein may relate to qubit-coupling structures that exhibit multiple resonant modes. Collectively, the multiple resonant modes may interfere with each other to suppress qubit-qubit coupling interactions. In addition, the coupling structure may enable a RIP gate through actuation of one of the resonant modes to promote qubit-qubit coupling interactions. Beneficially, quantum entanglement between qubits may be suppressed when the RIP gate is not operating.

[0019] In one or more embodiments, qubit-qubit decoupling can be achieved based on the respective electrical distances of the qubits along the resonator bus. In various embodiments, the qubit coupling structure may include multiple coupling paths, one of which is a resonator with a transmission line branch. In some embodiments, one of the coupling paths may include a quarter-wavelength superconducting waveguide having multiple impedances and capacitively coupled to the first and second qubits. Additionally, the coupling path of the qubit coupling structure may include a half-wavelength superconducting waveguide capacitively coupled to the qubits. In one or more embodiments, the coupling structure may further include direct capacitive coupling between the qubits. For example, the coupling path of the qubit coupling structure may include a first segment between the first capacitively coupled qubit and a capacitor and a second segment between the capacitor and the second capacitively coupled qubit. Additionally, the first segment, the second segment, or both may be coupled to a superconducting ground connection. Thereby, short coupling stubs may be established such that the even and odd modes of the resonator have different shapes, thereby establishing a zero entanglement rate at the qubit frequency.

[0020] 1 is a diagram of an exemplary, non-limiting first topology of a qubit-coupling structure 100 in accordance with one or more embodiments described herein. Repeated descriptions of similar elements used in other embodiments described herein are omitted for brevity. As shown in FIG. 1 , qubit-coupling structure 100 may include a resonator bus 102 coupled to a first qubit 104 and a second qubit 106. In various embodiments, qubit-coupling structure 100 may enable one or more RIP gates with respect to first qubit 104 and second qubit 106.

[0021] In one or more embodiments, the first qubit 104 and / or the second qubit 106 may be a fixed-frequency superconducting qubit, such as a transmon qubit. For example, the first qubit 104 and / or the second qubit 106 may comprise a first capacitive pad 108, a second capacitive pad 110, or one or more Josephson junctions 112, or a combination thereof. The first capacitive pad 108 and / or the second capacitive pad 110 may be comprised of one or more superconducting metals. As used herein, the term "superconducting" may refer to a characteristic of a material that exhibits superconducting properties below a superconducting critical temperature, such as aluminum (e.g., a superconducting critical temperature of 1.2 Kelvin) or niobium (e.g., a superconducting critical temperature of 9.3 Kelvin). In addition, those skilled in the art will recognize that other superconducting materials (e.g., hydride superconductors such as lithium / magnesium hydride alloys) may be used in the various embodiments described herein. Exemplary materials that may be configured within the first capacitive pad 108 and / or the second capacitive pad 110 may include, but are not limited to, aluminum, niobium, tantalum, combinations thereof, and / or the like.

[0022] 1 , one or more Josephson junctions 112 may be disposed between the first capacitive pad 108 and the second capacitive pad 110 of each qubit (e.g., the first qubit 104, the second qubit 106, or both). The one or more Josephson junctions 112 may establish a weak link between superconducting materials, for example, by means of an insulator material, a normal (e.g., non-superconducting) metallic material, a combination thereof, and / or the like. In various embodiments, the one or more Josephson junctions 112 may be characterized by a superconductor-insulator-superconductor (“SIS”) structure, a superconductor-normal metal-superconductor (“SNS”) structure, or a superconductor-constriction-superconductor (“SCS”) structure, or a combination thereof.

[0023] In various embodiments, the resonator bus 102 may be a superconducting transmission line, such as a length of coplanar waveguide. Exemplary materials that may be included within the resonator bus 102 may include, but are not limited to, aluminum, niobium, tantalum, combinations thereof, and / or the like. In one or more embodiments, the resonator bus 102 may be capacitively or inductively coupled to the first qubit 104, the second qubit 106, or both. For example, the resonator bus 102 may be capacitively coupled to the first capacitive pad 108 of the first qubit 104 and may be capacitively coupled to the first capacitive pad 108 of the second qubit 106 (e.g., as shown in the first exemplary topology illustrated in FIG. 1 ).

[0024] In one or more embodiments, the frequency of the first qubit 104 and / or the second qubit 106 may be significantly detuned from the frequency of the resonator bus 102. For example, the coupling structure 100 may be characterized by Equation 1 below:

number

number

[0025] In various embodiments, the resonator bus 102 may be passive. For example, the resonator bus 102 may miss photons and act as an effective qubit-qubit exchange coupling "J," whose operation is characterized by Equation 2 below:

number

[0026] However, qubit-qubit coupling "J" also establishes entanglement of the first qubit 104 and the second qubit 106 while the RIP gate is not operating, such as a ZZ interaction. For example, the ZZ interaction may be characterized by Equation 3 below:

number

[0027] The frequency of the resonator bus 102 may depend on the state of the first qubit 104 or the second qubit 106, or both, and the shift in frequency of the resonator bus 102 due to the qubits in the excited state may be characterized by “χ” in Equation 4 below:

number

number

[0028] In conventional coupling structures, increasing the χ value to obtain a significant RIP gate can result in an undesirable ZZ value. For example, in conventional coupling structures, applying an α value of −300 MHz for a Δ value of 1000 megahertz (MHz) can obtain a χ value of 10 MHz with a static ZZ value of 2 MHz. While a χ value of 10 MHz may be desirable, qubit-qubit entanglement characterized by a ZZ value of 2 MHz may cause the device to malfunction. In various embodiments described herein, qubit coupling structure 100 can enable a large χ value to obtain a significant RIP gate while minimizing the ZZ value to suppress qubit-qubit entanglement when the RIP gate is not operating.

[0029] For example, a first exemplary topology of qubit-coupling structure 100 (e.g., shown in FIG. 1 ) may control the ZZ interaction based on the electrical distance of first qubit 104 and / or second qubit 106 along the length of resonator bus 102. For example, resonator bus 102 may be a length of half-wavelength superconducting coplanar waveguide (“λ / 2 resonator”), and there may be zero qubit-qubit coupling across resonator bus 102 at half the resonance frequency of resonator bus 102. Setting first qubit 104 and second qubit 106 to the half-frequency may thereby couple first qubit 104 and second qubit 106 to the resonator bus 102 rather than to each other. However, setting first qubit 104 and second qubit 106 to the half-frequency may also suppress coupling between each qubit and resonator bus 102 because each qubit is significantly detuned from the resonance of resonator bus 102.

[0030] In one or more embodiments, the qubit-coupling structure 100 illustrated in the first topology can obtain zero qubit-qubit entanglement during ungated operation by adjusting the resonant frequency. For example, the electrical distance of each qubit along the length of the resonator bus 102 (e.g., a λ / 2 resonator) can control the difference between the zero qubit-qubit coupling frequency and the resonant frequency. Thus, by adjusting the placement of the first qubit 104 and / or the second qubit 106 along the resonator bus 102 (e.g., a λ / 2 resonator), the zero qubit-qubit coupling frequency can be brought closer to the resonance of the resonator bus 102. For example, additional transmission line length can be added relative to the position of the first qubit 104 along the resonator bus 102 compared to the position of the second qubit 106 along the resonator bus 102.

[0031] 2 is a diagram of an exemplary, non-limiting first microwave circuit 200 that can illustrate the first topology shown in FIG. 1 of qubit-coupling structure 100 according to one or more embodiments described herein. Repeated descriptions of similar elements used in other embodiments described herein are omitted for brevity. As shown in FIG. 2 , first qubit 104 can be coupled to resonator bus 102 (e.g., a λ / 2 resonator) via first bond line 201 (e.g., a superconducting transmission line made of one or more superconducting materials, such as aluminum, niobium, or tantalum, or a combination thereof) and / or first capacitor 202. Furthermore, second qubit 106 can be coupled to resonator bus 102 (e.g., a λ / 2 resonator) via second bond line 203 (e.g., a superconducting transmission line made of one or more superconducting materials, such as aluminum, niobium, or tantalum, or a combination thereof) and / or second capacitor 204. Additionally, the first microwave circuit 200 may include a drive port 206 capacitively coupled to the resonator bus 102 to drive the RIP gate. For example, photons 205 (e.g., represented by wavelength in FIG. 2 ) may be added and / or removed from the resonator bus 102 via the drive port 206. In various embodiments, the drive port 206 may be made of the same superconducting material as the resonator bus 102 and may include a third capacitor 208.

[0032] Additionally, the resonator bus 102 may include a first ideal transmission line element 210 (e.g., a delay-defined ideal transmission line (TLIND)) and / or a second ideal transmission line element 212 (e.g., a TLIND). As shown in FIG. 2, the first qubit 104 may have a greater electrical length along the resonator bus 102 than the second qubit 106 due to the incorporation of at least the first TLIND 210. Furthermore, as described above, the difference between the zero qubit-qubit coupling frequency and the qubit-resonator bus coupling frequency of the exemplary first microwave circuit 200 may be based on the additional electrical length associated with the first qubit 104.

[0033] 3A-3B are diagrams of exemplary, non-limiting graphs 300, 302 that may show how the qubit coupling structure 100 illustrated in the topology of FIG. 1 and / or the first microwave circuit 200 of FIG. 2, according to one or more embodiments described herein, can achieve a target zero qubit-qubit coupling frequency that enables strong qubit-resonator bus coupling. Repeated descriptions of similar elements used in other embodiments described herein are omitted for brevity. Graphs 300 and 302 may illustrate features of the first microwave circuit 200, where the second TLIND 212 has a Z value (e.g., the ratio of the complex voltage of a given wave to the complex current of the same wave) of 50 ohms and a delay value of 0.35 / 7 nanoseconds (nsec). Additionally, these scattering parameters may include a start at 1.0 gigahertz (GHz), a stop at 10 GHz, and a step of 0.01 GHz.

[0034] Graph 300 illustrates the characteristics of the first microwave circuit 200 without the first TLIND 210, and graph 302 illustrates the characteristics of the first microwave circuit 200 shown in FIG. 2 (e.g., with the first TLIND 210 having a Z value of 50 ohms and a delay value of 0.15 / 7 nsec). As shown in graph 300, the zero qubit-qubit coupling frequency may be at 5 GHz, and the qubit-resonator bus coupling frequency may be at 10 GHz. As shown in graph 302, the additional electrical distance provided by the first TLIND 210 may move the qubit-resonator bus coupling frequency to 7 GHz.

[0035] 4 is a diagram of an exemplary, non-limiting second topology of qubit coupling structure 100 according to one or more embodiments described herein. Repeated descriptions of similar elements used in other embodiments described herein are omitted for brevity. In one or more embodiments, qubit coupling structure 100 can include multiple coupling paths, thereby resulting in a degenerate multimode resonator. For example, the χ of each respective coupling path can be large, but the J value can be zero, as characterized by Equation 6 below:

number

[0036] For example, in one or more embodiments, the resonator bus 102 may be a quarter-wave superconducting coplanar waveguide (e.g., a λ / 4 resonator) having multiple impedances. Additionally, the qubit coupling structure 100 may include a superconducting transmission line branch 402. In one or more embodiments, the branch 402 may be a superconducting ground connection coupled to the resonator bus 102 (e.g., a λ / 4 resonator). In various embodiments, the qubit coupling structure 100 may obtain multiple coupling paths due to at least the branch 402, and the resonant modes of the multiple coupling paths may interfere with each other. For example, the multiple resonant modes exhibited by the multiple coupling paths may approximately cancel each other.

[0037] 5 is a diagram of an exemplary, non-limiting second microwave circuit 500 that can illustrate the second topology shown in FIG. 4 of the qubit-coupling structure 100 according to one or more embodiments described herein. Repeated descriptions of similar elements used in other embodiments described herein are omitted for brevity. As shown in FIG. 5 , the first qubit 104 can be coupled to the resonator bus 102 (e.g., a λ / 4 resonator) via a first bond line 201 and / or a first capacitor 202. Furthermore, the second qubit 106 can be coupled to the resonator bus 102 (e.g., a λ / 4 resonator) via a second bond line 203 and / or a second capacitor 204. Additionally, the exemplary second microwave circuit 500 can include a drive port 206, as described in various embodiments herein.

[0038] The resonator bus 102 may include a first coplanar waveguide element 506 and a second coplanar waveguide element 508. Additionally, the branch 402 may include a third coplanar waveguide element 510. In various embodiments, the first coplanar waveguide element 506 and the second coplanar waveguide element 508 may have a first length (“L1”). Furthermore, the third coplanar waveguide element 510 may have a second length (“L2”) that may be different from L1. For example, L2 may be less than L1.

[0039] 6A-6B are exemplary, non-limiting graphical illustrations that may show how multiple interferometric resonant modes may be obtained for the qubit-coupling structure 100 illustrated in the topology of FIG. 4 and / or the second microwave circuit 500 of FIG. 5, according to one or more embodiments described herein. Repeated descriptions of similar elements used in other embodiments described herein are omitted for brevity.

[0040] With reference to FIG. 6A , graph 600 may illustrate characteristics of a second microwave circuit 500 without branch 402, where L1 is equal to 4 millimeters (mm). Graph 602 may illustrate characteristics of a second microwave circuit 500 including branch 402, where L1 is equal to 3.6 mm and L2 is equal to 0.2 mm. The circuit state remained stable between graphs 600 and 602, except for the presence or absence of branch 402 and the corresponding L1 / L2 lengths. As shown in graph 600, without branch 402, the coupled structure may exhibit a single resonant mode. As shown in graph 602, the incorporation of branch 402 and the resulting multiple coupling paths may enable qubit coupled structure 100 to exhibit multi-mode resonance. Additionally, the microwave circuit without the branch 402 and the second microwave circuit 500 may exhibit similar self-inductance (e.g., 12.5 nanohenries (nH) compared to 13 nH) and χ values, while reducing the ZZ value.

[0041] With reference to FIG. 6B , graph 604 may illustrate the characteristics of the second microwave circuit 500 without the branch 402, where L1 is equal to 4.7 mm. Graph 606 may illustrate the characteristics of the second microwave circuit 500 including the branch 402, where L1 is equal to 4.5 mm and L2 is equal to 0.1 mm. The circuit state remained stable between graphs 604 and 606, except for the length of L1 / L2 corresponding to the presence or absence of the branch 402. As shown in graph 604, without the branch 402, the coupled structure may exhibit a single resonant mode. As shown in graph 606, the incorporation of the branch 402 and the resulting multiple coupling paths may enable the qubit-coupled structure 100 to exhibit multi-mode resonance. Additionally, the microwave circuit without the branch 402 and the second microwave circuit 500 may exhibit equivalent self-inductance (e.g., 12.5 nH) and χ values, while decreasing the ZZ value.

[0042] 7 is a diagram of an exemplary, non-limiting third topology of a qubit-coupling structure 100 according to one or more embodiments described herein. Repeated descriptions of similar elements used in other embodiments described herein are omitted for brevity. In one or more embodiments, various features of the first topology shown in FIG. 1 and the second topology shown in FIG. 4 may be combined. For example, the qubit-coupling structure 100 may include multiple embodiments of the resonator bus 102 described herein. For example, the qubit-coupling structure 100 may include a first resonator bus 102a and a second resonator bus 102b capacitively coupled to the first capacitive pad 108 of the first qubit 104 and the first capacitive pad 108 of the second qubit 106.

[0043] In various embodiments, the first resonator bus 102a (e.g., shown in FIG. 7 ) of the third topology of the qubit-coupling structure 100 may be a λ / 2 resonator. According to various embodiments described herein, the relationship between the zero qubit-qubit coupling frequency and the resonant frequency (e.g., a λ / 2 resonator) of the first resonator bus 102a may depend on the electrical distance of each qubit along the first resonator bus 102a. Furthermore, the second resonator bus 102b (e.g., shown in FIG. 7 ) of the third topology of the qubit-coupling structure 100 may be a λ / 4 resonator coupled (e.g., with a superconducting ground connection) to the branch 402. According to various embodiments described herein, the lengths L1 and L2 of the second resonator bus 102b and the branch 402 may further affect the establishment of multiple interfering resonant modes exhibited by the qubit-coupling structure 100.

[0044] 8 is a diagram of an exemplary, non-limiting third microwave circuit 800 that may illustrate the third topology shown in FIG. 7 of the qubit-coupled structure 100 according to one or more embodiments described herein. Repeated descriptions of similar elements used in other embodiments described herein are omitted for brevity. In various embodiments, the drive port 206 may be coupled to the first resonator bus 102a or the second resonator bus 102b, or both, to drive RIP gates across the qubit-coupled structure 100 of the exemplary microwave circuit 800.

[0045] 8, the first resonator bus 102a can be coupled to the first qubit 104 via one or more first coupled lines 201 and / or first capacitors 202, and the second resonator bus 102b can be coupled to the second qubit 106 via one or more second coupled lines 203 and / or second capacitors 204. The first resonator bus 102a can be a λ / 2 resonator having a coplanar waveguide (e.g., the third coplanar waveguide element 510). The second resonator bus 102b can be a λ / 4 resonator coupled to a superconducting ground connection and / or can include other coplanar waveguides (e.g., the second coplanar waveguide element 508). In various embodiments, the coplanar waveguides of the first resonator bus 102a may have a greater length than the coplanar waveguides of the second resonator bus 102b (e.g., according to various embodiments described herein, the third coplanar waveguide element 510 of the first resonator bus 102a may have a length L3 that is greater than the length L2 of the second coplanar waveguide element 508 of the second resonator bus 102b). For example, the first resonator bus 102a may include a coplanar waveguide having a length of 10 mm, and the second resonator bus 102b may include a coplanar waveguide having a length of 4.5 mm.

[0046] 9 is a diagram of an exemplary, non-limiting fourth topology of qubit-coupling structure 100 according to one or more embodiments described herein. Repetitive descriptions of similar elements used in other embodiments described herein are omitted for brevity. In one or more embodiments, qubit-coupling structure 100 may include a coupling stub 902 coupled to resonator bus 102.

[0047] 9 , the resonator bus 102 may include a fourth capacitor 904, which may define a first segment of the resonator bus 102 and a second segment of the resonator bus 102. The first segment may comprise a portion of the resonator bus 102 disposed between the first qubit 104 and the fourth capacitor 904. For example, the first segment may be capacitively coupled to the first qubit 104 and extend to the fourth capacitor 904. The second segment may comprise a portion of the resonator bus 102 disposed between the second qubit 106 and the fourth capacitor 904. For example, the second segment may be capacitively coupled to the second qubit 106 and extend to the fourth capacitor 904. In various embodiments, the resonator bus 102 may be a λ / 4 resonator.

[0048] The coupling stub 902 may be coupled to the first segment and the second segment of the resonator bus 102. In various embodiments, the coupling stub 902 may be a λ / 4 resonator. Further, in one or more embodiments, the coupling stub 902 may be a short circuit (e.g., as shown by the short connection 906 in FIG. 10 ). In one or more embodiments, the coupling stub 902 may be a superconducting ground connection.

[0049] FIG. 10 is a diagram of an exemplary, non-limiting fourth microwave circuit 1000 that can illustrate the fourth topology shown in FIG. 9 of the qubit-coupling structure 100 according to one or more embodiments described herein. Repeated descriptions of similar elements used in other embodiments described herein are omitted for brevity. As shown in FIG. 10 , the first qubit 104 can be coupled to the resonator bus 102 (e.g., a λ / 4 resonator) via a first bond line 201 and / or a first capacitor 202. Furthermore, the second qubit 106 can be coupled to the resonator bus 102 (e.g., a λ / 4 resonator) via a second bond line 203 and / or a second capacitor 204. Additionally, the exemplary second microwave circuit 500 can include a drive port 206, as described in various embodiments herein.

[0050] Additionally, a fourth capacitor 904 may be disposed along the resonator bus 102 between the first capacitor 202 and the second capacitor 204, thereby defining a first segment of the resonator bus 102 (e.g., coupled to the first qubit 104) and a second segment of the resonator bus 102 (e.g., coupled to the second qubit 106). The first segment of the resonator bus 102 may include a first coplanar waveguide element 506, and the second segment of the resonator bus 102 may include a second coplanar waveguide element 508. In various embodiments described herein, the first coplanar waveguide element 506 of the first segment and the second coplanar waveguide element 508 of the second segment may have the same length L1.

[0051] In various embodiments, the coupling stub 902 may include a fourth coplanar waveguide element 1002 coupled to the first segment and a fifth coplanar waveguide element 1004 coupled to the second segment. Further, the fourth coplanar waveguide element 1002 and / or the fifth coplanar waveguide element 1004 may be coupled to the third coplanar waveguide element 510 (e.g., having different lengths, L2). In addition, the fourth coplanar waveguide element 1002 and / or the fifth coplanar waveguide element 1004 may have the same length (“L3”). In one or more embodiments, L3 may be greater than L1 and L2. For example, the lengths of the coplanar waveguides may be characterized as L3 > L1 > L2.

[0052] 11 is a diagram of an exemplary, non-limiting graph 1100 that may show how the qubit-coupling structure 100 illustrated in the topology of FIG. 9 and / or the fourth microwave circuit 1000 of FIG. 10 may obtain multiple interferometric resonant modes, according to one or more embodiments described herein. Repeated descriptions of similar elements used in other embodiments described herein are omitted for brevity.

[0053] As described herein, the topology of the fourth qubit-coupling structure 100 illustrated in Figures 9 and 10 can result in a degenerate multimode resonator. For example, the qubit-coupling structure 100 can have multiple coupling paths via the resonator bus 102 and / or the coupling stubs 902. Furthermore, each of the coupling paths can exhibit resonant modes that can interfere with each other. For example, the even and odd resonant modes of the qubit-coupling structure 100 (e.g., a degenerate multimode resonator) shown in Figures 9-10 can add to nearly cancel the coupling interaction between the first qubit 104 and the second qubit 106 via the fourth capacitor 904. Additionally, shorted coupling stub 902 (e.g., via third coplanar waveguide element 510, fourth coplanar waveguide element 1002, and / or fourth coplanar waveguide element 1004, or a combination thereof) can cause the even resonant modes of qubit coupling structure 100 to have different shapes than the odd resonant modes, thereby achieving zero qubit-qubit coupling at the qubit frequency.

[0054] For example, graph 1100 illustrates the characteristics of the exemplary fourth microwave circuit 1000. Line 1102 can illustrate the J value, and line 1104 can illustrate the Z value. As shown in graph 1100, qubit coupling structure 100 exhibits two degenerate resonant modes at approximately 6.2 GHz and 6.5 GHz, separated by approximately 300 megahertz (MHz). Also shown in graph 1100, the zero qubit-qubit coupling frequency for exemplary fourth microwave circuit 1000 can occur at approximately 4.5 GHz. In various embodiments, the Z value can be inferred from the J value by assuming a 50 MHz delta between the first qubit 104 and the second qubit 106.

[0055] Also, the word "or" is intended to mean an inclusive "or" rather than an exclusive "or." That is, unless otherwise stated or clear from context, "X uses A or B" is intended to mean any of the natural inclusive permutations. That is, if X uses A; X uses B; or X uses both A and B, then "X uses A or B" is satisfied under any of the foregoing examples. Furthermore, unless otherwise stated or clear from such context where the singular form is specified, the articles "a" and "an" when used in this specification and the accompanying drawings should generally be construed to mean "one or more." As used herein, the terms "example" and / or "exemplary" are utilized to mean "serving as an example, instance, or illustration." For the avoidance of doubt, the subject matter disclosed herein is not limited by such examples. Additionally, any aspect or design described herein as "example" and / or "exemplary" is not necessarily to be construed as preferred or advantageous over other aspects or designs, and is not meant to exclude equivalent exemplary structures and techniques known to those skilled in the art.

[0056] It is, of course, not possible to describe for purposes of describing the present disclosure, components, products, or methods, or every conceivable combination thereof, but one skilled in the art will recognize that many additional combinations and permutations of the present disclosure are possible. Furthermore, the term "comprises" is to be construed when used as a transitional term in the claims, so that to the extent that terms such as "including," "having," "possessing," and the like are used in the detailed description, claims, appendices, and drawings, such terms are intended to be as inclusive as the term "comprises." The descriptions of various embodiments have been provided for illustrative purposes and are not intended to be exhaustive or limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein has been chosen to best explain the principles of the embodiments, practical applications or technical improvements of commercially available technology, or so that the disclosure will enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. 1. An apparatus comprising:

11. An apparatus comprising: a coupling structure coupled to a first qubit and a second qubit, the coupling structure having a plurality of coupling paths configured to selectively generate a plurality of resonant modes, at least one of the plurality of resonant modes causing coupling between the first qubit and the second qubit to enable resonator-induced phase gating operation, and other of the plurality of resonant modes suppressing coupling between the first qubit and the second qubit when the resonator-induced phase gating operation is not enabled, and one of the plurality of coupling paths is a resonator having a transmission line branch.

2. 10. The apparatus of claim 1, wherein the coupling path establishes a resonator-induced phase gate between the first qubit and the second qubit.

3. The apparatus of claim 2 , wherein the plurality of coupling paths collectively suppress coupling interactions between the first qubit and the second qubit.

4. 4. Apparatus according to any one of claims 1 to 3, wherein the transmission line branch is a section of transmission line having a superconducting ground connection.

5. The apparatus of claim 1 , wherein the coupling structure further comprises a drive port.

6. 6. The apparatus of claim 1, wherein the first qubit is coupled to a first end of the resonator and the second qubit is coupled to a point along a length of the resonator.

7. 7. The apparatus of claim 1, wherein the first qubit and the second qubit are coupled to the resonator by at least one coupling technique selected from the group consisting of capacitive coupling and inductive coupling.

8. 8. The apparatus of claim 1, wherein the resonator comprises a quarter wavelength superconducting coplanar waveguide having a plurality of sections with different impedances.

9. 1. An apparatus comprising:

11. An apparatus comprising: a coupling structure coupled to a first qubit and a second qubit, the coupling structure having a plurality of coupling paths configured to selectively generate a plurality of resonant modes, at least one of the plurality of resonant modes causing coupling between the first qubit and the second qubit to enable resonator-induced phase gating operation and other of the plurality of resonant modes suppressing coupling between the first qubit and the second qubit when the resonator-induced phase gating operation is not enabled, one coupling path of the plurality of coupling paths being a resonator, the first qubit being coupled to a first end of the resonator and the second qubit being coupled to a point along a length of the resonator.

10. 10. The apparatus of claim 9, wherein the coupling path establishes a resonator-induced phase gate between the first qubit and the second qubit.

11. 11. The apparatus of claim 9 or 10, wherein the multiple coupling paths collectively suppress coupling interactions between the first qubit and the second qubit.

12. 12. The apparatus of claim 9, wherein the first qubit and the second qubit are coupled to the resonator by at least one coupling technique selected from the group consisting of capacitive coupling and inductive coupling.

13. 13. The apparatus of claim 9, wherein the coupling structure further comprises a drive port.

14. 1. An apparatus comprising:

10. The apparatus of claim 1, wherein the coupling structure is coupled to a first qubit and a second qubit, the coupling structure having a plurality of coupling paths configured to selectively generate a plurality of resonant modes, at least one of the plurality of resonant modes causing coupling between the first qubit and the second qubit to enable resonator-induced phase gating operation and other of the plurality of resonant modes suppressing coupling between the first qubit and the second qubit when the resonator-induced phase gating operation is not enabled, and one of the plurality of coupling paths is a quarter-wave superconducting waveguide capacitively coupled to the first qubit and the second qubit, the quarter-wave superconducting waveguide comprising a plurality of portions with different impedances.

15. 15. The device of claim 14, wherein a fundamental resonance of the quarter-wave superconducting waveguide is below a frequency of the first qubit and a frequency of the second qubit, and the device exhibits multiple resonator modes that add in a canceling manner to couple between the first qubit and the second qubit.

16. a resonator-induced phase gate driving the quarter-wave superconducting waveguide with a first resonator mode from the plurality of resonator modes.

16. The apparatus of claim 15.

17. 17. The apparatus of claim 16, wherein the resonator-induced phase gate facilitates the coupling interaction between the first qubit and the second qubit.

18. 1. An apparatus comprising: a coupling structure coupled to a first qubit and a second qubit, the coupling structure having a plurality of coupling paths configured to selectively generate a plurality of resonant modes, at least one of the plurality of resonant modes causing coupling between the first qubit and the second qubit to enable resonator-induced phase gating operation, and other of the plurality of resonant modes suppressing coupling between the first qubit and the second qubit when the resonator-induced phase gating operation is not enabled, one of the plurality of coupling paths being a quarter-wave superconducting waveguide capacitively coupled to the first qubit and the second qubit, the quarter-wave superconducting waveguide comprising a plurality of portions with different impedances; a half-wavelength superconducting waveguide capacitively coupled to the first qubit and the second qubit; An apparatus comprising:

19. 20. The apparatus of claim 18, further comprising a superconducting ground connection coupled to the quarter wavelength superconducting waveguide to electrically ground.

20. 20. The apparatus of claim 19, wherein both the quarter-wavelength superconducting waveguide and the half-wavelength superconducting waveguide are coupled to a first capacitive pad of the first qubit and a first capacitive pad of the second qubit.

21. 21. The device of claim 19 or 20, wherein the device exhibits multiple resonator modes that add in a canceling manner to a coupling interaction between the first qubit and the second qubit.

22. a resonator-induced phase gate that drives the quarter-wavelength superconducting waveguide or the half-wavelength superconducting waveguide with a first resonator mode from the plurality of resonator modes; 22. The apparatus of claim 21.

23. 23. The apparatus of claim 22, wherein the resonator-induced phase gate facilitates the coupling interaction between the first qubit and the second qubit.

24. 1. An apparatus comprising: a coupling structure coupled to a first qubit and a second qubit, the coupling structure having a plurality of coupling paths configured to selectively generate a plurality of resonant modes, at least one of the plurality of resonant modes causing coupling between the first qubit and the second qubit to enable resonator-induced phase gating operation, and other of the plurality of resonant modes suppressing coupling between the first qubit and the second qubit when the resonator-induced phase gating operation is not enabled, one of the plurality of coupling paths being a quarter-wave superconducting waveguide capacitively coupled to the first qubit and the second qubit, the quarter-wave superconducting waveguide comprising a plurality of portions with different impedances; direct capacitive coupling between the first qubit and the second qubit; and An apparatus comprising:

25. 25. The apparatus of claim 24, wherein the quarter-wave superconducting waveguide has a first segment between the first qubit and a capacitor and a second segment between the capacitor and the second qubit, the apparatus further comprising a superconducting ground connection coupled to the first segment to electrical ground.

26. 26. The device of claim 25, wherein the device exhibits multiple resonator modes that add to cancel out coupling interactions between the first qubit and the second qubit.

27. 27. The apparatus of claim 26, further comprising a resonator-induced phase gate that drives the quarter-wave superconducting waveguide in a first resonator mode from the plurality of resonator modes.

28. 30. The apparatus of claim 27, wherein the resonator-induced phase gate facilitates the coupling interaction between the first qubit and the second qubit.

29. 1. A method comprising:

11. A method of coupling a first qubit and a second qubit using a coupling structure, the coupling structure having a plurality of coupling paths configured to selectively generate a plurality of resonant modes, at least one of the plurality of resonant modes causing coupling between the first qubit and the second qubit to enable resonator-induced phase gating operation, and other of the plurality of resonant modes suppressing coupling between the first qubit and the second qubit when the resonator-induced phase gating operation is not enabled, wherein one coupling path of the plurality of coupling paths is a resonator having a transmission line branch.

30. 30. The method of claim 29, comprising establishing a resonator-induced phase gate between the first qubit and the second qubit by the coupling path.

31. 31. The method of claim 29 or 30, comprising collectively suppressing coupling interactions between the first qubit and the second qubit by the multiple coupling paths.

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