Multimode couplers for improved connectivity

Abstract

Techniques and couplers for managing coupling between qubits are presented. A first tunable coupler qubit (TCQ) can include a first frequency mode and a second frequency mode. A second TCQ can include a third frequency mode and a fourth frequency mode. The first TCQ can be selectively coupled to a first qubit based on the first frequency mode and selectively coupled to a second TCQ based on the second and third frequency modes. The second TCQ can be selectively coupled to a second qubit based on the fourth frequency mode. When specific respective magnetic fluxes are applied to the first and second TCQs, ZZ interaction between the first and second qubits can be suppressed. When respective corrective magnetic fluxes are applied to the first and second TCQs to excite the respective frequency modes, coupling can occur, and ZZ interaction and an entangled gate can be created between the first and second qubits.

Description

[Background technology]

[0001] The present disclosure relates to quantum circuitry, and more particularly to multi-mode couplers for improved connectivity. Summary of the Invention

[0002] The following presents a summary to provide a basic understanding of one or more embodiments of the disclosed subject matter. This summary is not intended to identify key or critical elements or to delineate the scope of any particular embodiments or the claims. Its sole purpose is to present concepts in a simplified form as a prelude to the more detailed description that is presented later. One or more embodiments described herein present systems, devices, structures, methods, apparatus, and / or computer program products that can facilitate the creation and / or use of tunable multi-mode couplers that can manage interactions and coupling between quantum components, such as qubits.

[0003] According to certain embodiments, a system may include a first quantum component. The system may also include a first coupler qubit, which may be operable in a first mode associated with a first frequency and a second mode associated with a second frequency. The first coupler qubit may be selectively coupled to the first quantum component based on the first mode. The first coupler qubit may be selectively coupled to the second coupler qubit based on the second mode and based on a third mode operable on the second coupler qubit. The third mode may be associated with a third frequency. An advantage of the system may be that the system may have improved (e.g., increased, enhanced, or optimized) efficiency, reliability, and performance associated with interactions or couplings between quantum components (e.g., qubits or other quantum components).

[0004] In one or more embodiments of the above system, the first coupler qubit may include a Josephson junction and a superconducting quantum interference device associated with the Josephson junction, and the superconducting quantum interference device may be flux-tunable. In one or more embodiments, ZZ interaction and static ZZ interaction between the first qubit and the second qubit may be suppressed, and exchange interaction between the first qubit and the second qubit may be suppressed for a specified range of frequencies associated with the first qubit and the second qubit, based on the first coupler qubit being selectively coupled to the first quantum component (which may be a first qubit) via the first mode, the first coupler qubit being selectively coupled to the second coupler qubit via the second mode and the third mode, and the second coupler qubit being selectively coupled to the second qubit via the fourth mode.

[0005] In one or more embodiments of the above system, the system may include a coplanar waveguide resonator that may include a first port and a second port, wherein a first plate of a first capacitor component may be connected to a first coupler qubit, a second plate of the first capacitor component may be connected to the first port, a third plate of the second capacitor component may be connected to the second port, and a fourth plate of the second capacitor component may be connected to a second coupler qubit. In one or more embodiments of the above system, the system may include a third coupler qubit, a group of capacitor components that may have first, second, and third capacitor components, and a bus component that may be associated with the group of capacitor components, wherein the first coupler qubit may be associated with the first capacitor component, the second coupler qubit may be associated with the second capacitor component, and the third coupler qubit may be associated with the third capacitor component.

[0006] Advantages of the system may include the system being able to improve (e.g., increase, enhance, or optimize) connectivity between quantum components (e.g., qubits or other quantum components), improve the layout of electronic elements or quantum components of quantum circuitry, and improve management of interactions or coupling between quantum components, which may include improved mitigation or suppression of unwanted interactions, coupling, and entanglement between quantum components.

[0007] In some embodiments, the elements described in connection with the disclosed systems may be embodied in different forms, such as a device, a method, or otherwise.

[0008] These and other features will become apparent from the following detailed description of illustrative embodiments thereof, which is to be read in connection with the accompanying drawings. [Brief explanation of the drawings]

[0009] [Figure 1] FIG. 1 illustrates a block diagram of a non-limiting example system that can include a pair of coupler components that can manage interactions or coupling between quantum components, in accordance with various aspects and embodiments of the disclosed subject matter.

[0010] [Figure 2] 1 illustrates a block diagram of a non-limiting example mode structure of a coupler component mode, in accordance with various aspects and embodiments of the disclosed subject matter.

[0011] [Figure 3] FIG. 1 shows a diagram of a non-limiting example system that can include a pair of tunable coupler components that can manage interactions or coupling between qubits, in accordance with various aspects and embodiments of the disclosed subject matter.

[0012] [Figure 4] FIG. 4 shows a diagram of a non-limiting example device layout 400 of a system that can include a pair of tunable coupler components that can manage interactions or coupling between qubits, in accordance with various aspects and embodiments of the disclosed subject matter.

[0013] [Figure 5] FIG. 10 presents non-limiting exemplary graphical illustrations illustrating magnetic field tuning of ZZ interactions in a system that can include a pair of coupler components that can manage interactions or coupling between qubits, in accordance with various aspects and embodiments of the disclosed subject matter.

[0014] [Figure 6]FIG. 1 illustrates a diagram of a non-limiting example system in which multiple (e.g., four or more) coupler components can be coupled via a capacitive or co-planar waveguide (CPW) resonator bus component to provide improved connectivity between qubits and facilitate management of interactions or coupling between qubits, in accordance with various aspects and embodiments of the disclosed subject matter.

[0015] [Figure 7] FIG. 1 presents a non-limiting, example graphical illustration of the interaction between two tunable coupler qubits (TCQs) associated with a node when one of the TCQs is flux-tuned to transition the TCQ to an ON state while the other TCQ is maintained in an OFF state, according to various aspects and embodiments of the disclosed subject matter.

[0016] [Figure 8] FIG. 1 illustrates a diagram of a non-limiting example system that can include qubits and associated TCQs that can be associated with respective bus components to form a square lattice, thereby providing improved connectivity between the qubits and facilitating management of interactions or coupling between the qubits, according to various aspects and embodiments of the disclosed subject matter.

[0017] [Figure 9] FIG. 1 illustrates a diagram of a non-limiting example system that can include quadrupole transmon qubits (QTQs) and associated TCQs that can be associated with respective bus components to form a square lattice, thereby providing improved connectivity between such qubits and facilitating management of interactions or coupling between such qubits, according to various aspects and embodiments of the disclosed subject matter.

[0018] [Figure 10]1 illustrates a diagram of another non-limiting exemplary system that can include QTQs and associated TCQs that can be associated with respective bus components to form a square lattice, thereby providing improved connectivity between such QTQs and facilitating management of interactions or coupling between such QTQs, according to various aspects and embodiments of the disclosed subject matter.

[0019] [Figure 11] 1 illustrates a block diagram of a non-limiting example system that can employ CPW resonators that can enable long-distance (e.g., long-range) coupling between TCQs and / or between TCQs and bus components, according to various aspects and embodiments of the disclosed subject matter.

[0020] [Figure 12] 1 illustrates a block diagram of a non-limiting example system that can employ CPW resonators that can enable long-range coupling between TCQs across multiple dies, in accordance with various aspects and embodiments of the disclosed subject matter.

[0021] [Figure 13] 1 presents an exemplary graphical illustration related to long-range coupling of qubits associated with TCQs connected via CPW resonators, in accordance with various aspects and embodiments of the disclosed subject matter.

[0022] [Figure 14] FIG. 1 illustrates a block diagram of an exemplary system that may be utilized to create, form, or design a device including qubits, coupler components, and / or other quantum components, elements, or circuit configurations in accordance with various aspects and embodiments of the disclosed subject matter.

[0023] [Figure 15] FIG. 1 illustrates a flow diagram of a non-limiting, exemplary method in which a pair of TCQs can be employed to control interactions, couplings, or gates between components of a quantum circuit, according to various aspects and embodiments of the disclosed subject matter.

[0024] [Figure 16] FIG. 10 shows a flow diagram of another non-limiting exemplary method in which a pair of coupler components can be employed to control interactions, couplings, or gates between components of a quantum circuit, in accordance with various aspects and embodiments of the disclosed subject matter.

[0025] [Figure 17] 1 illustrates a block diagram of a non-limiting exemplary operating environment that can facilitate one or more embodiments described herein. DETAILED DESCRIPTION OF THE INVENTION

[0026] The following detailed description is illustrative only and is not intended to limit the embodiments and / or the application or uses of the embodiments, nor is it intended to be bound by any expressed or implied information presented in the Background or Summary sections above or in the Detailed Description section.

[0027] One or more embodiments will now be described with reference to the drawings, wherein like reference numerals are used to refer to like elements throughout. In the following 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 cases one or more embodiments may be practiced without these specific details.

[0028] Quantum computers can include groups of qubits that can perform quantum operations on data. Quantum circuits that include qubits can utilize couplers to enable interactions between qubits or coupling between pairs of qubits to create quantum logic gates. Couplers can also be used to enable interactions or coupling between other types of electronic elements in quantum circuits.

[0029] To facilitate description of various aspects and embodiments of the disclosed subject matter with respect to interactions, couplings, and gates, the following may provide definitions and / or context that may be relevant to the disclosed subject matter. An entanglement gate may include an operation that applies an external field (e.g., a microwave pulse) to a quantum processor that includes qubits to create an entangled state between two or more separate qubits. A controlled-phase (CPHASE) gate may be a particular type of entanglement gate that allows one qubit to acquire a phase shift if, and only if, both qubits are in an initial excited state.

[0030] A ZZ interaction may be a type of interaction between two qubits or modes in which excitation of one qubit can shift the transition frequency of the other qubit or mode. Thus, a ZZ interaction can equate a state-dependent shift in qubit frequency to a state-dependent phase shift, thereby representing a way to entangle two different qubits to create a CPHASE gate. A ZZ interaction may sometimes be referred to as longitudinal coupling or denoted as chi or 2-chi. A static ZZ interaction may be a type of ZZ interaction that can exist between two qubits or modes in the absence of any external microwave drive (e.g., microwave pulse). A static ZZ interaction may be an "always-on" interaction that can be unwanted (e.g., unnecessary) and detrimental to a system of qubits by inhibiting independent control of each qubit and creating unwanted entanglement.

[0031] Exchange interactions can be a type of interaction between quantum systems that can allow for the exchange of energy. If they exist between two qubits, applying a microwave pulse to one qubit can potentially excite the other qubit; thus, such interactions can be an unwanted form of crosstalk that can be detrimental to the quantum system.

[0032] For some existing quantum circuits and couplers, always-on interactions, such as static ZZ interactions, can occur between two qubits or modes, even in the absence of any external microwave drive. Such always-on interactions can be undesirable and detrimental to a system of qubits because they can inhibit independent control of each qubit and can create unwanted (e.g., unnecessary) entanglement between qubits.

[0033] It may be desirable to improve (e.g., increase, enhance, or optimize) the efficiency, reliability, and performance of coupler components, improve connectivity between qubits (or other quantum components), and improve the layout of electronic elements of quantum circuitry. It may also be desirable to improve management of interactions and coupling between qubits (or other quantum components), including reducing or suppressing unwanted interactions, coupling, and entanglement between qubits (or other quantum components).

[0034] The disclosed subject matter includes coupler components and techniques that can have several advantages and overcome various deficiencies of existing couplers and coupling techniques. The disclosed coupler components and techniques for coupling qubits can have improved (e.g., increased, enhanced, or optimized) efficiency, reliability, and performance compared to existing couplers and techniques, can improve connectivity between qubits (or other quantum components), can improve the layout of electronic elements of quantum circuitry, and can improve management of interactions and coupling between qubits (or other quantum components), including improved mitigation or suppression of unwanted interactions, coupling, and entanglement between qubits (or other quantum components).

[0035] To that end, various embodiments described herein relate to techniques for managing coupling between qubits. In some embodiments, tunable multi-mode couplers can be operated in pairs, which can provide improved (e.g., enhanced) connectivity and long-range interaction between qubits (e.g., fixed-frequency transmon qubits) or other types of quantum components. The system or device can include a first tunable coupler qubit (TCQ) that can include a first mode (e.g., a first "A" mode) associated with a first frequency (e.g., a first mode of oscillation) and a second mode (e.g., a first "B" mode) associated with a second frequency (e.g., a second mode of oscillation). The TCQ may also be referred to as a TCQ coupler. The system or device can also include a second TCQ that can include a third mode (e.g., a second "B" mode) associated with a third frequency and a fourth mode (e.g., a second "A" mode) associated with a fourth frequency. The first TCQ may be associated with (e.g., selectively connected or coupled to) a first quantum component (e.g., a qubit, resonator, or other electronic element) and a second TCQ. The second TCQ may be associated with a second quantum component. The first TCQ and second TCQ may be associated with (e.g., selectively connected or coupled to) each other, for example, by direct capacitive coupling, through a bus component, or via a coplanar waveguide (CPW), as described herein.

[0036] The frequencies associated with each mode may be the same or different from one another. For example, a first frequency associated with a first mode (e.g., a first "A" mode) may be the same or different from a fourth frequency associated with a fourth mode (e.g., a second "A" mode), and a second frequency associated with a second mode (e.g., a first "B" mode) may be the same or different from a third frequency associated with a third mode (e.g., a second "B" mode).

[0037] The first TCQ may be selectively coupled to a first qubit based on a first frequency mode and selectively coupled to a second TCQ based on second and third frequency modes. The second TCQ may be selectively coupled to a second qubit based on a fourth frequency mode. For example, when specific respective magnetic fluxes are applied to a first TCQ (e.g., a flux-tunable SQUID of the first TCQ) and a second TCQ (e.g., a flux-tunable SQUID of the second TCQ), this may result in a desired balance between the respective modes of the respective TCQs, and may desirably suppress interaction and coupling between the first qubit and the second qubit. For example, based on mode-selective coupling (e.g., utilizing a pair of TCQs, such as a first TCQ and a second TCQ), ZZ interaction or coupling, including static ZZ interaction, between the first qubit and the second qubit may be desirably suppressed, and exchange interaction between the first qubit and the second qubit may be desirably suppressed over a wide range of qubit frequencies between the qubits.

[0038] The first TCQ may be selectively coupled to a first qubit based on a first frequency mode and selectively coupled to a second TCQ based on second and third frequency modes. The second TCQ may be selectively coupled to a second qubit based on a fourth frequency mode. For example, when specific respective magnetic fluxes are applied to a first TCQ (e.g., a flux-tunable SQUID of the first TCQ) and a second TCQ (e.g., a flux-tunable SQUID of the second TCQ), this may result in a desired balance between the respective modes of the respective TCQs, and may desirably suppress interaction and coupling between the first qubit and the second qubit. For example, based on mode-selective coupling (e.g., utilizing a pair of TCQs, such as a first TCQ and a second TCQ), ZZ interaction or coupling, including static ZZ interaction, between the first qubit and the second qubit may be desirably suppressed, and exchange interaction between the first qubit and the second qubit may be desirably suppressed over a wide range of qubit frequencies between the qubits.

[0039] When applying respective corrective magnetic fluxes to the first and second TCQs to desirably adjust the tuning of the respective TCQs (e.g., adjusting the tuning of the respective SQUIDs of the respective TCQs), this may result in respective imbalances in the first and second TCQs (e.g., as described herein), which may excite respective modes of the first and second TCQs, thereby creating desired couplings, which may create ZZ interactions, entangled interactions and gates, and / or controlled phase (CPHASE) gates between the first and second qubits via interactions (e.g., couplings) between this pair of TCQs, interactions between the first qubit and the first TCQ, and interactions between the second qubit and the second TCQ. Coupling may be defined as an interaction between two systems (e.g., between a first system including a first qubit and / or a first TCQ and a second system including a second qubit and / or a second TCQ) strong enough to create a multi-qubit gate (e.g., between two qubits) and / or a desired exchange of information or energy between two electronic elements (e.g., electronic elements that may be qubits, resonators, or other desired electronic elements or components).

[0040] In some embodiments, four or more TCQs (e.g., a first TCQ, a second TCQ, and other TCQ couplers) can be coupled together (e.g., selectively coupled) via capacitive and / or CPW resonator buses as described herein. With regard to coupling TCQs together using CPW resonators, the CPW resonators can enable desirable long-range coupling of TCQs across the same integrated circuit (IC) chip (e.g., the same qubit chip or the same die) or between or across multiple IC chips using bump bonds.

[0041] In particular embodiments, the qubits may be quadrupole transmon qubits that can each be associated with (e.g., selectively coupled to) a TCQ. The quadrupole transmon qubits and TCQs may be arranged in a desirably dense square lattice that can enable desirable (e.g., improved, enhanced, or optimized) connectivity and selectivity between the quadrupole transmon qubits. The quadrupole transmon qubits may be associated with (e.g., selectively coupled to) any desired number of TCQs (e.g., four TCQs, or more or less than four TCQs) as described herein.

[0042] These and other aspects and embodiments of the disclosed subject matter will now be described with reference to the drawings.

[0043] 1 illustrates a block diagram of a non-limiting exemplary system 100 that can include a pair of coupler components that can manage interactions or coupling between quantum components (e.g., qubits, resonators, or other electronic components or elements) in accordance with various aspects and embodiments of the disclosed subject matter. System 100 can include various components and circuitry (e.g., quantum components and circuitry) that can be arranged to perform one or more desired functions, as described herein. System 100 can include or be part of, for example, a multi-qubit device or package that can have varying dimensions (e.g., an integrated circuit (IC) chip on which system 100 can reside can have varying dimensions), where the length of the device or package can range, for example, from approximately a few millimeters to approximately tens of millimeters, the width of the device or package can range, for example, from approximately a few millimeters to approximately tens of millimeters, and the thickness can range, for example, from approximately 1 millimeter (mm) to approximately 3 mm. It should be appreciated and understood that these dimensions of the device or package are exemplary, and that according to other embodiments, the device or package may have dimensions that differ (e.g., smaller or larger) than the exemplary dimensions described herein.

[0044] In some embodiments, system 100 may include a first quantum component (QC1) 102 and a second quantum component (QC2) 104 that may be formed as part of a quantum circuit that may be formed on one or more chip stacks that are formed on one or more dies (e.g., IC chips). First quantum component 102 and second quantum component 104 may be part of a group of quantum components of a quantum computer (e.g., a superconducting quantum computer). In particular embodiments, first quantum component 102 and second quantum component 104 may be transmon qubits or quadrupole transmon qubits, although in other embodiments, first quantum component 102 and second quantum component 104 may be different types of qubits. A qubit may include, for example, one or more Josephson junctions (JJs) and shunt capacitors that may be associated with one or more Josephson junctions. In some embodiments, first quantum component 102 and / or second quantum component 104 may be different types of quantum components, such as resonators or other types of electronic elements that may be employed in a quantum circuit.

[0045] It may be desirable (e.g., wanted, needed, or suitable) to manage (e.g., control) interactions, couplings, and / or gates between quantum components, such as quantum component 102 and second quantum component 104. According to various embodiments, system 100 may include a pair of coupler components (e.g., a pair of TCQs) including coupler components (CCs) 106 and 108 that can enable and manage interactions and couplings between first quantum component 102 and second quantum component 104. CCs 106 and 108 may be located between (e.g., logically or physically between) first quantum component 102 and second quantum component 104 in a quantum circuit. One end of CC 106 may be associated (e.g., directly or indirectly connected or coupled) with first quantum component 102, and the other end of CC 106 may be associated (e.g., directly or indirectly connected or coupled) with one end of CC 108. The other end of CC 108 may be associated with (e.g., directly or indirectly connected or coupled to) second quantum component 104. CCs 106 and 108 may control and enable inter-quantum component (e.g., inter-qubit) interactions (e.g., interactions between first quantum component 102 and second quantum component 104) that may allow for quantum logic gates or other desired types of interactions. In some embodiments, quantum components 102 and 104 may be coupled to CCs 106 and 108, respectively, using coupling capacitors, and / or CCs 106 and 108 may be coupled to each other using coupling capacitors, as described in more detail herein.

[0046] According to various embodiments, CC106 and CC108 may each be a TCQ (e.g., a flux-tunable TCQ) that can enable desirably tuning (e.g., modifying, adjusting, or changing) one or more parameters associated with CC106 and CC108 (e.g., frequency or another desired parameter) based on magnetic flux applied to CC106 and CC108, respectively, as described in more detail herein.

[0047] CC 106 may include JJ 110 and SQUID 112 (e.g., a flux-tunable SQUID), where SQUID 112 may include JJ 114 and JJ 116. CC 106 may also include capacitor (C) 118, which may be a shunt capacitor associated with JJ 110 and SQUID 112, capacitor 120 associated with JJ 110, and capacitor 122 associated with SQUID 112. CC 108 may include JJ 124 and SQUID 126 (e.g., a flux-tunable SQUID), where SQUID 126 may include JJ 128 and JJ 130. The CC 108 may also include a shunt capacitor 132 , which may be associated with the JJ 124 and the SQUID 126 , a capacitor 134 , which may be associated with the JJ 124 , and a capacitor 136 , which may be associated with the SQUID 126 .

[0048] In the CC 106, the JJ 110 and the SQUID 112 may be structured, designed, and / or arranged in relation to each other within the quantum circuit such that multiple vibrational modes may be created, which may include a first mode of oscillation (e.g., an “A” mode) 138 and a second mode of oscillation (e.g., a “B” mode) 140. The first mode of oscillation 138 may be associated with a first frequency, and the second mode of oscillation 140 may be associated with a second frequency. The second frequency associated with the second mode 140 may typically be higher than the first frequency associated with the first mode 138. The second mode 140 may also be referred to as a dark mode because it may not typically have a net dipole moment. The first mode 138 and the second mode 140 may be two distinct modes that may correspond to symmetric and antisymmetric combinations of excitations associated with the JJ 110 and the SQUID 112.

[0049] Similarly, in CC 108, JJ 124 and SQUID 126 may be structured, designed, and / or arranged in relation to one another within the quantum circuit such that multiple vibrational modes may be created, which may include a third mode of oscillation (e.g., another “B” mode) 142 and a fourth mode of oscillation (e.g., another “A” mode) 144. Third mode 142 may be associated with a third frequency, which may be different from or the same as the second frequency associated with second mode 140. Fourth mode 144 may be associated with a fourth frequency, which may be different from or the same as the first frequency associated with first mode 138. The third frequency associated with third mode 142 may typically be higher than the fourth frequency associated with fourth mode 144. Third mode 142 may also be referred to as a dark mode because it may not typically have a net dipole moment. The third mode 142 and the fourth mode 144 may be two distinct modes that may correspond to symmetric and antisymmetric combinations of excitations associated with the JJ 124 and the SQUID 126 .

[0050] Referring briefly to Figure 2 (in conjunction with Figure 1), Figure 2 illustrates a block diagram of a non-limiting example mode structure 200 for a mode of a CC (e.g., CC 106, CC 108), in accordance with various aspects and embodiments of the disclosed subject matter. The mode structure 200 can include an "A" mode structure 202 for the "A" mode (e.g., first mode 138) of CC 106 and a "B" mode structure 204 for the "B" mode (e.g., second mode 140).

[0051] The JJ 110 and SQUID 112 of CC 106 (e.g., a flux-tunable TCQ) may be associated with (e.g., connected to) respective capacitor pads (e.g., capacitor plates), such as capacitor pads 206, 208, and 210, of each capacitor of CC 106. As shown in “A” mode structure 202, in the “A” mode of CC 106, charge can flow from capacitor pad 210 to capacitor pad 208 (as indicated by reference numeral 212), and charge can also flow in the same direction from capacitor pad 208 to capacitor pad 206 (as indicated by reference numeral 214). As a result, no net charge accumulates on capacitor pad 208, which may be symmetric or antisymmetric depending on how the direction of charge is defined. As shown in “B” mode structure 204, in the “B” mode of CC 106, charge can flow from capacitor pad 208 to capacitor pad 206 and capacitor pad 210 (as indicated by reference numerals 216 and 218, respectively).

[0052] 1 , in some embodiments, the first quantum component 102 may be selectively coupled to the CC 106 based on a first mode 138 (e.g., the first quantum component 102 may be selectively coupled to the first (or “A”) mode 138 of the CC 106). The second quantum component 104 may be selectively coupled to the CC 108 based on a fourth mode 144 (e.g., the second quantum component 104 may be selectively coupled to the fourth (or other “A”) mode 144 of the CC 108). Additionally, the CC 106 and the CC 108 may be selectively coupled to each other based on the second (or “B”) mode 140 of the CC 106 and the third (or other “B”) mode 142 of the CC 108.

[0053] The pair of CCs 106 and 108 can desirably (e.g., preferably, improved, or optimally) manage the interactions (e.g., ZZ interactions, static ZZ interactions, exchange interactions, or other interactions), couplings, and gates (e.g., ZZ gates, entanglement gates, CPHASE gates, or other gates) between the first quantum component 102 and the second quantum component 104 to facilitate desirably managing the interactions and couplings between the first quantum component 102 and the second quantum component 104. Using the respective SQUIDs 112 and 126, the CCs 106 and 108 can be desirably tuned to facilitate exciting or not exciting respective modes (e.g., 138, 140, 142, 144), which can enable the CCs 106 and 108 to manage the interactions, couplings, and gates between the first quantum component 102 and the second quantum component 104.

[0054] To facilitate tuning of CCs 106 and 108, system 100 may include a coil component 146 that may be associated with and proximate to CC 106 and a coil component 148 that may be associated with and proximate to CC 108. Coil component 146 may be employed to apply a desired magnetic field or flux to CC 106 (e.g., SQUID 112 of CC 106) based on a current supplied to coil component 146. Coil component 148 may be employed to apply a desired magnetic field or flux to CC 108 (e.g., SQUID 126 of CC 108) based on a current supplied to coil component 148. The magnetic field created and applied by coil component 148 may be different from or the same as the magnetic flux created and applied by coil component 146, depending in part on the respective properties of or associated with each component (e.g., JJ, SQUID, or other component) of CC 106 and CC 108 (e.g., JJ barrier properties, component material properties, inductance, impedance, or other properties). Under a particular magnetic flux applied to CC106 and CC108, the respective modes (e.g., 138, 140, 142, 144) can be maintained or transitioned to a non-excited state, thereby suppressing coupling between the first quantum component 102 and the second quantum component 104 and / or suppressing interaction or coupling between the respective components of system 100 (e.g., between first quantum component 102 and CC106, between CC106 and CC108, and / or between second quantum component 104 and CC108).

[0055] For example, coil component 146 can apply magnetic flux to SQUID 112 of CC 106 in an amount that can cause the critical current of SQUID 112, and therefore a first energy (e.g., first Josephson energy) associated with SQUID 112, to be equal or at least substantially equal to the critical current of JJ 110 of CC 106, and therefore a second energy (e.g., second Josephson energy) associated with JJ 110. Coil component 148 can also apply magnetic flux to SQUID 126 of CC 108 in an amount that can cause the critical current of SQUID 126, and therefore a third energy (e.g., third Josephson energy) associated with SQUID 126, to be equal or at least substantially equal to the critical current of JJ 124 of CC 108, and therefore a fourth energy (e.g., fourth Josephson energy) associated with JJ 124. As a result, a balance between the first and second energies associated with CC106 and a balance between the third and fourth energies associated with CC108 can be achieved, which can provide and / or enhance the desired mode-selective coupling associated with CCs 106 and 108, which can cause or create a desired suppression (e.g., suppression) of the interaction or coupling (e.g., ZZ, static ZZ, and / or exchange interaction or coupling) between first quantum component 102 and second quantum component 104 until essentially or approximately zero interaction or coupling.

[0056] When the magnetic flux applied to CCs 106 and 108 by coil component 146 and coil component 148 is modified (e.g., changed or adjusted) to specific respective amounts of magnetic flux to adjust the tuning of CCs 106 and 108 (e.g., adjust the tuning associated with SQUID 112 and SQUID 126), the respective modes (e.g., 138, 140, 142, 144) can be transitioned to excited states, thereby allowing desired interactions or couplings between first quantum component 102 and second quantum component 104 (and interactions or couplings between other desired components).

[0057] For example, modifying the magnetic flux applied to the SQUID 112 of CC 106 may create an imbalance between a first energy associated with the SQUID 112 (e.g., such first energy may be modified based on the modified magnetic flux) and a second energy of the JJ 110 of CC 106. This imbalance may result in excitation of a mode of CC 106 and may alter a mode-selective coupling associated with CC 106, such that the first quantum component 102 may have a desired interaction or coupling with both the first and second modes of CC 106. Similarly, modifying the magnetic flux applied to the SQUID 126 of CC 108 may create an imbalance between a third energy associated with the SQUID 126 (e.g., such third energy may be modified based on the modified magnetic flux) and a fourth energy of the JJ 124 of CC 108. This imbalance may result in excitation of a mode of CC 108 and may alter the mode-selective coupling associated with CC 108, such that second quantum component 104 may have a desired interaction or coupling to both the third and fourth modes of CC 108. Such alteration of the mode-selective coupling associated with CCs 106 and 108 may also create or allow a desired coupling between CCs 106 and 108. As a result, a pair of CCs 106 and 108 employing mode-selective coupling may create a desired interaction, coupling, and / or gate (e.g., a ZZ interaction or coupling, an exchange interaction or coupling, an exchange gate, and / or a CPHASE gate) between first quantum component 102 and second quantum component 104 via CCs 106 and 108.

[0058] It should be appreciated and understood that in some embodiments, CCs 106 and 108 (e.g., TCQs) can include SQUIDs, but in certain other embodiments, CCs (e.g., TCQs) can utilize a single tunable JJ (e.g., a single electrostatic voltage-tunable JJ) instead of a SQUID in a CC (e.g., a SQUID including two JJs). Such a tunable JJ (e.g., a single electrostatic voltage-tunable JJ) can be tuned by applying a specific electrostatic voltage to the tunable JJ to adjust the tuning of the tunable JJ, for example, to facilitate switching the CC to an ON state (e.g., enabling desired interactions or coupling between quantum components) or an OFF state (e.g., inhibiting, suppressing, minimizing, or preventing undesired interactions or coupling between quantum components). For example, a conductive or capacitive pad or wire may be present in proximity to the single tunable JJ, and a specific voltage may be applied to the conductive or capacitive pad or wire, which can apply a specific electrostatic charge to the tunable JJ to adjust the tuning of the tunable JJ.

[0059] Referring to FIG. 3 , FIG. 3 illustrates a diagram of a non-limiting exemplary system 300 that may include a pair of TCQs capable of managing interactions or coupling between qubits, in accordance with various aspects and embodiments of the disclosed subject matter. System 300 may include a first qubit 302 and a second qubit 304 that may be formed as part of a quantum circuit that may be formed on one or more chip stacks formed on one or more dies (e.g., IC chips). In particular embodiments, first qubit 302 and second qubit 304 may be transmon qubits, while in other embodiments, first qubit 302 and second qubit 304 may be different types of qubits. First qubit 302 may include a JJ 306 and a capacitor 308 that may be in parallel with JJ 306. Second qubit 304 may include a JJ 310 and a capacitor 312 that may be in parallel with JJ 310.

[0060] System 300 may also include a first TCQ 314 and a second TCQ 316. The first qubit 302 may be associated (e.g., coupled) to the first TCQ 314 via coupling capacitors 318 and 320. The second qubit 304 may be associated (e.g., coupled) to the second TCQ 316 via coupling capacitors 322 and 324. The first TCQ 314 may be associated (e.g., coupled) to the second TCQ 316 via coupling capacitor 326.

[0061] The first TCQ 314 may include a JJ 328 and a SQUID 330 that may be associated with (e.g., connected to) the JJ 328. The SQUID 330 may include a JJ 332 and a JJ 334 that may be in parallel with the JJ 332. The SQUID 330 may be formed in part by respective currents that may flow through the JJ 332 and the JJ 334. The first TCQ 314 may also include a shunt capacitor 336 that may be in parallel with the JJ 328 and the SQUID 330. The first TCQ 314 may also include a capacitor 338 that may be in parallel with the SQUID 330 and a capacitor 340 that may be in parallel with the JJ 328.

[0062] The second TCQ 316 may include a JJ 342 and a SQUID 344, which may be associated with (e.g., connected to) JJ 342. The SQUID 344 may include a JJ 346 and a JJ 348, which may be in parallel with JJ 346. The SQUID 344 may be formed in part by respective currents that may flow through JJ 346 and JJ 348. The second TCQ 316 may also include a shunt capacitor 350, which may be in parallel with JJ 342 and the SQUID 344. The second TCQ 316 may also include a capacitor 352, which may be in parallel with the SQUID 344, and a capacitor 354, which may be in parallel with JJ 342.

[0063] The first TCQ 314 may include a first mode (e.g., an “A” mode) associated with a first frequency and a second mode (e.g., a “B” mode) associated with a second frequency. The second TCQ 316 may include a third mode (e.g., another “B” mode) associated with a third frequency and a fourth mode (e.g., another “A” mode) associated with a fourth frequency. When a desired (e.g., suitable or appropriate) magnetic flux is applied to the SQUID 330 of the first TCQ 314 (e.g., by a coil component (not shown in FIG. 3 but as described herein)), the first qubit 302 may couple only to the first mode (e.g., the “A” mode) of the first TCQ 314. When a desired (e.g., suitable or appropriate) magnetic flux is applied to the SQUID 344 of the second TCQ 316 (e.g., by a coil component (not shown in FIG. 3 but as described herein)), the second qubit 304 can couple only to the fourth mode (e.g., another “A” mode) of the second TCQ 316. Under the same respective magnetic fields, the first TCQ 314 and the second TCQ 316 can couple to each other only via the second and third modes (e.g., via their respective “B” modes). As a result, when TCQs 314 and 316 are under their respective magnetic fields, as described herein, a balance can be achieved between a first energy associated with SQUID 330 (e.g., a first Josephson energy) and a second energy associated with JJ 328 (e.g., the first energy and the second energy can be the same or substantially the same), and a balance can be achieved between a third energy associated with SQUID 344 and a fourth energy associated with JJ 342, thereby desirably suppressing interaction or coupling between first quantum bit 302 and second quantum bit 304.

[0064] When the respective magnetic fields applied to the first TCQ314 and the second TCQ316 are modified (e.g., by respective coil components) to desired respective corrective magnetic fields, this can create an imbalance between the first energy associated with SQUID330 (e.g., that which is modified by the corrective magnetic field) and the second energy associated with JJ328, and can create an imbalance between the third energy associated with SQUID344 (e.g., that which is modified by another corrective magnetic field) and the fourth energy associated with JJ342. As a result, the respective modes of the first TCQ 314 and the second TCQ 316 may be excited, and the mode-selective couplings of the first TCQ 314 and the second TCQ 316 may be altered, such that the first qubit 302 may have a desired interaction or coupling with both the first mode and the second mode of the first TCQ 314, and the second qubit 304 may have a desired interaction or coupling with both the third mode and the fourth mode of the second TCQ 316, and a desired interaction, coupling, and / or gate (e.g., a ZZ interaction or coupling, an exchange interaction or coupling, an exchange gate, and / or a CPHASE gate) may be created between the first qubit 302 and the second qubit 304 via the first TCQ 314 and the second TCQ 316.

[0065] Referring to Figure 4, Figure 4 shows a diagram of a non-limiting example device layout 400 (e.g., device geometry) of a system that may include a pair of TCQs that can manage interactions or coupling between qubits, in accordance with various aspects and embodiments of the disclosed subject matter. The device layout 400 of the system may include a layout of quantum circuitry that may include qubit 402, qubit 404, TCQ 406, TCQ 408, CPW 410, CPW 412, CPW 414, CPW 416, and coupling capacitor 418. Qubit 402 may include JJ 420. Qubit 404 may include JJ 422. TCQ 406 may include JJ 424 and SQUID 426. TCQ 408 may include JJ 428 and SQUID 430.

[0066] Each of TCQs 406 and 408 may include a respective "A" mode and a respective "B" mode, which may be associated with a respective frequency, as described herein. As described herein, qubit 402 may be selectively coupled to TCQ 406 based on the "A" mode of TCQ 406, and qubit 404 may be selectively coupled to TCQ 408 based on the "A" mode of TCQ 408. TCQs 406 and 408 may be selectively coupled to each other based on their respective "B" modes, as described herein.

[0067] As part of device layout 400, qubit 402 may be configured with a group of pads (e.g., conductive and / or capacitive pads), including pad 432, pad 434, pad 436, and pad 438, which may be located within and isolated from ground region 440. Also, as part of device layout 400, qubit 404 may be configured with another group of pads, including pad 442, pad 444, pad 446, and pad 448, which may be located within and isolated from ground region 450. Furthermore, as part of device layout 400, TCQ 406 may be configured with pads, including pad 452, pad 454, and pad 456, which may be located within and isolated from ground region 458. Also, as part of device layout 400, TCQ 408 may be configured with various pads, including pad 460, pad 462, and pad 464, which may be located within and isolated from ground region 466.

[0068] JJ 420 of qubit 402 may be connected to pad 432 and pad 434. JJ 422 of qubit 404 may be connected to pad 442 and pad 444. For TCQ 406, JJ 424 may be connected to pad 452 and pad 454, and SQUID 426 may be connected to pad 452 and pad 456. For TCQ 408, JJ 428 may be connected to pad 460 and pad 462, and SQUID 430 may be connected to pad 460 and pad 464. TCQs 406 and TCQ 408 may be selectively coupled to each other via coupling capacitor 418.

[0069] Qubit 402 may be selectively coupled to TCQ 406, as described herein. To facilitate such selective coupling, pad 436 of qubit 402 may be connected to CPW 410, which may be connected to pad 454 of TCQ 406, and pads 436 and 432 of qubit 402 may be capacitively associated or connected to one another. Also, to facilitate such selective coupling, pad 438 of qubit 402 may be connected to CPW 412, which may be connected to pad 456 of TCQ 406, and pads 438 and 434 of qubit 402 may be capacitively associated or connected to one another.

[0070] Qubit 404 may be selectively coupled to TCQ 408, as described herein. To facilitate such selective coupling, pad 446 of qubit 404 may be connected to CPW 414, which may be connected to pad 462 of TCQ 408, and pads 446 and 442 of qubit 404 may be capacitively associated or connected to one another. Also, to facilitate such selective coupling, pad 448 of qubit 404 may be connected to CPW 416, which may be connected to pad 464 of TCQ 408, and pads 448 and 444 of qubit 404 may be capacitively associated or connected to one another.

[0071] The system represented by device layout 400 may operate and / or function in the same or similar manner as other systems or devices described herein with respect to selectively coupling, optionally suppressing interactions or coupling between qubits, and optionally allowing interactions, couplings, or gates between qubits. It should be recognized and understood that exemplary device layout 400 is merely one exemplary device layout for a system that may include a pair of TCQs that may each be associated with a qubit to facilitate desired selective interactions or couplings of such qubits, and that in other embodiments, a variety of other device layouts may be utilized to achieve desired selective interactions or couplings of qubits in accordance with various aspects and embodiments of the disclosed subject matter.

[0072] Referring briefly to FIG. 5 (in conjunction with FIG. 3 ), FIG. 5 presents an illustration of a non-limiting, exemplary graph 500 illustrating magnetic field tuning of ZZ interactions in a system that may include a pair of coupler components capable of managing interaction or coupling between qubits, in accordance with various aspects and embodiments of the disclosed subject matter. Coupling may be defined as an interaction between two systems (e.g., between a first system including a first qubit and / or a first TCQ and a second system including a second qubit and / or a second TCQ) that is strong enough to create a multi-qubit gate (e.g., between two qubits) and / or a desired exchange of information or energy between two electronic elements (e.g., qubits, resonators, or other desired electronic elements or components). The exemplary graph 500 plots the ZZ interaction (in kilohertz (kHz)) between the first qubit 302 and the second qubit 304 along the y-axis of graph 500 versus the Josephson energy E along the x-axis of graph 500. j (units: gigahertz (GHz)). Graph line 502 shows the relationship between the various Josephson energies E j , a data point can be presented that indicates the amount of ZZ interaction between the first qubit 302 and the second qubit 304.

[0073] In this exemplary scenario, the critical current associated with JJ328 in the first TCQ314 and the critical current associated with JJ342 in the second TCQ316 both have Josephson energies E j =10 GHz. Also, in this example scenario, the frequencies associated with the first qubit 302 and the second qubit 304 may be approximately 5 GHz. The Josephson energies of the SQUID 330 of the first TCQ 314 and the SQUID 344 of the second TCQ 316 may be tuned (e.g., tuned, adjusted, or modified simultaneously or in parallel) via respective magnetic fluxes applied to the respective SQUIDs 330 and 344 (e.g., by respective coil components).

[0074] E of each of SQUID 330 and 344 j is equal to 10 GHz, based on the respective magnetic fields applied to SQUIDs 330 and 344 (e.g., by their respective coil components), the ZZ and exchange interactions between first qubit 302 and second qubit 304 may be desirably (e.g., favorably or significantly) suppressed, as shown by reference numeral 504 in graph 500. That is, pair of TCQs 314 and 316 may be effectively in an off position or state in which the ZZ and exchange interactions between first qubit 302 and second qubit 304 may be suppressed.

[0075] E of each of SQUID 330 and 344 j As E increases toward about 25 GHz, based on the respective corrective magnetic fields applied to SQUIDs 330 and 344 (e.g., by their respective coil components), the ZZ interaction between first qubit 302 and second qubit 304 desirably (e.g., significantly or preferably) increases, as shown by reference numeral 506 in graph 500, and ZZ > 10 megahertz (MHz) can be achieved. jincreases to about 25 GHz, the pair of TCQs 314 and 316 can be effectively in an on position or state where the ZZ and exchange interactions between the first qubit 302 and the second qubit 304 can be desirably increased.

[0076] 6 illustrates a diagram of a non-limiting example system 600 in which multiple (e.g., four or more) coupler components can be coupled via capacitive or CPW resonator bus components to provide improved connectivity between qubits and facilitate management of interactions or coupling between qubits, according to various aspects and embodiments of the disclosed subject matter. Repeated descriptions of similar elements used in other embodiments described herein have been or may be omitted for the sake of brevity.

[0077] Exemplary system 600 may include qubits 602, 604, 606, and 608. Exemplary system 600 may also include TCQs 610, 612, 614, and 616. Each of TCQs 610, 612, 614, and 616 may include an "A" vibrational mode and a "B" vibrational mode, which may be associated with a respective frequency. While system 600 includes four qubits and four TCQs, it should be appreciated and understood that in other embodiments, system 600 may include fewer or more than four qubits and fewer or more than four TCQs.

[0078] Qubit 602 may be associated (e.g., coupled) with TCQ 610 via coupling capacitors 618 and 620. Qubit 604 may be associated with TCQ 612 via coupling capacitors 622 and 624. Qubit 606 may be associated with TCQ 614 via coupling capacitors 626 and 628. Qubit 608 may be associated with TCQ 616 via coupling capacitors 630 and 632.

[0079] System 600 may include a bus component 634 that may be employed to facilitate selective interaction or coupling between each qubit (e.g., 602, 604, 606, or 608). According to various embodiments, bus component 634 may be a capacitive bus component or a CPW resonator bus component. Bus component 634 may be associated (e.g., coupled) with TCQ 610 via coupling capacitor 636, associated with TCQ 612 via coupling capacitor 638, associated with TCQ 614 via coupling capacitor 640, and associated with TCQ 616 via coupling capacitor 642.

[0080] Each qubit 602, 604, 606, and 608 can be selectively coupled to a respective TCQ 610, 612, 614, and 616 based on the respective "A" mode of each TCQ 610, 612, 614, and 616. Each TCQ 610, 612, 614, and 616 can be selectively coupled to each other based on the respective "B" mode of each TCQ 610, 612, 614, and 616 and via bus component 634.

[0081] System 600 may also include coil component 644, which may be located proximate to TCQ 610 (e.g., proximate to a SQUID (not shown in FIG. 6 ) of TCQ 610), coil component 646, which may be located proximate to TCQ 612, coil component 648, which may be located proximate to TCQ 614, and coil component 650, which may be located proximate to TCQ 616. Each of coil components 644, 646, 648, and 650 may apply a respective magnetic flux to each of TCQs 610, 612, 614, and 616 based on a respective input current, which may be provided to each of coil components 644, 646, 648, and 650, as described herein.

[0082] For example, if it is desirable to suppress interactions and coupling between all of the qubits 602, 604, 606, and 608 associated with bus component 634, coil components 644, 646, 648, and 650 can apply respective magnetic fluxes to each of the TCQs 610, 612, 614, and 616, which can result in a balance, for each TCQ, between the first Josephson energy associated with the SQUID of that TCQ and the second Josephson energy associated with the JJ of that TCQ (e.g., the first Josephson energy and the second Josephson energy can be the same or substantially the same), thereby desirably suppressing interactions or coupling between the qubits 602, 604, 606, and 608, as described herein.

[0083] If it is desirable to create an interaction, coupling, or gate between a pair of quantum bits connected to the same node (e.g., the same bus component 634), such interaction, coupling, or gate can be selectively implemented by system 600 by flux tuning only the TCQs associated with the pair of quantum bits by modifying the respective magnetic fluxes applied to those TCQs to excite their respective "B" modes and transition those TCQs to an ON state, while other TCQs associated with other quantum bits remain in an OFF state based on the respective magnetic fluxes applied to those other TCQs. For example, if it is desired to create an interaction, coupling, or gate between qubit 602 and qubit 604 associated with bus component 634 while suppressing interaction with other qubits 606 and 608 associated with bus component 634, a first magnetic flux applied to TCQ 610 by coil component 644 can be modified to a first modified magnetic flux based on a modified input current supplied to coil component 644 to flux tune the SQUID of TCQ 610 (e.g., modify the tuning of the SQUID), and a second magnetic flux applied to TCQ 612 by coil component 646 can be modified to a second modified magnetic flux based on another modified input current supplied to coil component 646 to flux tune the SQUID of TCQ 612. As described herein, the first corrective flux may create a Josephson energy imbalance between the SQUID and associated JJ of TCQ 610, and the second corrective flux may create a Josephson energy imbalance between the SQUID and associated JJ of TCQ 612. As a result, via the mode-selective coupling of TCQ 610 and TCQ 612 (as described herein) and via bus component 634, there may be a desired selective interaction, coupling, and / or gate (e.g., ZZ interaction and coupling, and / or entanglement interaction and gate) between qubit 602 and qubit 604.Other magnetic fluxes applied to other TCQs 614 and 616 by other coil components 648 and 650 may remain, such that interactions or coupling between other qubits 606 and 608 associated with those other TCQs may be suppressed with respect to those qubits 606 and 608 and qubits 602 and 604.

[0084] As another example, if it is desired to selectively create an interaction, coupling, or gate between qubit 604 and qubit 608 associated with bus component 634, while suppressing interaction with the other qubits 602 and 606 associated with bus component 634, coil components 646 and 650 can be controlled to apply respective corrective magnetic fluxes to respective TCQs 612 and 616, flux tuning only the TCQs 612 and 616 associated with qubits 604 and 608, exciting their respective "B" modes and transitioning those TCQs 612 and 616 to the on state, enabling such interaction, coupling, or gate between qubit 604 and qubit 608. Meanwhile, coil components 644 and 648 can continuously apply their respective magnetic fluxes to the other TCQs 610 and 614 to keep them in an off state (e.g., by keeping the "B" mode de-excited) and suppress interaction of qubit 602 and qubit 606 with each other or with the other qubits 604 and 608. System 600 can be utilized and managed to allow any desired selective interaction or coupling between any pair of qubits associated with bus component 634, while suppressing interaction or coupling between other qubits associated with bus component 634.

[0085] 7 (in conjunction with FIG. 6 ), FIG. 7 presents an illustration of a non-limiting, exemplary graph 700 illustrating the interaction between two qubits associated with TCQs when one of the respective TCQs associated with a node (e.g., a bus component) is flux-tuned to transition that TCQ to an ON state while the other TCQ is maintained in an OFF state, in accordance with various aspects and embodiments of the disclosed subject matter. The exemplary graph 700 represents the ZZ interaction (in kHz) between qubit 602 and qubit 606 along the y-axis of graph 700, as well as the Josephson energy E along the x-axis of graph 700. j (in GHz). Graph line 702 shows the relationship between the various Josephson energies E j For qubit 602 and qubit 606, a data point can be presented that indicates the amount of ZZ interaction between qubit 602 and qubit 606.

[0086] In this example scenario, the TCQ 610 associated with qubit 602 can be flux tuned to excite the "B" mode of the TCQ 610, transitioning it to an excited state and transitioning or placing the TCQ 610 in an ON state, while the TCQ 614 associated with qubit 606 can remain in an OFF state. j can be varied over a desired sweep range. The ZZ interaction between qubit 602 and qubit 606 can be calculated. Graph line 702 shows the ZZ interaction for various Josephson energies E j can represent the computational complexity of the ZZ interaction between qubit 602 and qubit 606 in terms of ZZ<1 kHz. In graph 700, it can be seen that ZZ<1 kHz for the entire sweep range, which can indicate a desirably minimal amount of unwanted entanglement between qubit 602 and qubit 606.

[0087] 8 illustrates a diagram of a non-limiting example system 800 that may include qubits (e.g., transmon qubits) and associated TCQs that may be associated with respective bus components to form a square lattice, thereby providing improved connectivity between the qubits and facilitating management of interactions or coupling between the qubits, according to various aspects and embodiments of the disclosed subject matter. Repeated descriptions of similar elements used in other embodiments described herein have been or may be omitted for the sake of brevity.

[0088] Exemplary system 800 may include a first qubit subgroup, which may include qubits 802, 804, 806, and 808, as part of a lattice containing the qubits. Exemplary system 800 may also include TCQs 810, 812, 814, and 816. Each of TCQs 810, 812, 814, and 816 may include an "A" vibration mode and a "B" vibration mode, which may be associated with a respective frequency. Qubit 802 may be associated (e.g., selectively coupled) with TCQ 810 via coupling capacitors 818 and 820. Qubit 804 may be associated with TCQ 812 via coupling capacitors 822 and 824. Qubit 806 may be associated with TCQ 814 via coupling capacitors 826 and 828. Qubit 808 may be associated with TCQ 816 via coupling capacitors 830 and 832.

[0089] System 800 may include a bus component 834 that may be employed to facilitate selective interaction or coupling between respective qubits (e.g., 802, 804, 806, or 808). According to various embodiments, bus component 834 may be a capacitive bus component or a CPW resonator bus component. Bus component 834 may be associated (e.g., coupled) with TCQ 810 via coupling capacitor 836, associated with TCQ 812 via coupling capacitor 838, associated with TCQ 814 via coupling capacitor 840, and associated with TCQ 816 via coupling capacitor 842.

[0090] Each qubit 802, 804, 806, and 808 may be selectively coupled to a respective TCQ 810, 812, 814, and 816 based on the respective "A" modes of each TCQ 810, 812, 814, and 816, as described herein. Each TCQ 810, 812, 814, and 816 may be selectively coupled to each other based on the respective "B" modes of each TCQ 810, 812, 814, and 816, as described herein, and via bus component 834.

[0091] Exemplary system 800 may also include a second qubit subgroup, which may include qubits 806, 844, 846, and 848, which may be associated with TCQs 850, 852, 854, and 856, respectively, as part of the lattice (e.g., via respective coupling capacitors). As can be seen, in the lattice, qubit 806 may be part of a first qubit subgroup and a second qubit subgroup. That is, qubit 806 and various other qubits in the lattice may each be associated with two TCQs (e.g., qubit 806 may be selectively coupled to TCQ 814 and TCQ 850). TCQs 850, 852, 854, and 856 may be associated with bus component 858 (e.g., via respective coupling capacitors). It should be appreciated and understood that this and other portions of the lattice associated with other subgroups of quantum bits may also include various other coupling capacitors for coupling each quantum bit to its respective TCQ and for coupling each TCQ to its respective bus component, but for simplicity and clarity, such coupling capacitors are not referenced numerically in FIG. 8 .

[0092] Each of the TCQs 850, 852, 854, and 856 can include an "A" vibration mode and a "B" vibration mode that can be associated with a respective frequency. Each qubit 806, 844, 846, and 848 can be selectively coupled to a respective TCQ 850, 852, 854, and 856 based on the respective "A" modes of each TCQ 850, 852, 854, and 856, as described herein. Each TCQ 850, 852, 854, and 856 can be selectively coupled to each other based on the respective "B" modes of each TCQ 850, 852, 854, and 856, as described herein, and via bus component 858.

[0093] Exemplary system 800 can also include a third qubit subgroup, which can include qubits 808, 860, 862, and 864, which can be associated with TCQs 866, 868, 870, and 872, respectively, as part of the lattice. As can be seen, in the lattice, qubit 808 can be part of a first qubit subgroup and a third qubit subgroup. TCQs 866, 868, 870, and 872 can be associated with a bus component 874 (e.g., via respective coupling capacitors). Each of TCQs 866, 868, 870, and 872 can include an “A” vibrational mode and a “B” vibrational mode, which can be associated with a respective frequency. Each qubit 808, 860, 862, and 864 can be selectively coupled to a respective TCQ 866, 868, 870, and 872 based on the respective "A" modes of each TCQ 866, 868, 870, and 872, as described herein. Each TCQ 866, 868, 870, and 872 can be selectively coupled to each other based on the respective "B" modes of each TCQ 866, 868, 870, and 872, as described herein, and via bus component 874.

[0094] Exemplary system 800 may also include a fourth qubit subgroup, which may include qubits 848, 860, 876, and 878, which may be associated with TCQs 880, 882, 884, and 886, respectively, as part of the lattice (e.g., via respective coupling capacitors). As can be seen, in the lattice, qubit 848 may be part of the second qubit subgroup and the fourth qubit subgroup, and qubit 860 may be part of the third qubit subgroup and the fourth qubit subgroup. TCQs 880, 882, 884, and 886 may be associated with bus component 888 (e.g., via respective coupling capacitors). Each of TCQs 880, 882, 884, and 886 may include an “A” vibrational mode and a “B” vibrational mode, which may be associated with a respective frequency. Each qubit 848, 860, 876, and 878 can be selectively coupled to a respective TCQ 880, 882, 884, and 886 based on the respective "A" modes of each TCQ 880, 882, 884, and 886, as described herein. Each TCQ 880, 882, 884, and 886 can be selectively coupled to each other based on the respective "B" modes of each TCQ 880, 882, 884, and 886, as described herein, and via bus component 888.

[0095] Similarly, in some embodiments, exemplary system 800 may further include, as part of the lattice, a fifth qubit subgroup 890 (which may include qubit 846 that is also part of the second qubit subgroup), where each qubit in fifth subgroup 890 may be associated with a respective TCQ that may be associated with a bus component; a sixth qubit subgroup 892 (which may include qubit 876 that is also part of the fourth qubit subgroup), where each qubit in sixth subgroup 892 may be associated with a respective TCQ that may be associated with a bus component; and / or another qubit subgroup, associated TCQ, and associated bus component.

[0096] If it is desirable to suppress interactions between all of the qubits of the lattice (e.g., qubits 802, 804, 806, 808, 844, 846, 848, . . . , 860, . . . , 876, 878, 880), then a respective magnetic field can be applied (e.g., by a respective coil component) to each TCQ associated with each qubit of the lattice (e.g., TCQs 810, 812, 814, 816, 850, 852, 854, 856, 866, . . . , 880, 882, 884, 886) to place each TCQ in an off state, as described herein. System 800 can also implement selective interaction or coupling between one or more desired pairs of qubits (e.g., qubit 802 and qubit 806; and / or qubit 844 and qubit 846; and / or qubit 848 and qubit 860) of the lattice by flux-tuning only the TCQs (e.g., TCQs 810 and TCQ 814; and / or TCQs 852 and TCQ 854; and / or TCQs 882 and TCQ 880, respectively) by modifying the respective magnetic fluxes applied to those TCQs (e.g., by respective coil components associated with those TCQs) to flux-tune those TCQs, exciting the respective "B" modes of only those TCQs, transitioning them to an excited state and transitioning those TCQs from an OFF state to an ON state, while other TCQs associated with other qubits remain in an OFF state based on the respective magnetic fluxes applied to those other TCQs associated with the lattice, as described herein. It should be appreciated and understood that for simplicity and clarity, each coil component associated with each TCQ (e.g., TCQs 810, 812, 814, 816, 850, 852, 854, 856, 866, ..., 880, 882, 884, 886) is not shown in FIG.

[0097] 9 illustrates a diagram of a non-limiting exemplary system 900 that may include quadrupole transmon qubits and associated TCQs that may be associated with respective bus components to form a square lattice (e.g., a desirably dense square lattice) to provide improved connectivity between such qubits and facilitate management of interactions or coupling between such qubits, according to various aspects and embodiments of the disclosed subject matter. System 900 may also desirably increase component density (e.g., increase the number of quantum components on a die) compared to existing quantum circuit configurations and techniques. Repeated descriptions of similar elements used in other embodiments described herein may be omitted or omitted for the sake of brevity.

[0098] The lattice of system 900 may include a group of quadrupole transmon qubits, including quadrupole transmon qubit (QTQ) 902. QTQ 902 (and each of the other QTQs) may include four capacitor pads, including capacitor pads 904, 906, 908, and 910, and a JJ 912. Capacitor pad 904 and capacitor pad 906 may be galvanically connected to each other, and capacitor pad 908 and capacitor pad 910 may be galvanically connected to each other. JJ 912 may be associated with (e.g., connected to) capacitor pads 904, 906, 908, and 910. JJ 912 may facilitate (e.g., enable) the connection of capacitor pads 904 and 906 to capacitor pads 908 and 910 under certain conditions. The QTQ902 can function like a transmon qubit, as described herein, except that the placement of the capacitor pads of the QTQ902 relative to the JJ912 allows the QTQ902 to have dipole interactions with up to four TCQs, rather than just two.

[0099] The example system 900 may include a first subgroup of QTQs, which may include QTQs 902, 914, 916, and 918, as part of a lattice (e.g., a square lattice). The example system 900 may also include TCQs 920, 922, 924, and 926. Each of the TCQs 920, 922, 924, and 926 may include an "A" vibration mode and a "B" vibration mode, which may be associated with a respective frequency. QTQ 902 may be associated (e.g., selectively coupled) with TCQ 920 (e.g., via a coupling capacitor). QTQ 914 may be associated with TCQ 922 (e.g., via a coupling capacitor). QTQ 916 may be associated with TCQ 924 (e.g., via a coupling capacitor). QTQ 918 may be associated with TCQ 926 (e.g., via a coupling capacitor). As disclosed, each of the QTQs (e.g., QTQ 902) may be associated with one or more TCQs (e.g., TCQ 920) via coupling capacitors (e.g., coupling capacitors 928 and 930). For simplicity and clarity, only some of the coupling capacitors are explicitly referred to using reference numbers in FIG. 9.

[0100] System 900 may include a bus component 932 that may be employed to facilitate selective interaction or coupling between respective QTQs 902, 914, 916, and 918, each associated with bus component 932 via a respective TCQ 920, 922, 924, and 926. According to various embodiments, bus component 932 may be a capacitive bus component or a CPW resonator bus component. Bus component 932 may be associated with (e.g., coupled to) TCQs 920, 922, 924, and 926 via respective coupling capacitors (e.g., coupling capacitor 934).

[0101] Each QTQ 902, 914, 916, and 918 may be selectively coupled to each TCQ 920, 922, 924, and 926 based on the respective "A" modes of each TCQ 920, 922, 924, and 926, as described herein. Each TCQ 920, 922, 924, and 926 may be selectively coupled to each other based on the respective "B" modes of each TCQ 920, 922, 924, and 926, as described herein, and via bus component 932.

[0102] The example system 900 may also include a second subgroup of QTQs, which may include QTQs 916, 936, 938, and 940, which may be associated with TCQs 942, 944, 946, and 948, respectively, as part of the lattice. As can be seen, in the lattice, QTQ 916 may be part of the first subgroup of QTQs and the second subgroup of QTQs. TCQs 942, 944, 946, and 948 may be associated with bass component 950 (e.g., via respective coupling capacitors). Each of TCQs 942, 944, 946, and 948 may include an “A” vibration mode and a “B” vibration mode, which may be associated with a respective frequency. Each QTQ 916, 936, 938, and 940 can be selectively coupled to each TCQ 942, 944, 946, and 948 based on the respective "A" modes of each TCQ 942, 944, 946, and 948, as described herein. Each TCQ 942, 944, 946, and 948 can be selectively coupled to each other based on the respective "B" modes of each TCQ 942, 944, 946, and 948, as described herein, and via bus component 950.

[0103] The exemplary system 900 may also include a third QTQ subgroup that may include QTQs 916, 918, 940, and 952, which may be associated with TCQs 954, 956, 958, and 960, respectively, as part of the lattice (e.g., via respective coupling capacitors). As can be seen, in the lattice, QTQ 916 may be part of the first, second, and third QTQ subgroups, QTQ 918 may be part of the first and third QTQ subgroups, and QTQ 940 may be part of the second and third QTQ subgroups. TCQs 954, 956, 958, and 960 may be associated with a bass component 962 (e.g., via respective coupling capacitors). Each of TCQs 954, 956, 958, and 960 may include an “A” vibration mode and a “B” vibration mode that may be associated with a respective frequency. Each QTQ 916, 918, 940, and 952 can be selectively coupled to each TCQ 954, 956, 958, and 960 based on the respective "A" modes of each TCQ 954, 956, 958, and 960, as described herein. Each TCQ 954, 956, 958, and 960 can be selectively coupled to each other based on the respective "B" modes of each TCQ 954, 956, 958, and 960, as described herein, and via bus component 962.

[0104] The lattice may also include other subgroups of QTQs, each of which may include a respective QTQ associated with a respective TCQ associated with a bus component. Given the disclosed structure and properties of QTQs, a QTQ (e.g., QTQ916) may have dipole interactions with up to four TCQs, rather than just two TCQs. For example, with respect to QTQ916, in addition to being associated (e.g., selectively coupled) with TCQ924, TCQ942, and TCQ956, QTQ916 may also be associated (e.g., via a coupling capacitor) with a fourth TCQ, TCQ964. TCQ964 may be associated (e.g., via a coupling capacitor) with bus component 966.

[0105] Additionally, QTQ 914 may be associated with TCQ 968 (e.g., via a coupling capacitor), which may be associated with bus component 966 (e.g., via a coupling capacitor). QTQ 936 may be associated with TCQ 970 (e.g., via a coupling capacitor), which may be associated with bus component 966 (e.g., via a coupling capacitor).

[0106] As a result, by QTQ 916 being associated with four TCQs (e.g., 924, 942, 956, and 964), which may be associated with four bus components (e.g., 932, 950, 962, and 966), QTQ 916 can selectively interact with (e.g., be selectively coupled to) seven or more QTQs (e.g., QTQs 902, 914, 918, 936, 938, 940, and 952, and / or another QTQ if the lattice is expanded). Also, in some embodiments, when a pair of QTQs (e.g., QTQs 902 and 914) associated with one bus component (e.g., bus component 932) interact with each other by having their associated TCQs (e.g., TCQs 920 and 926) switched to an on state (e.g., based on the application of a corrective magnetic flux thereto), if necessary, QTQ 916 can interact in parallel or simultaneously with QTQ 918 via bus component 962 by switching its associated TCQs (e.g., TCQs 956 and 954) to an on state, even when QTQs 902, 914, 916, and 918 are all associated with bus component 932.

[0107] If it is desirable to suppress interactions between all of the QTQs of the lattice (e.g., QTQs 902, 914, 916, 918, 936, 938, 940, and 952, and other QTQs), a respective magnetic field can be applied (e.g., by a respective coil component) to each TCQ associated with each QTQ of the lattice (e.g., TCQs 920, 922, 924, 926, 942, 944, 946, 948, 954, 956, 958, 960, 964, 968, and 970, and other TCQs), as described herein, to place each TCQ in an off state. System 900, as described herein, controls only the TCQs (e.g., TCQs 920 and TCQs 922; and / or TCQs 942 and TCQs 946; and / or TCQs 958 and TCQs 960, respectively) associated with one or more desired pairs of QTQs (e.g., QTQs 902 and 914; and / or QTQs 916 and 938; and / or QTQs 940 and 952) of the lattice, with the respective coil components applied to those TCQs. Selective interaction or coupling between one or more desired pairs of QTQs can also be implemented by flux tuning those TCQs by modifying their respective magnetic fluxes to excite the respective "B" modes of only those TCQs, transitioning them to an excited state and transitioning those TCQs from an off state to an on state, while other TCQs associated with other qubits remain in an off state based on the respective magnetic fluxes applied to those other TCQs associated with the lattice.

[0108] It should be appreciated and understood that for simplicity and clarity, each coil component associated with each TCQ (e.g., TCQs 920, 922, 924, 926, 942, 944, 946, 948, 954, 956, 958, 960, 964, 968, and 970) is not shown in Figure 9. It should also be appreciated and understood that in accordance with the disclosed subject matter, the grid of system 900 can be further extended in any direction or across multiple dies (e.g., via CPW resonators, which may desirably enable long-range coupling) to allow for more QTQs, TCQs, and bus components.

[0109] 10 illustrates a diagram of another non-limiting exemplary system 1000 that may include QTQs and associated TCQs that may be associated with respective bus components to form a square lattice, thereby providing improved connectivity between such QTQs and facilitating management of interactions or couplings between such QTQs, according to various aspects and embodiments of the disclosed subject matter. Repeated descriptions of similar elements used in other embodiments described herein may be omitted or omitted for the sake of brevity.

[0110] The grid of system 1000 may include a group of QTQs including QTQs 1002, 1004, 1006, 1008, 1010, 1012, 1014, 1016, and 1018. The difference between the grid of system 1000 of Figure 10 and the grid of system 900 of Figure 9 is that the grid of system 900 may provide increased density (e.g., more QTQs may be included in the same amount of space on the die) compared to the grid of system 1000.

[0111] The example system 1000 may also include TCQs 1020, 1022, 1024, 1026, 1028, 1030, 1032, 1034, 1036, 1038, 1040, 1042, 1044, 1046, 1048, 1050, 1052, 1054, 1056, 1058, 1060, 1062, 1064, and 1066. Each of the TCQs (e.g., 1020 through 1066) may include an "A" vibrational mode and a "B" vibrational mode, which may be associated with a respective frequency. The example system 1000 may further include bus components 1068 , 1070 , 1072 , 1074 , 1076 , 1078 , 1080 , 1082 , 1084 , 1086 , 1088 , and 1090 .

[0112] Each QTQ (e.g., 1002 through 1018) may be selectively coupled to a respective TCQ (e.g., 1020 through 1066) based on the respective "A" mode of each TCQ, as described herein. Each TCQ (e.g., 1020 through 1066) may be selectively coupled to each other based on the respective "B" mode of each TCQ and via respective bus components (e.g., 1068 through 1090), as described herein.

[0113] Each QTQ (e.g., 1002 through 1018) may be associated with (e.g., selectively coupled to) a respective TCQ (e.g., 1020 through 1066) via a respective coupling capacitor, as shown in system 1000 of Figure 10. Each TCQ (e.g., 1020 through 1066) may be coupled to a respective bus component (e.g., 1068 through 1099) via a respective coupling capacitor, as shown in system 1000 of Figure 10. For example, QTQ 1002 may be associated with (e.g., selectively coupled to) TCQs 1020, 1022, 1024, and 1026 via respective coupling capacitors (e.g., QTQ 1002 may be associated with TCQ 1020 via coupling capacitors 1092 and 1094). TCQs 1020, 1022, 1024, and 1026 may be associated with respective bus components 1068, 1070, 1072, and 1074 via respective coupling capacitors (e.g., TCQ 1020 may be associated with bus component 1068 via coupling capacitor 1096). For simplicity and clarity, only some of the coupling capacitors are explicitly referred to using reference numbers in FIG. 10.

[0114] Additionally, QTQ1004 may be associated with TCQ1032 (e.g., via a coupling capacitor), which may be associated with bus component 1068 (e.g., via a coupling capacitor). QTQ1006 may be associated with TCQ1036 (e.g., via a coupling capacitor), which may be associated with bus component 1070 (e.g., via a coupling capacitor). QTQ1008 may be associated with TCQ1042 (e.g., via a coupling capacitor), which may be associated with bus component 1072 (e.g., via a coupling capacitor). QTQ1010 may be associated with TCQ1048 (e.g., via a coupling capacitor), which may be associated with bus component 1074 (e.g., via a coupling capacitor).

[0115] System 1000 may employ subgroups of TCQs associated with respective bus components to desirably manage interactions and coupling between the QTQs. For example, if it is desired to suppress interactions between all QTQs (e.g., 1002 through 1018) in the lattice of system 1000, respective magnetic fields may be applied (e.g., by respective coil components) to each TCQ (e.g., 1020 through 1066) associated with each QTQ in the lattice to place each TCQ in an off state, as described herein. System 1000 can also implement desired selective interactions or couplings between one or more desired pairs of QTQs, as described herein, by flux tuning only the TCQs (e.g., TCQ1020 and TCQ1032; and / or TCQ1050 and TCQ1066; and / or another pair of TCQs) associated with one or more desired pairs of QTQs (e.g., QTQ1002 and QTQ1004; and / or QTQ1010 and QTQ1018; and / or another pair of QTQs) of the lattice by modifying the respective magnetic fluxes applied to those TCQs (e.g., by respective coil components associated with those TCQs), transitioning those TCQs from an off state to an on state, while leaving other TCQs associated with other qubits in an off state based on the respective magnetic fluxes applied to those other TCQs associated with the lattice.

[0116] It should be appreciated and understood that for simplicity and clarity, each coil component associated with each TCQ (e.g., 1020 through 1066) is not shown in Figure 9. It should also be appreciated and understood that in accordance with the disclosed subject matter, the grid of system 1000 can be further extended in any direction or across multiple dies (e.g., via CPW resonators that may desirably enable long-range coupling) to allow for more QTQs, TCQs, and bus components.

[0117] 11 illustrates a block diagram of a non-limiting example system 1100 that can employ CPW resonators that can enable long-distance (e.g., long-range) coupling between TCQs and / or between TCQs and bus components, according to various aspects and embodiments of the disclosed subject matter. Repeated descriptions of similar elements used in other embodiments described herein have been or may be omitted for the sake of brevity.

[0118] System 1100 may include qubit 1102, qubit 1104, TCQ 1106, and TCQ 1108. Qubit 1102 may be associated with TCQ 1106 via coupling capacitors 1110 and 1112. Qubit 1104 may be associated with TCQ 1108 via coupling capacitors 1114 and 1116. TCQs 1106 and 1108 may each include an “A” vibration mode and a “B” vibration mode, which may be associated with respective frequencies. As described herein, qubit 1102 may be selectively coupled to TCQ 1106 based on the “A” mode of TCQ 1106, and qubit 1104 may be selectively coupled to TCQ 1108 based on the “A” mode of TCQ 1108. The TCQs 1106 and 1108 can be selectively coupled to each other (and via the CPW resonator 1118) based on the respective "B" modes of the TCQs 1106 and 1108, as described herein.

[0119] In some embodiments, system 1100 can facilitate desired long-range coupling (e.g., selective coupling) between TCQ 1106 and TCQ 1108 between two dies or across the same die (e.g., an IC or qubit chip) using a CPW resonator 1118 of a desired length (e.g., a desirably long length that may be on the order of a few millimeters in length) having a desired resonance (e.g., about 5 GHz or other desired resonant frequency). CPW resonator 1118 can act as a bus between TCQ 1106 and TCQ 1108. In particular embodiments, TCQ 1106 can be coupled to CPW resonator 1118 via coupling capacitor 1120, and TCQ 1108 can be coupled to CPW resonator 1118 via coupling capacitor 1122.

[0120] According to various embodiments, the TCQs 1106 and 1108 may be coupled to the fundamental mode of the CPW resonator 1118 (e.g., a 5 GHz CPW resonator, or a CPW resonator having a fundamental mode associated with a frequency greater than or less than 5 GHz) or to a higher-order mode (when the length of the CPW resonator 1118 is relatively long). In some embodiments, the length of the CPW resonator 1118 may be adjusted so that the higher-order mode of the CPW resonator 1118 can be at about 5 GHz or another desired frequency greater than or less than 5 GHz.

[0121] In other embodiments, one or both of TCQs 1106 and / or 1108 may be selectively coupled to one another via one or more CPW resonators 1124 and / or 1126, which may be associated with a bus component 1128 via one or more respective coupling capacitors 1130 and / or 1132. In yet other embodiments, a qubit (e.g., qubit 1102) may be selectively coupled to a TCQ (e.g., TCQ 1106) via a CPW resonator of a desired length and resonance and via a coupling capacitor, which may be logically and / or physically positioned between the qubit and the TCQ.

[0122] The interaction and coupling between quantum bit 1102 and quantum bit 1104 can be selectively implemented or performed via TCQs 1106 and 1108 and via a CPW resonator (e.g., CPW resonator 1118) based on the respective magnetic fluxes or respective corrective magnetic fluxes applied to the respective TCQs 1106 and 1108 (e.g., by respective coil components), as described in more detail herein.

[0123] 12 illustrates a block diagram of a non-limiting example system 1200 that can employ CPW resonators that can enable long-range (e.g., long-distance) coupling between TCQs across multiple dies, in accordance with various aspects and embodiments of the disclosed subject matter. Repeated descriptions of similar elements used in other embodiments described herein have been or may be omitted for the sake of brevity.

[0124] System 1200 may include a first qubit (Q1) 1202 and a first TCQ (TCQ1) 1204, which may be formed on a first die 1206. System 1200 may also include a second qubit (Q2) 1208 and a second TCQ (TCQ2) 1210, which may be formed on a second die 1212. First qubit 1202 may be associated with first TCQ 1204 via coupling capacitors (C) 1214 and 1216. Second qubit 1208 may be associated with second TCQ 1210 via coupling capacitors 1218 and 1220. TCQs 1204 and 1210 may each include an “A” vibration mode and a “B” vibration mode, which may be associated with a respective frequency. As described herein, a first qubit 1202 may be selectively coupled to a first TCQ 1204 based on the "A" mode of the first TCQ 1204, and a second qubit 1208 may be selectively coupled to a second TCQ 1210 based on the "A" mode of the second TCQ 1210. TCQs 1204 and 1210 may be selectively coupled to each other (and via a CPW resonator) based on the respective "B" modes of TCQs 1204 and 1210, as described herein.

[0125] In some embodiments, the system 1200 may include a first CPW resonator 1222, which may be positioned or formed on the first die 1206. The first CPW resonator 1222 may be coupled to the first TCQ 1204 via a coupling capacitor 1224. The first CPW resonator 1222 may have a desired length and resonance (e.g., resonant frequency) as described herein. The first TCQ 1204 may be coupled to the first CPW resonator 1222 via a fundamental mode or a higher-order mode of the first CPW resonator 1222, which may be associated with a desired frequency.

[0126] In certain embodiments, the system 1200 may include a second CPW resonator 1226, which may be positioned or formed on the second die 1212. The second CPW resonator 1226 may be coupled to the second TCQ 1210 via a coupling capacitor 1228. The second CPW resonator 1226 may have a desired length and resonance (e.g., resonant frequency) as described herein. The second TCQ 1210 may be coupled to the second CPW resonator 1226 via a fundamental mode or a higher-order mode of the second CPW resonator 1226, which may be associated with a desired frequency.

[0127] In some embodiments, system 1200 can include bump bonds 1230 that can extend from first die 1206 to second die 1212. Bump bonds 1230 can be connected to first CPW resonator 1222 and second CPW resonator 1226 to connect first CPW resonator 1222 to second CPW resonator 1226. Bump bonds 1230 can be formed of a desired conductive material (e.g., a superconducting material such as indium, or other desired superconducting material).

[0128] The interaction and coupling between first qubit 1202 and second qubit 1208 can be selectively implemented or performed via TCQs 1204 and 1210, via CPW resonators 1222 and 1226, and via bump bond 1230 based on the respective magnetic fluxes or respective corrective magnetic fluxes applied to the respective TCQs 1204 and 1210 (e.g., by respective coil components), as described in more detail herein.

[0129] Briefly referring to FIG. 13 (in conjunction with FIG. 11 ), FIG. 13 presents an illustration of an exemplary graph 1300 related to long-range coupling of qubits associated with TCQs connected via CPW resonators, in accordance with various aspects and embodiments of the disclosed subject matter. Coupling may be defined as an interaction between two systems (e.g., between a first system including a first qubit and / or first TCQ and a second system including a second qubit and / or second TCQ) strong enough to create a multi-qubit gate (e.g., between the two qubits) and / or a desired exchange of information or energy between two electronic elements (e.g., qubits, resonators, or other desired electronic elements or components). Graph 1300 illustrates the Josephson energy E j The graph 1300 may include a graph 1302 relating to the frequency (F) (in GHz) associated with the modes of the qubits (e.g., 1102 and 1104) and the TCQ (e.g., 1106) as a function of the Josephson energy E j A graph 1304 relating to the ZZ interaction (in kHz) between qubits (eg, 1102 and 1104) as a function of (in GHz) may also be included.

[0130] Graph 1302 can include data points 1306 related to the frequency of a first qubit (e.g., 1102) as a function of Josephson energy; data points 1308 related to the frequency of a second qubit (e.g., 1104) as a function of Josephson energy; data points 1310 related to the frequency of the "A" mode of the TCQ (e.g., 1106) as a function of Josephson energy; and data points 1312 related to the frequency of the "B" mode of the TCQ (e.g., 1106) as a function of Josephson energy. Graph 1304, in an exemplary scenario, can be used to plot the frequency of a first qubit (e.g., 1102) as a function of Josephson energy; data points 1310 related to the frequency of a second qubit (e.g., 1104) as a function of Josephson energy; and data points 1312 related to the frequency of a "B" mode of the TCQ (e.g., 1106) as a function of Josephson energy. j , may include a data point 1314 indicating the amount of ZZ interaction between the first qubit and the second qubit.

[0131] Josephson energy E of a TCQ (e.g., 1106) SQUID j can be varied over a desired sweep range. In this exemplary scenario, a 5 GHz CPW resonator may be used as a bus between the TCQs (e.g., 1106 and 1108), with a coupling capacitor to the central paddle of either TCQ being 20 femtofarads. As can be seen in graph 1304 (e.g., data point 1314 on graph 1304), when the TCQ (e.g., 1106) is in the off position or state, the Z between the qubits (e.g., 1102 and 1104) may be desirably low (e.g., <1e-5 kHz), and when the TCQ (e.g., 1106) is in the on position or state, the Z interaction between the qubits (e.g., 1102 and 1104) may be desirably high (e.g., >10 MHz), as shown by reference numerals 1316 and 1318, respectively.

[0132] 14 illustrates a block diagram of an exemplary system 1400 that may be utilized to create, form, or design a device including qubits, coupler components (e.g., TCQs), and / or other quantum components, elements, or circuitry in accordance with various aspects and embodiments of the disclosed subject matter. System 1400 may include a processor component 1402 and a data store 1404. According to various embodiments, processor component 1402 may include or be associated with (e.g., communicatively connected to) device formation components 1406 that may be utilized to create, form, or design various components of or associated with device 1408 (or a system including one or more devices), including qubits, coupler components (e.g., TCQs), and associated quantum components, elements, or circuitry, as described in more detail herein. For example, device formation components 1406 may be utilized to create, form, or design various components of device 1408 (or a system), which may be formed or located on one or more chips 1410 (e.g., quantum computer or qubit device IC chips). The various components may include, for example, qubits 1412, coupler components 1414, JJs 1416, SQUIDs 1418, capacitors 1420, CPW resonators 1422, bump bonds 1424, and / or associated circuitry 1426.

[0133] As part of and to facilitate the creation, formation, or design of, or various components associated with, device 1408, device formation components 1406 can form or process substrates. As part of and to facilitate the creation, formation, or design of, or various components and / or circuitry associated with, device 1408, device formation components 1406 can also form, deposit, remove (e.g., selectively remove or etch), pattern, or process materials, including silicon or silicon-based materials (e.g., dielectric materials), superconducting materials (e.g., niobium-based, indium-based, aluminum-based, or other desired superconducting materials), or other materials for device 1408. For example, device formation components 1406 may employ and / or control a variety of processes, including fabrication processes, microfabrication processes, nanofabrication processes, material deposition processes (e.g., low-pressure chemical vapor deposition (LPCVD) processes), masking or photoresist processes, photolithography processes, chemical etching processes (e.g., reactive ion etching (RIE) processes, potassium hydroxide (KOH) etching processes), other etching or removal processes, epitaxial processes, material deformation processes, patterning processes, planarization processes (e.g., chemical mechanical planarization (CMP) processes), component formation processes, and / or other desired processes, to desirably form, deposit, remove (e.g., selectively remove or etch), pattern, or treat materials to facilitate the creation or formation of respective components or circuitry of device 1408.

[0134] The processor component 1402 may work in conjunction with other components (eg, a data store 1404 , a device formation component 1406 , or another component) to facilitate the performance of various functions of the system 1400 . The processor component 1402 may employ one or more processors, microprocessors, or controllers capable of processing data, such as information related to the design, creation, or formation of the quantum computer, qubit 1412, coupler component 1414, JJ 1416, SQUID 1418, capacitor 1420, CPW resonator 1422, bump bond 1424, waveguide, electrode, filter, other component or device, and / or associated circuit configuration 1426, as well as information related to circuit design criteria, circuit design algorithms, traffic flow, policies, protocols, interfaces, tools, and / or other information, to facilitate operation of the system 1400 and to control the flow of data between the system 1400 and other components associated (e.g., connected) to the system 1400 (e.g., computer components, computers, laptop computers, other computing or communication devices, or network devices).

[0135] The data store 1404 may store data structures (e.g., user data, metadata), code structures (e.g., modules, objects, hashes, classes, procedures) or instructions, information related to the design, creation, or formation of quantum computers, qubits 1412, coupler components 1414, JJs 1416, SQUIDs 1418, capacitors 1420, CPW resonators 1422, bump bonds 1424, waveguides, electrodes, filters, other components or devices, and / or associated circuit configurations 1426, and information related to circuit design criteria, circuit design algorithms, traffic flows, policies, protocols, interfaces, tools, and / or other information to facilitate control of operations associated with the system 1400. In an aspect, the processor component 1402 may be operatively coupled to the data store 1404 (e.g., via a memory bus) to store and retrieve information necessary to operate and / or at least partially provide functionality to the data store 1404, the device formation component 1406, or other components, and / or substantially any other operational aspect of the system 1400. The data store 1404 described herein may include volatile and / or non-volatile memory, as described herein.

[0136] Systems and / or devices have been described herein (or will be described) with respect to interactions between several components. It should be appreciated that such systems and components may include those components or subcomponents identified therein, some of the identified components or subcomponents, and / or additional components. Subcomponents may be implemented as components communicatively coupled to other components rather than being included within a parent component. Furthermore, one or more components and / or subcomponents may be combined into a single component that provides aggregate functionality. Components may interact with one or more other components not specifically described herein for simplicity, but known to those skilled in the art.

[0137] 15 illustrates a flow diagram of a non-limiting exemplary method 1500 in which a pair of TCQs can be employed to control interactions, couplings, or gates between components of a quantum circuit, according to various aspects and embodiments of the disclosed subject matter. Method 1500 can be performed, for example, by a system that includes or is operably coupled to the pair of TCQs. Repeated descriptions of similar elements used in other embodiments described herein may be omitted or omitted for the sake of brevity.

[0138] In 1502, a first electronic element can be selectively coupled to the first TCQ based on a first mode that can be operable on the first TCQ, and the first mode can be associated with a first frequency. In some embodiments, the first electronic element can be a qubit (e.g., a transmon qubit, a quadrupole transmon qubit, or other type of qubit), while in other embodiments, the first electronic element can be a different type of component, such as a resonator.

[0139] In 1504, the first TCQ may be selectively coupled to the second TCQ based on a second mode that may be operable on the first TCQ and a third mode that may be operable on the second TCQ, where the second mode may be associated with a second frequency and the third mode may be associated with a third frequency. The third frequency may be different or the same as the second frequency (and may be different from the first frequency). In some embodiments, the second TCQ may be selectively coupled to a second electronic element (e.g., a qubit, resonator, or other type of component) based on a fourth mode that may be operable on the second TCQ, where the fourth mode may be associated with a fourth frequency that may be different or the same as the first frequency (and may be different from the third frequency and the second frequency). Each selective coupling between each component (e.g., the first electronic element, the first TCQ, the second TCQ, and / or the second electronic element) can be controlled (e.g., enabled or permitted; or inhibited or suppressed) based on the respective magnetic fluxes that can be applied to the first TCQ and the second TCQ by the respective coil components, or respective modifications to the respective magnetic fluxes, as described herein.

[0140] 16 illustrates a flow diagram of another non-limiting exemplary method 1600 in which a pair of coupler components (e.g., TCQs) can be employed to control interactions, couplings, or gates between components of a quantum circuit, according to various aspects and embodiments of the disclosed subject matter. Method 1600 can be performed, for example, by a system that includes or is operably coupled to the pair of TCQs. Repeated descriptions of similar elements used in other embodiments described herein may be omitted or omitted for the sake of brevity.

[0141] At 1602, a first magnetic flux may be applied to a first coupler component, which may be associated with a first electronic element via a first mode associated with a first frequency and with a second coupler component via a second mode associated with a second frequency and a third mode associated with a third frequency. At 1604, a second magnetic flux may be applied to a second coupler component, which may be associated with the second electronic element via a fourth mode associated with a fourth frequency. The first coupler component may include a first mode (e.g., an "A" mode) associated with the first frequency and a second mode (e.g., a "B" mode) associated with the second frequency. The second coupler component may include a third mode (e.g., another "B" mode) associated with a third frequency and a fourth mode (e.g., another "A" mode) associated with a fourth frequency.

[0142] The first coupler component may be selectively coupled to or otherwise associated with a first electronic element (e.g., a qubit, resonator, or other type of electronic element) based on a first mode operable on the first coupler component. At the other end of the first coupler component, the first coupler component may be selectively coupled to or otherwise associated with a second coupler component based on a second mode operable on the first coupler component and a third mode operable on the second coupler component. At the other end of the second coupler component, the second coupler component may be selectively coupled to or otherwise associated with a second electronic element (e.g., a qubit, resonator, or other type of electronic element) based on a fourth mode operable on the second coupler component.

[0143] A first coil component can generate a first magnetic flux based on a first input current and can apply the first magnetic flux to the first coupler component, and a second coil component can generate a second magnetic flux based on a second input current and can apply the second magnetic flux to the second coupler component.

[0144] In 1606, interaction and coupling between the first electronic element and the second electronic element can be suppressed based on the respective modes of the first and second coupler components and based on application of a first magnetic flux to the first coupler component and application of a second magnetic flux to the second coupler component. The first magnetic flux applied to the first SQUID of the first coupler component can be a first amount of magnetic flux that can cause a critical current of the first SQUID, and therefore a first energy (e.g., a first Josephson energy) associated with the first SQUID, to be equal or at least substantially equal to a critical current of the JJ of the first coupler component, and therefore a second energy (e.g., a second Josephson energy) associated with the JJ. The second magnetic flux applied to the second SQUID of the second coupler component can be a second amount of magnetic flux that can cause the critical current of the second SQUID, and therefore the third energy (e.g., the third Josephson energy) associated with the second SQUID, to be equal or at least substantially equal to the critical current of the JJ of the second coupler component, and therefore the fourth energy (e.g., the fourth Josephson energy) associated with that JJ, thereby resulting in a balance between the first and second energies associated with the first coupler component and a balance between the third and fourth energies associated with the second coupler component, which can provide and / or enhance desired mode-selective coupling associated with the first and second coupler components, which can cause or create a desired suppression (e.g., suppression) of the interaction or coupling (e.g., ZZ, static ZZ, and / or exchange interaction or coupling) between the first electronic element and the second electronic element to essentially or approximately zero interaction or coupling.

[0145] At 1608, the first magnetic flux can be modified to a first modified magnetic flux. At 1610, the second magnetic flux can be modified to a second modified magnetic flux. At 1612, the first modified magnetic flux can be applied to a first coupler component. At 1614, the second modified magnetic flux can be applied to a second coupler component. The first coil component can modify the first magnetic flux to the first modified magnetic flux based on a modified first input current that can be input to the first coil component. The first coil component can apply the first modified magnetic flux to the first coupler component. The second coil component can modify the second magnetic flux to a second modified magnetic flux based on a modified second input current that can be input to the second coil component. The second coil component can apply the second modified magnetic flux to the second coupler component.

[0146] At 1616, an interaction, coupling, and / or gate may be created between the first electronic element and the second electronic element based on the respective modes of the first and second coupler components, and based on application of the first modified magnetic flux to the first coupler component and application of the second modified magnetic flux to the second coupler component. Modifying (e.g., changing or adjusting) the first modified magnetic flux applied to the first SQUID of the first coupler component may create an imbalance between a first energy associated with the first SQUID (e.g., modified based on the first modified magnetic flux) and a second energy of the JJ of the first coupler component, which may excite a “B” mode of the first coupler component, which may modify a mode-selective coupling associated with the first coupler component, such that the first electronic element may have a desired interaction or coupling with both the first mode and the second mode of the first coupler component.

[0147] Similarly, modifying the second magnetic flux to the second modifying magnetic flux applied to the second SQUID of the second coupler component can create an imbalance between a third energy associated with the second SQUID (e.g., modified based on the second modifying magnetic flux) and a fourth energy of the JJ of the second coupler component, exciting the "B" mode of the second coupler component, which can modify the mode-selective coupling associated with the second coupler component such that the second electronic element can have a desired interaction or coupling with both the third and fourth modes of the second coupler component. Modifying the mode-selective coupling associated with the first and second coupler components in this way can also create a desired coupling between the first and second coupler components. As a result, a desired interaction, coupling, and / or gate (e.g., a ZZ interaction or coupling, an exchange interaction or coupling, an exchange gate, and / or a CPHASE gate) can be created between the first electronic element and the second electronic element via the first and second coupler components.

[0148] For simplicity of explanation, these methods and / or computer-implemented methods are depicted and described as a series of acts. It is understood and appreciated that the disclosed subject matter is not limited by the depicted acts and / or the order of acts; for example, acts can occur in various orders and / or in parallel, along with other acts not shown and described herein. Moreover, not all depicted acts may be required to implement a computer-implemented method in accordance with the disclosed subject matter. Those skilled in the art will also understand and appreciate that a computer-implemented method can alternatively be represented as a series of interrelated states via a state diagram or events. Additionally, it is further appreciated that the computer-implemented methods disclosed hereinafter and throughout this specification can be stored on an article of manufacture to facilitate transporting and transferring such computer-implemented methods to a computer. As used herein, the term article of manufacture is intended to encompass a computer program accessible from any computer-readable device or storage medium.

[0149] To provide a context for various aspects of the disclosed subject matter, FIG. 17 and the following discussion are intended to provide a general description of a suitable environment in which various aspects of the disclosed subject matter may be implemented. FIG. 17 illustrates a block diagram of a non-limiting, exemplary operating environment that can facilitate one or more embodiments described herein. Repeated descriptions of similar elements used in other embodiments described herein may be omitted or omitted for the sake of brevity. Referring to FIG. 17, a suitable operating environment 1700 for implementing various aspects of the present disclosure may include a computer 1712. The computer 1712 may also include a processing unit 1714, a system memory 1716, and a system bus 1718. The system bus 1718 couples system components, including, but not limited to, the system memory 1716, to the processing unit 1714. The processing unit 1714 may be any of a variety of available processors. Dual microprocessors and other multi-processor architectures may also be employed as the processing unit 1714. The system bus 1718 may be any of several types of bus structures, including a memory bus or memory controller, a peripheral bus or external bus, and / or a local bus using any kind of available bus architecture, including, but not limited to, Industry Standard Architecture (ISA), MicroChannel Architecture (MSA), Enhanced ISA (EISA), Intelligent Drive Electronics (IDE), VESA Local Bus (VLB), Peripheral Component Interconnect (PCI), CardBus, Universal Serial Bus (USB), Advanced Graphics Port (AGP), FireWire (IEEE 1394), and Small Computer System Interface (SCSI). The system memory 1716 may also include volatile memory 1720 and nonvolatile memory 1722. The basic input / output system (BIOS), containing the basic routines for transferring information between elements within the computer 1712, such as during start-up, is stored in the nonvolatile memory 1722.By way of example, and not limitation, non-volatile memory 1722 may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), flash memory, or non-volatile random access memory (RAM) (e.g., ferroelectric RAM (FeRAM)). Volatile memory 1720 may also include random access memory (RAM) acting as external cache memory. By way of example, and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), sync link DRAM (SLDRAM), direct Rambus RAM (DRRAM), direct Rambus dynamic RAM (DRDRAM), and Rambus dynamic RAM (RDRAM).

[0150] Computer 1712 may also include removable / non-removable, volatile / non-volatile computer storage media. Figure 17, for example, illustrates disk storage 1724. Disk storage 1724 may include devices such as, but not limited to, a magnetic disk drive, a floppy disk drive, a tape drive, a Jaz drive, a Zip drive, an LS-100 drive, a flash memory card, or a memory stick. Disk storage 1724 may also include storage media separately or in combination with other storage media, including, but not limited to, an optical disk drive, such as a compact disc read-only memory (CD-ROM), a CD-recordable drive (CD-R drive), a CD-rewriteable drive (CD-RW drive), or a digital versatile disc read-only memory (DVD-ROM) drive. A removable or non-removable interface, such as interface 1726, is typically used to facilitate connection of disk storage 1724 to system bus 1718. Figure 17 also illustrates software that acts as an intermediary between a user and the basic computer resources described in preferred operating environment 1700. Such software may include, for example, operating system 1728. Operating system 1728, which may be stored on disk storage 1724, is responsible for controlling and allocating resources of the computer 1712. System applications 1730 take advantage of the management of resources by operating system 1728 through, for example, program modules 1732 and program data 1734 stored either in system memory 1716 or on disk storage 1724. It should be appreciated that the present disclosure may be implemented with various operating systems or combinations of operating systems. A user enters commands or information into the computer 1712 through input devices 1736.The input devices 1736 include, but are not limited to, pointing devices such as a mouse, trackball, stylus, touchpad, keyboard, microphone, joystick, gamepad, satellite dish, scanner, television tuner card, digital camera, digital video camera, webcam, and the like. These and other input devices connect to the processing unit 1714 through the system bus 1718 via interface ports 1738. Interface ports 1738 include, for example, serial ports, parallel ports, game ports, and universal serial buses (USB). The output devices 1740 use several of the same types of ports as the input devices 1736. Thus, for example, a USB port can be used to provide input to the computer 1712 and to output information from the computer 1712 to the output device(s) 1740. An output adapter 1742 is provided to illustrate that some output devices 1740, such as monitors, speakers, and printers, among other output devices 1740, require special adapters. Output adapters 1742 include, by way of illustration and not limitation, video and sound cards that provide a method of connection between output device 1740 and the system bus 1718. It should be noted that other devices and / or systems of devices provide both input and output capabilities, such as remote computer(s) 1744.

[0151] The computer 1712 can operate in a networked environment using logical connections to one or more remote computers, such as a remote computer 1744. The remote computer 1744 may be a computer, a server, a router, a network PC, a workstation, a microprocessor-based appliance, a peer device or other common network node, and the like, and may typically include many or all of the elements described relative to the computer 1712. For simplicity, only a memory storage device 1746 is shown with the remote computer 1744. The remote computer 1744 is logically connected to the computer 1712 through a network interface 1748 and then physically connected via communication connection 1750. The network interface 1748 encompasses wired and / or wireless communication networks such as a local area network (LAN), a wide area network (WAN), a cellular network, and the like. LAN technologies include Fiber Distributed Data Interface (FDDI), Copper Distributed Data Interface (CDDI), Ethernet, Token Ring, and the like. WAN technologies include, but are not limited to, point-to-point links, circuit-switched networks such as Integrated Services Digital Networks (ISDN) and its variations, packet-switched networks, and Digital Subscriber Lines (DSL). Communications connection(s) 1750 refers to the hardware / software employed to connect network interface 1748 to system bus 1718. While communications connection(s) 1750 are shown internal to computer 1712 for clarity of illustration, they may also be external to computer 1712. The hardware / software for connecting to network interface 1748 may also include, by way of example only, internal and external technologies such as modems, including ordinary telephone-grade modems, cable modems, and DSL modems, ISDN adapters, and Ethernet cards.

[0152] One or more embodiments may be systems, methods, apparatus, and / or computer program products of any conceivable level of technical detail of integration. A computer program product may include one or more computer-readable storage media having computer-readable program instructions for causing a processor to implement aspects of one or more embodiments. A computer-readable storage medium may be a tangible device capable of holding and storing instructions for use by an instruction-execution device. A computer-readable storage medium may be, for example, but not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. A non-exhaustive list of more specific examples of computer-readable storage media may include portable computer diskettes, hard disks, RAM, ROM, erasable programmable read-only memory (EPROM or flash memory), SRAM, portable CD-ROMs, digital versatile disks (DVDs), memory sticks, floppy disks, punch cards, or mechanically encoded devices such as ridge structures in grooves with instructions recorded thereon, and any suitable combination of the foregoing. As used herein, computer-readable storage media should not be construed as being transitory signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission medium (e.g., light pulses passing through a fiber optic cable), or electrical signals transmitted through wires.

[0153] The computer-readable program instructions described herein may be downloaded from a computer-readable storage medium to each computing / processing device or to an external computer or external storage device via a network, such as the Internet, a local area network, a wide area network, and / or a wireless network. The network may include copper transmission cables, optical fiber transmissions, wireless transmissions, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface within each computing / processing device receives the computer-readable program instructions from the network and forwards the computer-readable program instructions to a computer-readable storage medium within the respective computing / processing device for storage. The computer-readable program instructions for implementing operations of the disclosed subject matter may be assembler instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, state setting data, configuration data for configuring an integrated circuit, or either source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, or the like, and procedural programming languages ​​such as the “C” programming language or similar. The computer-readable program instructions may execute entirely on the user's computer, partially on the user's computer, as a stand-alone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the latter scenario, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be to an external computer (e.g., over the Internet using an Internet Service Provider).In some embodiments, electronic circuitry including, for example, programmable logic circuitry, a field programmable gate array (FPGA), or a programmable logic array (PLA) can execute computer readable program instructions by utilizing state information of the computer readable program instructions to personalize the electronic circuitry to perform aspects of the disclosed subject matter.

[0154] Aspects of the disclosed subject matter are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the present disclosure. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer-readable program instructions. These computer-readable program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, executed by the processor of the computer or other programmable data processing apparatus, produce a method for implementing the function(s) / act(s) specified in one or more blocks of the flowchart illustrations and / or block diagrams. These computer-readable program instructions can also be stored on a computer-readable storage medium that can instruct a computer, programmable data processing apparatus, and / or other device to function in a particular manner, such that a computer-readable storage medium having instructions stored thereon includes an article of manufacture containing instructions that implement aspects of the function(s) / act(s) specified in one or more blocks of the flowchart illustrations and / or block diagrams. Computer-readable program instructions may be loaded onto a computer, other programmable data processing apparatus, or other device and cause the computer, other programmable apparatus, or other device to perform a series of operational acts to produce a computer-implemented process, such that the instructions executing on the computer, other programmable apparatus, or other device implement the functions / acts specified in one or more blocks of the flowcharts and / or block diagrams.

[0155] The flowcharts and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the disclosed subject matter. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of instructions, including one or more executable instructions for implementing a specified logical function. In some alternative implementations, the functions noted in the blocks may occur out of the order noted in the figures. For example, two blocks shown in succession may be executed substantially in parallel, or the blocks may be executed in the reverse order, depending on the functionality involved. It will also be noted that each block of the block diagrams and / or flowchart diagrams, and combinations of blocks in the block diagrams and / or flowchart diagrams, may be implemented by a dedicated hardware-based system that performs the specified functions or acts or that implements a combination of dedicated hardware and computer instructions.

[0156] While the subject matter has been described above in the general context of computer-executable instructions for a computer program product executing on one computer and / or multiple computers, those skilled in the art will recognize that the present disclosure may also be implemented in combination with other program modules. Generally, program modules include routines, programs, components, data structures, etc. that perform particular tasks and / or implement particular abstract data types. Those skilled in the art will also recognize that the computer-implemented methods disclosed herein may be practiced with other computer system configurations, including single-processor or multiprocessor computer systems, minicomputing devices, mainframe computers, as well as computers, handheld computing devices (e.g., PDAs, phones), microprocessor-based or programmable consumer or industrial electronic devices, and the like. The illustrated aspects may also be practiced in distributed computing environments where tasks are performed by remote processing devices linked through a communications network. However, some, if not all, aspects of the present disclosure may be practiced on stand-alone computers. In a distributed computing environment, program modules may be located in local and remote memory storage devices.

[0157] As used herein, terms such as “component,” “system,” “platform,” and “interface” may refer to and / or include computer-related entities or entities associated with an operating machine having one or more specific functionalities. The entities disclosed herein may be hardware, a combination of hardware and software, software, or software in execution. For example, a component may be, but is not limited to, a process running on a processor, a processor, an object, an executable, a thread of execution, a program, and / or a computer. By way of illustration, both an application running on a server and the server may be a component. One or more components may reside within a process and / or thread of execution, and a component may be localized on one computer and / or distributed between two or more computers. In another example, each component may execute from various computer-readable media having various data structures stored thereon. Components may communicate via local and / or remote processes, such as according to signals comprising one or more data packets (e.g., data from one component interacting with another component via signals with other systems over a network such as a local system, a distributed system, and / or the Internet). As another example, a component may be a device having inherent functionality provided by mechanical parts operated by electrical or electronic circuitry operated by a software or firmware application executed by a processor. In such cases, the processor may be internal or external to the device and may execute at least a portion of the software or firmware application.As yet another example, a component may be a device that provides inherent functionality without mechanical parts through electronic components, where the electronic components may include a processor or other means for executing software or firmware that at least partially provides the functionality of the electronic component. In some aspects, a component may emulate the electronic component, for example, via a virtual machine in a cloud computing system.

[0158] Furthermore, the term "or" is intended to mean an inclusive "or," not an exclusive "or." That is, unless otherwise specified or clear from the context, "X employs A or B" is intended to mean any of the natural inclusive permutations. That is, if X employs A; X employs B; or X employs both A and B, then "X employs A or B" is satisfied under any of the aforementioned multiple examples. Furthermore, the articles "a" and "an," as used in this specification and the accompanying drawings, should generally be construed to mean "one or more," unless otherwise specified or clear from the context that the singular form is intended. 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. Furthermore, 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.

[0159] As employed herein, the term "processor" may refer to virtually any computing processing unit or device, including, but not limited to, a single-core processor; a single processor with software multithreading execution capabilities; a multi-core processor; a multi-core processor with software multithreading execution capabilities; a multi-core processor with hardware multithreading technology; a parallel platform; and a parallel platform with distributed shared memory. Additionally, a processor may refer to an integrated circuit, an application-specific integrated circuit (ASIC), a digital signal processor (DSP), a field-programmable gate array (FPGA), a programmable logic controller (PLC), a complex programmable logic device (CPLD), discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. Furthermore, a processor may utilize nanoscale architectures, such as, but not limited to, molecular and quantum dot-based transistors, switches, and gates, to optimize space usage or improve performance of user equipment. A processor may be implemented as a combination of computing processing units. In this disclosure, terms such as “memory,” “storage,” “data store,” “data storage,” “database,” and substantially any other information storage component associated with the operation and functionality of a component are utilized to refer to a “memory” or “memory component” entity embodied in a component that includes memory. It should be recognized that memory and / or memory components described herein may be either volatile memory or nonvolatile memory, or may include both volatile and nonvolatile memory. By way of illustration and not limitation, nonvolatile memory may include ROM, PROM, EPROM, EEPROM, flash memory, or nonvolatile RAM (e.g., FeRAM). Volatile memory may include, for example, RAM, which may act as external cache memory.By way of example, and not limitation, RAM is available in many forms, including SRAM, DRAM, SDRAM, DDR SDRAM, ESDRAM, SLDRAM, DRRAM, DRDRAM, and RDRAM. Additionally, the memory components of computer-implemented methods or systems disclosed herein are intended to include, but are not limited to, these and any other suitable types of memory.

[0160] The foregoing description includes merely exemplary systems and computer-implemented methods. Naturally, it is not possible to describe every conceivable combination of components or computer-implemented methods for purposes of describing the present disclosure, but one skilled in the art will recognize that many further combinations and permutations of the present disclosure are possible. Furthermore, to the extent that terms such as "comprises," "having," and "possessing" are used in the detailed description, claims, appendices, and drawings, such terms are intended to be inclusive in the same manner as "comprises" is interpreted when the term "comprises" is employed as a transitional term in a claim. While the description of various embodiments has been presented for illustrative purposes, it is not intended to be exhaustive or to be 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 was selected to best explain the principles of the embodiments, practical applications of, or technical improvements to, commercially available technologies, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. a first quantum component; and a first coupler qubit operable in a first mode associated with a first frequency and a second mode associated with a second frequency, wherein the first coupler qubit is selectively coupled to the first quantum component based on the first mode, and the first coupler qubit is selectively coupled to the second coupler qubit based on the second mode and based on a third mode operable on the second coupler qubit, the third mode being associated with a third frequency; A system comprising:

2. 10. The system of claim 1, wherein the first quantum component is a first qubit, the second coupler qubit is operable at a fourth mode associated with a fourth frequency, and the system further comprises a second qubit, wherein the second coupler qubit is selectively coupled to the second qubit based on the fourth mode.

3. 3. The system of claim 2, wherein ZZ interaction and static ZZ interaction between the first qubit and the second qubit are suppressed and exchange interaction between the first qubit and the second qubit is suppressed for a specified range of frequencies associated with the first qubit and the second qubit based on the first coupler qubit being selectively coupled to the first qubit via the first mode, the first coupler qubit being selectively coupled to the second coupler qubit via the second mode and the third mode, and the second coupler qubit being selectively coupled to the second qubit via the fourth mode.

4. 10. The system of claim 1, wherein the first coupler qubit comprises a Josephson junction and a superconducting quantum interference device associated with the Josephson junction, the superconducting quantum interference device being flux tunable.

5. a capacitor component having a first plate and a second plate, wherein the first plate is connected to the first coupler qubit and the second plate is connected to the second coupler qubit; 10. The system of any preceding claim, further comprising:

6. a first capacitor component having a first plate and a second plate; a second capacitor component having a third plate and a fourth plate; and a coplanar waveguide resonator having a first port and a second port, wherein the first plate is connected to the first coupler qubit, the second plate is connected to the first port, the third plate is connected to the second port, and the fourth plate is connected to the second coupler qubit; 10. The system of any preceding claim, further comprising:

7. a first die and a second die; and a bump bond, wherein the first coupler qubit, the first capacitor component, and a first portion of the coplanar waveguide resonator are on the first die, the second coupler qubit, the second capacitor component, and a second portion of the coplanar waveguide resonator are on the second die, and the first portion of the coplanar waveguide resonator and the second portion of the coplanar waveguide resonator are connected via the bump bond. The system of claim 6 further comprising:

8. a third coupler qubit; a capacitor component group having a first capacitor component, a second capacitor component, and a third capacitor component; and a bus component associated with the group of capacitor components, wherein the first coupler qubit is associated with the first capacitor component, the second coupler qubit is associated with the second capacitor component, and the third coupler qubit is associated with the third capacitor component; 10. The system of any preceding claim, further comprising:

9. 9. The system of claim 8, wherein the first capacitor component has a first plate and a second plate, the second capacitor component has a third plate and a fourth plate, the third capacitor component has a fifth plate and a sixth plate, the first plate is connected to the first coupler qubit, the third plate is connected to the second coupler qubit, the fifth plate is connected to the third coupler qubit, and the second plate, the fourth plate, and the sixth plate are connected to the bus component.

10. a first coplanar waveguide resonator having a first port and a second port; a second coplanar waveguide resonator having a third port and a fourth port; or a third coplanar waveguide resonator having a fifth port and a sixth port; Further provided with the first capacitor component has a first plate and a second plate, the second capacitor component has a third plate and a fourth plate, or the third capacitor component has a fifth plate and a sixth plate, and the first plate is connected to the first coupler qubit, or the third plate is connected to the second coupler qubit, or the fifth plate is connected to the third coupler qubit, the second plate is connected to the first port, the fourth plate is connected to the third port, or the sixth plate is connected to the fifth port, and the second port, the fourth port, or the sixth port is connected to the bus component. The system of claim 8.

11. the first quantum component is a quadrupole transmon qubit, the quadrupole transmon qubit having first, second, third and fourth capacitor pads associated with a Josephson junction; the second quantum component is a second coupler qubit; and the system further comprises: a third coupler qubit; and a fourth coupler qubit, wherein the first capacitor pad and the second capacitor pad of the quadrupole Transmon qubit are associated with the first coupler qubit, the second capacitor pad and the third capacitor pad of the quadrupole Transmon qubit are associated with the third coupler qubit, or the third capacitor pad and the fourth capacitor pad of the quadrupole Transmon qubit are associated with the fourth coupler qubit; Equipped with A system according to any preceding claim.

12. selectively coupling a first electronic element to a first tunable coupler qubit based on a first mode operable on the first tunable coupler qubit, where the first mode is associated with a first frequency; and selectively coupling the first tunable coupler qubit to the second tunable coupler qubit based on a second mode operable on the first tunable coupler qubit and a third mode operable on the second tunable coupler qubit, wherein the second mode is associated with a second frequency and the third mode is associated with a third frequency. A method for providing the above.

13. The first electronic element is a first qubit and the second tunable coupler qubit is operable in a fourth mode associated with a fourth frequency, and the method further comprises: selectively coupling the second tunable coupler qubit to a second qubit based on the fourth mode. Equipped with The method of claim 12.

14. applying a magnetic flux to a first superconducting quantum interference device of the first tunable coupler qubit, wherein said applying the magnetic flux enables a first critical current associated with the first superconducting quantum interference device to be equal to or substantially the same as a second critical current associated with a Josephson junction of the first tunable coupler qubit. The method of claim 13 further comprising:

15. suppressing at least one of ZZ coupling, static ZZ coupling, or exchange coupling between the first qubit and the second qubit based on the first critical current associated with the first superconducting quantum interference device being equal to or substantially the same as the second critical current associated with the Josephson junction. The method of claim 14 further comprising:

16. a first superconducting quantum interference device of the first tunable coupler qubit enabling the first tunable coupler qubit to be flux tunable, a second superconducting quantum interference device of the second tunable coupler qubit enabling the second tunable coupler qubit to be flux tunable, the magnetic flux is a first magnetic flux, and the Josephson junction is a first Josephson junction; and the method further comprises: modifying the first magnetic flux applied to the first superconducting quantum interference device of the first tunable coupler qubit; creating a first imbalance between a first energy associated with the first Josephson junction and a second energy associated with the first superconducting quantum interference device based on the modifying the first magnetic flux; modifying a second magnetic flux applied to a second superconducting quantum interference device of the second tunable coupler qubit, wherein the second tunable coupler qubit includes a second Josephson junction associated with the second superconducting quantum interference device; creating a second imbalance between a third energy associated with the second Josephson junction and a fourth energy associated with the second superconducting quantum interference device based on the modifying the second magnetic flux; and creating an entanglement gate between the first qubit and the second qubit based on the first imbalance and the second imbalance. The method of claim 14, comprising:

17. Based on the step of creating the entanglement gate, creating a first exchange coupling between the first qubit and the first tunable coupler qubit; creating a second exchange coupling between the second qubit and the second tunable coupler qubit; and creating a third exchange coupling between the first tunable coupler qubit and the second tunable coupler qubit; and generating a ZZ coupling between the first qubit and the second qubit based on the first exchange coupling, the second exchange coupling, and the third exchange coupling; The method of claim 16 further comprising:

18. 18. The method of claim 17, wherein a controlled phase gate between the first qubit and the second qubit is permitted based on the first exchange coupling, the second exchange coupling, and the third exchange coupling.

19. a first electronic component; a first tunable coupler qubit structured to be operable in a first mode of oscillation and a second mode of oscillation, wherein the first tunable coupler qubit is selectively coupled to the first electronic component based on the first mode; and a second tunable coupler qubit structured to be operable in a third mode of oscillation and a fourth mode of oscillation, wherein the first tunable coupler qubit is selectively coupled to the second tunable coupler qubit based on the second mode and the third mode; 1. A device comprising:

20. the first electronic component is a first qubit, the first mode is associated with a first frequency, the second mode is associated with a second frequency, the third mode is associated with a third frequency, and the fourth mode is associated with a fourth frequency, and the system further comprises: a second qubit, wherein the second tunable coupler qubit is selectively coupled to the second qubit based on the fourth mode; Equipped with a ZZ interaction or a static ZZ interaction between the first qubit and the second qubit is suppressed based on the first tunable coupler qubit being selectively coupled to the first qubit via the first mode, the first tunable coupler qubit being selectively coupled to the second tunable coupler qubit via the second mode and the third mode, and the second tunable coupler qubit being selectively coupled to the second qubit via the fourth mode, and an exchange interaction between the first qubit and the second qubit is suppressed for a specified range of frequencies associated with the first qubit and the second qubit.

20. The device of claim 19.

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