Mode selective coupler for frequency collision reduction

Abstract

Systems and techniques are provided that facilitate mode-selective couplers for frequency collision reduction. In various embodiments, a device can include a control qubit. In various aspects, the device can include a first target qubit coupled to the control qubit by a first mode-selective coupler. In various embodiments, the first mode-selective coupler can facilitate A-mode coupling between the control qubit and the first target qubit. In various embodiments, the device can include a second target qubit coupled to the control qubit by a second mode-selective coupler. In various aspects, the second mode-selective coupler can facilitate B-mode coupling between the control qubit and the second target qubit.

Description

Background Technology

[0001] This disclosure generally relates to superconducting qubits, and more specifically to mode-selective couplers for reducing frequency conflicts between superconducting qubits. Summary of the Invention

[0002] The following overview is presented to provide a basic understanding of one or more embodiments of the invention. This overview is not intended to identify key or essential elements, or to depict any scope of a particular embodiment or any scope of the claims. Its sole purpose is to present concepts in a simplified form as a prelude to the more detailed description that follows. In one or more embodiments described herein, devices, systems, computer-implemented methods, apparatuses, and / or computer program products are described that facilitate mode-selective couplers for frequency conflict reduction.

[0003] According to one or more embodiments, a device is provided. In various aspects, the device may include a control qubit. In various embodiments, the device may further include a first target qubit. In various cases, the first target qubit may be coupled to the control qubit via a first mode-selective coupler. In various aspects, the first mode-selective coupler may facilitate mode A coupling between the control qubit and the first target qubit. In various embodiments, the device may further include a second target qubit. In various aspects, the second target qubit may be coupled to the control qubit via a second mode-selective coupler. In various cases, the second mode-selective coupler may facilitate mode B coupling between the control qubit and the second target qubit. In various embodiments, the first mode-selective coupler may include a capacitor. In various embodiments, the capacitor may capacitively couple an intermediate capacitor pad of the control qubit to an intermediate capacitor pad of the first target qubit. In various embodiments, the second mode-selective coupler may include a first capacitor and a second capacitor. In various aspects, the first capacitor may capacitively couple an end capacitor pad of the control qubit to an end capacitor pad of the second target qubit. In various embodiments, the second capacitor can capacitively couple the end capacitor pad of the control qubit to the middle capacitor pad of the second target qubit.

[0004] According to one or more embodiments, a method is provided. In various aspects, the method may include providing a control qubit. In various embodiments, the method may further include coupling the control qubit to a first target qubit via a first mode-selective coupler. In various embodiments, the first mode-selective coupler may facilitate mode A coupling between the control qubit and the first target qubit. In various aspects, the method may further include coupling the control qubit to a second target qubit via a second mode-selective coupler. In various embodiments, the second mode-selective coupler may facilitate mode B coupling between the control qubit and the second target qubit. In various embodiments, the first mode-selective coupler may include a capacitor. In various embodiments, the capacitor may capacitively couple an intermediate capacitor pad of the control qubit to an intermediate capacitor pad of the first target qubit. In various embodiments, the second mode-selective coupler may include a first capacitor and a second capacitor. In various cases, the first capacitor may capacitively couple an end capacitor pad of the control qubit to an end capacitor pad of the second target qubit. In various respects, the second capacitor can capacitively couple the end capacitor pad of the control qubit to the middle capacitor pad of the second target qubit.

[0005] According to one or more embodiments, an apparatus is provided. In various aspects, the apparatus may include a first mode-selective coupler that facilitates mode A coupling between a control qubit and a first target qubit. In various aspects, the apparatus may further include a second mode-selective coupler that facilitates mode B coupling between the control qubit and the second target qubit. In various embodiments, the first mode-selective coupler may include a capacitor. In various aspects, the capacitor may capacitively couple an intermediate capacitor pad of the control qubit to an intermediate capacitor pad of the first target qubit. In various embodiments, the second mode-selective coupler may include a first capacitor and a second capacitor. In various aspects, the first capacitor may capacitively couple an end capacitor pad of the control qubit to an end capacitor pad of the second target qubit. In various cases, the second capacitor may capacitively couple an end capacitor pad of the control qubit to an intermediate capacitor pad of the second target qubit. Attached Figure Description

[0006] Figure 1 A circuit diagram of an exemplary non-limiting system for promoting A-mode coupling according to one or more embodiments described herein is shown.

[0007] Figure 2A block diagram of an example non-limiting system for promoting A-mode coupling according to one or more embodiments described herein is shown.

[0008] Figure 3 A circuit diagram of an example non-limiting system for promoting B-mode coupling according to one or more embodiments described herein is shown.

[0009] Figure 4 A block diagram of an example non-limiting system for promoting B-mode coupling according to one or more embodiments described herein is shown.

[0010] Figure 5 A block diagram of an exemplary non-limiting system for promoting mode-selective couplers for frequency conflict reduction according to one or more embodiments described herein is shown.

[0011] Figure 6 A flowchart is shown of an exemplary non-limiting method for promoting mode-selective couplers for frequency conflict reduction according to one or more embodiments described herein.

[0012] Figures 7 to 8 A graph illustrating example non-limiting simulation results of a system for promoting frequency conflict reduction of a mode-selective coupler according to one or more embodiments described herein is shown.

[0013] Figure 9 A block diagram of an exemplary non-limiting quantum computing lattice that facilitates mode-selective couplers for frequency conflict reduction according to one or more embodiments described herein is shown.

[0014] Figure 10 A flowchart is shown of an exemplary non-limiting method for promoting mode-selective couplers for frequency conflict reduction according to one or more embodiments described herein.

[0015] Figure 11 A block diagram is shown that illustrates an example non-limiting operating environment that may facilitate one or more embodiments described herein. Detailed Implementation

[0016] The following detailed description is illustrative only and is not intended to limit the embodiments and / or their application or use. Furthermore, it is not intended to be construed as being limited by any express or implied information presented in the preceding background or overview or specific embodiments sections.

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

[0018] Superconducting qubits are a promising technology for establishing large-scale quantum computing systems. In various embodiments, superconducting qubits can comprise one or more Josephson junctions shunted by one or more capacitors (e.g., macroscopic structures that can exhibit quantum mechanical behavior). In various embodiments, the quantum computing system can be formed based on a two-dimensional lattice of superconducting qubits (e.g., a quantum computing lattice), in which a pair of adjacent superconducting qubits can be coupled via a bus resonator (e.g., a microwave resonator). In various embodiments, the coupled pair of adjacent superconducting qubits can be entangled via a bi-qubit gate called a cross-resonant gate. In various aspects, a cross-resonant gate can be implemented by driving a superconducting qubit (called a control qubit) with a microwave pulse and / or tone at a switching frequency (e.g., an operating frequency and / or qubit frequency) of a neighboring and / or adjacent superconducting qubit (called a target qubit). In various embodiments, the control qubit can emit a pulse and / or tone toward the target qubit in response to being driven by the microwave pulse and / or tone. In various ways, the amplitude of the pulses and / or tones transmitted from the control qubit to the target qubit can depend on the state of the control qubit, thus entangled the two superconducting qubits. In other words, the target qubit can undergo qubit rotation at a rate dependent on the state of the control qubit.

[0019] To selectively entangle superconducting qubits, the neighbors of the control qubit (e.g., these target qubits) can have different (e.g., sufficiently separated) transition frequencies. For a quantum computing lattice where all superconducting qubits (e.g., except those on the boundaries / periphery of the lattice) have four neighboring and / or adjacent superconducting qubits, five different transition frequencies can be required (e.g., four separate transition frequencies for the four target qubits, and a fifth transition frequency for the control qubit). In various cases, the quantum computing lattice can be formed from single-mode qubits; that is, where any superconducting qubit in the quantum computing lattice has a single transition frequency (e.g., single-junction transport). In various cases, such a lattice can require five sets of differently fabricated superconducting qubits to achieve five different transition frequencies required for selective entanglement (e.g., generating the lattice from a first set of single-junction transport qubits with a first transition frequency, a second set with a second transition frequency, a third set with a third transition frequency, a fourth set with a fourth transition frequency, and a fifth set with a fifth transition frequency). In various aspects, a quantum computing lattice can include dozens and / or hundreds of superconducting qubits. When implementing many superconducting qubits, defects in nanofabrication techniques can make it difficult to reliably and / or consistently fabricate these five sets of different superconducting qubits (e.g., it may make it difficult to maintain all five sets of transition frequencies at their desired values). Selective entanglement cannot be achieved between the control qubit and these target qubits when two target qubits adjacent to and / or neighboring to the control qubit have similar transition frequencies. This can be referred to as target-based frequency conflict. In various aspects, target-based frequency conflict can negatively impact the performance of a quantum computing system.

[0020] For quantum computing lattices that include second-nearest neighbor connectivity in addition to nearest-nearest neighbor connectivity, more than five different transition frequencies can be required to facilitate selective cross-resonant entanglement (e.g., up to nine different transition frequencies can be required, thus necessitating nine different sets of superconducting qubits; one transition frequency for the control qubit, four different transition frequencies for the four nearest-nearest-neighbor target qubits, and four different transition frequencies for the four second-nearest-neighbor target qubits). In such cases, target-based frequency conflicts are even more likely to occur.

[0021] Those skilled in the art will recognize that what constitutes a frequency conflict can depend on the implementation details and / or operational context of the quantum computing system. In various respects, those skilled in the art will understand what similarity thresholds in the frequency transitions can constitute a frequency conflict, and / or will understand what dissimilarity thresholds in the frequency transitions can avoid frequency conflicts.

[0022] Some methods for reducing the number of target-based frequency collisions include reducing the connectivity of quantum computing lattices (e.g., reducing the average number of neighbors of a typical qubit in a quantum computing lattice). Quantum computing lattices with such reduced connectivity (called low-degree lattices) may be less likely to experience frequency collisions, but may also be less resilient to errors and therefore may require the implementation of quantum error-correcting codes. In various respects, systems and / or techniques for reducing frequency collisions without reducing lattice connectivity may be desirable.

[0023] Various embodiments of the present invention can solve one or more of these technical problems. In various aspects, embodiments of the present invention can provide quantum computing lattice architectures that can reduce the statistical probability of frequency collisions without correspondingly reducing lattice connectivity. Specifically, in various aspects, embodiments of the present invention can include generating quantum computing lattices based on double-junction transport qubits coupled via mode-selective couplers.

[0024] In various aspects, a dual-junction transport qubit can be a superconducting qubit comprising two capacitively shunt Josephson junctions coupled in series (e.g., a dual-junction transport qubit can be formed from two single-junction transport qubits connected and / or coupled in series). In other words, a dual-junction transport qubit can comprise a first Josephson junction and a second Josephson junction, wherein the first Josephson junction is coupled in series between a first capacitor pad and a second capacitor pad, and wherein the second Josephson junction is coupled in series between the second capacitor pad and a third capacitor pad. In various aspects, the second capacitor pad can be referred to as the intermediate capacitor pad of the dual-junction transport qubit, and the first and third capacitor pads can be referred to as the end capacitor pads of the dual-junction transport qubit. In various instances, a dual-junction transport qubit can support and / or exhibit two different excitation modes: mode A and mode B. In various aspects, these two different excitation modes can have two different spatial symmetries and / or two different transition frequencies (e.g., mode A transition frequency and mode B transition frequency). In various embodiments, double-junction transport qubits can be encoded in mode A (e.g., and therefore may have mode A switching frequencies) or mode B (e.g., and therefore may have mode B switching frequencies). In various aspects, short microwave pulses can be used to switch the double-junction transport qubit between encodings (e.g., a suitable microwave pulse can be applied to the double-junction transport qubit to switch it from mode A to mode B and / or from mode B to mode A). In various aspects, and as explained in more detail below, mode-selective coupling can be achieved between neighboring and / or adjacent double-junction transport qubits to promote selective cross-resonant entanglement. In some cases, mode-selective coupling can be achieved between the second nearest neighbor double-junction transport qubits to promote selective cross-resonant entanglement.

[0025] As described above, a quantum computing lattice including bus resonators between single-junction transport qubits can require five different fabricated qubit groups (e.g., one group corresponding to the control qubit and four different groups corresponding to the four different target qubits, which can have different conversion frequencies for a total of five conversion frequencies). On the other hand, in various cases and as further explained throughout this disclosure, a quantum computing lattice including mode-selective couplers between double-junction transport qubits can require three different fabricated qubit groups instead of five (e.g., a first group of double-junction transport qubits with a first A-mode conversion frequency and a first B-mode conversion frequency, a second group of double-junction transport qubits with a second A-mode conversion frequency and a second B-mode conversion frequency, and a third group of double-junction transport qubits with a third A-mode conversion frequency and a third B-mode conversion frequency, for a total of six different conversion frequencies).

[0026] In various cases, this reduction in the number of qubit groups to be fabricated in a quantum computing lattice can decrease the probability and / or prevalence of target-based frequency conflicts. After all, nanofabrication and / or microfabrication can, in various ways, include inherent and / or unintentional process variations that make it difficult to perfectly control the structural properties of superconducting qubits and thus their switching frequencies. When fabricating a larger number of different groups of superconducting qubits, there can be fewer and / or smaller differences in structural properties between one of these different groups and another. In some cases, inherent and / or unintentional process variations in nanofabrication and / or microfabrication can further reduce these already small and / or minor differences in structural properties, which can cause target-based frequency conflicts (e.g., causing the structural properties of one of these different groups of superconducting qubits to be too similar to those of another in the same group). On the other hand, when fabricating fewer numbers of different groups of superconducting qubits, there can be more and / or larger differences in structural properties between one of these different groups and another. In various cases, greater and / or more significant differences in these structural properties can help ensure that the structural properties of different groups of superconducting qubits can be sufficiently different, even when affected by process variations, in order to reduce the likelihood of target-based frequency conflicts.

[0027] In other words, generating five different superconducting qubit sets from a fixed pool of possible qubit structural properties can result in these five different sets having fewer and / or smaller structural differences, and these fewer and / or smaller structural differences can be more easily obscured by inherent and / or unintentional process variations during nanofabrication and / or microfabrication, thereby increasing the likelihood of target-based frequency conflicts. On the other hand, generating three different superconducting qubit sets from a fixed pool of possible qubit structural properties can result in these three different sets having more and / or larger structural differences (e.g., at least compared to generating five different qubit sets), and these more and / or larger structural differences can be less easily obscured by inherent and / or unintentional process variations during nanofabrication and / or microfabrication, thereby reducing the likelihood of target-based frequency conflicts. Thus, by reducing the number of different sets of superconducting qubits that need to be manufactured, the statistical probability of target-based frequency conflicts can be reduced.

[0028] Because various embodiments of the present invention can facilitate the generation of quantum computing lattices using three different sets of superconducting qubits instead of five, they can reduce the probability and / or prevalence of target-based frequency collisions. Furthermore, in various cases, this reduction in the probability and / or prevalence of target-based frequency collisions can be achieved without a corresponding reduction in lattice connectivity. For at least these reasons, various embodiments of the present invention constitute specific and tangible technical improvements in the field of superconducting qubit fabrication. Moreover, in various cases, this reduction in the probability and / or prevalence of target-based frequency collisions can be achieved without the use of magnetic flux (e.g., in various aspects, embodiments of the present invention can provide physical lattice architectures that are not susceptible to target-based frequency collisions, do not exhibit reduced connectivity, and do not require the use of magnetic flux to facilitate selective cross-resonant entanglement).

[0029] In various embodiments, one or more of these technical benefits can be facilitated by producing a quantum computing lattice based on bijunction transport qubits coupled using mode-selective couplers (e.g., architectures / structures that can facilitate mode-selective coupling between a pair of superconducting qubits). In various embodiments, the control qubit can be a bijunction transport qubit. That is, in various cases, the control qubit can include a first Josephson junction and a second Josephson junction, wherein the first Josephson junction is coupled in series between an end capacitor pad and an intermediate capacitor pad, and wherein the second Josephson junction is coupled in series between the intermediate capacitor pad and another end capacitor pad. Thus, in various cases, the control qubit can have two different switching frequencies: a first A-mode switching frequency and a first B-mode switching frequency. In various aspects, the control qubit can be coupled to a target qubit. In various embodiments, the target qubit can also be a bijunction transport qubit (e.g., having two Josephson junctions, two end capacitor pads, and an intermediate capacitor pad). Therefore, under various conditions, the target qubit can have two different switching frequencies: a second A-mode switching frequency and a second B-mode switching frequency.

[0030] In various cases, the control qubit can be coupled to the target qubit via a first mode-selective coupler. In various embodiments, the first mode-selective coupler can facilitate A-mode coupling between the control qubit and the target qubit (e.g., when coupled via the first mode-selective coupler, the A-mode of the control qubit can be coupled to and / or entangled with the A-mode of the target qubit, but the B-mode of the control qubit cannot be coupled to and / or entangled with the B-mode of the target qubit). In various embodiments, to facilitate this A-mode coupling, the first mode-selective coupler can include a capacitor that capacitively couples the intermediate capacitor pad of the control qubit to the intermediate capacitor pad of the target qubit. In various embodiments, the capacitor of the first mode-selective coupler can be any suitable microstructure and / or nanostructure exhibiting a net capacitance between the intermediate capacitor pads of the control qubit and the target qubit, such as a coplanar waveguide and / or continuous metal element suitably proximally located to the intermediate capacitor pads of the control qubit and the target qubit. In various cases, the capacitance of the capacitor can be less than the shunt capacitance value associated with the control qubit and less than the shunt capacitance value associated with the target qubit. In various aspects, those skilled in the art will understand how such a capacitor can be fabricated and / or implemented between the intermediate capacitor pad of the control qubit and the intermediate capacitor pad of the target qubit. In various embodiments, such a capacitor between the intermediate capacitor pad of the control qubit and the intermediate capacitor pad of the target qubit can facilitate A-mode coupling between the control qubit and the target qubit and / or can prevent B-mode coupling between the control qubit and the target qubit.

[0031] In various other cases, the control qubit may be coupled to the target qubit via a second mode-selective coupler instead of the first mode-selective coupler. In various embodiments, the second mode-selective coupler may facilitate B-mode coupling between the control qubit and the target qubit (e.g., when coupled via the second mode-selective coupler, the B-mode of the control qubit may be coupled to and / or entangled with the B-mode of the target qubit, but the A-mode of the control qubit may not be coupled to and / or entangled with the A-mode of the target qubit). In various cases, to facilitate B-mode coupling, the second mode-selective coupler may include a first capacitor and a second capacitor. In various cases, the first capacitor may capacitively couple the end capacitor pad of the control qubit to the end capacitor pad of the target qubit. In various cases, the second capacitor may capacitively couple the end capacitor pad of the control qubit to the middle capacitor pad of the target qubit. In various embodiments, the first capacitor of the second mode-selective coupler can be any suitable microstructure and / or nanostructure exhibiting net capacitance between the end capacitor pad of the control qubit and the end capacitor pad of the target qubit, such as a coplanar waveguide and / or continuous metal element suitably adjacent to the end capacitor pads of the control qubit and the target qubit. Similarly, in various embodiments, the second capacitor of the second mode-selective coupler can be any suitable microstructure and / or nanostructure exhibiting net capacitance between the end capacitor pad of the control qubit and the intermediate capacitor pad of the target qubit, such as a coplanar waveguide and / or continuous metal element suitably adjacent to the end capacitor pads of the control qubit and the intermediate capacitor pad of the target qubit. In various cases, the first capacitance of the first capacitor can be less than the shunt capacitance value associated with the control qubit and less than the shunt capacitance value associated with the target qubit. In various cases, the second capacitance of the second capacitor can be half of the first capacitance. In various aspects, those skilled in the art will understand how a first capacitor can be fabricated and / or implemented between the end capacitor pad of the control qubit and the end capacitor pad of the target qubit, and will also understand how a second capacitor can be fabricated and / or implemented between the end capacitor pad of the control qubit and the intermediate capacitor pad of the target qubit. In various embodiments, such a first capacitor between the end capacitor pad of the control qubit and the end capacitor pad of the target qubit, and such a second capacitor between the end capacitor pad of the control qubit and the intermediate capacitor pad of the target qubit, can facilitate B-mode coupling between the control qubit and the target qubit and / or can prevent A-mode coupling between the control qubit and the target qubit.

[0032] In various other embodiments, a control qubit can be coupled to a first target qubit and a second target qubit, all of which can be dual-junction transport qubits (e.g., the control qubit can have two Josephson junctions, two end capacitor pads, and a middle capacitor pad; the first target qubit can have two Josephson junctions, two end capacitor pads, and a middle capacitor pad; the second target qubit can have two Josephson junctions, two end capacitor pads, and a middle capacitor pad). Thus, the first target qubit can exhibit two different switching frequencies (e.g., an A-mode switching frequency denoted as f). A1 , where f A1 (can be any suitable frequency value) and B-mode conversion frequency (denoted as f) B1 , where f B1 Not equal to f A1 Similarly, the second target qubit can exhibit two different switching frequencies (e.g., the A-mode switching frequency (denoted as f)). A2 , where f A2 (This can be any suitable frequency value) and the B-mode conversion frequency (denoted as f). B2 , where f B2 Not equal to f A2 In various cases, the control qubit can be coupled to the first target qubit via the first mode-selective coupler, as described above (e.g., coupling the intermediate capacitor pad of the control qubit to a capacitor on the intermediate capacitor pad of the first target qubit), thereby promoting A-mode coupling between the control qubit and the first target qubit and thereby preventing B-mode coupling between the control qubit and the first target qubit. In various cases, the control qubit can be coupled to the second target qubit via the second mode-selective coupler, as described above (e.g., coupling the end capacitor pad of the control qubit to a first capacitor on the end capacitor pad of the second target qubit, and coupling the same end capacitor pad of the control qubit to a second capacitor on the intermediate capacitor pad of the second target qubit), thereby promoting B-mode coupling between the control qubit and the second target qubit and thereby preventing A-mode coupling between the control qubit and the second target qubit.

[0033] In various embodiments, the first target qubit and the second target qubit can be non-degenerate targets. That is, in some cases, the first target qubit and the second target qubit can have different structural properties such that f A1 Not equal to f A2 And make f B1 Not equal to f B2In this case, selective cross-resonant entanglement can be facilitated between the control qubit and the first target qubit and / or the second target qubit. Specifically, in some instances, the control qubit can be composed of qubits with a frequency f. A1 The control qubit can be driven by microwave pulses and / or tones. In this case, the control qubit can become entangled with the first target qubit (e.g., the microwave pulses and / or tones have frequencies that match the A-mode switching frequency of the first target qubit, and the first mode-selective coupler can facilitate A-mode coupling between the control qubit and the first target qubit, thereby resulting in entanglement). Furthermore, in this case, the control qubit can avoid becoming entangled with the second target qubit (e.g., because these targets are non-degenerate, they have frequencies f). A1 The microwave pulse and / or tone are related to the A-mode conversion frequency (f) of the second target qubit. A2 or B-mode conversion frequency (f AB2 (None of them match, thus preventing entanglement). In some instances, the control qubit can be composed of qubits with a frequency f. B2 The control qubit can be driven by microwave pulses and / or tones. In this case, the control qubit can become entangled with the second target qubit (e.g., the microwave pulses and / or tones have frequencies that match the B-mode switching frequency of the second target qubit, and the second-mode selective coupler can facilitate B-mode coupling between the control qubit and the second target qubit, thereby resulting in entanglement). Furthermore, in this case, the control qubit can avoid becoming entangled with the first target qubit (e.g., because these targets are non-degenerate, they have frequencies f). B2 The microwave pulse and / or tone are related to the A-mode conversion frequency (f) of the first target qubit. A1 or B-mode conversion frequency (f B1 (None of them match). In various respects, note that in some cases, the frequency f is... B1 The microwave pulse and / or tone can prevent the control qubit from becoming entangled with the first target qubit or the second target qubit (e.g., the frequency of the microwave pulse and / or tone does not match the A-mode transition frequency or B-mode transition frequency of the second target qubit; although the frequency of the microwave pulse and / or tone matches the B-mode transition frequency of the first target qubit, the first mode-selective coupler can prevent B-mode coupling between the control qubit and the first target qubit). Similarly, in various aspects, note that in some cases, a frequency f... A2The microwave pulse and / or tone can prevent the control qubit from becoming entangled with the first target qubit or the second target qubit (e.g., the frequency of the microwave pulse and / or tone does not match the A-mode switching frequency or the B-mode switching frequency of the first target qubit; although the frequency of the microwave pulse and / or tone matches the A-mode switching frequency of the second target qubit, the second mode selective coupler can prevent A-mode coupling between the control qubit and the second target qubit).

[0034] In various embodiments, the first target qubit and the second target qubit can be degenerate targets. That is, in some cases, the first target qubit and the second target qubit can have similar and / or identical structural properties, such that f A1 equal to and / or substantially equal to f A2 And make f B1 equal to and / or substantially equal to f B2 Even in this case, selective entanglement can be promoted between the control qubit and the first target qubit and / or the second target qubit. Specifically, in some instances, the control qubit can be composed of qubits with a frequency f. A1 =f A2 The control qubit can be driven by microwave pulses and / or tones. In this case, the control qubit can become entangled with the first target qubit but not with the second target qubit. After all, the microwave pulses and / or tones have frequencies that match the A-mode transition frequency of the first target qubit, and the first mode-selective coupler can facilitate A-mode coupling between the control qubit and the first target qubit. Although the microwave pulses and / or tones also have frequencies that match the A-mode transition frequency of the second target qubit (e.g., because they are degenerate targets), the second mode-selective coupler can prevent A-mode coupling between the control qubit and the second target qubit. In some instances, the control qubit can be driven by a frequency f. B1 =f B2 The control qubit is driven by microwave pulses and / or tones. In this case, the control qubit can become entangled with the second target qubit but not with the first target qubit. After all, the microwave pulses and / or tones have frequencies that match the B-mode transition frequency of the second target qubit, and the second mode-selective coupler can facilitate B-mode coupling between the control qubit and the second target qubit. Although the microwave pulses and / or tones also have frequencies that match the B-mode transition frequency of the first target qubit (e.g., because they are degenerate targets), the first mode-selective coupler can prevent B-mode coupling between the control qubit and the first target qubit.

[0035] Therefore, even when using degenerate targets, embodiments of the present invention can promote selective cross-resonant entanglement. In stark contrast, degenerate targets in quantum computing lattices employing single-junction transport qubits coupled to a bus resonator will not experience selective cross-resonant entanglement.

[0036] In various embodiments, the control qubit can be further coupled to a third target qubit and a fourth target qubit. In various cases, the third target qubit and the fourth target qubit can be dual-junction transport qubits (e.g., the third target qubit can have two Josephson junctions, two end capacitor pads, and an intermediate capacitor pad; the fourth target qubit can have two Josephson junctions, two end capacitor pads, and an intermediate capacitor pad). In various aspects, the third target qubit and the fourth target qubit can be degenerate targets (e.g., they can be similar to and / or identical to each other) and can be non-degenerate with the first target qubit and the second target qubit. In various aspects, another instance of the first mode-selective coupler can couple the control qubit to the third target qubit, and another instance of the second mode-selective coupler can couple the control qubit to the fourth target qubit. Therefore, in various instances, mode A coupling between the control qubit and the third target qubit can be facilitated, and mode B coupling between the control qubit and the fourth target qubit can be facilitated. In various embodiments, selective cross-resonant entanglement can be facilitated between the control qubit and the third target qubit and / or the fourth target qubit, as described above with respect to the first and second target qubits.

[0037] That is, in various respects, the control qubit can be coupled to four target qubits (e.g., the first, second, third, and fourth target qubits), thereby promoting A-mode coupling between the control qubit and two of these target qubits (e.g., the first and third target qubits), and thus promoting B-mode coupling between the control qubit and the other two of these target qubits (e.g., the second and fourth target qubits). With this configuration, selective cross-resonant entanglement can be promoted between the control qubit and any of the four target qubits, despite the fact that the first and second target qubits are degenerate, and despite the fact that the third and fourth target qubits are degenerate. This is because in such a case there can be two pairs of degenerate targets, and in the quantum computing lattice there can be three different sets of superconducting qubits (e.g., the set corresponding to the control qubit, the set corresponding to the degenerate first and second target qubits, and the set corresponding to the degenerate third and fourth target qubits), instead of five different sets of superconducting qubits. In various respects, this reduction in the number of different groups of superconducting qubits required to form a quantum computing lattice can decrease the probability and / or prevalence of target-based frequency collisions without correspondingly reducing lattice connectivity. Thus, various embodiments of the present invention constitute concrete and tangible technical improvements in the field of superconducting qubit fabrication.

[0038] To help clarify the above discussion, consider the following non-limiting illustrative example. Consider a control qubit and four target qubits W, X, Y, and Z. Assume the control qubit and the four target qubits W, X, Y, and Z are double-junction transport qubits. Furthermore, assume that target qubits W and X are degenerate, and that target qubits Y and Z are also degenerate. In this case, the illustration involves only three types and / or sets of qubits: a first type and / or set corresponding to the control qubit, a second type and / or set corresponding to the degenerate target qubits W and X, and a third type and / or set corresponding to the degenerate target qubits Y and Z. Assume the control qubit is coupled to the target qubit via a mode-selective coupler that promotes mode A coupling, and assume the control qubit is coupled to the target qubit X via a mode-selective coupler that promotes mode B coupling. Similarly, suppose the control qubit is coupled to the target qubit Y by a mode-selective coupler that promotes mode A coupling, and suppose the control qubit is coupled to the target qubit Z by a mode-selective coupler that promotes mode B coupling.

[0039] Selective cross-resonant entanglement can be promoted in various ways. In some cases, the control qubit can be driven by microwave pulses and / or tones having frequencies corresponding to the A-mode transition frequency of the target qubit W. Because the frequency of the microwave pulses and / or tones matches the A-mode transition frequency of the target qubit W, and because A-mode coupling between the control qubit and the target qubit W is promoted, the control qubit can become entangled with the target qubit W. Note that in this case, the control qubit can avoid entanglement with the target qubit X. After all, even if the microwave pulses and / or tones have frequencies matching the A-mode transition frequency of the target qubit X (e.g., W and X are degenerate targets), A-mode coupling between the control qubit and the target qubit X is not promoted; instead, only B-mode coupling between the control qubit and the target qubit X is promoted. Furthermore, note that in this case, the control qubit can avoid entanglement with these target qubits Y and Z because their A-mode transition frequencies and their B-mode transition frequencies do not match the frequencies of the microwave pulse and / or tone (e.g., Y and Z may be non-degenerate with W and X).

[0040] In various cases, the control qubit can be driven by a microwave pulse and / or tone having a frequency corresponding to the B-mode transition frequency of the target qubit X. Because the frequency of the microwave pulse and / or tone matches the B-mode transition frequency of the target qubit X, and because B-mode coupling between the control qubit and the target qubit X is promoted, the control qubit can become entangled with the target qubit X. Note that in this case, the control qubit can avoid entanglement with the target qubit W. After all, even if the microwave pulse and / or tone has a frequency matching the B-mode transition frequency of the target qubit W (e.g., W and X are degenerate targets), B-mode coupling between the control qubit and the target qubit W is not promoted; instead, only A-mode coupling between the control qubit and the target qubit W is promoted. Furthermore, note that in this case, the control qubit can avoid entanglement with these target qubits Y and Z because their A-mode transition frequencies and their B-mode transition frequencies do not match the frequency of the microwave pulse and / or tone (e.g., Y and Z may not be degenerate with W and X).

[0041] In various cases, the control qubit can be driven by microwave pulses and / or tones having frequencies corresponding to the A-mode transition frequency of the target qubit Y. Because the frequency of the microwave pulses and / or tones matches the A-mode transition frequency of the target qubit Y, and because A-mode coupling between the control qubit and the target qubit Y is promoted, the control qubit can become entangled with the target qubit Y. Note that in this case, the control qubit can avoid entanglement with the target qubit Z. After all, even if the microwave pulses and / or tones have frequencies matching the A-mode transition frequency of the target qubit Z (e.g., Y and Z are degenerate targets), A-mode coupling between the control qubit and the target qubit Z is not promoted; instead, only B-mode coupling is facilitated between the control qubit and the target qubit Z. Furthermore, note that in this case, the control qubit can avoid entanglement with these target qubits W and X because their A-mode transition frequencies and their B-mode transition frequencies do not match the frequencies of the microwave pulse and / or tone (e.g., W and X may be non-degenerate with Y and Z).

[0042] In various cases, the control qubit can be driven by a microwave pulse and / or tone having a frequency corresponding to the B-mode transition frequency of the target qubit Z. Because the frequency of the microwave pulse and / or tone matches the B-mode transition frequency of the target qubit Z, and because B-mode coupling between the control qubit and the target qubit Z is promoted, the control qubit can become entangled with the target qubit Z. Note that in this case, the control qubit can avoid entanglement with the target qubit Y. After all, even if the microwave pulse and / or tone has a frequency matching the B-mode transition frequency of the target qubit Y (e.g., Y and Z are degenerate targets), B-mode coupling between the control qubit and the target qubit Y is not promoted; instead, only A-mode coupling between the control qubit and the target qubit Y is promoted. Furthermore, note that the control qubit can avoid entanglement with these target qubits W and X because their A-mode transition frequencies and their B-mode transition frequencies do not match the frequency of the microwave pulse and / or tone (e.g., W and X may not be degenerate with Y and Z).

[0043] As illustrated by this non-limiting illustrative example, various embodiments of the invention can promote selective cross-resonant entanglement using as few as three different sets of superconducting qubits, rather than requiring up to five different sets of superconducting qubits. This reduction in the number of different sets of superconducting qubits required to promote selective cross-resonant entanglement can, in different cases, reduce the statistical probability of target-based frequency conflicts without correspondingly reducing lattice connectivity.

[0044] Various embodiments of the present invention include novel systems, architectures, and / or techniques for facilitating mode-selective coupling for frequency collision reduction, which are not abstract, not natural phenomena, not natural laws, and cannot be performed by humans as a set of mental behaviors. Instead, various embodiments of the present invention include systems, architectures, and / or techniques for facilitating frequency collision reduction without requiring a corresponding reduction in lattice connectivity. Frequency collisions can negatively impact the performance of quantum computing lattices. While some techniques can reduce the probability of frequency collisions by reducing lattice connectivity (e.g., by reducing the number of connections in a quantum computing lattice), such low-density lattices are more susceptible to errors. Various embodiments of the present invention can reduce the statistical probability of frequency collisions without reducing lattice connectivity. Specifically, a control qubit can be coupled to a first target qubit via a first mode-selective coupler that can facilitate A-mode coupling between the control qubit and the first target qubit (e.g., a suitable structure of such a first mode-selective coupler is disclosed herein). Similarly, the control qubit can be coupled to a second target qubit via a second mode-selective coupler, which can facilitate mode B coupling between the control qubit and the second target qubit (e.g., a suitable structure for such a second mode-selective coupling is disclosed herein). In various respects, the first and second mode-selective couplers can allow selective cross-resonant entanglement to occur, even when the first and second target qubits are degenerate. In a nearest-neighbor connected quantum computing lattice composed of double-junction transport qubits (e.g., where each non-peripheral qubit is coupled to all four of its neighboring qubits), such first and second mode-selective couplers can allow selective cross-resonant entanglement with as few as three sets of different superconducting qubits. That is, various embodiments of the invention can reduce the number of different sets of qubits required to achieve selective cross-resonant entanglement in a nearest-neighbor connected quantum computing lattice. This reduction in the number of different sets of qubits can correspondingly reduce the chance of frequency collisions occurring within the quantum computing lattice. Thus, various embodiments of the present invention can improve the performance of quantum computing systems (e.g., reduce the probability of target-based frequency collisions), and therefore various embodiments of the present invention constitute specific and tangible technical improvements in the field of superconducting qubit fabrication.

[0045] In all respects, it should be understood that the accompanying drawings of this disclosure are exemplary and not restrictive, and are not necessarily drawn to scale.

[0046] Figure 1A circuit diagram of an exemplary non-limiting system 100 that facilitates mode-A coupling according to one or more embodiments described herein is shown. As shown, system 100 may include dual-junction transport qubits 102 and 104.

[0047] In various embodiments, the dual-junction transport qubit 102 may include a Josephson junction 106 shunt by capacitor 110. In various cases, the dual-junction transport qubit 102 may also include a Josephson junction 108 shunt by capacitor 112. In various embodiments, the dual-junction transport qubit 102 may further include capacitor 114 that shunts both Josephson junction 106 and Josephson junction 108. In various aspects, the dual-junction transport qubit 102 can be considered to include two series-coupled single-junction transport qubits such that they share a capacitor pad. Specifically, the Josephson junction 106 shunt by capacitor 110 can be considered to be shunt by a first capacitor pad and a second capacitor pad (in Figure 1 The first single-junction transport qubit is formed (not shown in the image). In various respects, the first capacitor pad and the second capacitor pad can shunt the Josephson junction 106 to form a capacitor 110. Furthermore, the Josephson junction 108 shunt by capacitor 112 can be considered as being formed by the second capacitor pad and a third capacitor pad (in the image). Figure 1 The second single-junction transport qubit (not shown) is formed. In various aspects, the second and third capacitor pads can shunt the Josephson junction 108 to form capacitor 112. Furthermore, the first and third capacitor pads can shunt both Josephson junctions 106 and 108 to form capacitor 114. In various aspects, the physical structure of the double-junction transport qubit 102 can be discussed below. Figure 2 It is described more clearly in the text.

[0048] In various contexts, the dual-junction transport qubit 102 can support and / or exhibit two distinct excitation modes. These two distinct excitation modes may be referred to as mode A and mode B. Mode A may be associated with the mode A transition frequency of the dual-junction transport qubit 102. Similarly, mode B may be associated with the mode B transition frequency of the dual-junction transport qubit 102. The mode A transition frequency may differ from and / or be unequal to the mode B transition frequency. As will be understood by those skilled in the art, the mode A transition frequency and / or mode B transition frequency of the dual-junction transport qubit 102 can be set and / or controlled during manufacturing, subject to inherent and / or unintentional process variations.

[0049] In some embodiments, the dual-junction transport qubit 102 can be encoded in mode A and / or mode B. In various aspects, when the dual-junction transport qubit 102 is encoded in mode A, it can exhibit mode A switching frequencies and can avoid exhibiting mode B switching frequencies. In various aspects, when the dual-junction transport qubit 102 is encoded in mode B, it can exhibit mode B switching frequencies and can avoid exhibiting mode A switching frequencies.

[0050] In various respects, as will be understood by those skilled in the art, the dual-junction transport qubit 102 can be encoded into mode A and / or mode B by short microwave pulses (e.g., the dual-junction transport qubit 102 can be switched from mode A to mode B and / or from mode B to mode A).

[0051] In various embodiments, the dual-junction transport qubit 104 can be similar to the dual-junction transport qubit 102. That is, in various aspects, the dual-junction transport qubit 104 can include a Josephson junction 116 shunt by capacitor 120. In various cases, the dual-junction transport qubit 104 can also include a Josephson junction 118 shunt by capacitor 122. In various embodiments, the dual-junction transport qubit 104 can further include a capacitor 124 that shunts both Josephson junction 116 and Josephson junction 118. In various aspects, the dual-junction transport qubit 104 can be considered to include two series-coupled single-junction transport qubits such that they share a capacitor pad. Specifically, the Josephson junction 116 shunt by capacitor 120 can be considered to be separated by a first capacitor pad and a second capacitor pad (separated from the first and second capacitor pads of the dual-junction transport qubit 102, and in...). Figure 1 The first single-junction transport qubit (not shown in the diagram) is formed. In various respects, the first capacitor pad and the second capacitor pad can shunt the Josephson junction 116 to form a capacitor 120. Furthermore, the Josephson junction 118 shunt by capacitor 122 can be considered as being formed by the second capacitor pad and the third capacitor pad (separated from the second and third capacitor pads of the dual-junction transport qubit 102, and...). Figure 1 The second single-junction transport qubit (not shown) is formed. In various aspects, the second and third capacitor pads can shunt the Josephson junction 118 to form capacitor 122. Furthermore, the first and third capacitor pads can shunt both Josephson junctions 116 and 118 to form capacitor 124. In various aspects, the physical structure of the double-junction transport qubit 104 can be discussed below. Figure 2 It is described more clearly in the text.

[0052] In various instances, the dual-junction transport qubit 104 can support and / or exhibit two different excitation modes. These two different excitation modes may be referred to as mode A and mode B in various aspects. Mode A may be associated with the mode A transition frequency of the dual-junction transport qubit 104. Similarly, mode B may be associated with the mode B transition frequency of the dual-junction transport qubit 104. The mode A transition frequency may be different from and / or not equal to the mode B transition frequency in various aspects. The mode A transition frequency and mode B transition frequency of the dual-junction transport qubit 104 may be different from and / or not equal to the mode A transition frequency and mode B transition frequency of the dual-junction transport qubit 102, respectively.

[0053] In some embodiments, as with dual-junction transport qubit 102, dual-junction transport qubit 104 can be encoded in A-mode and / or B-mode. In various cases, short microwave pulses can be used to switch between A-mode and B-mode encoding, as understood by those skilled in the art. As will be understood by those skilled in the art, the A-mode switching frequency and / or B-mode switching frequency of dual-junction transport qubit 104 can be set and / or controlled during manufacturing, subject to inherent and / or unintentional process variations.

[0054] In various embodiments, the dual-junction transport qubit 102 can be coupled to the dual-junction transport qubit 104 via a first mode-selective coupler 126. In various aspects, the first mode-selective coupler 126 can facilitate A-mode coupling between the dual-junction transport qubit 102 and the dual-junction transport qubit 104. In other words, the first mode-selective coupler 126 can function such that the A-mode excitation of the dual-junction transport qubit 102 can be coupled to and / or entangled with the A-mode excitation of the dual-junction transport qubit 104, and that the B-mode excitation of the dual-junction transport qubit 102 cannot be coupled to and / or entangled with the B-mode excitation of the dual-junction transport qubit 104. In various aspects, as shown, the first mode-selective coupler 126 may include a capacitor 128. In various aspects, the capacitor 128 can capacitively couple an intermediate capacitor pad (e.g., a second capacitor pad) of the dual-junction transport qubit 102 to an intermediate capacitor pad (e.g., a second capacitor pad) of the dual-junction transport qubit 104. In various respects, the capacitance of capacitor 128 can be smaller than the shunt capacitance of dual-junction transport qubit 102 (e.g., smaller than the capacitance of capacitor 110, smaller than the capacitance of capacitor 112, and smaller than the capacitance of capacitor 114) and smaller than the shunt capacitance of dual-junction transport qubit 104 (e.g., smaller than the capacitance of capacitor 120, smaller than the capacitance of capacitor 122, and smaller than the capacitance of capacitor 124). In various respects, this capacitive coupling structure can facilitate A-mode coupling between dual-junction transport qubit 102 and dual-junction transport qubit 104 while preventing B-mode coupling between dual-junction transport qubit 102 and dual-junction transport qubit 104. In various cases, the structure of the first mode-selective coupler 126 can be discussed below. Figure 2 It is described more clearly in the text.

[0055] In various respects, the dual-junction transport qubit 102 can act as a control qubit, while the dual-junction transport qubit 104 can act as a target qubit. In various respects, the cross-resonance direction can be said to extend along the first-mode selective coupler 126 from the dual-junction transport qubit 102 to the dual-junction transport qubit 104.

[0056] Figure 2 A block diagram of an example non-limiting system 200 that can facilitate mode-A coupling according to one or more embodiments described herein is shown. In various aspects, Figure 2 It can be shown that it is achievable Figure 1 The physical structure / architecture of the circuit shown.

[0057] In various respects, system 200 may include dual-junction transport qubits 102 and 104, which may be coupled together via a first mode-selective coupler 126. As explained above, Figure 1 A circuit diagram depicts the dual-junction transport qubit 102, the dual-junction transport qubit 104, and the first-mode selective coupler 126. On the other hand, Figure 2 The physical structure and / or architecture that can be used to implement the dual-junction transport qubit 102, the dual-junction transport qubit 104, and the first mode selective coupler 126 are described.

[0058] In various embodiments, the dual-junction transport qubit 102 may include a Josephson junction 106, a Josephson junction 108, end capacitor pads 202 and 204, and an intermediate capacitor pad 206. As shown, in various aspects, the end capacitor pad 202 may be coupled to the Josephson junction 106. Similarly, as shown, the intermediate capacitor pad 206 may be coupled to the Josephson junction 106, such that the end capacitor pad 202, the Josephson junction 106, and the intermediate capacitor pad 206 may be connected in series with each other. In various aspects, the end capacitor pad 202 and the intermediate capacitor pad 206 can be considered as shunting the Josephson junction 106. In other words, in various aspects, the end capacitor pad 202 and the intermediate capacitor pad 206 may collectively form and / or serve as capacitor 110.

[0059] As shown, in various aspects, the Josephson junction 108 can be coupled to the intermediate capacitor pad 206. Similarly, as shown, the end capacitor pad 204 can be coupled to the Josephson junction 108, such that the intermediate capacitor pad 206, the Josephson junction 108, and the end capacitor pad 204 can be connected in series with each other. In various aspects, the intermediate capacitor pad 206 and the end capacitor pad 204 can be considered as shunting the Josephson junction 108. In other words, in various aspects, the intermediate capacitor pad 206 and the end capacitor pad 204 can be collectively formed and / or used as capacitor 112.

[0060] As shown, in various aspects, the end capacitor pad 202, Josephson junction 106, intermediate capacitor pad 206, Josephson junction 108, and end capacitor pad 204 can be coupled together such that they are all in series with each other. In various instances, the end capacitor pad 202 and the end capacitor pad 204 can be considered as shunting both the Josephson junction 106 and the Josephson junction 108. In other words, in various aspects, the end capacitor pad 202 and the end capacitor pad 204 can be collectively formed and / or used as capacitor 114.

[0061] In various respects, as described above, this two-junction transport qubit 102 can be considered as two series-coupled single-junction transport qubits sharing an intermediate capacitor pad. Specifically, the end capacitor pad 202, the Josephson junction 106, and the intermediate capacitor pad 206 can be considered as a first single-junction transport qubit. Similarly, the intermediate capacitor pad 206, the Josephson junction 108, and the end capacitor pad 204 can be considered as a second single-junction transport qubit connected in series with the first single-junction transport qubit. As shown, the first and second single-junction transport qubits can share the intermediate capacitor pad 206.

[0062] In various embodiments, the end capacitor pad 202, the intermediate capacitor pad 206, and the end capacitor pad 204 can be composed of any suitable material for forming shunt capacitors in a quantum computing system (e.g., any suitable superconducting material, such as niobium). Although Figure 2 The end capacitor pad 202, intermediate capacitor pad 206, and end capacitor pad 204 are described as being made of the same material, but this is not limiting and is for illustrative purposes only. In various aspects, the end capacitor pad 202, intermediate capacitor pad 206, and end capacitor pad 204 may comprise different materials. In various embodiments, the end capacitor pad 202, intermediate capacitor pad 206, and end capacitor pad 204 may have any suitable size, shape, and / or dimension. Although Figure 2 End capacitor pads 202 and 204 are described as having similar dimensions, shapes, and / or sizes, but this is non-limiting and illustrative only. In various aspects, end capacitor pads 202 and 204 may have different sizes, shapes, and / or sizes. In various aspects, as shown, intermediate capacitor pad 206 may be H-shaped. In various aspects, this H-shape can provide additional surface area for coupling purposes. That is, in some cases, this H-shape can increase the side surface area of ​​intermediate capacitor pad 206 that can be used to couple any other suitable quantum computing components and / or circuits (e.g., capacitive coupling, direct coupling, and / or otherwise) to intermediate capacitor pad 206. In various embodiments, intermediate capacitor pad 206 may have any other suitable size, shape, and / or size.

[0063] As described above, in various embodiments, the dual-junction transport qubit 102 can exhibit two different excitation modes: mode A and mode B. In various aspects, the mode structure for mode A excitation can be as follows: a bright mode component in the end capacitor pad 202, a dark mode component in the intermediate capacitor pad 206, and a bright mode component in the end capacitor pad 204. In various aspects, the mode structure for mode B excitation can be as follows: a dark mode component in the end capacitor pad 202, neutral and / or zero mode components in the intermediate capacitor pad 206, and a bright mode component in the end capacitor pad 204.

[0064] In various embodiments, the dual-junction transport qubit 104 may exhibit a structure and / or architecture similar to that of the dual-junction transport qubit 102. In various aspects, the dual-junction transport qubit 104 may include a Josephson junction 116, a Josephson junction 118, end capacitor pads 208 and 210, and an intermediate capacitor pad 212. As shown, in various aspects, the end capacitor pad 208 may be coupled to the Josephson junction 116. Similarly, as shown, the intermediate capacitor pad 212 may be coupled to the Josephson junction 116, such that the end capacitor pad 208, the Josephson junction 116, and the intermediate capacitor pad 212 may be connected in series. In various aspects, the end capacitor pad 208 and the intermediate capacitor pad 212 can be considered as shunting the Josephson junction 116. In other words, in various aspects, the end capacitor pad 208 and the intermediate capacitor pad 212 may collectively form and / or act as capacitor 120.

[0065] As shown, in various aspects, the Josephson junction 118 can be coupled to the intermediate capacitor pad 212. Similarly, as shown, the end capacitor pad 210 can be coupled to the Josephson junction 118, such that the intermediate capacitor pad 212, the Josephson junction 118, and the end capacitor pad 210 can be connected in series with each other. In various aspects, the intermediate capacitor pad 212 and the end capacitor pad 210 can be considered as shunting the Josephson junction 118. In other words, in various aspects, the intermediate capacitor pad 212 and the end capacitor pad 210 can collectively form and / or serve as capacitor 122.

[0066] As shown, in various aspects, end capacitor pad 208, Josephson junction 116, intermediate capacitor pad 212, Josephson junction 118, and end capacitor pad 210 can be coupled together such that they are all in series with each other. In various embodiments, the end capacitor pad 208 and the end capacitor pad 210 can be considered as shunting both the Josephson junction 116 and the Josephson junction 118. In other words, in various aspects, end capacitor pad 208 and end capacitor pad 210 can be collectively formed and / or used as capacitor 124.

[0067] In various respects, as described above, these dual-junction transport qubits 104 can be considered as two series-coupled single-junction transport qubits sharing an intermediate capacitor pad. Specifically, the end capacitor pad 208, the Josephson junction 116, and the intermediate capacitor pad 212 can be considered as a first single-junction transport qubit. Similarly, the intermediate capacitor pad 212, the Josephson junction 118, and the end capacitor pad 210 can be considered as a second single-junction transport qubit connected in series with the first single-junction transport qubit. As shown, the first single-junction transport qubit and the second single-junction transport qubit can share the intermediate capacitor pad 212.

[0068] In various respects, the size, shape, dimensions and / or material of the end capacitor pad 208, the intermediate capacitor pad 212 and the end capacitor pad 210 may be as described above with respect to the end capacitor pad 202, the intermediate capacitor pad 206 and the end capacitor pad 204.

[0069] In various embodiments, the mode structure for A-mode excitation of the dual-junction transport qubit 104 can be as described above regarding the mode structure for A-mode excitation of the dual-junction transport qubit 102. Similarly, in various aspects, the mode structure for B-mode excitation of the dual-junction transport qubit 104 can be as described above regarding the mode structure for B-mode excitation of the dual-junction transport qubit 102.

[0070] In various embodiments, as shown, the first mode-selective coupler 126 may include capacitor pad 214, capacitor pad 216, and transmission line 218. In various aspects, capacitor pad 214 may be capacitively coupled to intermediate capacitor pad 206, and capacitor pad 216 may be capacitively coupled to intermediate capacitor pad 212. In various aspects, transmission line 218 may directly couple capacitor pad 214 to capacitor pad 216. In various cases, capacitor pad 214, capacitor pad 216, and transmission line 218 may collectively exhibit a net capacitance. In other words, capacitor pad 214, capacitor pad 216, and transmission line 218 may collectively form and / or act as capacitor 128 in various cases. As described above, the capacitance of capacitor 128 (e.g., the net capacitance of capacitor pads 214, 216, and transmission line 218) can be less than the shunt capacitance of dual-junction transport qubit 102 (e.g., less than the capacitance of capacitor 110, capacitor 112, and capacitor 114) and can be less than the shunt capacitance of dual-junction transport qubit 104 (e.g., less than the capacitance of capacitor 120, capacitor 122, and capacitor 124).

[0071] In various embodiments, capacitor pads 214 and 216 can be composed of any suitable material (e.g., any suitable superconducting material, such as niobium) used for forming capacitors and / or capacitive connections in a quantum computing system. Although Figure 2 Capacitor pads 214 and 216 are described as being made of the same material, but this is not limiting and is for illustrative purposes only. In various aspects, capacitor pads 214 and 216 may comprise different materials. In various embodiments, capacitor pads 214 and 216 may have any suitable size, shape, and / or dimensions. Although Figure 2 Capacitor pads 214 and 216 are described as having similar dimensions, shapes, and / or sizes, but this is non-limiting and illustrative only. In various respects, capacitor pads 214 and 216 may have different sizes, shapes, and / or dimensions. In various respects, transmission line 218 may be composed of any suitable conductive material used in quantum computing systems (e.g., any suitable superconducting material, such as niobium). Although Figure 2 Transmission line 218 is depicted as straight, but this is non-limiting and for illustrative purposes only. In various respects, transmission line 218 may have any suitable size, shape, and / or dimensions.

[0072] In various aspects, the first mode-selective coupler 126 can have the same characteristics as... Figure 2The structure and / or architecture may differ from those depicted in the description (e.g., it may have components different from capacitor pad 214, capacitor pad 216, and transmission line 218). Specifically, in various embodiments, the first mode-selective coupler 126 may be any suitable structure, architecture, and / or quantum circuit component, such as a coplanar waveguide, representing the net capacitance between intermediate capacitor pad 206 and intermediate capacitor pad 212. In other words, the first mode-selective coupler 126 may be any suitable structure that serves as a capacitor between intermediate capacitor pad 206 and intermediate capacitor pad 212 and / or otherwise capacitively couples intermediate capacitor pad 206 to intermediate capacitor pad 212.

[0073] In various respects, as described above, the net capacitive coupling between intermediate capacitor pad 206 and intermediate capacitor pad 212 can facilitate A-mode coupling between the dual-junction transport qubit 102 and the dual-junction transport qubit 104. Furthermore, in various respects, as described above, the net capacitive coupling between intermediate capacitor pad 206 and intermediate capacitor pad 212 can prevent B-mode coupling between the dual-junction transport qubit 102 and the dual-junction transport qubit 104.

[0074] Figure 3 A circuit diagram of an exemplary non-limiting system 300 that facilitates mode-B coupling according to one or more embodiments described herein is shown. As shown, system 300 may include dual-junction transport qubit 102 and dual-junction transport qubit 104 as described above.

[0075] In various embodiments, the double-junction transport qubit 102 can be coupled to the double-junction transport qubit 104 via a second mode-selective coupler 302. In various aspects, the second mode-selective coupler 302 can facilitate B-mode coupling between the double-junction transport qubit 102 and the double-junction transport qubit 104. In other words, the second mode-selective coupler 302 can function such that the B-mode excitation of the double-junction transport qubit 102 can be coupled to and / or entangled with the B-mode excitation of the double-junction transport qubit 104, and that the A-mode excitation of the double-junction transport qubit 102 cannot be coupled to and / or entangled with the A-mode excitation of the double-junction transport qubit 104. In various aspects, as shown, the second mode-selective coupler 302 may include capacitors 304 and 306. In various aspects, capacitor 304 can capacitively couple the end capacitor pad (e.g., the first capacitor pad) of the dual-junction transport qubit 102 to the end capacitor pad (e.g., the first capacitor pad) of the dual-junction transport qubit 104. In various aspects, capacitor 306 can capacitively couple the end capacitor pad (e.g., the first capacitor pad) of the dual-junction transport qubit 102 to the intermediate capacitor pad (e.g., the second capacitor pad) of the dual-junction transport qubit 104. In various aspects, the capacitance of capacitor 304 can be less than the shunt capacitance value of the dual-junction transport qubit 102 (e.g., less than the capacitance of capacitor 110, less than the capacitance of capacitor 112, and less than the capacitance of capacitor 114) and less than the shunt capacitance value of the dual-junction transport qubit 104 (e.g., less than the capacitance of capacitor 120, less than the capacitance of capacitor 122, and less than the capacitance of capacitor 124). In various cases, the capacitance of capacitor 306 can be half the capacitance of capacitor 304. In various respects, this capacitive coupling structure can facilitate B-mode coupling between the dual-junction transport qubit 102 and the dual-junction transport qubit 104, while preventing A-mode coupling between the two qubits 102 and 104. In various cases, the structure of the second mode-selective coupler 302 can be more clearly described in the following discussion. Figure 4 middle.

[0076] In various respects, the dual-junction transport qubit 102 can act as a control qubit, while the dual-junction transport qubit 104 can act as a target qubit. In various respects, it can be said that the cross-resonance direction extends from the dual-junction transport qubit 102 to the dual-junction transport qubit 104 along the second-mode selective coupler 302.

[0077] Figure 4 A block diagram of an example non-limiting system 400 that facilitates B-mode coupling according to one or more embodiments described herein is shown. In various aspects, Figure 4 It can be shown that it is achievable Figure 3 The physical structure / architecture of the circuit described in the document.

[0078] In various respects, system 400 may include the dual-junction transport qubit 102 and dual-junction transport qubit 104 as described above, which can be coupled together via a second mode-selective coupler 302. As explained above, Figure 3 A circuit diagram depicts the dual-junction transport qubit 102, the dual-junction transport qubit 104, and the second-mode selective coupler 302. On the other hand, Figure 4 The physical structure and / or architecture that can be used to realize the dual-junction transport qubit 102, the dual-junction transport qubit 104, and the second-mode selective coupler 302 are described.

[0079] In various embodiments, as shown, the second mode-selective coupler 302 may include capacitor pad 402, capacitor pad 404, capacitor pad 408, transmission line 406, and transmission line 410. In various aspects, capacitor pad 402 may be capacitively coupled to end capacitor pad 202, capacitor pad 404 may be capacitively coupled to end capacitor pad 210, and capacitor pad 408 may be capacitively coupled to intermediate capacitor pad 212. In various aspects, transmission line 406 may directly couple capacitor pad 402 to capacitor pad 404. In various cases, capacitor pad 402, capacitor pad 404, and transmission line 406 may exhibit net capacitance. In other words, capacitor pad 402, capacitor pad 404, and transmission line 406 may, in various cases, collectively form and / or act as capacitor 304. As described above, the capacitance of capacitor 304 (e.g., the net capacitance of capacitor pad 402, capacitor pad 404, and transmission line 406) can be less than the shunt capacitance value of dual-junction transport qubit 102 (e.g., less than the capacitance of capacitor 110, less than the capacitance of capacitor 112, and less than the capacitance of capacitor 114) and can be less than the shunt capacitance value of dual-junction transport qubit 104 (e.g., less than the capacitance of capacitor 120, less than the capacitance of capacitor 122, and less than the capacitance of capacitor 124).

[0080] In various respects, transmission line 410 can directly couple capacitor pad 402 to capacitor pad 408. In various cases, capacitor pad 402, capacitor pad 408, and transmission line 410 can exhibit a net capacitance. In other words, capacitor pad 402, capacitor pad 408, and transmission line 410 can collectively form and / or serve as capacitor 306 in various cases. As mentioned above, the capacitance of capacitor 306 (e.g., the net capacitance of capacitor pad 402, capacitor pad 408, and transmission line 410) can be half the capacitance of capacitor 304 (e.g., half the net capacitance of capacitor pad 402, capacitor pad 404, and transmission line 406).

[0081] In various embodiments, capacitor pads 402, 404, and 408 can be made of any suitable material for forming capacitors and / or capacitive connections in a quantum computing system (e.g., any suitable superconducting material, such as niobium). Although Figure 4 Capacitor pads 402, 404, and 408 are described as being made of the same material, but this is not limiting and is for illustrative purposes only. In various aspects, capacitor pads 402, 404, and 408 may comprise different materials. In various embodiments, capacitor pads 402, 404, and 408 may have any suitable size, shape, and / or dimensions. Although Figure 4 Capacitor pads 402, 404, and 408 are described as having similar dimensions, shapes, and / or sizes, but this is non-limiting and illustrative only. In various aspects, capacitor pads 402, 404, and 408 may have different sizes, shapes, and / or dimensions. In various aspects, transmission lines 406 and 410 may be composed of any suitable conductive material for quantum computing systems (e.g., any suitable superconducting material, such as niobium). In various aspects, transmission lines 406 and 410 may comprise different materials. Although... Figure 4 Transmission lines 406 and 410 are depicted as straight, but this is non-limiting and for illustrative purposes only. In various respects, transmission lines 406 and 410 may have any suitable size, shape, and / or dimensions. Although Figure 4 Transmission lines 406 and 410 are described as being coupled to capacitor pad 402, but this is not limiting and is for illustrative purposes only. In various cases, capacitor pad 402 may be coupled to transmission line 406 but not to transmission line 410 (e.g., in this case, the second mode-selective coupler 302 may include a fourth capacitor pad (not shown) capacitively coupled to end capacitor pad 202 and directly coupled to transmission line 410). In various cases, capacitor pad 402 may be coupled to transmission line 410 but not to transmission line 406 (e.g., in this case, the second mode-selective coupler 302 may include a fourth capacitor pad (not shown) capacitively coupled to end capacitor pad 202 and directly coupled to transmission line 406).

[0082] In various embodiments, the second mode-selective coupler 302 may have the same characteristics as... Figure 4The structures and / or architectures depicted may differ from those described herein (e.g., they may have components different from capacitor pads 402, 404, 408, transmission line 406, and transmission line 410). Specifically, in various embodiments, the second mode-selective coupler 302 may be any suitable structure, architecture, and / or quantum circuit component that exhibits a first net capacitance, such as a coplanar waveguide, between end capacitor pads 202 and 210, and a second net capacitance, such as a coplanar waveguide, between end capacitor pads 202 and intermediate capacitor pads 212. In other words, the second mode-selective coupler 302 may be any suitable structure that serves as a first capacitor between end capacitor pads 202 and 210 and as a second capacitor between end capacitor pads 202 and intermediate capacitor pads 212. In other words, the second mode selective coupler 302 can be any suitable structure that capacitively couples the end capacitor pad 202 to the end capacitor pad 210 and capacitively couples the end capacitor pad 202 to the intermediate capacitor pad 212.

[0083] In various aspects, the first net capacitive coupling between end capacitor pads 202 and 210, as described above, and the second net capacitive coupling between end capacitor pads 202 and intermediate capacitor pads 212, as described above, can facilitate B-mode coupling between the dual-junction transport qubits 102 and 104. Furthermore, in various aspects, the first net capacitive coupling between end capacitor pads 202 and 210, as described above, and the second net capacitive coupling between end capacitor pads 202 and intermediate capacitor pads 212, as described above, can prevent A-mode coupling between the dual-junction transport qubits 102 and 104.

[0084] although Figure 4 The second mode-selective coupler 302 is shown to capacitively couple end capacitor pad 202 to end capacitor pad 210, but this is non-limiting and for illustrative purposes only. In various respects, the second mode-selective coupler 302 can capacitively couple any end capacitor pad of the dual-junction transport qubit 102 (e.g., end capacitor pad 202 and / or end capacitor pad 204) to any end capacitor pad of the dual-junction transport qubit 104 (e.g., end capacitor pad 208 and / or end capacitor pad 210). Although Figure 4A second mode-selective coupler 302 is shown that can capacitively couple end capacitor pads 202 to intermediate capacitor pads 212, but this is non-limiting and for illustrative purposes only. In various respects, the second mode-selective coupler 302 can capacitively couple any end capacitor pad of the dual-junction transport qubit 102 to the intermediate capacitor pad 212 of the dual-junction transport qubit 104, provided that the same end capacitor pad of the dual-junction transport qubit 102 is capacitively coupled to the end capacitor pad of the dual-junction transport qubit 104.

[0085] In various aspects, the dual-junction transport qubit 102 can act as a control qubit, while the dual-junction transport qubit 104 can act as a target qubit.

[0086] Figure 5 A block diagram of an exemplary non-limiting system 500 for facilitating the reduction of frequency interference in a mode-selective coupler according to one or more embodiments described herein is shown. In various aspects, Figure 5 The first mode selective coupler 126 and the second mode selective coupler 302 can be implemented to couple multiple target qubits together to a control qubit in order to promote selective cross-resonance entanglement.

[0087] In various embodiments, system 500 may include a control qubit 502, a first target qubit 504, and a second target qubit 506. In various aspects, the control qubit 502, the first target qubit 504, and the second target qubit 506 may be dual-junction transport qubits, as described above. That is, in various aspects, the control qubit 502 may include an end capacitor pad 512, a Josephson junction 508, an intermediate capacitor pad 514, a Josephson junction 510, and an end capacitor pad 516, all of which are coupled together in series. Similarly, the first target qubit 504 may include an end capacitor pad 522, a Josephson junction 518, an intermediate capacitor pad 524, a Josephson junction 520, and an end capacitor pad 526, all of which are coupled together in series. Similarly, the second target qubit 506 may include an end capacitor pad 532, a Josephson junction 528, an intermediate capacitor pad 534, a Josephson junction 530, and an end capacitor pad 536, all of which are coupled together in series.

[0088] As described above, since the first target qubit 504 is a double-junction transport qubit, it can have both an A-mode switching frequency and a B-mode switching frequency. Similarly, since the second target qubit 506 is a double-junction transport qubit, it can have both an A-mode switching frequency and a B-mode switching frequency.

[0089] In various cases, the first target qubit 504 and the second target qubit 506 can be degenerate. That is, in some cases, the A-mode conversion frequency of the first target qubit 504 can be equal to the A-mode conversion frequency of the second target qubit 506, and the B-mode conversion frequency of the first target qubit 504 can be equal to the B-mode conversion frequency of the second target qubit 506.

[0090] As shown, in various embodiments, control qubit 502 can be coupled to first target qubit 504 via a first mode-selective coupler 126. That is, the first mode-selective coupler 126 can capacitively couple intermediate capacitor pad 514 to intermediate capacitor pad 524. Similarly, as shown, in various embodiments, control qubit 502 can be coupled to second target qubit 506 via a second mode-selective coupler 302. That is, the second mode-selective coupler 302 can capacitively couple end capacitor pad 516 to end capacitor pad 532 and can capacitively couple end capacitor pad 516 to intermediate capacitor pad 534. Due to the first mode-selective coupler 126, mode A coupling between control qubit 502 and first target qubit 504 can be facilitated, and mode B coupling between control qubit 502 and first target qubit 504 can be prevented. Similarly, due to the second mode selective coupler 302, B-mode coupling between the control qubit 502 and the second target qubit 506 can be facilitated, while A-mode coupling between the control qubit 502 and the second target qubit 506 can be prevented.

[0091] In various embodiments, system 500 can facilitate selective cross-resonant entanglement, although in practice the first target qubit 504 and the second target qubit 506 can be degenerate. Specifically, in various cases, control qubit 502 can be driven by microwave pulses and / or tones having a frequency equal to the A-mode switching frequency of the first target qubit 504. Since the frequency and / or tone of the microwave pulses are equal to the A-mode switching frequency of the first target qubit 504, and since the first mode-selective coupler 126 can facilitate A-mode coupling between control qubit 502 and the first target qubit 504, control qubit 502 can become entangled with the first target qubit 504. Note that in this case, control qubit 502 can avoid becoming entangled with the second target qubit 506. This is because, although the microwave pulse and / or tone have a frequency equal to the A-mode switching frequency of the second target qubit 506 (e.g., the first target qubit 504 and the second target qubit 506 may be degenerate), the second mode selective coupler 302 can prevent A-mode coupling between the control qubit 502 and the second target qubit 506.

[0092] In various other cases, the control qubit 502 can be driven by microwave pulses and / or tones having a frequency equal to the B-mode transition frequency of the second target qubit 506. Since the frequency and / or tone of the microwave pulses are equal to the B-mode transition frequency of the second target qubit 506, and since the second mode-selective coupler 302 can facilitate B-mode coupling between the control qubit 502 and the second target qubit 506, the control qubit 502 can become entangled with the second target qubit 506. Note that in this case, the control qubit 502 can avoid entanglement with the first target qubit 504. This is because, although the microwave pulses and / or tones have a frequency equal to the B-mode transition frequency of the first target qubit 504 (e.g., the first target qubit 504 and the second target qubit 506 can be degenerate), the first mode-selective coupler 126 can prevent B-mode coupling between the control qubit 502 and the first target qubit 504.

[0093] Thus, as explained above, the first mode-selective coupler 126 and the second mode-selective coupler 302 can work together to facilitate selective cross-resonant entanglement, even with degeneracy targets. Furthermore, no magnetic flux and / or reduced connectivity is required to facilitate this selective cross-resonant entanglement. As mentioned above, when degeneracy targets are involved, a quantum computing lattice using only a single-junction transport qubit coupled by a bus resonator cannot facilitate selective cross-resonant entanglement. This highlights the specific and tangible technical benefits of the various embodiments of the invention.

[0094] Figure 6 A flowchart is shown of an exemplary non-limiting method 600 for facilitating the reduction of frequency conflicts in a mode-selective coupler according to one or more embodiments described herein.

[0095] In various embodiments, action 602 may include forming a control qubit (e.g., 502), a first target qubit (e.g., 504), and a second target qubit (e.g., 506), wherein the control qubit, the first target qubit, and the second target qubit are double-junction transport qubits. In various aspects, any suitable microfabrication and / or nanofabrication techniques may be used to form and / or manufacture the control qubit, the first target qubit, and the second target qubit. In various aspects, the first target qubit and the second target qubit may be degenerate (e.g., may have the same A-mode conversion frequency and the same B-mode conversion frequency).

[0096] In various aspects, action 604 may include capacitively coupling an intermediate capacitor pad (e.g., 514) of the control qubit to an intermediate capacitor pad (e.g., 524) of the first target qubit, thereby facilitating A-mode coupling between the control qubit and the first target qubit.

[0097] In various instances, action 606 may include capacitively coupling an end capacitor pad (e.g., 516) of the control qubit to an end capacitor pad (e.g., 532) of the second target qubit, and capacitively coupling the same end capacitor pad of the control qubit to an intermediate capacitor pad (e.g., 534) of the second target qubit, thereby facilitating B-mode coupling between the control qubit and the second target qubit.

[0098] In various embodiments, action 608 may include applying a first micro-wave modulation corresponding to the A-mode excitation frequency (e.g., the A-mode switching frequency of the first target qubit 504) to the control qubit, thereby causing the first target qubit to become entangled with the control qubit.

[0099] In various embodiments, action 610 may include applying a second micro-wave modulation corresponding to the B-mode excitation frequency (e.g., the B-mode switching frequency of the second target qubit 506) to the control qubit, thereby causing the second target qubit to become entangled with the control qubit.

[0100] Figures 7 to 8 Plots illustrating exemplary, non-limiting simulation results of a system for a mode-selective coupler that can facilitate frequency conflict reduction according to one or more embodiments described herein are shown. In various aspects, Figures 7 to 8 The selective cross-resonance entanglement behavior of system 500 is shown.

[0101] Figure 7 Graphs 702 and 704 are depicted. In various aspects, graph 702 can represent the oscillatory behavior (e.g., Z-oscillation) of the first target qubit 504 when the control qubit 502 is driven by a microwave pulse and / or tone having a frequency matching the A-mode switching frequency of the first target qubit 504. In various aspects, graph 704 can represent the oscillatory behavior (e.g., Z-oscillation) of the second target qubit 506 when the control qubit 502 is driven by a microwave pulse and / or tone having a frequency matching the A-mode switching frequency of the first target qubit 504.

[0102] As shown in graph 702, when the control qubit 502 is driven by a microwave pulse and / or tone having a frequency matching the A-mode transition frequency of the first target qubit 504, the first target qubit 504 undergoes Rabi oscillations. Specifically, when the control qubit 502 is in a 0 state and is driven by a microwave pulse and / or tone matching the A-mode transition frequency of the first target qubit 504, the first target qubit 504 exhibits oscillatory behavior 706. Furthermore, when the control qubit 502 is in a 1 state and is driven by a microwave pulse and / or tone matching the A-mode transition frequency of the first target qubit 504, the first target qubit 504 exhibits oscillatory behavior 708.

[0103] As shown in graph 704, when the control qubit 502 is driven by a microwave pulse and / or tone having a frequency matching the A-mode transition frequency of the first target qubit 504, the second target qubit 506 does not experience Rabi oscillations. Specifically, when the control qubit 502 is in a 0 state and is driven by a microwave pulse and / or tone matching the A-mode transition frequency of the first target qubit 504, the second target qubit 506 exhibits oscillatory behavior 710. Furthermore, when the control qubit 502 is in a 1 state and is driven by a microwave pulse and / or tone matching the A-mode transition frequency of the first target qubit 504, the second target qubit 506 exhibits oscillatory behavior 712.

[0104] Thus, as illustrated in graphs 702 and 704, when the control qubit 502 is driven by a microwave pulse and / or tone matching the A-mode switching frequency of the first target qubit 504, the first target qubit 504 can exhibit Rabi oscillations, and the second target qubit 506 can exhibit non-Rabi oscillation behavior. In other words, the first target qubit 504 can become entangled with the control qubit 502, and the second target qubit 506 can avoid becoming entangled with the control qubit 502. In various respects, this selective cross-resonant entanglement is caused by the first mode-selective coupler 126 coupling the control qubit 502 to the first target qubit 504 and the second mode-selective coupler 302 coupling the control qubit 502 to the second target qubit 506. Furthermore, the fact that the first target qubit 504 and the second target qubit 506 can be degenerate can facilitate this selective cross-resonant entanglement.

[0105] Figure 8 Similar to Figure 7 . Figure 8Graphs 802 and 804 are depicted. In various aspects, graph 802 can represent the oscillatory behavior (e.g., Z-oscillation) of the first target qubit 504 when the control qubit 502 is driven by a microwave pulse and / or tone having a frequency matching the B-mode switching frequency of the second target qubit 506. In various aspects, graph 804 can represent the oscillatory behavior (e.g., Z-oscillation) of the second target qubit 506 when the control qubit 502 is driven by a microwave pulse and / or tone having a frequency matching the B-mode switching frequency of the second target qubit 506.

[0106] As shown in graph 802, when the control qubit 502 is driven by a microwave pulse and / or tone having a frequency matching the B-mode transition frequency of the second target qubit 506, the first target qubit 504 does not experience Rabi oscillations. Specifically, when the control qubit 502 is in state 0 and driven by a microwave pulse and / or tone matching the B-mode transition frequency of the second target qubit 506, the first target qubit 504 exhibits oscillatory behavior 806. Furthermore, when the control qubit 502 is in state 2 and driven by a microwave pulse and / or tone matching the B-mode transition frequency of the second target qubit 506, the first target qubit 504 exhibits oscillatory behavior 808.

[0107] As shown in graph 804, when the control qubit 502 is driven by a microwave pulse and / or tone having a frequency matching the B-mode transition frequency of the second target qubit 506, the second target qubit 506 does indeed experience Rabi oscillations. Specifically, when the control qubit 502 is in state 0 and driven by a microwave pulse and / or tone matching the B-mode transition frequency of the second target qubit 506, the second target qubit 506 exhibits oscillatory behavior 810. Furthermore, when the control qubit 502 is in state 2 and driven by a microwave pulse and / or tone matching the B-mode transition frequency of the second target qubit 506, the second target qubit 506 exhibits oscillatory behavior 812.

[0108] Thus, as shown in graphs 802 and 804, when the control qubit 502 is driven by a microwave pulse and / or tone matching the B-mode switching frequency of the second target qubit 506, the second target qubit 506 can exhibit Rabi oscillations, and the first target qubit 504 can exhibit non-Rabi oscillation behavior. In other words, the second target qubit 506 can become entangled with the control qubit 502, and the first target qubit 504 can avoid becoming entangled with the control qubit 502. In various respects, this selective cross-resonant entanglement is caused by the first mode-selective coupler 126 coupling the control qubit 502 to the first target qubit 504 and the second mode-selective coupler 302 coupling the control qubit 502 to the second target qubit 506. Furthermore, the fact that the first target qubit 504 and the second target qubit 506 can be degenerate can facilitate this selective cross-resonant entanglement.

[0109] Figure 9 A block diagram of an exemplary non-limiting quantum computing lattice 900, which can facilitate mode-selective couplers for frequency conflict reduction, is shown according to one or more embodiments described herein. In various aspects, Figure 9 It can be shown how the first mode selective coupler 126 and the second mode selective coupler 302 can be implemented across a quantum computing lattice to facilitate selective cross-resonance entanglement.

[0110] In various embodiments, the quantum computing lattice 900 may include dual-junction transport qubits 902, 904, 906, 908, 910, 912, 914, and 916. In various aspects, the dual-junction transport qubits 902, 904, 906, 908, 910, 912, 914, and 916 may be constructed as described above with respect to dual-junction transport qubits 102 and / or 104.

[0111] In various aspects, as shown, the dual-junction transport qubit 908 can be coupled to its adjacent qubits: namely, dual-junction transport qubits 902, 904, 912, and 914. Specifically, dual-junction transport qubit 908 can be coupled to dual-junction transport qubit 902 via the second mode-selective coupler 302, to dual-junction transport qubit 904 via the first mode-selective coupler 126, to dual-junction transport qubit 914 via the second mode-selective coupler 302, and to dual-junction transport qubit 912 via the first mode-selective coupler 126. Therefore, B-mode coupling can be promoted between dual-junction transport qubits 908 and 902, A-mode coupling can be promoted between dual-junction transport qubits 908 and 904, B-mode coupling can be promoted between dual-junction transport qubits 908 and 914, and A-mode coupling can be promoted between dual-junction transport qubits 908 and 912. Similarly, dual-junction transport qubit 910 can be coupled to dual-junction transport qubit 904 via a second mode-selective coupler 302, to dual-junction transport qubit 906 via a first mode-selective coupler 126, to dual-junction transport qubit 916 via a second mode-selective coupler 302, and to dual-junction transport qubit 914 via a first mode-selective coupler 126. This can promote B-mode coupling between the dual-junction transmission qubit 910 and the dual-junction transmission qubit 904, promote A-mode coupling between the dual-junction transmission qubit 910 and the dual-junction transmission qubit 906, promote B-mode coupling between the dual-junction transmission qubit 910 and the dual-junction transmission qubit 916, and promote A-mode coupling between the dual-junction transmission qubit 910 and the dual-junction transmission qubit 914.

[0112] In various respects, the dual-junction transport qubit 908 can be considered as a control qubit with four target qubits: the dual-junction transport qubits 902, 904, 912, and 914. Similarly, in various respects, the dual-junction transport qubit 910 can be considered as a control qubit with four target qubits: the dual-junction transport qubits 904, 906, 914, and 916.

[0113] In various respects, the dual-junction transport qubits 902, 904, and 906 can be degenerate. In various respects, the dual-junction transport qubits 908 and 910 can be degenerate. In various respects, the dual-junction transport qubits 912, 914, and 916 can be degenerate. That is, in various cases, the quantum computing lattice 900 can include three different sets of superconducting qubits instead of five different sets of superconducting qubits. In several different respects, when the first mode-selective coupler 126 and the second mode-selective coupler 302 are implemented, these three different sets of superconducting qubits can be sufficient to facilitate selective cross-resonant entanglement.

[0114] Consider the following example. Suppose that a dual-junction transport qubit 908 is driven by a micro-wave harmonic and / or pulse that matches the A-mode switching frequency of a dual-junction transport qubit 904. In this case, because the micro-wave harmonic and / or pulse matches the A-mode switching frequency of the dual-junction transport qubit 904, and because the dual-junction transport qubit 908 is coupled to the dual-junction transport qubit 904 via a first mode-selective coupler 126, the dual-junction transport qubit 904 can become entangled with the dual-junction transport qubit 908. Note that in this case, the dual-junction transport qubit 902 can avoid becoming entangled with the dual-junction transport qubit 908. After all, the dual-junction transport qubit 908 is coupled to the dual-junction transport qubit 902 via the second mode-selective coupler 302, which prevents A-mode coupling between the dual-junction transport qubit 908 and the dual-junction transport qubit 902. Furthermore, note that in this case, the dual-junction transport qubits 912 and 914 can also avoid becoming entangled with the dual-junction transport qubit 908. After all, the microwave pulse and / or tone has a frequency that does not match the A-mode transition frequency or the B-mode transition frequency of the two junction transport qubits 912 and 914 (e.g., the two junction transport qubits 912 and 914 may not be degenerate with the two junction transport qubits 902 and 904).

[0115] Suppose that the dual-junction transport qubit 908 is instead driven by a micro-wave harmonic and / or pulse that matches the B-mode transition frequency of the dual-junction transport qubit 902. In this case, because the micro-wave harmonic and / or pulse matches the B-mode transition frequency of the dual-junction transport qubit 902, and because the dual-junction transport qubit 908 is coupled to the dual-junction transport qubit 902 by the second mode-selective coupler 302, the dual-junction transport qubit 902 can become entangled with the dual-junction transport qubit 908. Note that in this case, the dual-junction transport qubit 904 can avoid becoming entangled with the dual-junction transport qubit 908. After all, the dual-junction transport qubit 908 is coupled to the dual-junction transport qubit 904 through the first mode-selective coupler 126, which can prevent B-mode coupling between the dual-junction transport qubit 908 and the dual-junction transport qubit 904. Furthermore, note that in this case, the dual-junction transport qubits 912 and 914 can also avoid becoming entangled with the dual-junction transport qubit 908. After all, the microwave pulse and / or tone has a frequency that does not match the A-mode switching frequency or the B-mode switching frequency of the two junction transport qubits 912 and 914 (e.g., the two junction transport qubits 912 and 914 may not be degenerate with the two junction transport qubits 902 and 904).

[0116] Suppose that the dual-junction transport qubit 908 is instead driven by a micro-wave harmonic and / or pulse that matches the A-mode transition frequency of the dual-junction transport qubit 912. In this case, because the micro-wave harmonic and / or pulse matches the A-mode transition frequency of the dual-junction transport qubit 912, and because the dual-junction transport qubit 908 is coupled to the dual-junction transport qubit 912 via the first mode-selective coupler 126, the dual-junction transport qubit 912 can become entangled with the dual-junction transport qubit 908. Note that in this case, the dual-junction transport qubit 914 can avoid becoming entangled with the dual-junction transport qubit 908. After all, the dual-junction transport qubit 908 is coupled to the dual-junction transport qubit 914 via the second mode-selective coupler 302, which can prevent A-mode coupling between the dual-junction transport qubit 908 and the dual-junction transport qubit 914. Furthermore, note that in this case, the dual-junction transport qubits 902 and 904 can also avoid becoming entangled with the dual-junction transport qubit 908. After all, the microwave pulse and / or tone has a frequency that does not match the A-mode conversion frequency or B-mode conversion frequency of the two junction transport qubits 902 and 904 (e.g., the two junction transport qubits 912 and 914 may not be degenerate with the two junction transport qubits 902 and 904).

[0117] Suppose that the dual-junction transport qubit 908 is instead driven by a micro-wave harmonic and / or pulse that matches the B-mode transition frequency of the dual-junction transport qubit 914. In this case, because the micro-wave harmonic and / or pulse matches the B-mode transition frequency of the dual-junction transport qubit 914, and because the dual-junction transport qubit 908 is coupled to the dual-junction transport qubit 914 by the second mode-selective coupler 302, the dual-junction transport qubit 914 can become entangled with the dual-junction transport qubit 908. Note that in this case, the dual-junction transport qubit 912 can avoid becoming entangled with the dual-junction transport qubit 908. After all, the dual-junction transport qubit 908 is coupled to the dual-junction transport qubit 912 through the first mode-selective coupler 126, which can prevent B-mode coupling between the dual-junction transport qubit 908 and the dual-junction transport qubit 912. Furthermore, note that in this case, the dual-junction transport qubits 902 and 904 can also avoid becoming entangled with the dual-junction transport qubit 908. After all, the microwave pulse and / or tone has a frequency that does not match the A-mode conversion frequency or B-mode conversion frequency of the two junction transport qubits 902 and 904 (e.g., the two junction transport qubits 912 and 914 may not be degenerate with the two junction transport qubits 902 and 904).

[0118] Thus, as illustrated in the non-limiting illustrative examples above, selective cross-resonant entanglement can be promoted in the quantum computing lattice 900 using as few as three different sets of superconducting qubits (e.g., a first set of degenerate double-junction transport qubits 902, 904, and 906; a second set of degenerate double-junction transport qubits 908 and 910; and a third set of degenerate double-junction transport qubits 912, 914, and 916). Because fewer different sets of superconducting qubits are required to promote selective cross-resonant entanglement compared to the usual five sets, various embodiments of the present invention can reduce the statistical probability of target-based frequency collisions occurring in the quantum computing lattice 900.

[0119] In various respects, the quantum computing lattice 900 may include any suitable number of superconducting qubits, and / or may be arranged in any suitable shape and / or manner. In various respects, the quantum computing lattice 900 may be fabricated on any suitable quantum computing substrate (e.g., a silicon substrate) using any suitable nanofabrication and / or microfabrication techniques.

[0120] Figure 10 A flowchart is shown of an exemplary non-limiting method 1000 for a mode-selective coupler that facilitates frequency conflict reduction according to one or more embodiments described herein.

[0121] In various embodiments, action 1002 may include providing a control qubit (e.g., 502). Such provision can be facilitated by any suitable microfabrication and / or nanofabrication techniques. The control qubit can be provided on any suitable quantum computing substrate.

[0122] In various embodiments, action 1004 may include coupling the control qubit to a first target qubit (e.g., 504) by a first mode-selective coupler (e.g., 126) that facilitates A-mode coupling.

[0123] In various aspects, action 1006 may include coupling the control qubit to a second target qubit (e.g., 506) by a second mode-selective coupler (e.g., 302) that facilitates B-mode coupling.

[0124] In various embodiments, action 1008 may include driving the control qubit with a first micro-wave modulation corresponding to the A-mode excitation frequency (e.g., the A-mode switching frequency of the first target qubit 504), thereby causing the first target qubit to become entangled with the control qubit.

[0125] In various embodiments, action 1010 may include driving the control qubit with a second micro-wave modulation corresponding to the B-mode excitation frequency (e.g., the B-mode switching frequency of the second target qubit 506), thereby causing the second target qubit to become entangled with the control qubit.

[0126] As illustrated herein, various embodiments of the invention can provide mode-selective coupling between dual-junction transport qubits in a quantum computing lattice, which can allow for independent driving of even degenerate targets using cross-resonant gates. By implementing the mode-selective coupler as illustrated herein, several embodiments of the invention can generate nearest-neighbor connected quantum computing lattices using as few as three different superconducting qubit groups instead of the usual five. This reduction in the number of different groups of qubits can reduce the probability and / or prevalence of target-based frequency collisions occurring in the quantum computing lattice. In various respects, the suppression and / or reduction of target-based frequency collisions can allow for increased yields of multi-qubit devices and reduced levels of crosstalk between qubits.

[0127] In various respects, embodiments of the invention can be implemented in any suitable quantum computing lattice employing any appropriate level of lattice connectivity. For example, in some cases, a second nearest neighbor connected quantum computing lattice can be considered, where all non-peripheral qubits are coupled to eight neighboring qubits. In this case, embodiments of the invention can facilitate selective cross-resonant entanglement with as few as five different sets of qubits, rather than the nine different sets of qubits commonly found when second nearest neighbor connections are included.

[0128] In various aspects, embodiments of the present invention can reduce target-based frequency conflicts by mode-selective coupling between tunable coupler qubits (“TCQs”) in a square lattice. In various aspects, mode-selective coupling can allow driving cross-resonant entangled gates between a type of excitation mode.

[0129] In various aspects, methods for suppressing qubit conflicts in a qubit lattice may include providing tunable coupler qubits (“TCQs”) having at least two junctions arranged in any suitable lattice configuration. The method may further include coupling a TCQ within the lattice to two adjacent TCQs of the lattice via a first type of mode-selective coupling. The method may further include coupling a TCQ within the lattice to two other adjacent TCQs of the lattice via a second type of mode-selective coupling. In various aspects, the first and second types of mode-selective coupling can reduce the set of qubit frequencies required to avoid target-based frequency conflicts.

[0130] To provide additional background for the various embodiments described herein, Figure 11 The following discussion is intended to provide a general description of a suitable computing environment 1100 in which various embodiments of the embodiments described herein may be implemented. While the embodiments have been described above in the general context of computer-executable instructions that can run on one or more computers, those skilled in the art will recognize that the embodiments may also be implemented in combination with other program modules and / or as a combination of hardware and software.

[0131] Typically, program modules include routines, programs, components, data structures, etc., that perform specific tasks or implement specific abstract data types. Furthermore, those skilled in the art will recognize that the methods of this invention can be practiced with other computer system configurations, including single-processor or multi-processor computer systems, minicomputers, mainframe computers, Internet of Things (IoT) devices, distributed computing systems, and personal computers, handheld computing devices, microprocessor-based or programmable consumer electronics, each of which can be operatively coupled to one or more associated devices.

[0132] The embodiments illustrated in this document can also be implemented in a distributed computing environment, where some tasks are performed by remote processing devices linked via a communication network. In a distributed computing environment, program modules can reside on both local and remote storage devices.

[0133] Computing devices typically include a variety of media, which may include computer-readable storage media, machine-readable storage media, and / or communication media, these two terms being used differently from each other herein. A computer-readable storage medium or a machine-readable storage medium can be any available storage medium accessible by a computer, and includes volatile and non-volatile media, removable and non-removable media. By way of example and not limitation, a computer-readable storage medium or a machine-readable storage medium can be implemented in combination with any method or technique used for storing information such as computer-readable or machine-readable instructions, program modules, structured data, or unstructured data.

[0134] Computer-readable storage media may include, but is not limited to: random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, compact disc read-only memory (CDROM), digital universal disc (DVD), Blu-ray disc (BD) or other optical disc storage, magnetic tape cassettes, magnetic tape, disk storage or other magnetic storage devices, solid-state drives or other solid-state storage devices, or other tangible and / or non-transient media that can be used to store desired information. In this regard, the terms “tangible” or “non-transient” as used herein with respect to storage, memory, or computer-readable media shall be understood to exclude only the propagation of transient signals themselves as a modifier, and shall not waive the rights to all standard storage, memory, or computer-readable media that do not only propagate transient signals themselves.

[0135] A computer-readable storage medium can be accessed by one or more local or remote computing devices, for example via access requests, queries or other data retrieval protocols, for various operations with respect to the information stored in the medium.

[0136] Communication media typically embody computer-readable instructions, data structures, program modules, or other structured or unstructured data as data signals such as modulated data signals (e.g., carrier waves or other transmission mechanisms), and include any medium for delivering or transmitting information. The term "modulated data signal" refers to a signal whose characteristics are set or altered in a manner that encodes information in one or more signals. By way of example and not limitation, communication media include wired media, such as wired networks or direct-line connections, and wireless media, such as acoustic, RF, infrared, and other wireless media.

[0137] Refer again Figure 11An exemplary environment 1100 for implementing various embodiments of the aspects described herein includes a computer 1102, which includes a processing unit 1104, system memory 1106, and a system bus 1108. The system bus 1108 couples system components, including but not limited to system memory 1106, to the processing unit 1104. The processing unit 1104 can be any of various commercial processors. Dual microprocessors and other multiprocessor architectures can also be used as the processing unit 1104.

[0138] System bus 1108 can be any of several types of bus structures capable of further interconnecting to a memory bus (with or without a memory controller), a peripheral bus, and a local bus using any of a variety of commercially available bus architectures. System memory 1106 includes ROM 1110 and RAM 1112. The Basic Input / Output System (BIOS) can be stored in non-volatile memory such as ROM, erasable programmable read-only memory (EPROM), or EEPROM. The BIOS contains basic routines such as those that help transfer information between components within computer 1102 during startup. RAM 1112 may also include high-speed RAM, such as static RAM for caching data.

[0139] Computer 1102 further includes an internal hard disk drive (HDD) 1114 (e.g., EIDE, SATA), one or more external storage devices 1116 (e.g., floppy disk drive (FDD) 1116, memory stick or flash drive reader, memory card reader, etc.), and a drive 1120 (e.g., a solid-state drive, optical disc drive, which can read from or write to a disk 1122 such as a CD-ROM, DVD, BD, etc.). Alternatively, in cases involving a solid-state drive, disk 1122 is not included unless it is separate. Although the internal HDD 1114 is shown as being located within computer 1102, the internal HDD 1114 may also be configured for external use in a suitable chassis (not shown). Additionally, although not shown in environment 1100, a solid-state drive (SSD) may be used as a supplement to or replacement for HDD 1114. HDD 1114, external storage device 1116, and drive 1120 can be connected to system bus 1108 via HDD interface 1124, external storage interface 1126, and drive interface 1128, respectively. Interface 1124 for the external drive implementation may include at least one or both of Universal Serial Bus (USB) and Institute of Electrical and Electronics Engineers (IEEE) 1394 interface technologies. Other external drive connection technologies are contemplated in the embodiments described herein.

[0140] The drive and its associated computer-readable storage medium provide non-volatile storage of data, data structures, computer-executable instructions, etc. For computer 1102, the drive and storage medium accommodate any data stored in a suitable digital format. Although the above description of computer-readable storage media refers to a corresponding type of storage device, those skilled in the art will understand that other types of computer-readable storage media (whether currently existing or developed in the future) may also be used in the example operating environment, and further, any such storage medium may contain computer-executable instructions for performing the methods described herein.

[0141] Multiple program modules may be stored in the drive and RAM 1112, including an operating system 1130, one or more application programs 1132, other program modules 1134, and program data 1136. All or part of the operating system, application programs, modules, and / or data may also be cached in RAM 1112. The systems and methods described herein can be implemented using different commercially available operating systems or combinations of operating systems.

[0142] Computer 1102 may optionally include emulation technology. For example, a hypervisor (not shown) or other intermediary may emulate the hardware environment of operating system 1130, and the emulated hardware may optionally be compatible with... Figure 11 The hardware shown is different. In such an embodiment, operating system 1130 may include one of a plurality of virtual machines (VMs) hosted at computer 1102. Furthermore, operating system 1130 may provide a runtime environment, such as the Java Runtime Environment or the .NET Framework, to application 1132. A runtime environment is a consistent execution environment that allows application 1132 to run on any operating system that includes a runtime environment. Similarly, operating system 1130 may support containers, and application 1132 may be in the form of a container, which is a lightweight, standalone, executable software package including, for example, code, runtime, system tools, system libraries, and application settings.

[0143] Furthermore, computer 1102 may enable a security module, such as a Trusted Processing Module (TPM). For example, with a TPM, before loading the boot component, the boot component hashes the boot component in time and waits for the result to match a security value. This process can occur at any layer of the computer 1102's code execution stack, such as at the application execution level or at the operating system (OS) kernel level, thereby achieving security at any code execution level.

[0144] Users can input commands and information into computer 1102 through one or more wired / wireless input devices (e.g., keyboard 1138, touchscreen 1140) and pointing devices (such as mouse 1142). Other input devices (not shown) may include microphones, infrared (IR) remote controls, radio frequency (RF) remote controls, or other remote controls, joysticks, virtual reality controllers and / or virtual reality headsets, game controllers, styluses, image input devices (e.g., cameras), gesture sensor input devices, visual motion sensor input devices, emotion or face detection devices, biometric input devices (e.g., fingerprint or iris scanners), or the like. These and other input devices are typically connected to processing unit 1104 via input device interface 1144, which can be coupled to system bus 1108, but can be connected via other interfaces such as parallel ports, IEEE 1394 serial ports, game ports, USB ports, IR interfaces, etc. Interfaces, etc.

[0145] Monitor 1146 or other types of display devices can also be connected to system bus 1108 via an interface such as video adapter 1148. In addition to monitor 1146, computers typically include other peripheral output devices (not shown), such as speakers, printers, etc.

[0146] Computer 1102 can operate in a networked environment via logical connections to one or more remote computers (such as remote computer 1150) via wired and / or wireless communications. Remote computer 1150 may be a workstation, server computer, router, personal computer, laptop computer, microprocessor-based entertainment device, peer-to-peer device, or other common network node, and typically includes many or all of the elements described relative to computer 1102; however, for brevity, only memory / storage device 1152 is shown. The depicted logical connections include wired / wireless connections to a local area network (LAN) 1154 and / or a larger network such as a wide area network (WAN) 1156. Such LAN and WAN networking environments are common in offices and companies and facilitate enterprise-wide computer networks, such as intranets, all of which can connect to global communication networks, such as the Internet.

[0147] When used in a LAN networking environment, computer 1102 can connect to local area network 1154 via a wired and / or wireless communication network interface or adapter 1158. Adapter 1158 facilitates wired or wireless communication to LAN 1154, which may also include a wireless access point (AP) deployed thereon for communicating with adapter 1158 in wireless mode.

[0148] When used in a WAN networking environment, computer 1102 may include modem 1160 or may be connected to a communication server on WAN 1156 via other means (such as via the Internet) for establishing communication on WAN 1156. Modem 1160, which may be internal or external and wired or wireless, may be connected to system bus 1108 via input device interface 1144. In a networking environment, program modules depicted relative to computer 1102 or portions thereof may be stored in remote memory / storage device 1152. It should be understood that the network connection shown is an example, and other means for establishing communication links between computers may be used.

[0149] When used in a LAN or WAN networking environment, computer 1102 can access cloud storage systems or other network-based storage systems as a supplement to or replacement of the external storage device 1116 described above, such as, but not limited to, network virtual machines providing one or more aspects of information storage or processing. Generally, the connection between computer 1102 and the cloud storage system can be established, for example, via adapter 1158 or modem 1160 through LAN 1154 or WAN 1156. When computer 1102 is connected to the associated cloud storage system, external storage interface 1126 can manage the storage provided by the cloud storage system by means of adapter 1158 and / or modem 1160, as it will manage other types of external storage. For example, external storage interface 1126 can be configured to provide access to cloud storage sources, as if those sources were physically connected to computer 1102.

[0150] Computer 1102 is operable to communicate with any wireless device or entity operably placed in wireless communication, such as a printer, scanner, desktop and / or laptop computer, portable data assistant, communications satellite, any device or location associated with a wirelessly detectable tag (e.g., self-service terminal, newsstand, store shelf, etc.), and telephone. This may include Wi-Fi and Wireless technology. Therefore, communication can be a predefined structure like a traditional network, or simply self-organizing communication between at least two devices.

[0151] This invention can be a system, method, apparatus, and / or computer program product at any possible level of technical detail integration. A computer program product may include a computer-readable storage medium (or media) having computer-readable program instructions thereon for causing a processor to execute aspects of the invention. A computer-readable storage medium may be a tangible device capable of retaining and storing instructions for use by an instruction execution device. A computer-readable storage medium may be, for example, but not limited to, electronic storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination thereof. A non-exhaustive list of more specific examples of computer-readable storage media may also include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disk read-only memory (CD-ROM), digital universal disk (DVD), memory sticks, floppy disks, mechanical encoding devices such as punch cards, or protrusions in slots having instructions recorded thereon, and any suitable combination thereof. As used herein, computer-readable storage media should not be construed as transient signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses passing through fiber optic cables), or electrical signals transmitted through wires.

[0152] The computer-readable program instructions described herein can be downloaded from a computer-readable storage medium to a corresponding computing / processing device via a network (e.g., the Internet, a local area network, a wide area network, and / or a wireless network), or downloaded to an external computer or external storage device. The network may include copper transmission cables, optical transmission fibers, wireless transmissions, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to a computer-readable storage medium within the corresponding computing / processing device. The computer-readable program instructions used to perform the operations of this invention may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, status setting data, integrated circuit configuration data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​(such as Smalltalk, C++, etc.) and procedural programming languages ​​(such as the "C" programming language or similar programming languages). Computer-readable program instructions may execute entirely on a user's computer, partially on a user's computer, as a standalone software package, partially on a user's computer and partially on a remote computer, or entirely on a remote computer or server. In the latter case, the remote computer may be connected to the user's computer via any type of network (including a local area network (LAN) or a wide area network (WAN)) or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuitry including, for example, programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs) may be personalized to execute computer-readable program instructions by utilizing state information of the computer-readable program instructions in order to perform aspects of the present invention.

[0153] The present invention will now be described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It should 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, special-purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions / actions specified in one or more blocks of the flowchart illustrations and / or block diagrams. These computer-readable program instructions can also be stored in a computer-readable storage medium that causes a computer, programmable data processing apparatus, and / or other device to operate in a particular manner, such that the computer-readable storage medium storing the instructions comprises an article of manufacture containing instructions for implementing aspects of the functions / actions specified in one or more blocks of the flowchart illustrations and / or block diagrams. Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operations to be performed on the computer, other programmable apparatus, or other device to produce computer-implemented processing, such that the instructions executed on the computer, other programmable apparatus, or other device perform the functions / actions specified in one or more boxes of a flowchart and / or block diagram.

[0154] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. 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 marked in the blocks may occur in a different order than indicated in the figures. For example, depending on the functions involved, two consecutively shown blocks may actually be executed substantially simultaneously, or these blocks may sometimes be executed in reverse order. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or action or executes a combination of dedicated hardware and computer instructions.

[0155] While the subject matter has been described above in the general context of computer-executable instructions running on a computer and / or a computer program product on a computer, those skilled in the art will recognize that this disclosure can also be implemented in combination with other program modules. Typically, program modules include routines, programs, components, data structures, etc., that perform specific tasks and / or implement specific abstract data types. Furthermore, those skilled in the art will recognize that the computer implementation methods of the present invention can be practiced with other computer system configurations, including single-processor or multi-processor computer systems, small computing devices, mainframe computers, and computers, handheld computing devices (e.g., PDAs, telephones), microprocessor-based or programmable consumer or industrial electronic products, etc. The aspects shown can also be implemented in a distributed computing environment, where tasks are performed by remote processing devices linked via a communication network. However, some (if not all) aspects of the present invention can be practiced on a standalone computer. In a distributed computing environment, program modules can reside in both local and remote memory storage devices.

[0156] As used herein, the terms “component,” “system,” “platform,” “interface,” etc., may refer to and / or include computer-related entities or entities associated with an operating machine having one or more specific functions. 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 file, a thread of execution, a program, and / or a computer. For illustration, both an application running on a server and the server itself can be components. One or more components may reside within a process and / or a thread of execution, and components may reside on a single computer and / or be distributed across two or more computers. In another instance, a corresponding component may be executed from a different computer-readable medium having different data structures stored thereon. Components may communicate via local and / or remote processes, such as according to a signal having one or more data packets (e.g., data from a component interacting with another component in a local system, a distributed system, and / or data from a component interacting with other systems across a network such as the Internet via that signal). As another example, a component may be a device having specific functions provided by mechanical parts operated by electrical or electronic circuitry, which is operated by a software or firmware application executed by a processor. In such a case, the processor can be internal or external to the device and can execute at least a portion of the software or firmware application. As another example, the component can be a device that provides a specific function through electronic components without mechanical parts, wherein the electronic components can include a processor or other means for performing software or firmware that at least partially endows the electronic components with the functions. In one aspect, the component can be emulated via a virtual machine, for example, within a cloud computing system.

[0157] Furthermore, the term "or" is intended to mean an inclusive "or" rather than an exclusive "or." That is, unless otherwise specified or clear from the context, "X adopts A or B" is intended to mean any natural inclusive permutation. That is, if X adopts A; X adopts B; or X adopts both A and B, then "X adopts A or B" is satisfied in any of the foregoing cases. Additionally, the articles "a" and "an" as used in the subject matter specification and figures should generally be interpreted as meaning "one or more," unless otherwise specified or clearly indicated from the context to the singular form. As used herein, the terms "example" and / or "exemplary" are used to indicate that something is used as an instance, example, or illustration. For the avoidance of doubt, the subject matter disclosed herein is not limited to such examples. Furthermore, any aspect or design described herein as an "example" and / or "exemplary" is not necessarily to be construed as superior to or better than other aspects or designs, nor does it imply the exclusion of equivalent exemplary structures and techniques known to those skilled in the art.

[0158] As used herein, the term "processor" can refer to substantially any computing processing unit or device, including but not limited to a single-core processor; a single processor with software multithreading capabilities; a multi-core processor; a multi-core processor with software multithreading capabilities; a multi-core processor with hardware multithreading technology; a parallel platform; and a parallel platform with distributed shared memory. Additionally, "processor" can refer to an integrated circuit, application-specific integrated circuit (ASIC), digital signal processor (DSP), field-programmable gate array (FPGA), programmable logic controller (PLC), 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, processors can utilize nanoscale architectures, such as, but not limited to, molecular and quantum dot-based transistors, switches, and gates, to optimize space utilization or enhance the performance of user equipment. Processors can also be implemented as a combination of computing processing units. In this disclosure, terms such as “storage,” “data storage,” “database,” “database,” and substantially any other information storage component, used in connection with the operation and function of a component, are used to refer to a “memory component,” an entity embodied in “memory,” or a component that includes memory. It should be understood that the memory and / or memory components described herein can be volatile or non-volatile memory, or may include both volatile and non-volatile memory. By way of example and not limitation, non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable ROM (EEPROM), flash memory, or non-volatile random access memory (RAM) (e.g., ferroelectric RAM (FeRAM)). Volatile memory may include, for example, RAM that can act as an external cache memory. By way of illustration and not limitation, RAM may be available in many forms, such as synchronous RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM), direct Rambus, etc. RAM (DRRAM), Direct Rambus Dynamic RAM (DRDRAM), and Rambus Dynamic RAM (RDRAM). Additionally, the memory components of the systems or computer-implemented methods disclosed herein inherently include (but are not limited to) these and any other suitable types of memory.

[0159] The above description includes only examples of systems and computer-implemented methods. Of course, for the purposes of describing this disclosure, it is impossible to describe every conceivable combination of components or computer-implemented method; however, those skilled in the art will recognize that many further combinations and substitutions of this disclosure are possible. Furthermore, the terms “comprising,” “having,” “possessing,” etc., used in the detailed description, claims, appendices, and drawings are intended to be inclusive in a manner similar to the term “including,” since “including” is interpreted as a transitional word in the claims.

[0160] Various embodiments have been described for illustrative purposes, but are not intended to be exhaustive or limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein has been chosen to best explain the principles of the embodiments, their practical application, or technical improvements to technologies found in the market, or to enable those skilled in the art to understand the embodiments disclosed herein.

Claims

1. A device comprising: A control qubit, the control qubit being coupled to a first mode-selective coupler and a second mode-selective coupler; A first target qubit is coupled to a first mode-selective coupler, wherein the first mode-selective coupler allows A-mode coupling between the control qubit and the first target qubit and prevents B-mode coupling between the control qubit and the first target qubit; as well as A second target qubit is coupled to a second mode-selective coupler, wherein the second mode-selective coupler allows B-mode coupling between the control qubit and the second target qubit, and prevents A-mode coupling between the control qubit and the second target qubit.

2. The device according to claim 1, wherein the control qubit, the first target qubit, and the second target qubit are dual-junction transport qubits.

3. The device of claim 2, wherein the first mode-selective coupler includes a capacitor that capacitively couples the intermediate capacitor pad of the control qubit to the intermediate capacitor pad of the first target qubit.

4. The device according to claim 3, wherein the capacitor has a capacitance smaller than the shunt capacitance value of the control qubit and smaller than the shunt capacitance value of the first target qubit.

5. The device of claim 2, and having the features of claim 2, wherein the second mode-selective coupler comprises a first capacitor and a second capacitor, the first capacitor capacitively coupling the end capacitor pad of the control qubit to the end capacitor pad of the second target qubit, and the second capacitor capacitively coupling the end capacitor pad of the control qubit to the intermediate capacitor pad of the second target qubit.

6. The device of claim 5, wherein the first capacitor has a first capacitance smaller than the shunt capacitance value of the control qubit and smaller than the shunt capacitance value of the second target qubit, and wherein the second capacitor has a second capacitance that is half the first capacitance.

7. The device according to claim 1, wherein the first target qubit and the second target qubit are degenerate targets.

8. The device of claim 7, wherein when the control qubit is driven by a first micro-wave modulation corresponding to the A-mode excitation frequency of the degenerate target, the first target qubit is entangled with the control qubit, and wherein when the control qubit is driven by a second micro-wave modulation corresponding to the B-mode excitation frequency of the degenerate target, the second target qubit is entangled with the control qubit.

9. A method comprising: Provides control qubits; The control qubit is coupled to a first target qubit via a first mode-selective coupler, which allows mode A coupling between the control qubit and the first target qubit and prevents mode B coupling between them; and The control qubit is coupled to the second target qubit via a second mode-selective coupler, which allows B-mode coupling between the control qubit and the second target qubit and prevents A-mode coupling between the control qubit and the second target qubit.

10. The method of claim 9, wherein the control qubit, the first target qubit, and the second target qubit are dual-junction transport qubits.

11. The method of claim 10, wherein the first mode-selective coupler comprises a capacitor capacitively coupling an intermediate capacitor pad of the control qubit to an intermediate capacitor pad of the first target qubit.

12. The method of claim 11, wherein the capacitor has a capacitance smaller than the shunt capacitance of the control qubit and smaller than the shunt capacitance of the first target qubit.

13. The method of claim 10, wherein the second mode-selective coupler comprises a first capacitor and a second capacitor, the first capacitor capacitively coupling the end capacitor pad of the control qubit to the end capacitor pad of the second target qubit, and the second capacitor capacitively coupling the end capacitor pad of the control qubit to the middle capacitor pad of the second target qubit.

14. The method of claim 13, wherein the first capacitor has a first capacitance, the first capacitance being less than the shunt capacitance of the control qubit and less than the shunt capacitance of the second target qubit, and wherein the second capacitor has a second capacitance, the second capacitance being half the first capacitance.

15. The method of claim 9, wherein the first target qubit and the second target qubit are degenerate targets.

16. The method of claim 15, further comprising: The control qubit is driven by a first micro-wave modulation of the A-mode excitation frequency corresponding to the degeneracy target, thereby causing the first target qubit to become entangled with the control qubit. as well as The control qubit is driven by a second micro-wave modulation of the B-mode excitation frequency corresponding to the degenerate target, thereby causing the second target qubit to become entangled with the control qubit.

17. An apparatus comprising: Control qubits; A first mode-selective coupler, which allows mode A coupling between the control qubit and the first target qubit and prevents mode B coupling between the control qubit and the first target qubit; as well as A second mode-selective coupler allows B-mode coupling between the control qubit and the second target qubit and prevents A-mode coupling between the control qubit and the second target qubit. The second mode-selective coupler couples the end capacitor pad of the control qubit to the middle capacitor pad of the second target qubit.

18. The apparatus of claim 17, wherein the first mode-selective coupler includes a capacitor that couples an intermediate capacitor pad of the control qubit to an intermediate capacitor pad of the first target qubit, wherein the capacitance of the capacitor is less than the shunt capacitance of the control qubit and less than the shunt capacitance of the second target qubit.

19. The apparatus of claim 17, wherein the second mode-selective coupler comprises a first capacitor and a second capacitor, the first capacitor coupling an end capacitor pad of the control qubit to an end capacitor pad of the second target qubit, the second capacitor coupling the end capacitor pad of the control qubit to an intermediate capacitor pad of the second target qubit, wherein a first capacitance of the first capacitor is less than the shunt capacitance of the control qubit and less than the shunt capacitance of the second target qubit, and wherein a second capacitance of the second capacitor is half the first capacitance.

20. The apparatus of claim 17, wherein the first target qubit and the second target qubit are degenerate targets, wherein the first target qubit is entangled with the control qubit when the control qubit is driven by a first micro-wave modulation corresponding to the A-mode excitation frequency of the degenerate target, and wherein the second target qubit is entangled with the control qubit when the control qubit is driven by a second micro-wave modulation corresponding to the B-mode excitation frequency of the degenerate target.

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