Multiresonant coupling architecture for reducing ZZ interaction

Abstract

Systems and techniques are provided to facilitate multi-resonant couplers that maintain ZX interactions while reducing ZZ interactions. In various embodiments, a first qubit may have a first operating frequency and a second qubit may have a second operating frequency, and the multi-resonant architecture may couple the first qubit to the second qubit.

Description

Technical Field

[0001] This disclosure generally relates to superconducting qubits, and more specifically to a multi-resonant coupling architecture that reduces ZZ interactions between superconducting qubits while achieving cross-resonant gates through ZX interactions. Background Technology

[0002] Quantum computing systems can be constructed from various arrangements of superconducting qubits. In various instances, the qubits can have a fixed operating frequency (e.g., a transmon-type qubit with a single Josephson junction can have a fixed operating frequency) and can be arranged in a two-dimensional array on any suitable quantum computing substrate. In various aspects, any qubit in such a two-dimensional array can be coupled to some and / or all of its nearest-neighbor qubits, and / or to some and / or all of its second-nearest-neighbor qubits.

[0003] Conventionally, qubits are coupled together via microwave resonators of a fixed frequency (e.g., bus resonators). That is, the first and second qubits are conventionally coupled by a single fixed-frequency resonator, wherein a first end of the single fixed-frequency resonator is capacitively coupled to the first qubit, and a second end of the single fixed-frequency resonator is capacitively coupled to the second qubit. Such coupling allows the first and second qubits to exhibit strong ZX interactions and / or high coherence from cross-resonance, which can improve the operation of the entire quantum computing system. In various instances, qubit devices comprising more than 50 qubits have been successfully implemented based on such cross-resonance interactions, where these qubits are driven by micro-tuning at the frequencies of adjacent qubits.

[0004] However, a significant drawback of conventional couplers is that they introduce always-on ZZ interactions between the coupled qubits. This weak ZZ error accumulates between any pair of conventionally coupled qubits and erodes the desired cross-resonance mechanism used for two-qubit gates. In other words, this ZZ error suppresses the effectiveness and / or performance of quantum computing systems. Conventional systems and / or techniques for handling always-on ZZ errors include echoing and tunable frequency coupling elements. Echoing involves using additional pulses to cancel the ZZ interaction. However, these pulses take time to materialize, which can significantly consume the coherence budget due to the finite coherence time. Tunable frequency couplers can be used to reduce and / or eliminate ZZ interactions. However, adding tunable frequency elements to quantum computing systems often leads to coherence degradation. In other words, conventional systems and / or techniques for reducing always-on ZZ interactions have a corresponding negative impact on coherence time.

[0005] In various instances, embodiments of the present invention can solve one or more of the problems in the prior art. Summary of the Invention

[0006] 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 multi-resonant coupling architectures for reducing ZZ interactions.

[0007] According to one or more embodiments, a device is provided. The device may include a first qubit, a second qubit, and a multi-resonant architecture. In various aspects, the multi-resonant architecture may include a first resonator capacitively coupling the first qubit to the second qubit and a second resonator capacitively coupling the first qubit to the second qubit. In various embodiments, the first qubit may have a first operating frequency, and the second qubit may have a second operating frequency. In various cases, the first resonator may have a first resonant frequency lower than both the first and second operating frequencies. In various aspects, the second resonator may have a second resonant frequency greater than both the first and second operating frequencies. In various embodiments, the first and second resonators may be λ / 2 resonators, and the first and second resonators may be connected in parallel. In various embodiments, the first resonant frequency may be about 3 gigahertz (GHz), the second resonant frequency may be about 6 GHz, and the first and second operating frequencies may be between 4.5 GHz and 5.5 GHz. In various instances, the first resonant frequency, the second resonant frequency, the first operating frequency, and the second operating frequency may be fixed.

[0008] According to one or more embodiments, a device is provided. The device may include a first qubit, a second qubit, and a multi-resonance architecture. In various aspects, the multi-resonance architecture may include a resonator. In various instances, a first end of the resonator may be capacitively coupled to the first and second qubits. In various aspects, a second end of the resonator may be coupled to ground. In various embodiments, the first qubit may have a first operating frequency, and the second qubit may have a second operating frequency. In various cases, the resonator may have a first harmonic frequency less than both the first and second operating frequencies. In various aspects, the resonator may have a second harmonic frequency greater than both the first and second operating frequencies. In various embodiments, the resonator may be a λ / 4 resonator. In various embodiments, the first harmonic frequency may be about 2 GHz, the second harmonic frequency may be about 6 GHz, and the first and second operating frequencies may be between 4.5 GHz and 5.5 GHz. In various instances, the first harmonic frequency, the second harmonic frequency, the first operating frequency, and the second operating frequency may be fixed.

[0009] According to one or more embodiments, a device is provided. The device may include a first qubit, a second qubit, and a multi-resonant architecture. In various aspects, the multi-resonant architecture may include a resonator and a differential direct coupler. In various instances, the resonator may capacitively couple the first qubit to the second qubit, and the differential direct coupler may capacitively couple the first qubit to the second qubit. In various cases, the differential direct coupler may capacitively couple the opposite pads of the first qubit and the second qubit. In various embodiments, the first qubit may have a first operating frequency, and the second qubit may have a second operating frequency. In various cases, the resonator may have a resonant frequency greater than both the first and second operating frequencies. In various embodiments, the resonator may be a λ / 2 resonator, and the resonator and the differential direct coupler may be connected in parallel. In various embodiments, the resonant frequency may be approximately 6 gigahertz (GHz), and the first and second operating frequencies may be between 4.5 GHz and 5.5 GHz. In various instances, the resonant frequency, the first operating frequency, and the second operating frequency may be fixed.

[0010] According to one or more embodiments, a device is provided. The device may include a first qubit, a second qubit, and a multi-resonant architecture. In various aspects, the multi-resonant architecture may include a resonator and a direct coupler. In various instances, a first end of the resonator may be capacitively coupled to the first and second qubits, and a second end of the resonator may be coupled to ground. In various aspects, the direct coupler may capacitively couple the first qubit to the second qubit. In various cases, the direct coupler may capacitively couple a common pad of the first and second qubits. In various embodiments, the first qubit may have a first operating frequency, and the second qubit may have a second operating frequency. In various cases, the resonator may have a resonant frequency greater than both the first and second operating frequencies. In various embodiments, the resonator may be a λ / 4 resonator. In various embodiments, the resonant frequency may be approximately 6 gigahertz (GHz), and the first and second operating frequencies may be between 4.5 GHz and 5.5 GHz. In various instances, the resonant frequency, the first operating frequency, and the second operating frequency may be fixed.

[0011] According to one or more embodiments, an apparatus is provided. The apparatus may include a first transmon-type qubit having a first operating frequency, a second transmon-type qubit having a second operating frequency, and a multi-resonant architecture. In various aspects, the multi-resonant architecture may capacitively couple the first transmon-type qubit to the second transmon-type qubit. In various instances, the multi-resonant architecture may have a first resonant frequency less than both the first and second operating frequencies, and may have a second resonant frequency greater than both the first and second operating frequencies. In various embodiments, the multi-resonant architecture may include a first λ / 2 resonator capacitively coupled to the first and second transmon-type qubits, wherein the first λ / 2 resonator exhibits the first resonant frequency. In various instances, the multi-resonant architecture may include a second λ / 2 resonator capacitively coupled to the first and second transmon-type qubits, wherein the second λ / 2 resonator exhibits the second resonant frequency. In various cases, the first and second λ / 2 resonators may be connected in parallel. In various other embodiments, the multi-resonant architecture may include a λ / 4 resonator. In various instances, the first terminal of the λ / 4 resonator can be coupled between a coupling capacitor for the first transmon qubit and a coupling capacitor for the second transmon qubit, and the second terminal of the λ / 4 resonator can be shorted to ground. In various cases, the first harmonic of the λ / 4 resonator can be the first resonant frequency, and the second harmonic of the λ / 4 resonator can be the second resonant frequency.

[0012] As described above, a pair of fixed-frequency qubits are conventionally coupled together via a fixed-frequency microwave resonator. Specifically, for the first and second qubits, the first end of the fixed-frequency microwave resonator is capacitively coupled to the first qubit, and the second end is capacitively coupled to the second qubit. This coupling structure can lead to high coherence and / or strong ZX interactions between the first and second qubits. However, this coupling structure also generates a persistent ZZ interaction between the first and second qubits. This ZZ interaction can negatively affect the performance of the quantum computing system comprising the first and second qubits. Therefore, eliminating, minimizing, suppressing, and / or reducing this ZZ interaction can improve the operation of the quantum computing system.

[0013] As described above, there are two main conventional systems and / or techniques for suppressing and / or reducing ZZ interactions. The first conventional system and / or technique is echoing. Echoing involves injecting additional pulses into the quantum computing system to resist, cancel, and / or destructively interfere with the ZZ interaction. However, injecting these pulses takes time, and the time spent injecting them can consume the coherence budget of the quantum computing system. The second conventional system and / or technique for handling ZZ interactions is using tunable frequency elements. Introducing tunable frequency elements into the quantum computing system can eliminate and / or reduce ZZ interactions. However, the use and / or complexity of tunable frequency elements introduce a corresponding degradation in coherence. In other words, conventional systems and / or techniques reduce ZZ interactions between a pair of coupled qubits at the cost of reduced coherence time.

[0014] Various embodiments of the present invention can address one or more of the problems in the prior art. In various aspects, embodiments of the present invention can provide a multiresonant coupling architecture that can couple a first qubit to a second qubit. In various instances, such a multiresonant coupling architecture can reduce ZZ interactions between the first and second qubits without reducing the coupling strength and / or ZX interactions between the first and second qubits. In various instances, such a multiresonant coupling architecture can include fixed-frequency and / or untunable elements, and therefore such a multiresonant coupling architecture can avoid introducing the coherence degradation typically associated with tunable-frequency elements into the quantum computing system. Furthermore, in various aspects, such a multiresonant coupling architecture can eliminate the need for echo injection into the quantum computing system. In other words, unlike conventional systems and / or techniques, various embodiments of the present invention can provide a multiresonant coupling architecture that can reduce ZZ interactions between coupled qubits without introducing a corresponding reduction in coherence time.

[0015] Various multi-resonant coupling architectures can be implemented to achieve these improved results. Consider a first qubit having a first operating frequency and a second qubit having a second operating frequency. In some embodiments, the multi-resonant coupling architecture may include a first λ / 2 resonator and a second λ / 2 resonator. In various instances, a first end of the first λ / 2 resonator may be coupled to a first coupling capacitor of the first qubit, and a second end of the first λ / 2 resonator may be coupled to a first coupling capacitor of the second qubit. Similarly, a first end of the second λ / 2 resonator may be coupled to a second coupling capacitor of the first qubit, and a second end of the second λ / 2 resonator may be coupled to a second coupling capacitor of the second qubit. In other words, the first λ / 2 resonator can capacitively couple the first qubit to the second qubit, and the second λ / 2 resonator can capacitively couple the first qubit to the second qubit, such that the first λ / 2 resonator and the second λ / 2 resonator are in parallel. In various instances, the first λ / 2 resonator may exhibit a first resonant frequency that is lower than both the first and second operating frequencies. In various aspects, the second λ / 2 resonator may exhibit a second resonant frequency that is higher than both the first and second operating frequencies. Furthermore, in various aspects, the first and second resonant frequencies can be fixed. In various embodiments, such a multi-resonant coupling architecture can reduce (e.g., in some cases, by orders of magnitude and / or more) the ZZ interaction between the first and second qubits without correspondingly reducing the coupling strength and / or cross-resonant gate velocity between the first and second qubits. Moreover, such a multi-resonant coupling architecture avoids introducing coherence degradation (e.g., echo and / or tunable frequency elements may not be required).

[0016] In other embodiments, the multi-resonant coupling architecture may include a λ / 4 resonator. In various aspects, a first end of the λ / 4 resonator may be coupled to a coupling capacitor of a first qubit, and the first end of the λ / 4 resonator may also be coupled to a coupling capacitor of a second qubit. That is, in various aspects, the first end of the λ / 4 resonator may be capacitively coupled to both the first and second qubits. In various instances, the second end of the λ / 4 resonator may be coupled to ground. In various aspects, the λ / 4 resonator may exhibit a first harmonic frequency lower than both the first and second operating frequencies. In various instances, the λ / 4 resonator may exhibit a second harmonic frequency higher than both the first and second operating frequencies. Furthermore, in various aspects, the first and second harmonic frequencies may be fixed. In various embodiments, such a multi-resonant coupling architecture can reduce (e.g., in some cases, by orders of magnitude and / or more) the ZZ interaction between the first and second qubits without correspondingly reducing the coupling strength and / or cross-resonant gate velocity between the first and second qubits. Furthermore, this multi-resonant coupling architecture avoids introducing coherence degradation (e.g., echo and / or tunable frequency elements may not be required).

[0017] In other embodiments, the multi-resonant coupling architecture may include a λ / 2 resonator and a differential direct coupler. In various instances, a first end of the λ / 2 resonator may be coupled to a first coupling capacitor of a first qubit, and a second end of the λ / 2 resonator may be coupled to a first coupling capacitor of a second qubit. Similarly, a first end of the differential direct coupler may be coupled to a second coupling capacitor of a first qubit, and a second end of the differential direct coupler may be coupled to a second coupling capacitor of a second qubit. In other words, the λ / 2 resonator can capacitively couple the first qubit to the second qubit, and the differential direct coupler can capacitively couple the first qubit to the second qubit, such that the λ / 2 resonator and the differential direct coupler are connected in parallel. In various aspects, the differential direct coupler may couple the opposite pads of the first qubit and the second qubit. In various cases, the λ / 2 resonator may exhibit a resonant frequency greater than a first operating frequency and greater than a second operating frequency. Furthermore, in various aspects, the resonant frequency may be fixed. In various embodiments, such a multi-resonant coupling architecture can reduce (e.g., in some cases, by orders of magnitude and / or more) the ZZ interaction between the first and second qubits without correspondingly reducing the coupling strength and / or cross-resonant gate velocity between the first and second qubits. Furthermore, this multi-resonant coupling architecture avoids introducing coherence degradation (e.g., echo and / or tunable frequency elements may not be required).

[0018] In other embodiments, the multi-resonant coupling architecture may include a λ / 4 resonator and a direct coupler. In various aspects, a first end of the λ / 4 resonator may be coupled to a first coupling capacitor of a first qubit, and the first end of the λ / 4 resonator may also be coupled to a first coupling capacitor of a second qubit. That is, in various aspects, the first end of the λ / 4 resonator may be capacitively coupled to both the first and second qubits. In various instances, the second end of the λ / 4 resonator may be coupled to ground. In various cases, the first end of the direct coupler may be coupled to a second coupling capacitor of the first qubit, and the second end of the direct coupler may be coupled to a second coupling capacitor of the second qubit. In various cases, the direct coupler may couple the common pad of the first and second qubits. In various aspects, the λ / 4 resonator may exhibit a resonant frequency greater than a first operating frequency and greater than a second operating frequency. Furthermore, in various aspects, the resonant frequency may be fixed. In various embodiments, such a multi-resonant coupling architecture can reduce (e.g., in some cases, by orders of magnitude and / or more) the ZZ interaction between the first and second qubits without correspondingly reducing the coupling strength and / or cross-resonant gate velocity between the first and second qubits. Furthermore, this multi-resonant coupling architecture avoids introducing coherence degradation (e.g., echo and / or tunable frequency elements may not be required).

[0019] Therefore, unlike conventional systems and / or techniques, various embodiments of the present invention can provide a multi-resonant coupling architecture that can reduce ZZ interactions between coupled qubits without correspondingly reducing coherence time. Thus, various embodiments of the present invention constitute a substantial technical improvement over the prior art. Attached Figure Description

[0020] Figure 1 A block diagram of an example non-limiting system comprising two resonators that promotes the reduction of ZZ interactions according to one or more embodiments described herein is shown.

[0021] Figure 2 A block diagram of an example non-limiting system including a resonator that promotes the reduction of ZZ interactions according to one or more embodiments described herein is shown.

[0022] Figure 3 A block diagram of an example non-limiting system comprising a resonator and a differential direct coupler that facilitates the reduction of ZZ interactions according to one or more embodiments described herein is shown.

[0023] Figure 4 A block diagram of an example non-limiting system comprising a resonator and a direct coupler is shown, which facilitates the reduction of ZZ interactions according to one or more embodiments described herein.

[0024] Figures 5-6 Example non-limiting graphs are shown depicting the reduction of ZZ interactions facilitated by one or more embodiments described herein.

[0025] Figure 7 A block diagram of an example non-limiting qubit array that promotes the reduction of ZZ interactions according to one or more embodiments described herein is shown.

[0026] Figure 8 A flowchart illustrating an example non-limiting method comprising two resonators for promoting the reduction of ZZ interactions according to one or more embodiments described herein is shown.

[0027] Figure 9 A flowchart illustrating an example non-limiting method comprising a resonator for promoting the reduction of ZZ interactions according to one or more embodiments described herein is shown.

[0028] Figure 10 A flowchart illustrating an example non-limiting method comprising a resonator and a differential direct coupler for promoting the reduction of ZZ interactions according to one or more embodiments described herein.

[0029] Figure 11 A flowchart illustrating an example non-limiting method comprising a resonator and a direct coupler for promoting the reduction of ZZ interactions according to one or more embodiments described herein.

[0030] Figure 12 A flowchart illustrating an example non-limiting method for promoting the reduction of ZZ interactions according to one or more embodiments described herein.

[0031] Figure 13 A block diagram illustrating an example non-limiting operating environment that may facilitate one or more embodiments described herein is shown. Detailed Implementation

[0032] 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 bound by any express or implied information presented in the prior art or invention description section or the detailed description section.

[0033] 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 clear that one or more embodiments may be practiced without these specific details in various circumstances.

[0034] As in conventional systems and / or techniques, consider two transmon-type qubits coupled by a bus resonator of a fixed frequency. The coupling strength can be quantized by the exchange coupling J, which can be given by the following equation:

[0035]

[0036] Where Δ1 is the difference between the operating frequency of the first transmon qubit and the resonant frequency of the fixed-frequency bus resonator, Δ2 is the difference between the operating frequency of the second transmon qubit and the resonant frequency of the fixed-frequency bus resonator, g1 is the coupling strength between the first transmon qubit and the fixed-frequency bus resonator, and g2 is the coupling strength between the second transmon qubit and the fixed-frequency bus resonator. Also consider two transmon qubits coupled by a direct coupler; a direct coupler is any suitable, short transmission line segment (e.g., short in the sense that its resonant frequency is greater than about 30 GHz), which can produce coupling independent of the qubit frequency at the typical transmon qubit frequency of about 5 GHz. In this case, the qubit coupling is also given by a specific value of J determined by the geometry of the direct coupler. In both examples, the Hamiltonian H of these conventionally coupled qubits (e.g., coupled by a single fixed-frequency microwave resonator or two qubits coupled by a direct coupler) can be described by the following equation:

[0037]

[0038] Where i can take the value 1 or 2 to represent the first transmon type qubit or the second transmon type qubit, and ω i It is the resonant frequency of the i-th transmon-type qubit, where α represents the number of excitations in the i-th transmon type qubit, where α i It is the anharmonicity of the i-th transmon-type qubit, and in which This indicates the exchange coupling between qubit 1 and qubit 2. It is the annihilation operator of the i-th qubit, and (This is the i-th qubit generating operator). In this Hamiltonian, the always-on ZZ interaction can be given as:

[0039]

[0040] Where Δ represents the detuning between the two qubits, and all other symbols are defined in the two equations above. This arises from the fact that the sum of the energies of the |00> and |11> states of the two transmon qubits differs from the sum of the energies of the |01> and |10> states. While a low ZZ interaction between the two transmon qubits is desirable, a high coupling strength between them is also desirable, because conversely, the ZX interaction from qubit 1 to qubit 2 (e.g., the strength of cross-resonance) is given by the following:

[0041]

[0042] Where J, α1, and Δ are as defined above, and Ω1 is the cross-resonance drive intensity applied to qubit 1. As shown in the equations above, one way to increase the ratio of ZX to ZZ (i.e., to increase the ratio of desired to unwanted interactions) is to decrease J. However, this increases the total gate operation time, resulting in a degradation in fidelity due to loss of coherence.

[0043] As described above, conventional systems and / or techniques for reducing, suppressing, eliminating, and / or minimizing ZZ interactions without reducing, suppressing, eliminating, and / or minimizing ZX interactions implement echo-emitting and / or tunable frequency elements. Echo-emitting involves injecting multiple pulse signals into the quantum computing system to resist, cancel, cancel, correct, and / or destructively interfere with ZZ interactions. However, time is required to inject such pulse signals into the quantum computing system, and this time can consume the already finite coherence budget of the quantum computing system. Tunable frequency elements can be used to improve ZZ interactions. However, tunable frequency elements are also associated with coherence degradation. Thus, conventional systems and / or techniques reduce ZZ interactions at the expense of reducing coherence time. However, various embodiments of the present invention can reduce ZZ interactions without correspondingly reducing coherence time.

[0044] The inventors of various embodiments of the present invention recognize that, in various instances, the ZZ interaction can be reduced and / or canceled while maintaining the finite J by incorporating a second coupler mode. In various instances, the Hamiltonian H when the second coupler mode is incorporated can be described by the following equation:

[0045]

[0046] Where i can take the value 1 or 2 to represent the first transmon type qubit or the second transmon type qubit, and ω i α i , As defined above, j is the summation over the number of resonator modes that couple the first transmon type qubit to the second transmon type qubit, where γ j It is the frequency of the resonator mode, where It is the number of excitations in the resonator mode, where g ij This represents the coupling between the i-th transmon-type qubit and the coupler mode j, and where... This represents the exchange between the i-th transmon-type qubit and the coupler mode j. In this form, the remaining J0 coupling terms are due to the direct coupler (if present).

[0047] Various embodiments of the present invention can provide a multi-resonant coupling architecture that reduces ZZ interactions between two qubits while maintaining finite exchange coupling J without a corresponding reduction in coherence time. Again, consider a first qubit with a first operating frequency and a second qubit with a second operating frequency. In various aspects, the multi-resonant architecture can capacitively couple the first qubit to the second qubit. In various instances, the multi-resonant architecture can have a first pole greater than both the first and second operating frequencies. In various instances, the multi-resonant architecture can have a second pole less than both the first and second operating frequencies. In various cases, the multi-resonant architecture can have a direct coupling term (e.g., a direct coupler capacitively coupling the first qubit to the second qubit) instead of a second pole. In various instances, the multi-resonant architecture can exhibit zero ZZ interactions and zero exchange coupling J at the first set of qubit frequencies. In various aspects, the multi-resonant architecture can exhibit zero ZZ interactions and non-zero exchange coupling J at the second set of qubit frequencies. In various cases, the multi-resonant architecture can be untunable.

[0048] In various embodiments, the multi-resonant architecture may include a first resonator and a second resonator. In various instances, the first resonator may capacitively couple a first qubit to a second qubit. That is, a first end of the first resonator may be coupled to a first coupling capacitor of the first qubit, and a second end of the first resonator may be coupled to a first coupling capacitor of the second qubit. Similarly, the second resonator may capacitively couple a first qubit to a second qubit. That is, a first end of the second resonator may be coupled to a second coupling capacitor of the first qubit, and a second end of the second resonator may be coupled to a second coupling capacitor of the second qubit. In various instances, the first resonator may be connected in parallel with the second resonator. In various aspects, both the first and second resonators may be λ / 2 resonators. In various instances, the first resonator may have a first resonant frequency that is less than a first operating frequency of the first qubit and less than a second operating frequency of the second qubit. In various cases, the second resonator may have a second resonant frequency that is greater than the first operating frequency of the first qubit and greater than the second operating frequency of the second qubit. In various instances, the first resonant frequency can be approximately 3 GHz, the second resonant frequency can be approximately 6 GHz, and the first and second operating frequencies can be in the range of 4.5 GHz to 5.5 GHz. In various instances, the first resonator and / or the second resonator can be non-tunable. In various aspects, such a multi-resonant architecture can reduce (e.g., in some cases, by orders of magnitude and / or more) the ZZ interaction between the first and second qubits, without correspondingly reducing the ZX interaction and / or exchange coupling J between the first and second qubits. Furthermore, such a multi-resonant architecture can achieve this result without implementing multi-pulse echoes and / or without tunable frequency elements. Thus, such a multi-resonant architecture can reduce ZZ interactions in various instances without the accompanying coherence degradation of conventional systems and / or techniques.

[0049] In various other embodiments, the multi-resonant architecture may include a resonator. In various instances, a first end of the resonator may be capacitively coupled to a coupling capacitor of a first qubit and capacitively coupled to a coupling capacitor of a second qubit. That is, the first end of the resonator may be capacitively coupled to both the first and second qubits. In various instances, a second end of the resonator may be coupled to ground. In various aspects, the resonator may be a λ / 4 resonator. In various instances, the resonator may have a first harmonic frequency that is less than a first operating frequency of the first qubit and less than a second operating frequency of the second qubit. In various cases, the resonator may have a second harmonic frequency that is greater than the first operating frequency of the first qubit and greater than the second operating frequency of the second qubit. In various instances, the first harmonic frequency may be about 2 GHz, the second harmonic frequency may be about 6 GHz, and the first and second operating frequencies may be in the range of 4.5 GHz to 5.5 GHz. In various instances, the resonator may be non-tunable. In various respects, such a multiresonant architecture can reduce (e.g., in some cases, by orders of magnitude and / or more) the ZZ interaction between the first and second qubits, without correspondingly reducing the ZX interaction and / or exchange coupling J between the first and second qubits. Furthermore, such a multiresonant architecture can achieve this result without implementing multipulse echoes and / or without tunable frequency elements. Thus, such a multiresonant architecture can reduce ZZ interactions in various instances without the accompanying coherence degradation of conventional systems and / or techniques.

[0050] In various other embodiments, the multi-resonant architecture may include a resonator and a differential direct coupler. In various instances, the resonator may capacitively couple a first qubit to a second qubit. That is, a first end of the resonator may be coupled to a first coupling capacitor of the first qubit, and a second end of the resonator may be coupled to a first coupling capacitor of the second qubit. Similarly, in various instances, the differential direct coupler may capacitively couple a first qubit to a second qubit. That is, a first end of the differential direct coupler may be coupled to a second coupling capacitor of the first qubit, and a second end of the differential direct coupler may be coupled to a second coupling capacitor of the second qubit. In various instances, the differential direct coupler may couple the first qubit and the second qubit together at opposite pads. In various cases, the resonator may be connected in parallel with the differential direct coupler. In various aspects, the resonator may be a λ / 2 resonator. In various instances, the resonator may have a resonant frequency greater than a first operating frequency of the first qubit and greater than a second operating frequency of the second qubit. In various instances, the resonant frequency can be approximately 6 GHz, and the first and second operating frequencies can range from 4.5 GHz to 5.5 GHz. In various instances, the resonator can be non-tunable. In various aspects, the differential direct coupler can be any suitable, short transmission line segment (e.g., short in the sense that its resonant frequency is greater than approximately 30 GHz), which can produce frequency-independent coupling at a typical transmon-type qubit frequency of approximately 5 GHz. In various aspects, such a multi-resonant architecture can reduce (e.g., in some cases, by orders of magnitude and / or more) the ZZ interaction between the first and second qubits without correspondingly reducing the ZX interaction and / or exchange coupling J between the first and second qubits. Furthermore, such a multi-resonant architecture can achieve this result without implementing multi-pulse echoes and / or without tunable frequency elements. Thus, such a multi-resonant architecture can reduce ZZ interactions in various instances without the associated coherence degradation of conventional systems and / or techniques.

[0051] In various other embodiments, the multi-resonant architecture may include a resonator and a direct coupler. In various instances, a first end of the resonator may be capacitively coupled to both a first qubit and a second qubit. That is, the first end of the resonator may be coupled to a first coupling capacitor of the first qubit, and the first end of the resonator may also be coupled to a first coupling capacitor of the second qubit. In various aspects, the direct coupler may capacitively couple the first qubit to the second qubit. That is, a first end of the direct coupler may be coupled to a second coupling capacitor of the first qubit, and a second end of the direct coupler may be coupled to a second coupling capacitor of the second qubit. In various instances, the direct coupler may couple the common pads of the first and second qubits together. In various aspects, the resonator may be a λ / 4 resonator. In various instances, the resonator may have a resonant frequency greater than a first operating frequency of the first qubit and greater than a second operating frequency of the second qubit. In various instances, the resonant frequency may be approximately 6 GHz, and the first and second operating frequencies may be in the range of 4.5 GHz to 5.5 GHz. In various instances, the resonator may be non-tunable. In various respects, the direct coupler can be any suitable, short transmission line segment (e.g., short in the sense that its resonant frequency is greater than about 30 GHz), which can produce frequency-independent coupling at a typical transmon-type qubit frequency of about 5 GHz. In various respects, such a multiresonant architecture can reduce (e.g., in some cases, by orders of magnitude and / or more) the ZZ interaction between the first and second qubits, without correspondingly reducing the ZX interaction and / or exchange coupling J between the first and second qubits. Furthermore, such a multiresonant architecture can achieve this result without implementing multipulse echoes and / or without tunable frequency elements. Thus, such a multiresonant architecture can reduce ZZ interactions in various instances without the accompanying coherence degradation of conventional systems and / or techniques.

[0052] Various embodiments of the present invention include novel systems and / or techniques for promoting multiresonant coupling architectures for reducing ZZ interactions, which are not abstract, not natural phenomena, not natural laws, and cannot be performed by humans as a set of mental actions. Instead, various embodiments of the present invention include systems and / or techniques for promoting the reduction of ZZ interactions that do not correspondingly reduce ZX interactions and / or exchange coupling J, do not require multipulse echoes, and / or do not require tunable frequency elements. Reduction of ZX interactions negatively impacts the performance of quantum computing systems. Furthermore, implementing echoes and / or tunable frequency elements negatively impacts the coherence budget of quantum computing systems. Because various embodiments of the present invention can reduce ZZ interactions without correspondingly reducing ZX interactions and without requiring the implementation of echoes and / or tunable frequency elements, they can reduce unwanted ZZ interactions while maintaining non-zero exchange coupling J without the coherence degradation typically associated with conventional systems and / or techniques. In other words, embodiments of the present invention provide novel qubit coupling architectures that can be implemented in quantum computing systems (e.g., on quantum computing chips / substrates) to improve the performance and / or operation of quantum computing systems. Therefore, the various embodiments of the present invention constitute substantial technical improvements over the prior art.

[0053] 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.

[0054] Figure 1 A block diagram of an example non-limiting system 100 comprising two resonators, which can facilitate the reduction of ZZ interactions according to one or more embodiments described herein, is shown. As illustrated, in various aspects, system 100 may include a first qubit 102 and a second qubit 104. Figure 1 As shown, the first qubit 102 can be a fixed-frequency transmon-type qubit. That is, the first qubit 102 can include a Josephson junction 118 shunt by capacitor 120. However, in various instances, the first qubit 102 can be any suitable type of superconducting qubit (e.g., charge qubit, phase qubit, flux qubit). In various aspects, the first qubit 102 can be any suitable fixed-frequency superconducting qubit (e.g., a qubit whose operating frequency is not tunable). Similarly, as... Figure 1As shown, the second qubit 104 can be a fixed-frequency transmon-type qubit. That is, the second qubit 104 can include a Josephson junction 122 shunt by capacitor 124. However, in various instances, the second qubit 104 can be any suitable type of superconducting qubit (e.g., charge qubit, phase qubit, flux qubit). In various aspects, the second qubit 104 can be any suitable fixed-frequency superconducting qubit (e.g., a qubit whose operating frequency is not tunable).

[0055] In various other embodiments, the first qubit 102 and / or the second qubit 104 may be tunable and / or weakly tunable.

[0056] In various embodiments, the first qubit 102 may have a first operating frequency. In various embodiments, the second qubit 104 may have a second operating frequency. In various aspects, the first operating frequency may have any suitable value, and the second operating frequency may have any suitable value. In various embodiments, the first operating frequency may be in the range of 4.5 GHz to 5.5 GHz. In various aspects, the second operating frequency may be in the range of 4.5 GHz to 5.5 GHz. In various embodiments, the first and second operating frequencies may be separated by approximately 150 MHz (e.g., a 150 MHz detuning and / or frequency separation, as measured within any suitable measurement resolution and / or measurement error). For example, the first operating frequency may be approximately 150 MHz smaller than the second operating frequency. In various embodiments, the first qubit 102 may have any suitable anharmonicity, the second qubit 104 may have any suitable anharmonicity, and the first qubit 102 and the second qubit 104 may be in a straddling regime, wherein their frequency separation is less than the anharmonicity of the two qubits.

[0057] In various embodiments, the first qubit 102 may have a first coupling capacitor 108 and a second coupling capacitor 114. Similarly, the second qubit 104 may have a first coupling capacitor 110 and a second coupling capacitor 116. In various instances, coupling capacitors 108, 110, 114, and 116 may be any suitable coupling capacitor used in a quantum computing system.

[0058] In various instances, system 100 may include a first resonator 106 and a second resonator 112. In various aspects, the first resonator 106 may be any suitable fixed-frequency microwave resonator (e.g., a bus resonator) used in a quantum computing system. In various aspects, the first resonator 106 may be any suitable λ / 2 resonator. Similarly, in various instances, the second resonator 112 may be any suitable fixed-frequency microwave resonator (e.g., a bus resonator) used in a quantum computing system. In various aspects, the second resonator 112 may be any suitable λ / 2 resonator.

[0059] As shown in the figure, in various embodiments, the first resonator 106 can capacitively couple the first qubit 102 to the second qubit 104. Specifically, in various instances, the first resonator 106 may have a first end (e.g., as shown in the figure). Figure 1 The left end of the first resonator 106 depicted) and the second end (e.g., as Figure 1 The right-hand end of the depicted first resonator 106. In various cases, the first end of the first resonator 106 may be coupled to the first coupling capacitor 108 of the first qubit 102. In various aspects, the second end of the first resonator 106 may be coupled to the first coupling capacitor 110 of the second qubit 104. Similarly, in various embodiments, the second resonator 112 may capacitively couple the first qubit 102 to the second qubit 104. Specifically, in various instances, the second resonator 112 may have a first end (e.g., as shown in the diagram). Figure 1 The left-hand end of the second resonator 112 (as depicted) and the second end (e.g., as Figure 1 (The right-hand end of the depicted second resonator 112). In various cases, the first end of the second resonator 112 can be coupled to the second coupling capacitor 114 of the first qubit 102. In various aspects, the second end of the second resonator 112 can be coupled to the second coupling capacitor 116 of the second qubit 104.

[0060] As shown in the figure, in various instances, the first resonator 106 and the second resonator 112 can be connected in parallel (e.g., the opposite of series connection).

[0061] In various embodiments, the first resonator 106 may have a first resonant frequency. In various cases, the first resonant frequency may be less than the first operating frequency of the first qubit 102. In various examples, the first resonant frequency may also be less than the second operating frequency of the second qubit 104. In various embodiments, the second resonator 112 may have a second resonant frequency. In various cases, the second resonant frequency may be greater than the first operating frequency of the first qubit 102. In various examples, the second resonant frequency may also be greater than the second operating frequency of the second qubit 104. In various embodiments, the first resonant frequency may be approximately 3 GHz (e.g., the first resonant frequency may be within any suitable measurement resolution and / or measurement error of 3 GHz). In various examples, the second resonant frequency may be approximately 6 GHz (e.g., the second resonant frequency may be within any suitable measurement resolution and / or measurement error of 6 GHz). In various aspects, the resonant frequency of a fixed-frequency microwave resonator may depend on the shape and / or size of the fixed-frequency microwave resonator (e.g., a low resonant frequency can be obtained with a long microwave resonator, while a high resonant frequency can be obtained with a short microwave resonator).

[0062] In various instances, the first resonator 106, the second resonator 112, and the coupling capacitors 108, 110, 114, and 116 can be considered as a multi-resonant coupling architecture 126. As explained above, the multi-resonant coupling architecture 126 can reduce the ZZ interaction between the first qubit 102 and the second qubit 104 without correspondingly reducing the ZX interaction (e.g., exchange coupling J) between them. Furthermore, the multi-resonant coupling architecture 126 does not require the injection of multi-pulse echoes into the system 100. Moreover, the multi-resonant coupling architecture 126 can be constructed without tunable frequency elements (e.g., the first resonator 106 and the second resonator 112 can be fixed-frequency microwave resonators). Thus, in various aspects, the multi-resonant coupling architecture 126 can reduce the ZZ interaction between the first qubit 102 and the second qubit 104 without correspondingly reducing the coherence time of the system 100. Therefore, the multi-resonant coupling architecture 126 can constitute a substantial and tangible technical improvement relative to conventional systems and / or techniques.

[0063] Figure 2 A block diagram of an example non-limiting system 200 including a resonator, which can facilitate the reduction of ZZ interactions according to one or more embodiments described herein, is shown. As shown, in various aspects, system 200 may include a first qubit 102 and a second qubit 104, substantially as described above.

[0064] As shown, in various embodiments, the first qubit 102 may have a coupling capacitor 208. Similarly, the second qubit 104 may have a coupling capacitor 210. In various instances, coupling capacitors 208 and 210 may be any suitable coupling capacitor used in a quantum computing system.

[0065] In various instances, system 200 may include resonator 202. In various aspects, resonator 202 may be any suitable fixed-frequency microwave resonator (e.g., a bus resonator) used in quantum computing systems. In various aspects, resonator 202 may be any suitable λ / 4 resonator. In various instances, resonator 202 may be a long, low-frequency λ / 4 resonator.

[0066] As shown in the figure, in various embodiments, the resonator 202 may have a first terminal 204 and a second terminal 206. In various examples, the first terminal 204 of the resonator 202 may be capacitively coupled to a first qubit 102 and may be capacitively coupled to a second qubit 104. Specifically, in various aspects, the first terminal 204 of the resonator 202 may be coupled to a coupling capacitor 208 of the first qubit 102. Furthermore, the first terminal 204 of the resonator 202 may also be coupled to a coupling capacitor 210 of the second qubit 104. In various examples, the second terminal 206 of the resonator 202 may be coupled and / or shorted to ground 212.

[0067] In various embodiments, resonator 202 may have a first harmonic frequency. In various cases, the first harmonic frequency may be less than a first operating frequency of the first qubit 102. In various instances, the first harmonic frequency may also be less than a second operating frequency of the second qubit 104. In various embodiments, resonator 202 may have a second harmonic frequency. In various cases, the second harmonic frequency may be greater than the first operating frequency of the first qubit 102. In various instances, the second harmonic frequency may also be greater than the second operating frequency of the second qubit 104. In various embodiments, the first harmonic frequency may be about 2 GHz (e.g., the first harmonic frequency may be within any suitable measurement resolution and / or measurement error of 2 GHz). In various instances, the second harmonic frequency may be about 6 GHz (e.g., the second harmonic frequency may be within any suitable measurement resolution and / or measurement error of 6 GHz). In other words, system 200 may have a single resonant element (e.g., resonator 202) and may also have two resonants (e.g., a first harmonic frequency and a second harmonic frequency).

[0068] In various instances, resonator 202, ground 212, and coupling capacitors 208 and 210 can be considered as a multi-resonant coupling architecture 214. As explained above, the multi-resonant coupling architecture 214 can reduce the ZZ interaction between the first qubit 102 and the second qubit 104 without correspondingly reducing the ZX interaction (e.g., exchange coupling J) between them. Furthermore, the multi-resonant coupling architecture 214 does not require the injection of multi-pulse echoes into the system 200. Moreover, the multi-resonant coupling architecture 214 can be constructed without tunable frequency elements (e.g., resonator 202 can be a fixed-frequency microwave resonator). Thus, in various aspects, the multi-resonant coupling architecture 214 can reduce the ZZ interaction between the first qubit 102 and the second qubit 104 without correspondingly reducing the coherence time of the system 200. Therefore, the multi-resonant coupling architecture 214 can constitute a substantial and tangible technical improvement relative to conventional systems and / or techniques.

[0069] Figure 3 A block diagram of an example non-limiting system 300 comprising a resonator and a differential direct coupler, which can facilitate the reduction of ZZ interactions according to one or more embodiments described herein, is shown. As shown, in various aspects, system 300 may include a first qubit 102 and a second qubit 104, substantially as described above.

[0070] As shown, in various embodiments, the first qubit 102 may have a first coupling capacitor 312 and may have a second coupling capacitor 318. Similarly, the second qubit 104 may have a first coupling capacitor 314 and may have a second coupling capacitor 320. In various instances, coupling capacitors 312, 314, 318, and 320 may be any suitable coupling capacitor used in a quantum computing system.

[0071] Furthermore, in various embodiments, the first qubit 102 may have a first pad / node 302 and may also have a second pad / node 304. Similarly, the second qubit 104 may have a first pad / node 306 and may also have a second pad / node 308. In various embodiments, the first pad / node 302 of the first qubit 102 may be considered to be common to the second pad / node 308 of the second qubit 104 (e.g., common qubit pads and / or nodes). Furthermore, the first pad / node 302 of the first qubit 102 may be considered to be opposite to the first pad / node 306 of the second qubit 104 (e.g., opposite qubit pads and / or nodes). Similarly, in various embodiments, the second pad / node 304 of the first qubit 102 may be considered to be common to the first pad / node 306 of the second qubit 104 (e.g., common qubit pads and / or nodes). Additionally, the second pad / node 304 of the first qubit 102 can be considered to be the opposite of the second pad / node 308 of the second qubit 104 (e.g., opposite qubit pads and / or nodes).

[0072] In various instances, system 300 may include resonator 310 and differential direct coupler 316. In various aspects, resonator 310 may be any suitable fixed-frequency microwave resonator (e.g., a bus resonator) used in a quantum computing system. In various aspects, resonator 310 may be any suitable λ / 2 resonator. In various instances, differential direct coupler 316 may be any suitable direct coupling and / or wiring used in a quantum computing system.

[0073] As shown, in various embodiments, resonator 310 can capacitively couple the first qubit 102 to the second qubit 104. Specifically, in various instances, resonator 310 may have a first end (e.g., as shown in the diagram). Figure 3 The left end of the resonator 310 depicted in the image) and the second end (e.g., as shown in the image) Figure 3 The right-hand end of the resonator 310 depicted in the image. In various cases, the first end of the resonator 310 can be coupled to the first coupling capacitor 312 of the first qubit 102. In various aspects, the second end of the resonator 310 can be coupled to the first coupling capacitor 314 of the second qubit 104. Similarly, in various embodiments, the differential direct coupler 316 can capacitively couple the first qubit 102 to the second qubit 104. Specifically, in various instances, the differential direct coupler 316 can have a first end (e.g., as shown in the image). Figure 3 The left-hand end of the depicted differential direct coupler 316 and the second end (e.g., as shown) Figure 3(The right-hand end of the depicted differential direct coupler 316). In various cases, the first end of the differential direct coupler 316 can be coupled to the second coupling capacitor 318 of the first qubit 102. In various aspects, the second end of the differential direct coupler 316 can be coupled to the second coupling capacitor 320 of the second qubit 104. As shown, in various instances, the second coupling capacitor 318 of the first qubit 102 can be coupled to the first pad / node 302 of the first qubit 102. Also as shown, the second coupling capacitor 320 of the second qubit 104 can be coupled to the first pad / node 306 of the second qubit 104. Thus, in various embodiments, the differential direct coupler 316 can be considered as capacitively coupling the opposite pads / nodes of the first qubit 102 and the second qubit 104 together (e.g., the differential direct coupler 316 ultimately couples the first pad / node 302 of the first qubit 102 to the first pad / node 306 of the second qubit 104, wherein the first pad / node 302 of the first qubit 102 is considered to be opposite to the first pad / node 306 of the second qubit 104).

[0074] As shown in the figure, in various instances, the resonator 310 and the differential direct coupler 316 can be connected in parallel (e.g., the opposite of series connection).

[0075] In various embodiments, resonator 310 may have a resonant frequency. In various cases, this resonant frequency may be greater than a first operating frequency of the first qubit 102. In various instances, this resonant frequency may also be greater than a second operating frequency of the second qubit 104. In various embodiments, this resonant frequency may be approximately 6 GHz (e.g., this resonant frequency may be within any suitable measurement resolution and / or measurement error of 6 GHz). In various aspects, differential direct coupler 316 may be any suitable, short transmission line segment (e.g., short in the sense that its resonant frequency is greater than approximately 30 GHz), which can induce frequency-independent coupling at a typical transmon-type qubit frequency of approximately 5 GHz.

[0076] In various instances, resonator 310, differential direct coupler 316, and coupling capacitors 312, 314, 318, and 320 can be considered as a multi-resonant coupling architecture 322. As explained above, the multi-resonant coupling architecture 322 can reduce the ZZ interaction between the first qubit 102 and the second qubit 104 without correspondingly reducing the ZX interaction (e.g., exchange coupling J) between the first qubit 102 and the second qubit 104. Furthermore, the multi-resonant coupling architecture 322 does not require the injection of multi-pulse echoes into system 300. Moreover, the multi-resonant coupling architecture 322 can be constructed without tunable frequency elements (e.g., resonator 310 can be a fixed-frequency microwave resonator, and differential direct coupler 316 can be any suitable, short transmission line segment (e.g., short in the sense that its resonant frequency is greater than about 30 GHz), which can induce frequency-independent coupling at a typical transmon-type qubit frequency of about 5 GHz, or can be considered as a non-resonant structure). Thus, in various aspects, the multi-resonant coupling architecture 322 can reduce the ZZ interaction between the first qubit 102 and the second qubit 104 without correspondingly reducing the coherence time of the system 300. Furthermore, in various embodiments, the differential direct coupler 316 can be a short and / or compact direct coupler, and the resonator 310 can be a short microwave resonator (e.g., a microwave resonator capable of producing a high resonant frequency similar to 6 GHz can be shorter and / or more compact than a microwave resonator capable of producing a low resonant frequency similar to 3 GHz). Therefore, in various instances, the multi-resonant coupling architecture 322 can be very compact compared to conventional systems and / or techniques (and thus suitable for scaling to large device sizes). Therefore, the multi-resonant coupling architecture 322 can constitute a substantial and tangible technical improvement relative to conventional systems and / or techniques.

[0077] Figure 4 A block diagram of an example non-limiting system 400 comprising a resonator and a direct coupler, which can facilitate the reduction of ZZ interactions according to one or more embodiments described herein, is shown. As shown, in various aspects, system 400 may include a first qubit 102 and a second qubit 104, substantially as described above.

[0078] As shown, in various embodiments, the first qubit 102 may have a first coupling capacitor 408 and may have a second coupling capacitor 416. Similarly, the second qubit 104 may have a first coupling capacitor 410 and may have a second coupling capacitor 418. In various instances, coupling capacitors 408, 410, 416, and 418 may be any suitable coupling capacitor used in a quantum computing system.

[0079] Furthermore, in various embodiments, the first qubit 102 may have a first pad / node 302 and may have a second pad / node 304, substantially as described above. Similarly, the second qubit 104 may have a first pad / node 306 and may have a second pad / node 308, substantially as described above. As explained above, in various embodiments, the first pad / node 302 of the first qubit 102 may be considered common to the second pad / node 308 of the second qubit 104 (e.g., common qubit pads and / or nodes). Furthermore, the first pad / node 302 of the first qubit 102 may be considered opposite to the first pad / node 306 of the second qubit 104 (e.g., opposite qubit pads and / or nodes). Similarly, in various embodiments, the second pad / node 304 of the first qubit 102 may be considered common to the first pad / node 306 of the second qubit 104 (e.g., common qubit pads and / or nodes). Additionally, the second pad / node 304 of the first qubit 102 can be considered to be the opposite of the second pad / node 308 of the second qubit 104 (e.g., opposite qubit pads and / or nodes).

[0080] In various instances, system 400 may include resonator 402 and direct coupler 414. In various aspects, resonator 402 may be any suitable fixed-frequency microwave resonator (e.g., a bus resonator) used in a quantum computing system. In various aspects, resonator 402 may be any suitable λ / 4 resonator. In various instances, direct coupler 414 may be any suitable direct coupling and / or wiring used in a quantum computing system.

[0081] As shown in the figure, in various embodiments, resonator 402 may have a first terminal 404 and a second terminal 406. In various cases, the first terminal 404 of resonator 402 may be capacitively coupled to a first qubit 102 and capacitively coupled to a second qubit 104. Specifically, in various examples, the first terminal 404 of resonator 402 may be coupled to a first coupling capacitor 408 of the first qubit 102. Additionally, in various aspects, the first terminal 404 of resonator 402 may also be coupled to a first coupling capacitor 410 of the second qubit 104. In various examples, the second terminal 406 of resonator 402 may be coupled and / or shorted to ground 412.

[0082] In various embodiments, the direct coupler 414 can capacitively couple the first qubit 102 to the second qubit 104. Specifically, in various instances, the direct coupler 414 may have a first end (e.g., as shown in the image). Figure 4 The left end of the depicted direct coupler 414) and the second end (e.g., as Figure 4(The right-hand end of the depicted direct coupler 414). In various cases, the first end of the direct coupler 414 can be coupled to the second coupling capacitor 416 of the first qubit 102. In various aspects, the second end of the direct coupler 414 can be coupled to the second coupling capacitor 418 of the second qubit 104. As shown, in various instances, the second coupling capacitor 416 of the first qubit 102 can be coupled to the second pad / node 304 of the first qubit 102. Also as shown, the second coupling capacitor 418 of the second qubit 104 can be coupled to the first pad / node 306 of the second qubit 104. Thus, in various embodiments, the direct coupler 414 can be considered as capacitively coupling the common pads / nodes of the first qubit 102 and the second qubit 104 together (e.g., the direct coupler 414 ultimately couples the second pad / node 304 of the first qubit 102 to the first pad / node 306 of the second qubit 104, wherein the second pad / node 304 of the first qubit 102 is considered to be common to the first pad / node 306 of the second qubit 104).

[0083] In various embodiments, resonator 402 may have a resonant frequency. In various cases, this resonant frequency may be greater than a first operating frequency of the first qubit 102. In various instances, this resonant frequency may also be greater than a second operating frequency of the second qubit 104. In various embodiments, this resonant frequency may be approximately 6 GHz (e.g., this resonant frequency may be within any suitable measurement resolution and / or measurement error of 6 GHz). In various aspects, direct coupler 414 may be any suitable, short transmission line segment (e.g., short in the sense that its resonant frequency is greater than approximately 30 GHz), which can induce frequency-independent coupling at a typical transmon-type qubit frequency of approximately 5 GHz.

[0084] In various instances, resonator 402, direct coupler 414, ground 412, and coupling capacitors 408, 410, 416, and 418 can be considered as a multi-resonant coupling architecture 420. As explained above, the multi-resonant coupling architecture 420 can reduce the ZZ interaction between the first qubit 102 and the second qubit 104 without correspondingly reducing the ZX interaction (e.g., exchange coupling J) between the first qubit 102 and the second qubit 104. Furthermore, the multi-resonant coupling architecture 420 does not require the injection of multi-pulse echoes into the system 400. Moreover, the multi-resonant coupling architecture 420 can be constructed without tunable frequency elements (e.g., resonator 402 can be a fixed-frequency microwave resonator, and direct coupler 414 can be any suitable, short transmission line segment (e.g., short in the sense that its resonant frequency is greater than about 30 GHz), which can induce frequency-independent coupling at a typical transmon-type qubit frequency of about 5 GHz, or can be considered as a non-resonant structure). Thus, in various aspects, the multi-resonant coupling architecture 420 can reduce the ZZ interaction between the first qubit 102 and the second qubit 104 without correspondingly reducing the coherence time of the system 400. Furthermore, in various embodiments, the direct coupler 414 can be a short and / or compact direct coupler, and the resonator 402 can be a short microwave resonator (e.g., a microwave resonator with a high resonant frequency similar to 6 GHz can be shorter and / or more compact than a microwave resonator with a low resonant frequency similar to 2 GHz). Therefore, in various instances, the multi-resonant coupling architecture 420 can be very compact compared to conventional systems and / or techniques (and thus suitable for scaling to large device sizes). Therefore, the multi-resonant coupling architecture 420 can constitute a substantial and tangible technical improvement relative to conventional systems and / or techniques.

[0085] Figures 5-6 Example non-limiting graphs 500 and 600 are shown, depicting the reduction of ZZ interactions facilitated by one or more embodiments described herein.

[0086] like Figures 5-6As shown, graph 500 depicts computational simulation results for various embodiments of the present invention, and graph 600 depicts computational simulation results for various embodiments of the present invention compared to computational simulation results for conventional qubit coupling techniques. The inventors of various embodiments of the present invention run these computational simulations to calculate and / or approximate the ZX interaction (e.g., coupling strength and / or exchange coupling J) between two fixed-frequency superconducting qubits, and to calculate and / or approximate the ZZ interaction between these two fixed-frequency superconducting qubits. In some simulations, the inventors assume that the two fixed-frequency superconducting qubits are conventionally coupled. In other simulations, the inventors assume that the two fixed-frequency superconducting qubits are coupled via a multiresonant coupling architecture such as multiresonant coupling architecture 420. For these simulations, the inventors used the following values: g = 80 MHz, where g represents the coupling strength between the transmon-type qubit and the bus resonator; f0 = 5000 MHz, where f0 represents the frequency of the upper transmon-type qubit; α = -320 MHz, where α represents the anharmonicity of the transmon-type qubit; ω = 6100 MHz, where ω represents the frequency of the bus resonator; and J0 = 4.5 MHz, where J0 represents the exchange interaction of the transmon direct coupler. Furthermore, the frequency separation between the two fixed-frequency superconducting qubits was set at 150 MHz. In all aspects, the simulations were run with a drive signal set to 60 MHz.

[0087] Graph 500 depicts a subset of simulation results for various embodiments of the multi-resonant coupling architecture 420. As shown, graph 500 includes line 502, which indicates and / or corresponds to the value of the ZX interaction between the two qubits as a function of the operating frequency of the upper qubit when the qubits are coupled through the multi-resonant coupling architecture 420. That is, line 502 corresponds to the value of the ZX interaction between the two qubits as a function of the operating frequency of the upper qubit when the qubits are coupled through the multi-resonant coupling architecture 420. Figure 5 The variable "ZX (60MHz drive)" is labeled in the legend. Similarly, as shown, graph 500 includes line 504, which indicates the value of the ZZ interaction between the two qubits as a function of the operating frequency of the upper qubit when the qubits are coupled through the multi-resonant coupling architecture 420. That is, line 504 corresponds to... Figure 5The variable "ZZ" is labeled in the legend. As indicated by reference numeral 506, there is a specific range of upper qubit operating frequencies (e.g., between 5150 MHz and 5200 MHz) where the ZZ interaction is significantly reduced (e.g., zero ZZ interaction) and the ZX interaction is not significantly reduced (e.g., non-zero ZX interaction). In other words, graph 500 shows specific frequency bands where various embodiments of the invention cause a significant reduction in ZZ interaction without a corresponding reduction in ZX interaction. This reduction in ZZ interaction without a corresponding reduction in ZX interaction is facilitated by various embodiments of the invention. Furthermore, since various embodiments of the invention do not require echo-emitting and / or tunable frequency elements, they can facilitate such ZZ reduction without the corresponding coherence degradation typically associated with conventional systems and / or techniques.

[0088] Graph 600 is similar to Graph 500 because it depicts simulation results for various embodiments of the multi-resonant coupling architecture 420. However, Graph 600 depicts these results over a larger frequency band (e.g., from 4 GHz to 5.75 GHz for the upper qubit operating frequency) and also includes results associated with conventional coupling techniques. As shown, Graph 600 includes line 602, which indicates and / or corresponds to the value of the ZX interaction between the two qubits as a function of the upper qubit operating frequency when the qubits are conventionally coupled. That is, line 602 corresponds to the value of the ZX interaction between the two qubits as a function of the upper qubit operating frequency, as shown in... Figure 6 The variable "J (impedance)" is labeled in the legend. Graph 600 also includes line 604, which indicates and / or corresponds to the value of the ZZ interaction between the two qubits as a function of the operating frequency of the upper qubit when the two qubits are conventionally coupled. That is, line 604 corresponds to the value of the ZZ interaction between the two qubits as a function of the operating frequency of the upper qubit, as shown in... Figure 6 The variable "ZZ (impedance)" is labeled in the legend. As shown, conventional coupling techniques can lead to a significant reduction in both ZX and ZZ interactions in a specific frequency band (e.g., between 4.5 GHz and 4.75 GHz). However, as shown, there is no frequency band where conventional coupling techniques result in a significant decrease in ZZ interactions without a corresponding decrease in ZX interactions. As shown, conventional coupling techniques only produce low ZZ interactions at operating points where ZX interactions are also weak. However, as shown, various embodiments of the present invention can produce operating points where ZZ interactions are weak but ZX interactions are non-zero and / or not weak.

[0089] As shown, graph 600 includes line 606, which indicates and / or corresponds to the value of the ZX interaction between the two qubits as a function of the operating frequency of the upper qubit when the qubits are coupled through the multi-resonant coupling architecture 420. That is, line 606 corresponds to the value of the ZX interaction between the two qubits as a function of the operating frequency of the upper qubit. Figure 6 The variable "J(gs)" is labeled in the legend. Furthermore, graph 600 includes line 608, which indicates and / or corresponds to the value of the ZZ interaction between the two qubits as a function of the operating frequency of the upper qubit when the qubits are coupled through the multi-resonant coupling architecture 420. That is, line 608 corresponds to the value of the ZZ interaction between the two qubits as a function of the operating frequency of the upper qubit. Figure 6 The variable “ZZ(gs)” is labeled in the legend. As shown, various embodiments of the multiresonant coupling architecture 420 can significantly reduce both ZX and ZZ interactions in a specific frequency band (e.g., between 4.5 GHz and 4.75 GHz). Similarly, as illustrated, various embodiments of the multiresonant coupling architecture 420 can significantly reduce ZZ interactions in different frequency bands (e.g., between 5 GHz and 5.25 GHz) without a corresponding reduction in ZX interactions.

[0090] These results can be compared to demonstrate the benefits of various embodiments of the invention relative to conventional systems and / or techniques. As shown, line 606 is nearly identical to line 602. In other words, the multiresonant coupling architecture 420 provides nearly the same ZX interactions (e.g., coupling strength and / or exchange coupling J) as conventional coupling techniques. However, as shown, for a wide bandwidth (e.g., from about 4.8 GHz to 5.75 GHz), line 608 is significantly lower than line 604. In fact, as shown in graph 600, from about 5 GHz to 5.75 GHz, line 608 is almost an entire order of magnitude lower than line 604, and in a narrow bandwidth between about 5 GHz and 5.25 GHz, line 608 is almost two orders of magnitude lower than line 604, as shown. This improved performance clearly demonstrates that the various embodiments of the invention constitute a substantial and tangible technical improvement relative to the prior art.

[0091] Note that graphs 500 and 600 are exemplary and not limiting. In various aspects, based on the various parameters corresponding to the multi-resonant coupling architecture used for coupling qubits and / or based on the operating environment of the coupled qubits (e.g., different resonant frequencies of λ / 2 and / or λ / 4 couplers, different drive signals), zero ZZ interactions and non-zero ZX interactions can occur with respect to... Figures 5-6 The different upper qubit operating frequencies depicted are shown in the figures. Furthermore, note that graphs 500 and 600 show specific simulation results for various embodiments of the multiresonant coupling architecture 420. However, the inventors obtained very similar simulation results for various other embodiments of the invention (e.g., for multiresonant coupling architectures 126, 214, and 322). Since the results are almost identical, other simulation results have been omitted for brevity.

[0092] Figure 7A block diagram of an example non-limiting qubit array 700 that can promote the reduction of ZZ interactions according to one or more embodiments described herein is shown.

[0093] like Figure 7 As shown, various embodiments of the invention can be implemented to create a qubit array 700 (e.g., a two-dimensional array of coupled qubits). As illustrated, in various aspects, the qubit array 700 may include qubits Q1 to Q4. In various aspects, qubits Q1 to Q4 may be superconducting qubits of any suitable type and / or combination of types (e.g., qubits Q1 to Q4 may be qubits of the same type, and / or may be qubits of different types). In various instances, the qubit array 700 may be a square and / or a lattice array (e.g., two rows of two qubits). In various aspects, the qubit array 700 may be arranged in any other suitable configuration and / or shape (e.g., rectangular, triangular, circular). Although... Figure 7 Only four qubits (e.g., Q1 to Q4) in the qubit array 700 are depicted, but this is for illustrative purposes only. In various instances, any suitable number of qubits can be implemented in the qubit array 700. In various aspects, qubits Q1 to Q4 can be arranged in the qubit array 700 on any suitable quantum computing substrate (not shown).

[0094] As illustrated, in various embodiments, any qubit in the qubit array 700 can be coupled to some and / or all of its nearest-neighbor qubits (and / or in some cases, some and / or all of its second-nearest-neighbor qubits) via any suitable multi-resonant coupling architecture as described herein. For example, as shown, qubit Q1 can be coupled via as described regarding Figure 1 The explained multi-resonant coupling architecture 126 is coupled to qubit Q2. As shown, qubit Q1 can also be coupled via, as described above... Figure 3 The explained multi-resonant coupling architecture 322 is coupled to the qubit Q3 (e.g., for simplicity of illustration, Figure 7 The differential characteristics of the multi-resonant coupling architecture 322 are not shown; however, such differential characteristics are related to... Figure 3 (Fully depicted and described). As shown in the figure, the qubit Q2 can also be described as follows: Figure 4 The explained multi-resonant coupling architecture 420 is coupled to qubit Q4. As shown in the figure, qubit Q3 can be coupled to qubit Q4 via, as described above. Figure 2 The explained multi-resonant coupling architecture 214 is coupled to the qubit Q4. Although in Figure 7 Although not shown in the diagram, one or more conventional couplers can be implemented in the qubit array 700 in various instances.

[0095] In all aspects, Figure 7It describes how it can be implemented. Figures 1-4 Non-limiting examples of one or more of the multi-resonant coupling architectures (e.g., multi-resonant coupling architectures 126, 214, 322 and 420) depicted in the diagram to create two-dimensional arrays of coupled qubits with reduced ZZ interactions.

[0096] Figure 8 A flowchart of an example non-limiting method 800 comprising two resonators that can promote the reduction of ZZ interactions according to one or more embodiments described herein is shown.

[0097] In various embodiments, action 802 may include capacitively coupling a first qubit (e.g., 102) to a second qubit (e.g., 104) via a first resonator (e.g., 106). In various instances, the first qubit may have a first operating frequency, and the second qubit may have a second operating frequency. In various aspects, the first resonator may have a first resonant frequency that is less than both the first and second operating frequencies.

[0098] In various instances, action 804 may include capacitively coupling the first qubit to the second qubit via a second resonator (e.g., 112) connected in parallel with the first resonator. In various instances, the second resonator may have a second resonant frequency greater than both the first and second operating frequencies. In various aspects, the first and second resonators may be λ / 2 resonators. In various instances, the first resonant frequency, the second resonant frequency, the first operating frequency, and the second operating frequency may be fixed.

[0099] Figure 9 A flowchart of an example non-limiting method 900 comprising a resonator that can promote the reduction of ZZ interactions according to one or more embodiments described herein is shown.

[0100] In various embodiments, action 902 may include capacitively coupling a first end (e.g., 204) of a resonator (e.g., 202) to a first qubit (e.g., 102) and a second qubit (e.g., 104). In various instances, the first qubit may have a first operating frequency, and the second qubit may have a second operating frequency.

[0101] In various instances, action 904 may include coupling a second end of the resonator (e.g., 206) to ground (e.g., 212). In various instances, the resonator may have a first harmonic frequency less than a first operating frequency and less than a second operating frequency. In various aspects, the resonator may have a second harmonic frequency greater than a first operating frequency and greater than a second operating frequency. In various instances, the resonator may be a λ / 4 resonator. In various instances, the first harmonic frequency, the second harmonic frequency, the first operating frequency, and the second operating frequency may be fixed.

[0102] Figure 10 A flowchart of an example non-limiting method 1000 comprising a resonator and a differential direct coupler that can promote the reduction of ZZ interactions according to one or more embodiments described herein is shown.

[0103] In various embodiments, action 1002 may include capacitively coupling a first qubit (e.g., 102) to a second qubit (e.g., 104) via a resonator (e.g., 310). In various instances, the first qubit may have a first operating frequency, the second qubit may have a second operating frequency, and the resonator may have a resonant frequency greater than both the first and second operating frequencies.

[0104] In various instances, action 1004 may include capacitively coupling the first qubit to the second qubit via a differential direct coupler (e.g., 316) connected in parallel with the resonator. In various instances, the differential direct coupler may capacitively couple the opposite pads of the first and second qubits (e.g., 302 and 306). In various cases, the resonator may be a λ / 2 resonator. In various instances, the resonant frequency, the first operating frequency, and the second operating frequency may be fixed.

[0105] Figure 11 A flowchart is shown of an example non-limiting method 1100 comprising a resonator and a direct coupler that can promote the reduction of ZZ interactions according to one or more embodiments described herein.

[0106] In various embodiments, action 1102 may include capacitively coupling a first qubit (e.g., 102) to a second qubit (e.g., 104) via a resonator (e.g., 402). In various cases, a first end of the resonator (e.g., 404) may be capacitively coupled to both the first and second qubits, and a second end of the resonator (e.g., 406) may be coupled to ground (e.g., 412). In various cases, the first qubit may have a first operating frequency, the second qubit may have a second operating frequency, and the resonator may have a resonant frequency greater than both the first and second operating frequencies.

[0107] In various instances, action 1104 may include capacitively coupling the first qubit to the second qubit via a direct coupler (e.g., 414). In various instances, the direct coupler may capacitively couple the common pads of the first and second qubits (e.g., 304 and 306). In various cases, the resonator may be a λ / 4 resonator. In various instances, the resonant frequency, the first operating frequency, and the second operating frequency may be fixed.

[0108] Figure 12 A flowchart is shown of an example non-limiting method 1200 that can promote the reduction of ZZ interactions according to one or more embodiments described herein.

[0109] In various embodiments, action 1202 may include using a non-tunable multi-resonant architecture (e.g., as...) Figures 1-4 The coupling architecture shown capacitively couples a first qubit (e.g., 102) to a second qubit (e.g., 104). In various instances, the multi-resonant architecture may include a first pole that is greater than both the first operating frequency of the first qubit and the second operating frequency of the second qubit (e.g., in...). Figure 1 In the second resonant frequency of the second resonator 112, the second resonant frequency can be that of the first pole; in Figure 2 In the process, the second harmonic frequency of resonator 202 can be the first harmonic frequency; in Figure 3 In the middle, the resonant frequency of resonator 310 can be the first pole; in Figure 4 In this context, the resonant frequency of resonator 402 can be a first pole. In various aspects, the multi-resonant architecture may include a second pole, which is less than both the first and second operating frequencies (e.g., in...). Figure 1 In the first resonant frequency of the first resonator 106, the first resonant frequency can be the second frequency; in Figure 2 In this context, the first harmonic frequency of resonator 202 can be the second harmonic frequency. In various other respects, the multi-resonant architecture may alternatively include directly coupled terms (e.g., Figure 3 Differential direct coupler 316 or Figure 4 The direct coupler 414 in the middle is used instead of the second pole. In various cases, the multi-resonant architecture can be at the first set of qubit frequencies (e.g., such as...). Figure 6 As shown, zero coupling strength and zero ZZ interaction are exhibited between 4.5 GHz and 4.75 GHz. In various instances, multi-resonant architectures can be used at a second set of qubit frequencies (e.g., such as...). Figure 6 As shown, it exhibits non-zero coupling strength and zero ZZ interaction between 5 GHz and 5.25 GHz.

[0110] Various embodiments of the present invention can reduce unwanted ZZ interactions while maintaining desired ZX interactions. In various instances, this can be achieved through a multi-resonant coupling architecture with two fixed-frequency elements. In various aspects, the detuning between these two fixed-frequency elements and the qubits can be different, which can promote the suppression of ZZ interactions. In various other instances, this can be achieved through a multi-element coupler comprising a resonator and a short capacitive coupler. In various instances, the interactions between the two qubits and these elements can be different, which can lead to the cancellation of unwanted ZZ interactions in certain frequency bands.

[0111] In various instances, the following sample experiments can be performed. Two qubits can be coupled together through any embodiment of the invention (e.g., through any multiresonant coupling architecture discussed herein). The qubits can be weakly tunable, allowing the parameters and / or performance of the multiresonant coupling architecture to be studied. For various combinations of qubit frequency pairs, the exchange coupling J and ZZ interactions can be tested and / or recorded (e.g., J can be estimated from the ZX rate of the cross-resonance; the ZZ interaction can be measured via the Pi-Ramsey experiment). This allows the ZZ cancellation point to be pinpointed for a given coupler. The weakly tunable qubit can then be tuned to the desired state using an ac-Stark offset. Finally, the cross-resonant gate can be operated with the qubit within the ZZ cancellation bandwidth.

[0112] In some cases, a multi-resonant coupling architecture may include two λ / 2 resonators (e.g., such as...). Figure 1 As shown in the figure, one has a resonant frequency of 4 GHz, while the other has a resonant frequency of 6 GHz.

[0113] In some cases, multi-resonant coupled architectures may include a single λ / 4 resonator (e.g., such as...). Figure 2 As shown, this single λ / 4 resonator has 2 GHz first harmonics and 6 GHz second harmonics that can be combined to reduce and / or suppress ZZ interactions.

[0114] In some cases, multi-resonant coupling architectures may include a 6 GHz λ / 2 resonator and direct capacitive connections between differential pads of qubits (e.g., as shown in the image). Figure 3 (As shown). In various instances, the coupling through these two paths can be balanced such that the exchange coupling J approaches zero near the upper qubit operating frequency of 4.7 GHz, which can induce zero ZZ interaction and non-zero exchange coupling J at approximately 5 GHz.

[0115] In some cases, multi-resonant coupling architectures may include a 6 GHz λ / 4 resonator and direct capacitive connections between common pads of qubits (e.g., as shown in the image). Figure 4(As shown).

[0116] Various embodiments of the present invention can provide a multi-resonant coupling architecture that may include one or more coupling elements whose frequency response results in the cancellation of state-dependent coupling at the qubit frequency, while maintaining limited state-independent coupling.

[0117] To provide additional context for the various embodiments described herein, Figure 13 The following discussion is intended to provide a general description of a suitable computing environment 1300 in which various embodiments of the embodiments described herein may be implemented. Although 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.

[0118] 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.

[0119] 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.

[0120] 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.

[0121] Computer-readable storage media may include, but are 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” used herein to describe storage, memory, or computer-readable media should be understood to exclude only the propagation of transient signals themselves as a modifier, and do not waive the rights to all standard storage, memory, or computer-readable media that do not only propagate transient signals themselves.

[0122] A computer-readable storage medium can be accessed by one or more local or remote computing devices, for example, through access requests, queries or other data retrieval protocols, for various operations relative to the information stored in the medium.

[0123] 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" or multiple modulated data signals refers to a signal whose one or more 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).

[0124] Refer again Figure 13 An exemplary environment 1300 for implementing various embodiments of the aspects described herein includes a computer 1302, which includes a processing unit 1304, system memory 1306, and a system bus 1308. The system bus 1308 couples system components, including but not limited to system memory 1306, to the processing unit 1304. The processing unit 1304 can be any processor from a variety of commercially available processors. Dual microprocessors and other multiprocessor architectures can also be used as the processing unit 1304.

[0125] System bus 1308 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 1306 includes ROM 1310 and RAM 1312. The Basic Input / Output System (BIOS) can be stored in non-volatile memory such as ROM, erasable programmable read-only memory (EPROM), EEPROM, etc. The BIOS contains basic routines such as those that help pass information between components within computer 1302 during startup. RAM 1312 may also include high-speed RAM (such as static RAM for caching data).

[0126] Computer 1302 further includes an internal hard disk drive (HDD) 1314 (e.g., EIDE, SATA), one or more external storage devices 1316 (e.g., floppy disk drive (FDD) 1316, memory stick or flash memory drive reader, memory card reader, etc.), and a drive 1320 (e.g., a solid-state drive, optical disc drive, which can read from or write to a disk 1322 such as a CD-ROM, DVD, BD, etc.). Alternatively, in cases involving solid-state drives, disk 1322 will not be included unless it is separate. Although the internal HDD 1314 is illustrated as being located within computer 1302, the internal HDD 1314 may also be configured for external use in a suitable chassis (not shown). Additionally, although not shown in environment 1300, a solid-state drive (SSD) may be used as a supplement to or replacement for HDD 1314. HDD 1314, one or more external storage devices 1316, and drive 1320 can be connected to system bus 1308 via HDD interface 1324, external storage interface 1326, and drive interface 1328, respectively. Interface 1324 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 connectivity technologies are contemplated in the embodiments described herein.

[0127] The driver and its associated computer-readable storage medium provide non-volatile storage of data, data structures, computer-executable instructions, etc. For computer 1302, the driver 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.

[0128] Multiple program modules may be stored in the driver and RAM 1312, including an operating system 1330, one or more application programs 1332, other program modules 1334, and program data 1336. All or part of the operating system, applications, modules, and / or data may also be cached in RAM 1312. The systems and methods described herein can be implemented using various commercially available operating systems or combinations of operating systems.

[0129] Computer 1302 may optionally include emulation technology. For example, a hypervisor (not shown) or other intermediary may emulate the hardware environment used for operating system 1330, and the emulated hardware may optionally be compatible with... Figure 13 The hardware shown is different. In this embodiment, the operating system 1330 may include one of a plurality of virtual machines (VMs) hosted on the computer 1302. Furthermore, the operating system 1330 may provide a runtime environment for the application 1332, such as the Java Runtime Environment or the .NET Framework. A runtime environment is a consistent execution environment that allows the application 1332 to run on any operating system that includes a runtime environment. Similarly, the operating system 1330 may support containers, and the application 1332 may be in the form of containers, which are lightweight, standalone, executable software packages that include, for example, code, runtime, system tools, system libraries, and settings for the application.

[0130] Furthermore, computer 1302 may enable a security module, such as a Trusted Processing Module (TPM). For example, with a TPM, before loading the next startup component, the startup component hashes the next startup component in time and waits for the result to match a security value. This process can occur at any layer of the computer 1302'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.

[0131] Users can input commands and information into computer 1302 through one or more wired / wireless input devices (e.g., keyboard 1338, touchscreen 1340, and pointing devices such as mouse 1342). 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, gamepads, styluses, image input devices (e.g., one or more cameras), gesture sensor input devices, visual motion sensor input devices, emotion or face detection devices, biometric input devices (e.g., fingerprint or iris scanners), etc. These and other input devices are often connected to processing unit 1304 via input device interface 1344, which can be coupled to system bus 1308, but can be connected via other interfaces such as parallel ports, IEEE 1394 serial ports, game ports, USB ports, IR interfaces, etc. Interfaces, etc.

[0132] Monitor 1346 or other types of display devices can also be connected to system bus 1308 via an interface such as video adapter 1348. In addition to monitor 1346, computers typically include other peripheral output devices (not shown), such as speakers, printers, etc.

[0133] Computer 1302 can operate in a networked environment via a logical connection to one or more remote computers (such as remote computers 1350, either wired or wirelessly). Remote computers 1350 can be workstations, server computers, routers, personal computers, portable computers, microprocessor-based entertainment devices, peer-to-peer devices, or other public network nodes, and typically include many or all of the elements described relative to computer 1302; however, for brevity, only memory / storage device 1352 is shown. The depicted logical connections include wired / wireless connections to a local area network (LAN) 1354 and / or a larger network (e.g., a wide area network (WAN) 1356). 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.

[0134] When used in a LAN networking environment, computer 1302 can connect to local network 1354 via a wired and / or wireless communication network interface or adapter 1358. Adapter 1358 facilitates wired or wireless communication to LAN 1354, which may also include a wireless access point (AP) deployed thereon for communicating with adapter 1358 in wireless mode.

[0135] When used in a WAN networking environment, computer 1302 may include modem 1360 or be connected to a communication server on WAN 1356 via other means (such as via the Internet) for establishing communication on WAN 1356. Modem 1360 (which may be internal or external, and may be a wired or wireless device) may be connected to system bus 1308 via input device interface 1344. In a networking environment, program modules depicted relative to computer 1302 or portions thereof may be stored in remote memory / storage device 1352. It should be understood that the network connection shown is an example, and other means of establishing communication links between computers may be used.

[0136] When used in a LAN or WAN networking environment, computer 1302 can access cloud storage systems or other network-based storage systems as a supplement to or replacement of external storage device 1316 as described above, such as, but not limited to, network virtual machines providing one or more aspects of information storage or processing. Typically, the connection between computer 1302 and the cloud storage system can be established, for example, on LAN 1354 or WAN 1356 via adapter 1358 or modem 1360, respectively. When computer 1302 is connected to the associated cloud storage system, external storage interface 1326 can manage the storage provided by the cloud storage system by means of adapter 1358 and / or modem 1360, just like other types of external storage. For example, external storage interface 1326 can be configured to provide access to cloud storage sources as if those sources were physically connected to computer 1302.

[0137] Computer 1302 may be operable to communicate with any wireless device or entity operably deployed in wireless communications, such as printers, scanners, desktop and / or laptop computers, portable data assistants, communications satellites, any piece of equipment or location associated with a wirelessly detectable tag (e.g., self-service kiosks, newsstands, store shelves, etc.), and telephones. This may include Wi-Fi and Wireless technology. Therefore, communication can be a predefined structure like a conventional network, or simply self-organizing communication between at least two devices.

[0138] 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 one or more computer-readable storage 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 apparatus. 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 of the foregoing. 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 punched cards or raised structures with instructions recorded thereon in slots, and any suitable combination of the foregoing. 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.

[0139] The computer-readable program instructions described herein can be downloaded from a computer-readable storage medium to a corresponding computing / processing device, or downloaded via a network (e.g., the Internet, a local area network, a wide area network, and / or a wireless network) to an external computer or external storage device. The network may include copper cables, optical 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, configuration data for integrated circuits, 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 through 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.

[0140] This document describes aspects of the invention with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer-readable program instructions. These computer-readable program instructions can be provided to a processor of a general-purpose computer, 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 can direct a computer, programmable data processing apparatus, and / or other devices to operate in a particular manner, such that the computer-readable storage medium in which the instructions are stored includes an article of writing containing instructions that implement 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 that execute 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.

[0141] 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 one or more specified logical functions. In some alternative implementations, the functions marked in the blocks may occur in a non-linear order. 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 performs a combination of dedicated hardware and computer instructions.

[0142] While the subject matter has been described above in the general context of computer-executable instructions for computer program products running on computers and / or multiple computers, 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 devices, 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 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.

[0143] 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, processor, object, executable file, execution thread, program, and / or computer running on a processor. 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 execution thread, and components may reside on a single computer and / or be distributed across two or more computers. In another example, a corresponding component may be executed from various computer-readable media having various data structures stored thereon. Components may communicate via local and / or remote processes, such as according to signals 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 means of providing specific functionality 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 functionality. In one aspect, the component can be emulated by, for example, a virtual machine within a cloud computing system.

[0144] 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 of the natural inclusive arrangements. 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 this specification and the accompanying drawings 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 example, instance, 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 "example" and / or "exemplary" is not necessarily to be construed as preferred or advantageous relative to other aspects or designs, nor does it imply the exclusion of equivalent exemplary structures and techniques known to those skilled in the art.

[0145] 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 "memory," "memory device," "database," "data storage device," "database," and substantially any other information storage component, in relation to 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 illustration 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 serve 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 (DDR SDRAM), enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM), direct Rambus RAM (DRRAM), direct Rambus dynamic RAM (DRDRAM), and Rambus dynamic RAM (RDRAM). Furthermore, the memory components of the systems or computer-implemented methods disclosed herein are intended to include (but are not limited to) these and any other suitable types of memory.

[0146] 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 methods; however, those skilled in the art will recognize that many further combinations and substitutions of this disclosure are possible. Furthermore, the use of terms such as “comprising,” “having,” “possessing,” etc., in the detailed description, claims, appendices, and drawings is intended to be inclusive in a manner similar to the interpretation of the term “comprising” when used as a transitional word in the claims.

[0147] 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 relative to technologies found in the market, or to enable those skilled in the art to understand the embodiments disclosed herein.

Claims

1. A quantum bit device, comprising: First quantum bit; Second qubit; as well as A multi-resonant architecture, comprising a first resonator capacitively coupling a first qubit to a second qubit, and a second resonator capacitively coupling the first qubit to the second qubit. The first qubit has a first operating frequency, the second qubit has a second operating frequency, the first resonator has a first resonant frequency that is lower than the first and second operating frequencies, and the second resonator has a second resonant frequency that is higher than the first and second operating frequencies.

2. The qubit device of claim 1, wherein, The first resonator and the second resonator are λ / 2 resonators, and the first resonator and the second resonator are connected in parallel.

3. The qubit device of claim 1 or 2, wherein, The first resonant frequency is about 3 GHz, the second resonant frequency is about 6 GHz, and the first and second operating frequencies are between 4.5 GHz and 5.5 GHz.

4. The qubit device of claim 1 or 2, wherein, The first resonant frequency, the second resonant frequency, the first operating frequency, and the second operating frequency are fixed.

5. A quantum bit device, comprising: First quantum bit; Second qubit; as well as A multi-resonance architecture including a resonator, wherein a first end of the resonator is capacitively coupled to a first qubit and a second qubit, and wherein a second end of the resonator is coupled to ground. The first qubit has a first operating frequency, the second qubit has a second operating frequency, the resonator has a first harmonic frequency that is lower than the first and second operating frequencies, and the resonator has a second harmonic frequency that is higher than the first and second operating frequencies.

6. The quantum bit device according to claim 5, wherein, The resonator is a λ / 4 resonator.

7. The quantum bit device according to claim 5 or 6, wherein, The first harmonic frequency is about 2 GHz, the second harmonic frequency is about 6 GHz, and the first and second operating frequencies are between 4.5 GHz and 5.5 GHz.

8. The quantum bit device according to claim 5 or 6, wherein, The first harmonic frequency, the second harmonic frequency, the first operating frequency, and the second operating frequency are fixed.

9. A quantum bit device, comprising: First quantum bit; Second qubit; as well as A multi-resonant architecture includes a resonator capacitively coupling a first qubit to a second qubit and a differential direct coupler capacitively coupling the first qubit to the second qubit, wherein the differential direct coupler capacitively couples the opposite pads of the first qubit and the second qubit, and the differential direct coupler is configured to cause coupling independent of the operating frequency of the qubit.

10. The quantum bit device according to claim 9, wherein, The first qubit has a first operating frequency, wherein the second qubit has a second operating frequency, and wherein the resonator has a resonant frequency greater than the first operating frequency and the second operating frequency.

11. The quantum bit device according to claim 9 or 10, wherein, The resonator is a λ / 2 resonator, and the resonator and the differential direct coupler are connected in parallel.

12. The quantum bit device according to claim 10, wherein, The resonant frequency is approximately 6 GHz, and the first and second operating frequencies are between 4.5 GHz and 5.5 GHz.

13. The quantum bit device according to claim 10, wherein, The resonant frequency, the first operating frequency, and the second operating frequency are fixed.

14. A qubit device, comprising: First quantum bit; Second qubit; as well as A multi-resonant architecture includes a resonator and a direct coupler, wherein a first end of the resonator is capacitively coupled to a first qubit and a second qubit, a second end of the resonator is coupled to ground, the direct coupler capacitively couples the first qubit to the second qubit, and the direct coupler capacitively couples the common pads of the first and second qubits, and the direct coupler is configured to cause coupling independent of the operating frequency of the qubits.

15. The quantum bit device according to claim 14, wherein, The first qubit has a first operating frequency, wherein the second qubit has a second operating frequency, and wherein the resonator has a resonant frequency greater than the first operating frequency and the second operating frequency.

16. The quantum bit device according to claim 14 or 15, wherein, The resonator is a λ / 4 resonator.

17. The quantum bit device according to claim 15, wherein, The resonant frequency is approximately 6 GHz, and the first and second operating frequencies are between 4.5 GHz and 5.5 GHz.

18. The quantum bit device according to claim 15, wherein, The resonant frequency, the first operating frequency, and the second operating frequency are fixed.

19. A qubit device, comprising: A first transmon-type qubit with a first operating frequency; A second transmon-type qubit having a second operating frequency, wherein the second transmon-type qubit is an adjacent qubit to the first transmon-type qubit; and A multi-resonant architecture that capacitively couples a first transmon qubit to a second transmon qubit, wherein the multi-resonant architecture has a first resonant frequency less than a first operating frequency and a second operating frequency and a second resonant frequency greater than the first operating frequency and the second operating frequency.

20. The qubit device according to claim 19, wherein, The multi-resonant architecture includes a first λ / 2 resonator capacitively coupled to a first transmon qubit and a second transmon qubit, and a second λ / 2 resonator capacitively coupled to the first transmon qubit and the second transmon qubit, wherein the first λ / 2 resonator and the second λ / 2 resonator are connected in parallel, wherein the first λ / 2 resonator exhibits a first resonant frequency, and wherein the second λ / 2 resonator exhibits a second resonant frequency.

21. The qubit device according to claim 20, wherein, The first resonant frequency is approximately 3 gigahertz, and the second resonant frequency is approximately 6 gigahertz.

22. The qubit device according to claim 19, wherein, The multi-resonance architecture includes a λ / 4 resonator, wherein the first end of the λ / 4 resonator is coupled between a coupling capacitor of a first transmon type qubit and a coupling capacitor of a second transmon type qubit, wherein the second end of the λ / 4 resonator is shorted to ground, wherein the first harmonic of the λ / 4 resonator is the first resonant frequency, and wherein the second harmonic of the λ / 4 resonator is the second resonant frequency.

23. The qubit device according to claim 22, wherein, The first harmonic is about 2 gigahertz, and the second harmonic is about 6 gigahertz.

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