Tunable inter-resonator coupling circuit and quantum computing device including the same

Abstract

The present invention relates generally to the field of quantum computing, and in particular to a tunable inter-resonator coupling circuit that provides both direct and indirect coupling between linear or nonlinear resonators. The indirect coupling is provided by using a tunable coupling element that comprises two ungrounded superconducting islands. Since the superconducting islands are ungrounded, it is possible to provide the resonators and the superconducting islands with coupling frequencies of different signs, which in turn allows the interaction between the first and second resonators to be controlled more efficiently. Moreover, the design, calibration, and operation of a circuit with such a tunable coupling element is significantly easier and simpler compared to existing analogues, while providing the same or even better performance. A quantum computing device using one or more such circuits is also provided.

Description

[Technical field]

[0001] The present invention relates generally to the field of quantum computing. In particular, the present invention relates to tunable inter-resonator coupling circuits and quantum computing devices using one or more such circuits. [Background technology]

[0002] Quantum computing devices, also called quantum computers, use quantum mechanical phenomena such as superposition and entanglement to perform required quantum computing operations. Unlike traditional computers that manipulate information in the form of bits (e.g., "1" or "0"), quantum computers manipulate information using qubits. Qubits can refer to the fundamental unit of quantum information as well as quantum devices used to store one or more qubits of information (e.g., a superposition of "0" and "1").

[0003] Quantum computers can be implemented based on superconducting circuits comprising superconducting qubits and / or resonators. Tunable interaction between superconducting qubits or resonators is desirable for most quantum computing operations (e.g., large-scale quantum computation and simulation). It can be achieved by inserting additional circuit elements between the superconducting qubits or resonators, namely tunable couplers that allow the states of the superconducting qubits or resonators to interact with each other in a controlled manner. In other words, tunable couplers placed between the superconducting qubits or resonators allow quantum gates to be implemented.

[0004] A variety of tunable couplers have been previously designed and experimentally demonstrated. For example, according to one existing tunable coupler setup, two superconducting qubits are capacitively coupled both directly and indirectly. The indirect interaction is mediated by the tunable coupler itself. When the tunable coupler is implemented as a single island transmon, the sign of the indirect interaction is different from the sign of the direct interaction at coupler frequencies higher than the qubit frequency. As a result, the direct and indirect coupling terms may cancel each other out at a certain coupler frequency (also called the idle frequency). However, in this tunable coupler setup, the idle frequency is always above the qubit frequency, which may adversely affect the operation speed and accuracy of two-qubit gates implemented based on such tunable couplers. Summary of the Invention

[0005] This Summary is provided to introduce a selection of concepts in a simplified form that are further described below in the Detailed Description. This Summary is not intended to identify key features of the invention, nor is it intended to be used to limit the scope of the invention.

[0006] The object of the present invention is to provide a technical solution that allows tunable coupling between linear or nonlinear resonators.

[0007] The above object is achieved by means of the features of the attached independent claims. Further embodiments and examples are evident from the dependent claims, the detailed description and the accompanying drawings.

[0008] According to a first aspect, a tunable inter-resonator coupling circuit is provided. The circuit comprises a first resonator and a second resonator. The first resonator is linear or nonlinear, and the second resonator is linear or nonlinear. The first resonator and the second resonator have a direct coupling therebetween. The circuit further comprises a tunable coupling element arranged to provide an indirect coupling between the first resonator and the second resonator. The tunable coupling element comprises a first superconducting island and a second superconducting island, both of which are not grounded. The indirect coupling comprises (i) a first coupling between the first resonator and the first superconducting island, (ii) a Josephson coupling between the first superconducting island and the second superconducting island, and (iii) a second coupling between the second resonator and the second superconducting island. Since the superconducting island is floating, i.e. not grounded, it is possible to provide the resonator and the superconducting island with coupling frequencies of different signs, which in turn allows the interaction between the first and second resonators to be controlled more efficiently. Moreover, the design, calibration and operation of the circuit according to the first aspect is significantly easier and simpler compared to existing analogues, while at the same time providing the same or even better performance.

[0009] In one embodiment of the first aspect, each of the first and second resonators is linear and implemented as one of a harmonic oscillator, a coplanar waveguide resonator, and a lumped element resonator. These linear resonators may be used as a quantum bus or may be used to store qubit states. In this embodiment, a tunable coupler may enable on-demand transfer of quantum information between the linear resonators.

[0010] In another embodiment of the first aspect, each of the first and second resonators is implemented as a superconducting qubit, which may allow implementing a two-qubit gate based on the circuit according to the first aspect.

[0011] In one embodiment of the first aspect, the direct coupling is implemented as a non-galvanic (e.g., capacitive or inductive) coupling between the first resonator and the second resonator. Such a capacitive coupling may increase circuit performance.

[0012] In one embodiment of the first aspect, the first coupling is implemented as a capacitive coupling between the first resonator and the first superconducting island, and the second coupling is implemented as a capacitive coupling between the second resonator and the second superconducting island. Such a capacitive coupling is easier to implement by using conventional techniques, as compared to, for example, an inductive coupling.

[0013] In one embodiment of the first aspect, the tunable coupling element is implemented as a transmon qubit, which is less sensitive to control and signal noise compared to other standard qubit implementations.

[0014] In one embodiment of the first aspect, the first resonator has a first frequency and the second resonator has a second frequency. In this embodiment, the tunable coupling element has an idle frequency below each of the first and second frequencies. Because the idle frequency of the entire coupling element is below the frequency of the resonators, it is possible to design the coupling element such that its sweet spot is located at (or near) the operating point of a two-qubit gate implemented by using a superconducting qubit as a nonlinear resonator in a circuit according to the first aspect. This may reduce gate errors resulting from decoherence of the coupling element.

[0015] In one embodiment of the first aspect, the circuit further comprises a first readout resonator and a second readout resonator. The first readout resonator is configured to read out the first resonator and has a first operating frequency. The second readout resonator is configured to read out the second resonator and has a second operating frequency. Each of the first operating frequency and the second operating frequency exceeds each of an idle frequency of the tunable coupling element, a first frequency of the first resonator, and a second frequency of the second resonator. In this case, the coupling element will not resonate with the readout resonator during circuit operation (or gate operation if the resonator is represented by a superconducting qubit) that would otherwise adversely affect overall circuit operation.

[0016] In an embodiment of the first aspect, the indirect coupling further comprises a third coupling between the second resonator and the first superconducting island, and a fourth coupling between the first resonator and the second superconducting island. The use of these additional couplings can increase the applicability and flexibility of the circuit according to the first aspect.

[0017] In one embodiment of the first aspect, the third coupling is implemented as a capacitive coupling between the second resonator and the first superconducting island, and the fourth coupling is implemented as a capacitive coupling between the first resonator and the second superconducting island. By using such capacitive couplings, the circuit according to the first aspect can be made more compact.

[0018] In one embodiment of the first aspect, at least one of the first superconducting island and the second superconducting island has a capacitive coupling to ground, which may allow the tunable coupling element to be shielded from other circuit elements, thereby reducing crosstalk.

[0019] According to a second aspect, a quantum computing device is provided, comprising at least one circuit according to the first aspect and a control unit configured to perform a quantum computing operation by using the at least one circuit. The use of such one or more tunable inter-resonator coupling circuits in the quantum computing device may increase the computational accuracy and processing speed of the quantum computing device.

[0020] Other features and advantages of the present invention will become apparent from a reading of the following detailed description and a review of the accompanying drawings.

[0021] The invention will now be described with reference to the accompanying drawings. [Brief description of the drawings]

[0022] [Figure 1] FIG. 1 shows a block diagram of a tunable inter-qubit coupling circuit according to the prior art. [Diagram 2] 1 shows a block diagram of another tunable inter-qubit coupling circuit according to the prior art. [Diagram 3] 1 shows a block diagram of yet another tunable inter-qubit coupling circuit according to the prior art. [Figure 4] 1 shows a block diagram of a tunable inter-resonator coupling circuit in accordance with a first illustrative embodiment of the present invention; [Diagram 5] FIG. 4 shows a block diagram of a tunable inter-resonator coupling circuit in accordance with a second illustrative embodiment of the present invention. [Figure 6] FIG. 13 shows a block diagram of a tunable inter-resonator coupling circuit in accordance with a third illustrative embodiment of the present invention. [Figure 7] 1 shows a block diagram of a quantum computing device in accordance with one illustrative embodiment of the present invention. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0023] Various embodiments of the present invention will be further described in more detail with reference to the accompanying drawings. However, the present invention may be embodied in many other forms and should not be construed as being limited to any particular structure or function discussed in the following description. On the contrary, these embodiments are provided for the purpose of providing a thorough and complete description of the present invention.

[0024] According to the detailed description of the present invention, it will be apparent to those skilled in the art that the scope of the present invention encompasses any embodiment thereof disclosed herein, regardless of whether the embodiment is implemented independently or in cooperation with any other embodiment of the present invention. For example, the circuits and devices disclosed herein can be actually implemented by using any number of the embodiments provided herein. Furthermore, it should be understood that any embodiment of the present invention can be implemented using one or more of the elements presented in the appended claims.

[0025] The word "exemplary" is used herein to mean "used as an example." Unless specifically stated otherwise, any embodiment described herein as "exemplary" is not to be construed as preferred or advantageous over other embodiments.

[0026] Any positioning terminology, such as "left", "right", "up", "down", etc., may be used herein for convenience to describe the relationship of one element or feature to one or more other elements or features according to the figures. It should be clear that the positioning terminology is intended to encompass different orientations of the circuits disclosed herein in addition to the orientation(s) illustrated in the figures. As an example, if the circuit in the figures were imaginatively rotated 90 degrees clockwise, elements or features described as "left" and "right" relative to other elements or features would be oriented "above" and "below" the other elements or features, respectively. Thus, the positioning terminology used herein should not be construed as any limitation of the present invention.

[0027] Although numerical terminology such as "first," "second," and the like may be used herein to describe various embodiments and features thereof, it should be understood that the embodiments and features thereof should not be limited by this numerical terminology. This numerical terminology is used herein only to distinguish one embodiment or feature from another embodiment or feature. Thus, a first embodiment discussed below can be referred to as a second embodiment, and vice versa, without departing from the teachings of the present invention.

[0028] As used in the embodiments disclosed herein, a tunable inter-resonator coupling circuit may refer to a quantum circuit in which linear or nonlinear resonators are coupled together in a controlled manner. A non-limiting example of a linear resonator may include a harmonic oscillator, which is well known in the art (for this reason, a description of which is omitted herein). A non-limiting example of a nonlinear resonator may include a superconducting qubit.

[0029] As used in the embodiments disclosed herein, a superconducting qubit may refer to a superconducting quantum device configured to store one or more quantum bits (or qubits for short) of information. In this sense, a superconducting qubit serves as a quantum information storage and processing device. The source of nonlinearity in a superconducting qubit may be represented by one or more Josephson junctions. The term "Josephson junction" is used herein in its ordinary sense and may refer to a quantum mechanical device made of two superconducting electrodes separated by a barrier (e.g., a thin insulating tunnel barrier, an ordinary metal, a semiconductor, a ferromagnetic material, etc.).

[0030] According to embodiments disclosed herein, a quantum computing device, also referred to as a quantum computer, may refer to a device configured to perform different quantum computing operations (e.g., qubit operations such as reading the state of a superconducting qubit, initializing the state of a superconducting qubit, and entangling the state of a superconducting qubit with the state of other superconducting qubits in the quantum computing device, etc.) by using the tunable inter-resonator coupling circuit disclosed herein. Examples of existing implementations of such quantum computing devices may include superconducting quantum computers, trapped ion quantum computers, quantum computers based on spins in semiconductors, quantum computers based on cavity quantum electrodynamics, optical photon quantum computers, quantum computers based on defect centers in diamond, etc.

[0031] It should be noted that there are many tunable inter-qubit coupling circuits (also called tunable couplers) in the prior art. They are primarily used to implement quantum gates, allowing the states of qubits to interact with each other in a controlled manner. Some of the existing tunable inter-qubit coupling circuits are discussed below with reference to Figures 1-3.

[0032] 1 shows a block diagram of a tunable inter-qubit coupling circuit 100 according to the prior art. The circuit 100 comprises a first superconducting qubit 102, a second superconducting qubit 104, and a tunable coupling element 106. The first superconducting qubit 102 and the second superconducting qubit 104 are grounded and implemented similarly to each other, i.e., each of them comprises a parallel connection of a capacitor (C1 or C2, respectively) and two Josephson junctions (schematically shown as crosses in FIG. 1). The first superconducting qubit 102 and the second superconducting qubit 104 are coupled to a capacitor C1 or C2 in parallel with a tunable coupling element 106. 12Additionally, the first superconducting qubit 102 and the second superconducting qubit 104 are indirectly coupled to each other via a tunable coupling element 106. The tunable coupling element 106 comprises a grounded superconducting portion 108 and a superconducting island 110. Note that the term "superconducting island" as used herein may refer to a circuit component, all of whose parts are galvanically connected to each other with negligible self-inductance at all operating frequencies of the circuit. The (upper) grounded superconducting portion 108 is coupled to a capacitor C c and a (lower) superconducting island 110 on one side of the two Josephson junctions, which is a capacitor C c and on the other side of the two Josephson junctions. Thus, there is a Josephson junction between the grounded superconducting portion 108 and the superconducting island 110. Furthermore, the superconducting island 110 is ungrounded or floating, and a capacitor C 1c is coupled to the first superconducting qubit 102 via a capacitor C 2c to the second superconducting qubit 104 via

[0033] The Josephson junctions used in the circuit 100 provide anharmonicity between the first and second superconducting qubits 102, 104 and the tunable coupling element 106. However, if the first and second superconducting qubits 102, 104 and the tunable coupling element 106 all have negative anharmonicity (which is typically observed for such a transmon regime), this can lead to the following problems: the idle frequency of the tunable coupling element 106 exceeds the qubit frequency of the superconducting qubits 102, 104; the tunable coupling element 106 may become resonant with a readout resonator (which may additionally be connected to the circuit 100) during operation of the circuit 100 if the readout resonator has a frequency above the qubit frequency; During operation of the circuit 100, decoherence of the tunable coupling element 106 may also lead to a situation where the operating frequency of the tunable coupling element 106 is far away from its flux sweet spot (note that the sweet spot is a frequency of the tunable coupling element 106 that has no first-order sensitivity to the tuning parameter, which may be represented by the magnetic flux through the superconducting quantum interference device (SQUID) loop in the case of a transmon qubit, and by the charge bias in the case of a Cooper pair box (CPB) qubit. For example, when using a transmon with a symmetric SQUID, the sweet spot is at the maximum qubit frequency); Coupling of the tunable coupling element 106 to a higher excitation state may reduce the operating speed of the circuit 100.

[0034] 2 shows a block diagram of a tunable inter-qubit coupling circuit 200 according to the prior art. Similar to circuit 100, circuit 200 comprises a first superconducting qubit 202, a second superconducting qubit 204, and a tunable coupling element 206. The first superconducting qubit 202 is implemented similarly to the first superconducting qubit 102 and the second superconducting qubit 104. In particular, the first superconducting qubit 202 is grounded and comprises a parallel connection of a capacitor C1 and two Josephson junctions. At the same time, unlike circuit 100, the second superconducting qubit 204 is not grounded and is therefore connected differently in circuit 200 compared to the connection of the first superconducting qubit 202. The tunable coupling element 206 comprises a grounded superconducting portion 208 and a (non-grounded) superconducting island 210 arranged in the circuit 200 in the same manner as the grounded superconducting portion 108 and the superconducting island 110, respectively, in the circuit 100. The first superconducting qubit 202 and the second superconducting qubit 204 also have a capacitor C 12 , and indirectly coupled to each other via a tunable coupling element 206. The indirect coupling is achieved by coupling the 1c and C 2cHowever, circuit 200 lacks some of the benefits that may be provided if grounded superconducting portion 208 is replaced with an ungrounded superconducting island.

[0035] 3 shows a block diagram of a tunable inter-qubit coupling circuit 300 according to the prior art. Similar to circuits 100 and 200, circuit 300 comprises a first superconducting qubit 302, a second superconducting qubit 304, and a tunable coupling element 306. The first superconducting qubit 302 and the second superconducting qubit 304 are implemented similarly to the first superconducting qubit 102 and the second superconducting qubit 104 in circuit 100, respectively. However, the tunable coupling element 306 is connected differently between the first superconducting qubit 302 and the second superconducting qubit 304 compared to the tunable coupling elements 106, 206. More specifically, the tunable coupling element 306 is provided in circuit 300 such that there is no direct coupling between the first superconducting qubit 302 and the second superconducting qubit 304. The first superconducting qubit 302 and the second superconducting qubit 304 are only indirectly coupled to each other via a first superconducting island 308 and a second superconducting island 310, both of which are contained in a tunable coupling element 306. The first superconducting island 308 and the second superconducting island 310 are both ungrounded and each of them is coupled to a capacitor C 1cu , C 2cu , C 1cb , and C 2cb 3. The first superconducting qubit 302 and the second superconducting qubit 304 are coupled to each other via a Josephson coupling between the first superconducting island 308 and the second superconducting island 310. However, the circuit 300 lacks an effective direct inter-qubit coupling. For example, the capacitor C 12Due to the lack of a capacitor, a two-qubit gate based on circuit 300 may have limited speed of operation compared to a similar circuit with such a capacitor. Moreover, some practical scalable multi-qubit systems require a capacitor C large enough to provide a high speed two-qubit gate. 1cu and C 1cb It is not possible to place

[0036] The illustrative embodiments disclosed herein provide technical solutions that allow to mitigate or even eliminate the above-mentioned drawbacks of the prior art. In particular, the technical solutions disclosed herein involve providing both direct and indirect coupling between linear or nonlinear resonators in a quantum circuit. The indirect coupling is provided by using a tunable coupling element comprising two ungrounded superconducting islands. Since the superconducting islands are ungrounded, it is possible to provide the resonators and the superconducting islands with coupling frequencies of different signs, which in turn allows the interaction between the first and second resonators to be controlled more efficiently. Moreover, the design, calibration, and operation of such a quantum circuit with a tunable coupling element is easier compared to existing analogues, while providing the same or even better performance.

[0037] FIG. 4 shows a block diagram of a tunable inter-resonator coupling circuit 400 according to a first illustrative embodiment of the present invention. The circuit 400 comprises a first nonlinear resonator 402, a second nonlinear resonator 404, and a tunable coupling element 406. In this illustrative embodiment, each of the first nonlinear resonator 402 and the second nonlinear resonator 404 is implemented as a superconducting qubit (similar to that shown in FIG. 1). For this reason, the circuit 400 can be used to implement a two-qubit gate. However, the circuit 400 is not limited to this application, and can be used, for example, to implement a gate based on two or more linear resonators (e.g., harmonic oscillators as described below with reference to FIG. 5), or the circuit 400 can be used to implement a quantum gate between qutrits (in a three-level quantum system) or qudits (in a d-level quantum system). Qudits and qutrits have an infinite amount of energy levels and are therefore supported by nonlinear resonators. It should also be noted that a qubit can be formed when restricting the operation of a nonlinear resonator to its two lowest energy eigenstates.

[0038] Referring back to FIG. 4, the first superconducting qubit 402 and the second superconducting qubit 404 are coupled to a capacitor C 12 4 and 5. The first and second superconducting islands 408 and 410 are directly coupled to each other via a ground potential and indirectly coupled to each other via a tunable coupling element 406. The tunable coupling element 406 comprises a first superconducting island 408 and a second superconducting island 410, both of which are ungrounded. Moreover, the first and second superconducting islands 408 and 410 are arranged in the circuit 400 such that each of them is directly coupled to only one of the first and second superconducting qubits 402 and 404. More specifically, there is a first non-galvanic coupling between the first superconducting qubit 402 and the first superconducting island 408, and there is a second non-galvanic coupling between the second superconducting qubit 404 and the second superconducting island 410. The first and second non-galvanic couplings are both capacitive, i.e., a capacitor C 1c and C 2c4 , respectively. However, in some other embodiments, at least one of the first non-galvanic coupling, the second non-galvanic coupling, and the direct coupling between the first superconducting qubit 402 and the second superconducting qubit 404 may be inductive, if necessary and depending on the particular application. Moreover, in some other embodiments, the direct coupling itself may be implemented as a galvanic coupling, and at least one of the first non-galvanic coupling and the second non-galvanic coupling may be replaced with a galvanic coupling. The first superconducting island 408 and the second superconducting island 410 are coupled to each other via a Josephson junction (see the cross in FIG. 4 ), i.e., have a Josephson coupling between them. From this, the indirect coupling between the first superconducting qubit 402 and the second superconducting qubit 404 comprises the first non-galvanic coupling, the Josephson coupling, and the second non-galvanic coupling described above.

[0039] As can be seen from FIG. 4, the arrangement area of ​​the first superconducting island 408 is the capacitor C 1c One plate of the capacitor C c The second superconducting island 410 is bounded by one plate of the capacitor C 2c One plate of the capacitor C cand two Josephson junctions. Such an arrangement of the first superconducting island 408 and the second superconducting island 410 is given by way of example only. In some other embodiments, the first superconducting island 408 and the second superconducting island 410 may be arranged such that the indirect coupling between the first superconducting qubit 402 and the second superconducting qubit 404 comprises an additional third (galvanic or non-galvanic) coupling between the second superconducting qubit 404 and the first superconducting island 408, and an additional fourth (galvanic or non-galvanic) coupling between the first superconducting qubit 402 and the second superconducting island 410. Again, the third and fourth couplings may be capacitive or inductive, if necessary and depending on the particular application. By using these additional couplings, it is possible to increase the applicability and flexibility of the circuit 400. Additionally, one or both of the superconducting islands 408 and 410 may also have a coupling to ground via an additional capacitor.

[0040] Furthermore, tunable coupling element 406 may be configured such that its idle frequency is below the qubit frequencies of first superconducting qubit 402 and second superconducting qubit 404. In this case, tunable coupling element 406 may have a sweet spot located at (or near) the operating point of a two-qubit gate (implemented based on circuit 400). This may reduce gate errors resulting from decoherence of coupling element 406.

[0041] In one embodiment, tunable coupling element 406 may be implemented as a transmon qubit. By using a transmon qubit as a "mediator" between first superconducting qubit 402 and second superconducting qubit 404, it is possible to reduce sensitivity to charge noise.

[0042] In one embodiment, the circuit 400 may further comprise a first readout resonator and a second readout resonator (not shown). The first readout resonator is configured to read out the first resonator and has a first operating frequency. The second readout resonator is configured to read out the second resonator and has a second operating frequency. Each of the first operating frequency and the second operating frequency may be set to a value higher than the value of the operating frequency of the tunable coupling element 406. In this case, during operation of the circuit 400, there is no resonance between the tunable coupling element 406 and the readout resonator that would otherwise adversely affect the operation of the circuit 400.

[0043] FIG. 5 shows a block diagram of a tunable inter-resonator coupling circuit 500 according to a second illustrative embodiment of the present invention. The circuit 500 comprises a first linear resonator 502, a second linear resonator 504, and a tunable coupling element 506. The tunable coupling element 506 comprises a first superconducting island 508 and a second superconducting island 510, which are implemented and arranged in the same manner as the first superconducting island 408 and the second superconducting island 410 in the circuit 400, respectively. At the same time, the circuit 500 differs from the circuit 400 by the presence of a linear resonator (but not a nonlinear resonator). In particular, the first and second linear resonators 502 and 504 are shown in FIG. 5 as harmonic oscillators. In some other embodiments, at least one of the first linear resonator 502 and the second linear resonator 504 may be implemented as a coplanar waveguide resonator or a lumped element resonator. Circuit 500 may have similar advantages as circuit 400 , and the embodiments discussed above with respect to circuit 400 may be equally relevant to circuit 500 .

[0044] FIG. 6 shows a block diagram of a tunable inter-resonator coupling circuit 600 according to a third illustrative embodiment of the present invention. The circuit 600 comprises a first resonator 602, a second resonator 604, and a tunable coupling element 606. The tunable coupling element 606 comprises a first superconducting island 608 and a second superconducting island 610, which are implemented and arranged in the same manner as the superconducting islands in the circuit 400 or the circuit 500. At the same time, the circuit 600 differs from the circuits 400 and 500 in that the first resonator 602 and the second resonator 604 are of different types. More specifically, the first resonator 602 is nonlinear and is implemented as a superconducting qubit, and the second resonator 604 is linear and is implemented as a harmonic oscillator. It should be clear that the first resonator 602 can be of linear type and the second resonator 604 can be of nonlinear type, if necessary. In circuit 600, the second resonator 604 (i.e., a harmonic oscillator) can be used as a quantum bus for the first resonator 602 (i.e., a superconducting qubit), which can be very valuable in some applications.

[0045] FIG. 7 shows a block diagram of a quantum computing device 700 according to one illustrative embodiment of the present invention. The device 700 comprises a tunable inter-resonator coupling circuit 702 and a control unit 704. The circuit 702 may be implemented as one of the circuits 400, 500, and 600. The control unit 704 is configured to perform a quantum computing operation by using the circuit 702. The device 700 may further comprise a memory 706 storing executable instructions 708, which, when executed by the control unit 704, may cause the control unit 704 to perform a quantum computing operation. The control unit 704 may also store a result(s) of the quantum computing operation in the memory 706. It should be noted that the number, arrangement, and interconnection of the building elements constituting the device 700 shown in FIG. 7 are not intended to be any limitation of the present disclosure, but are merely used to provide a general idea of ​​how the building elements may be implemented within the device 700. For example, device 700 may comprise two or more circuits 702, each implemented as circuit 400, 500, or 600, or may comprise any combination of circuits 400, 500, and 600, depending on the quantum computing operation to be performed.

[0046] The control unit 704 may refer to a central processing unit (CPU), a general purpose processor, a special purpose processor, a microcontroller, a microprocessor, an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), a digital signal processor (DSP), a complex programmable logic device, etc. It is also noted that the control unit 704 may be implemented as any combination of one or more of the foregoing. As an example, the control unit 704 may be a combination of two or more microprocessors.

[0047] The memory 706 may be implemented as any classical non-volatile or volatile memory used in modern electronic computing machines. By way of example, non-volatile memory may include read only memory (ROM), ferroelectric random access memory (RAM), programmable ROM (PROM), electrically erasable PROM (EEPROM), solid state drive (SSD), flash memory, magnetic disk storage (such as hard drives and magnetic tape), optical disk storage (such as CDs, DVDs, and Blu-ray disks), etc. For volatile memory, examples include dynamic RAM, synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), static RAM, etc.

[0048] The executable instructions 708 stored in memory 706 may be configured as computer-executable code that causes the control unit 704 to perform quantum computing operations by using the circuitry 702. The computer-executable code for performing the quantum computing operations may be written in any combination of one or more programming languages, such as Java, C++, etc. In some examples, the computer-executable code may be in the form of a high-level language or in a pre-compiled form and generated on the fly by an interpreter (also pre-stored in memory 706).

[0049] Although exemplary embodiments of the present invention have been described herein, it should be noted that various changes and modifications can be made in the embodiments of the present invention without departing from the scope of legal protection defined by the appended claims. In the appended claims, the word "comprises" does not exclude other elements or operations, and the indefinite articles "a" or "an" do not exclude a plurality. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage. The following is a summary of the claims as originally filed: [C1] A tunable inter-resonator coupling circuit, comprising: a first resonator, wherein said first resonator is linear or non-linear, a second resonator, where the second resonator is linear or nonlinear, and the first resonator and the second resonator have a direct coupling between them, a tunable coupling element arranged to provide an indirect coupling between the first resonator and the second resonator; the tunable coupling element comprises a first superconducting island and a second superconducting island, both of which are ungrounded; The indirect coupling comprises: (i) a first coupling between the first resonator and the first superconducting island; (ii) a Josephson coupling between the first superconducting island and the second superconducting island; and (iii) a second coupling between the second resonator and the second superconducting island. [C2] The circuit of C1, wherein each of the first resonator and the second resonator is implemented as one of a harmonic oscillator, a coplanar waveguide resonator, and a lumped element resonator. [C3] The circuit of C1, wherein each of the first resonator and the second resonator is implemented as a superconducting qubit. [C4] The circuit of any one of C1 to C3, wherein the direct coupling is implemented as a non-galvanic coupling between the first resonator and the second resonator. [C5] The circuit of any one of C1 to C4, wherein the first coupling is implemented as a capacitive coupling between the first resonator and the first superconducting island, and the second coupling is implemented as a capacitive coupling between the second resonator and the second superconducting island. [C6] The circuit of any one of C1 to C5, wherein the tunable coupling element is implemented as a transmon qubit. [C7] The circuit described in any one of C1 to C6, wherein the first resonator has a first frequency, the second resonator has a second frequency, and the tunable coupling element has an idling frequency lower than each of the first frequency and the second frequency. [C8] - a first readout resonator configured to read out the first resonator, where the first readout resonator has a first operating frequency; a second readout resonator configured to read out the second resonator, where the second readout resonator has a second operating frequency; wherein each of the first operating frequency and the second operating frequency is greater than each of the idle frequency of the tunable coupling element, the first frequency of the first resonator, and the second frequency of the second resonator. [C9] The circuit described in any one of C1 to C8, wherein the indirect coupling further includes a third coupling between the second resonator and the first superconducting island, and a fourth coupling between the first resonator and the second superconducting island. [C10] The circuit of C9, wherein the third coupling is implemented as a capacitive coupling between the second resonator and the first superconducting island, and the fourth coupling is implemented as a capacitive coupling between the first resonator and the second superconducting island. [C11] The circuit of any one of C1-10, wherein at least one of the first superconducting island and the second superconducting island has a capacitive coupling to ground. [C12] A quantum computing device comprising at least one tunable inter-resonator coupling circuit according to any one of C1 to C11, and a control unit configured to perform a quantum computing operation by using the at least one tunable inter-resonator coupling circuit.

Claims

1. A tunable inter-resonator coupling circuit (400, 500, 600), comprising: a first resonator (402, 502, 602), where said first resonator (402, 502, 602) is linear or non-linear and has a first frequency; a second resonator (404, 504, 604), where the second resonator (404, 504, 604) is linear or non-linear and has a second frequency, and the first resonator (402, 502, 602) and the second resonator (404, 504, 604) have a direct coupling between them, a tunable coupling element (406, 506, 606) arranged to provide an indirect coupling between the first resonator (402, 502, 602) and the second resonator (404, 504, 604), wherein the tunable coupling element (406, 506, 606) has an idle frequency below each of the first frequency and the second frequency; a first readout resonator configured to read out said first resonator (402, 502, 602), where said first readout resonator has a first operating frequency; a second readout resonator configured to read out said second resonator (404, 504, 604), where said second readout resonator has a second operating frequency; the tunable coupling element (406, 506, 606) comprises a first superconducting island (408, 508, 608) and a second superconducting island (410, 510, 610), both of which are ungrounded; the indirect coupling comprises: (i) a first coupling between the first resonator (402, 502, 602) and the first superconducting island (408, 508, 608); (ii) a Josephson coupling between the first superconducting island (408, 508, 608) and the second superconducting island (410, 510, 610); and (iii) a second coupling between the second resonator (404, 504, 604) and the second superconducting island (410, 510, 610); A tunable inter-resonator coupling circuit, wherein each of the first operating frequency and the second operating frequency exceeds each of the idle frequency of the tunable coupling element (406, 506, 606), the first frequency of the first resonator (402, 502, 602), and the second frequency of the second resonator (404, 504, 604).

2. 10. The circuit of claim 1, wherein each of the first resonator and the second resonator is implemented as one of a harmonic oscillator, a coplanar waveguide resonator, and a lumped element resonator.

3. The circuit of claim 1 , wherein each of the first resonator and the second resonator is implemented as a superconducting qubit.

4. The circuit (400, 500, 600) of any one of claims 1 to 3, wherein the direct coupling is implemented as a non-galvanic coupling between the first resonator (402, 502, 602) and the second resonator (404, 504, 604).

5. The circuit (400, 500, 600) of any one of claims 1 to 4, wherein the first coupling is implemented as a capacitive coupling between the first resonator (402, 502, 602) and the first superconducting island (408, 508, 608) and the second coupling is implemented as a capacitive coupling between the second resonator (404, 504, 604) and the second superconducting island (410, 510, 610).

6. The circuit (400, 500, 600) of any one of claims 1 to 5, wherein the tunable coupling element (406, 506, 606) is implemented as a transmon qubit.

7. The circuit (400, 500, 600) of any one of claims 1 to 6, wherein the indirect coupling further comprises a third coupling between the second resonator (404, 504, 604) and the first superconducting island (408, 508, 608) and a fourth coupling between the first resonator (402, 502, 602) and the second superconducting island (410, 510, 610).

8. 8. The circuit (400, 500, 600) of claim 7, wherein the third coupling is implemented as a capacitive coupling between the second resonator (404, 504, 604) and the first superconducting island (408, 508, 608) and the fourth coupling is implemented as a capacitive coupling between the first resonator (402, 502, 602) and the second superconducting island (410, 510, 610).

9. The circuit (400, 500, 600) of any one of claims 1 to 8, wherein at least one of the first superconducting island (408, 508, 608) and the second superconducting island (410, 510, 610) has a capacitive coupling to ground.

10. A quantum computing device (700) comprising at least one tunable inter-resonator coupling circuit (400, 500, 600) according to any one of claims 1 to 9, and a control unit (704) configured to perform quantum computing operations by using the at least one tunable inter-resonator coupling circuit (400, 500, 600).

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