Arrangements and methods for coupling to qubits - Patents.com

Abstract

An arrangement for coupling to a qubit comprises the qubit and another circuit element controllably coupled to and isolated from the qubit. A network of resonators is provided between the qubit and the other circuit element. The network of resonators includes a plurality of resonators, including linear and / or nonlinear resonators. At least two of the plurality of resonators have the same circuit topology but different frequency responses.

Description

[Technical field]

[0001] The present disclosure relates to quantum computing. More particularly, the present disclosure relates to arrangements and methods for coupling to qubits such that the strength of the coupling can be very effectively defined by appropriate tuning. Furthermore, the present disclosure relates to quantum computing systems. [Background technology]

[0002] Qubits are the basic circuit elements used in quantum computing. Figure 1 shows an example of qubits 101 and 102. Controllable coupling to qubits is needed for a variety of reasons. One such reason is the need to controllably reset a qubit by coupling it to a quantum circuit refrigerator (QCR), which absorbs the qubit's energy and obtains its ground state. See QCRs 103 and 104, respectively. In some cases, one may want to initialize a qubit to a thermal state by coupling it to a controllable heat bath. Controllable coupling between qubits is also needed to perform quantum logic gates.

[0003] FIG. 2 shows a schematic diagram of a quantum computing system including multiple qubits 201, 202, 203, and 204. Controllable coupling may need to occur between any pair of qubits while other qubits need to be as unaffected as possible. This can be particularly challenging in so-called grid addressing of qubits, where the control signal lines form a grid and each qubit is affected by at least two separate control signal lines. In grid addressing, the control signal directed to a particular qubit is obtained from the combined effect of the signals on at least two respective control signal lines, while all subsequent qubits along each individual signal line need to be unaffected. However, it has been found that even low-level effects of individual control signals can cause undesirable crosstalk due to insufficient blocking effect of couplings that should remain "off".

[0004] Figure 3 shows the case where two so-called ancilla qubits 301 and 302 are located on either side of the qubit 303 used for the actual computation. The ancilla qubits can be used for parity measurements as part of quantum error correction. In particular, if autonomous error correction can be utilized, no readout of the ancilla qubits 301 and 302 is necessary, and a simple unconditional high-fidelity reset is sufficient. This can be achieved by controllably coupling the ancilla qubits to the respective QCRs 304 or 305.

[0005] Figure 4 shows a known method of initializing a qubit using a coupler, published in T. Yoshioka, JSTsai: “Fast unconditional initialization for superconducting qubit and resonator using quantum-circuit refrigerator”, Appl. Phys. Lett. 119, 124003 (2021). The qubit includes a superconducting loop broken by two Josephson junctions 401 and 402. The coupler includes a resonator 403 capacitively coupled at one end to the qubit and at the other end to a photon absorption circuit. The photon absorption circuit includes two SIN (superconductor-insulator-normal metal) junctions 404 and 405 in the loop and a bias voltage source 406, the low potential side of which is grounded. A first control signal source 407 can be used to excite the qubits |e,0>→|f,0> and |f,0>→|g,1> to transfer energy from the qubits to the resonator 403 as part of the reset process. A second control signal source 408 can be used to perform a read operation using the resonator 403. The circuit shown in FIG. 4 can be used successfully to unconditionally reset a qubit, but at the cost of continuous unnecessary energy decay, which in turn adversely affects the thermal relaxation time T1 of the qubit. The need to go through an energy transfer process to perform the reset limits the speed of the reset.

[0006] Further adverse effects of known coupling to qubits become more evident in larger quantum computing systems, which calls for miniaturization of all circuit hardware. Short distances between circuit elements often create more difficult problems with unwanted crosstalk. Also, the smaller the circuit elements, the more difficult it is to make them precisely enough. Inevitable variations in the manufacturing process often cause initial deviations from the desired frequency characteristics, increasing the need for subsequent laborious adjustments. [Prior art documents] [Non-patent literature]

[0007] [Non-Patent Document 1] T. Yoshioka, JSTsai: “Fast unconditional initialization for superconducting qubit and resonator using quantum-circuit refrigerator”, Appl. Phys. Lett. 119, 124003 (2021) Summary of the Invention [Problem to be solved by the invention]

[0008] 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 or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter.

[0009] It is an object to provide an arrangement and a method for coupling to a qubit, and a quantum computing system, where the coupling exhibits a large difference in coupling strength between the on and off states. These and other objects are achieved by the features of the independent claims. Further implementations are evident from the dependent claims, the description and the figures. [Means for solving the problem]

[0010] According to a first aspect, an arrangement for coupling to a quantum bit comprises the quantum bit and other circuit elements controllably coupled to and isolated from the quantum bit to perform a quantum computing operation. A network of resonators is provided between the quantum bit and the other circuit elements. The network of resonators comprises a plurality of resonators, including linear and / or nonlinear resonators. At least two of the plurality of resonators have the same circuit topology but different frequency responses.

[0011] According to one embodiment, the other circuit element is a quantum circuit refrigerator, which has at least the advantage that coupling through a network of resonators can be very effectively used to reset qubits.

[0012] According to one embodiment, the other circuit element is another qubit, which includes at least the advantage that coupling through a network of resonators can be used to allow desired pairs or groups of qubits to interact with each other, while effectively preventing other qubits from participating in undesired interactions.

[0013] According to one embodiment, the network of resonators comprises a plurality of the resonators coupled in series between the qubit and the other circuit elements, which includes at least the advantage that couplings can be relatively simply designed by replicating a similar topology as many times as desired, without concern for small variations that may be introduced by manufacturing tolerances.

[0014] According to one embodiment, there are at least six of the resonators coupled in series between the qubit and the other circuit elements, which includes at least the advantage that advantageously wide passbands and / or stopbands can be achieved in the frequency response of the network of resonators.

[0015] According to one embodiment, each of the resonators comprises a capacitively shunted Josephson junction, which includes the advantage that at least some of the fabrication steps used to fabricate the resonators may be the same as, or at least very similar to, those used to fabricate other circuit elements, such as qubits in a quantum computing system.

[0016] According to one embodiment, each of the resonators includes a quantum bit, which includes the advantage that at least some of the fabrication steps used to fabricate the resonators may be the same as, or at least very similar to, those used to fabricate other circuit elements, such as computational qubits in a quantum computing system.

[0017] According to one embodiment, the network of resonators includes at least one series-coupled LC resonator as part of a connection between the qubit and the other circuit element, and at least one LC resonator between the connection and ground, which includes at least the advantage that the network of resonators can have a wide range of different properties while maintaining a relatively small footprint on a substrate.

[0018] According to one embodiment, there may be three LC resonators between the connection and ground, one of which is coupled between the midpoint of the series-coupled LC resonators and ground, which includes at least the advantage that a network of resonators can be constructed with a good understanding of its possible frequency characteristics.

[0019] According to a second aspect, there is provided a quantum computing system comprising a plurality of qubits, at least one of which forms part of an arrangement of the type described above.

[0020] According to one embodiment, the plurality of qubits form an array, each qubit in the array can then form part of an arrangement of the type described above, the qubits in the array forming together said other circuit elements, this includes at least the advantage that quantum computing systems with a very large number of qubits can be built with advantageous coupling properties between the qubits.

[0021] According to one embodiment, the qubits in the array are addressable via a grid addressing scheme that includes a grid of addressing lines in at least two different directions through the array, such that combinations of control signals via the grid addressing scheme are configured to selectively define which qubits in the array become coupled together via the network of resonators. This includes at least the advantage that relatively few control signal lines, i.e. addressing lines, are required to control a large number of qubits.

[0022] According to a third aspect, there is provided a method for coupling to a quantum bit, the method comprising the steps of controllably coupling and decoupling the quantum bit with other circuit elements to perform a quantum computing operation, and communicating the controllable coupling through a network of resonators between the quantum bit and the other circuit elements. The network of resonators includes a plurality of resonators, including linear and / or nonlinear resonators. At least two of the plurality of resonators have the same circuit topology but different frequency responses.

[0023] According to one embodiment, the resonator is a static resonator and the controllable coupling and decoupling is achieved by tuning the operating frequency of at least one of the qubits and the other circuit elements, which includes at least the advantage that a relatively simple structure is required to achieve coupling.

[0024] According to one embodiment, among the plurality of resonators there is at least one frequency-tunable resonator. The controllable coupling and decoupling may then involve tuning one or more resonant frequencies of such at least one frequency-tunable resonator. This includes at least the advantage that a more versatile system can be built than with only static resonators.

[0025] In the following, exemplary embodiments are explained in more detail with reference to the accompanying figures and drawings. [Brief description of the drawings]

[0026] [Figure 1] FIG. 1 illustrates two qubits, two QCRs, and their mutual coupling. [Diagram 2] FIG. 1 illustrates four qubits and their mutual couplings. [Diagram 3] FIG. 2 illustrates a computation qubit, two ancilla qubits, and two QCRs used to reset the ancilla qubits. [Figure 4] FIG. 2 illustrates a qubit, a resonator, and an energy absorption circuit. [Diagram 5] FIG. 1 illustrates the principle of using a coupler between a qubit and another circuit element. [Figure 6] FIG. 2 illustrates an example of a coupler between a qubit and another circuit element. [Figure 7] FIG. 2 illustrates an example of a coupler between a qubit and another circuit element. [Figure 8] FIG. 2 illustrates an example of the frequency response of a coupler between a qubit and another circuit element. [Figure 9] FIG. 1 illustrates the principle of using a coupler network between a qubit and another circuit element. [Figure 10] FIG. 2 illustrates an example of a coupler network between a quantum bit and another circuit element. [Figure 11] FIG. 13 illustrates a comparison of the frequency response of a coupler between a qubit and another circuit element and a coupler network. [Figure 12] FIG. 2 illustrates an example of a coupler network between a quantum bit and another circuit element. [Figure 13] FIG. 13 shows the frequency response of the arrangement of FIG. 12 in two different examples. [Figure 14] FIG. 2 illustrates an example of a coupler network between a quantum bit and another circuit element. [Figure 15] FIG. 13 illustrates a comparison of the frequency response of a coupler between a qubit and another circuit element and a coupler network. [Figure 16] FIG. 1 illustrates an array of grid-addressable qubits and couplers between them. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0027] In the following description, reference is made to the accompanying drawings which form a part hereof, and in which is shown by way of illustration specific embodiments in which the present disclosure may be arranged. It is to be understood that other embodiments may be utilized and structural or logical changes may be made without departing from the scope of the present disclosure. Therefore, the following detailed description is not to be taken in a limiting sense, and the scope of the present disclosure is defined by the appended claims.

[0028] For example, it should be understood that disclosure related to a described method may also apply to a corresponding device or system configured to perform that method, and vice versa. For example, where certain method steps are described, the corresponding device may include units that perform the described method steps, even if such units are not explicitly described or shown in the figures. Conversely, for example, where a particular apparatus is described in terms of functional units, the corresponding method may include steps that perform the described functions, even if such steps are not explicitly described or shown in the figures. Furthermore, it should be understood that features of the various exemplary aspects described herein may be combined with each other, unless otherwise specified.

[0029] 5 is a generalized schematic diagram of a quantum circuit that can use a coupler 501 to selectively couple a source 502 of RF energy to a destination 503. In the following discussion, the emphasis is on the selectivity of the coupling, so the exact nature of the source 502 and destination 503 is not important, and the coupling shall be as effective as possible when established or in an "on" state, and the "off" state of the coupling shall block the transmission of RF energy in the frequency range of interest as effectively as possible. In many cases, for illustrative purposes, the source 502 can be considered a qubit. The destination 503 can be, for example, another qubit, a QCR, or some other circuit element to which the source 502 is selectively coupled using the coupler 501.

[0030] Making the coupling selective may involve using a tunable coupler between a fixed-frequency source and a fixed-frequency destination. Also, so-called parked-frequency sources or destinations may be considered "fixed-frequency" in this respect, where parking means intentionally maintaining a circuit element at a selected resonant frequency, even though it could be tuned to a different resonant frequency if desired. Alternatively, the coupler may have a fixed-frequency characteristic, and making the coupling selective may involve tuning at least one of the source and destination. Also, the source, coupler, and destination may all be tunable. The source, coupler, and destination system may be evaluated in terms of the frequency response of the coupling. Such a frequency response may include a passband, the center frequency of which is the frequency at which the coupling is most efficient. Similarly, the frequency response may include a stopband, the center frequency of which is the frequency at which the coupling most effectively blocks the propagation of RF energy.

[0031] Figures 6 and 7 show examples of couplers that can be used to realize an arrangement like that of Figure 5. The coupler of Figure 6 is a so-called MIT style coupler, where a flux qubit 601 is connected to the midpoint of a capacitively shunted series chain of two capacitive elements. A tuning signal through a nearby inductance creates a magnetic flux that induces a compensating current in the flux qubit 601, creating a superposition of clockwise and counterclockwise loop currents, which changes the overall resonant properties of the coupler 501. In Figure 7, the coupler 501 is implemented as a capacitively shunted Josephson junction 701.

[0032] Figure 8 shows an example of the frequency response of coupling implemented with a known coupler according to the principle shown in Figure 5. The graph in Figure 8 shows the S21 parameter value as a function of frequency for coupling from source to destination. The importance of the S21 parameter value in evaluating the efficiency of coupling can be shown by considering both the source and destination as qubits. The coupling rate (i.e. the time it takes for two qubits to exchange a population of microwave quanta) is proportional to |S21| and not |S21|^2, especially for small values. Some leveling is seen at larger values ​​compared to |S21|. This does not change the main concept, but to compensate for the leveling, it may be advantageous to design the coupler a little deeper than if no leveling occurred. For practically controllable coupling, a fairly deep off-state is required. If the on-state coupling rate is 50 MHz, it is expected that S21 needs to be reduced by about -150 dB from the corresponding on-state value to reach a coupling rate of 1 Hz in the off-state.

[0033] In Figure 8, the on-state occurs at about 3.98 GHz, and the off-state occurs at about 5.69 GHz. However, both the on-state frequency band and (especially) the off-state frequency band have very sharp peak shapes in Figure 8, which means that very precise tuning to the intended frequencies is required. Couplers such as those in Figures 6 and 7 are called narrowband couplers for this reason.

[0034] At this point, one may recall the difficulties mentioned in the description of the prior art: when the physical dimensions of quantum circuit elements are reduced, it becomes increasingly difficult to manufacture said quantum circuit elements accurately enough to consistently achieve the required accuracy in frequency characteristics, especially when a large number of quantum circuit elements have to be manufactured on a common substrate.

[0035] FIG. 9 shows a schematic arrangement for coupling to a source 502, which may be a qubit. As in FIG. 5, the element shown as destination 503 is another circuit element that is controllably coupled to and isolated from the qubit (or source 502) to perform a quantum computing operation. Instead of a single coupler as in FIG. 5, the arrangement of FIG. 9 includes a coupler network 901 between the source 502 and the destination 503. The coupler network 901 is composed of a network of resonators between the source 502 and the destination 503. The network of resonators includes a plurality of resonators, including linear and / or nonlinear resonators. At least two of the plurality of resonators have the same circuit topology but different frequency responses.

[0036] The drawbacks of the prior art discussed above are in some ways turned to advantages in Fig. 9. Because it is difficult to manufacture two resonators exactly alike based on circuit topology so that they have the same frequency response, Fig. 9 intentionally allows the frequency responses to differ. It turns out that the natural variations in frequency characteristics caused by statistical variations in the manufacturing process can result in a more favorable frequency response when a network of resonators is used as a coupler than individual resonators. When resonators in a network are taken together, they can form so-called wideband couplers, examples of which are described in more detail below.

[0037] Figure 10 shows an example of applying the principles shown in Figure 9. In the arrangement of Figure 10, a coupler network 901 between a source 502 and a destination 503 includes six couplers of the type shown in Figure 7 coupled in series. For illustrative purposes, one of the six couplers is designated by reference numeral 1001 in Figure 10. Since each of the couplers is itself a resonator, Figure 10 essentially shows a network of resonators (coupled in series) between a source (or qubit) 502 and a destination (or other circuit element) 503. In the embodiment of Figure 10, each resonator includes a capacitively shunted Josephson junction.

[0038] FIG. 11 shows the frequency response, expressed as the S21 parameter value as a function of frequency, of a combination made with the narrowband single resonator coupler 501 of FIG. 7 (graph 1101) and the wideband six resonator coupler network 901 of FIG. 10 (graph 1102). Both have a wide passband centered at about 4.25 GHz and a narrow stopband centered at about 4.53 GHz. However, the upper end of the passband in graph 1102, at about 4.38 GHz, drops off much more sharply than in graph 1101, and the stopband is deeper and wider. This shows that the wideband six resonator coupler network 901 of FIG. 10 provides very effective coupling at the passband frequencies while very effectively blocking all unwanted transmissions of RF energy at the stopband frequencies. In addition, the nominal stop frequency of the wideband six-resonator coupler network 901 of FIG. 10 does not need to match unwanted resonant frequencies (e.g., resonant frequencies of nearby qubits that are not currently coupled anywhere) particularly precisely, compared to the similar requirement when coupled with the narrowband single-resonator coupler 501 of FIG. 7.

[0039] The significant width of the stopband of the six-resonator coupler network 901 of FIG. 10 is represented by the deep valley in graph 1102 and is also useful in the presence of multiple unwanted resonant frequencies that should not currently be coupled, as long as all such unwanted resonant frequencies are close enough to each other that they fall within the useful width of the stopband of graph 1102.

[0040] The number of resonators coupled in series between the source and destination affects the width of the stopband and the steepness of the band edges in the frequency response. In an advantageous embodiment such as that of Figure 10, there are at least six resonators coupled in series between the source 502 and destination 503.

[0041] 12 shows another embodiment in which coupler network 901 includes a network of resonators coupled in series between a source 502 and a destination 503. In this embodiment, each of the resonators includes a qubit, and in particular, each of the resonators is a so-called MIT style coupler with a flux qubit connected to the midpoint of a capacitive shunt series chain of two capacitive elements. In the embodiment of FIG. 12, there are eight resonators coupled in series between the source 502 and the destination 503. A common control signal line 1201 can be used to tune all eight resonators simultaneously.

[0042] Figure 13 shows the frequency response, expressed as the S21 parameter value as a function of frequency, for couplings made with the wideband eight-resonator coupler network 901 of Figure 12 for two different control signal values. In both cases, there is a relatively wide passband whose edges drop off sufficiently sharply at least below the -100 dB level, and relatively sharply below the -150 dB level, to effectively cut off couplings of unwanted resonant frequencies. The value of the S21 parameter remains sufficiently close to 0 dB throughout the passband, which is more than 100 MHz wide.

[0043] Other forms of resonators may be used in the coupler network than those shown in Figures 10 and 12. Figure 14 shows an embodiment in which the network of resonators in coupler network 901 includes at least one series coupled LC resonator 1401 as part of a connection between source 502 and destination 503, and at least one LC resonator between said connection and ground. In the embodiment of Figure 14, there are three of said LC resonators 1402, 1403, and 1404 between said connection and ground.

[0044] FIG. 15 shows a comparison of the frequency response, expressed as the S21 parameter value as a function of frequency, of coupling made with a narrowband single resonator coupler (graph 1501) and with the wideband four resonator coupler network 901 of FIG. 14 (graph 1502). Again, it can be seen that using wideband couplers it is easier to achieve the desired combination of passbands and stopbands, but it is still not entirely straightforward, especially when only a few elements of some types are available, for example due to manufacturing issues. For example, in FIG. 15 the desired S21 parameter value of -150 dB for the intended stopband is not yet reached, but perhaps one more resonator would be needed or a narrower band would have to be accepted. However, it should be noted that even two different "off" frequencies with a somewhat insufficient off state between them can be useful for wideband couplers, since a "spectator qubit" or other circuit element with which coupling should not currently take place can spend most of its important time at these two "off" frequencies even if it has to quickly pass through a non-ideal frequency.

[0045] In the above example, we described coupling via a network of resonators between a source and a destination. As already hinted at above, the source could be a qubit and the destination could be, for example, a QCR. In such a case, controllably coupling the qubit to the QCR could be used to unconditionally reset the qubit. As another example, the destination could be a controllable heat bath, in which case the controllable coupling could be used to initialize the qubit to a thermal state by coupling it to the controllable heat bath.

[0046] Similar controllable coupling through a network of resonators can also be used between two (or more) qubits to perform quantum computing gates. In general, a quantum computing system may include multiple qubits, at least one of which forms part of an arrangement of the type described above. By way of example, a quantum computing system according to an embodiment will now be described with reference to FIG.

[0047] In Fig. 16, a number of qubits belonging to a quantum computing system form an array. Each of said qubits 1601, 1602, 1603, and 1604 shown in Fig. 16 is a transmon, although other types of qubits may be employed. In Fig. 16, shunt capacitors are omitted to simplify the graphical representation. Each qubit in the array forms part of an arrangement of the type described above, such that the qubits 1601, 1602, 1603, and 1604 in the array form "other circuit elements" with respect to each other. In other words, a controllable coupling through a network of resonators may be formed between desired pairs of qubits in the array.

[0048] In the embodiment of FIG. 16, the qubits are tunable, i.e. addressable, by a grid addressing scheme that includes a grid of addressing lines. In this embodiment, the addressing lines run in two different directions. See horizontal addressing lines 1611 and 1612, and vertical addressing lines 1613 and 1614. It is also possible to provide a grid of addressing lines that pass through the array in two or more different directions. The basic idea of ​​grid addressing is that a combination of control signals is used through the addressing lines of the grid addressing scheme to interact with the qubits. For example, a small magnitude control signal passing only through the upper horizontal addressing line 1611, or only through the left vertical addressing line 1613, will not cause significant interaction with any of the qubits 1601, 1602, or 1603, even if they are arranged along said addressing lines (although some small, unintended interaction cannot be completely avoided). Sending such a small magnitude control signal simultaneously over both addressing lines 1611 and 1613 produces a control signal combination at the top left qubit 1601 that is strong enough to induce the desired interaction with the qubit.

[0049] In addition to the qubits, the quantum computing system of FIG. 16 includes a resonator between the qubits. Here, we can first consider what happens in a quantum computing system when the resonator is a single resonator of the type shown in FIG. 7 and FIG. 10, constituting a narrowband coupler between the qubits. As an example, we can assume that resonator 1621 is utilized to couple qubits 1601 and 1602 by tuning said qubits to match the on-frequency of resonator 1621. A combination of control signals via addressing lines 1611 and 1613 is used to tune qubit 1601, and a combination of control signals via addressing lines 1611 and 1613 is used to tune qubit 1602. Qubits 1603 and 1604 are unaffected, but some degree of interaction inevitably occurs. A small magnitude control signal via addressing line 1613 partially tunes qubit 1603, and the same occurs between addressing line 1614 and qubit 1604. Considering that resonators 1621, 1622, 1623, and 1624 are narrowband couplers, partial tuning of qubits 1613 and 1614 will likely move them out of the narrow off-frequency peaks in the frequency responses of at least some of resonators 1622, 1623, and 1624, causing unintended interactions between pairs of qubits in a quantum computing system.

[0050] Alternatively, it may be assumed that each possible coupling between a pair of qubits may pass through a resonator that constitutes the network. For example, the resonator shown as 1621 in FIG. 16 and constituting a narrowband coupler may be replaced with a network of resonators following the general approach shown in, for example, FIG. 10 or FIG. 14. A combination of control signals via addressing lines may again be used to selectively tune a desired pair of qubits to resonate in a known passband of the corresponding resonator network, while also being used to maintain other qubits of the array at one or more frequencies that coincide with one or more stopbands of the resonator network. In such an embodiment, the combination of control signals via addressing lines is configured to selectively define which qubits in the array are coupled through the network of resonators.

[0051] Compared to a solution with only a single narrowband coupler between qubits, in a modified quantum computing system as described above, the off-state of coupling can be wider in frequency and the coupling blocking capability can be deeper. As already mentioned, this is advantageous because, despite the goal of avoiding the interaction of low-level individual control signals with "spectator" qubits, some unintended detuning can still occur that would move the affected qubit away from the exact resonant frequency in the absence of any control signal at all. A wider stopband can be more effective to cover the frequencies of such slightly detuned spectator qubits as well.

[0052] Any ranges or device values ​​described herein may be expanded or modified without losing the effect sought, and any embodiment may be combined with another embodiment unless expressly prohibited.

[0053] Although the subject matter has been described in language specific to structural features and / or acts, it should be understood that the subject matter defined in the appended claims is not necessarily limited to the specific features or acts described above. Rather, the specific features and acts described above are disclosed as example ways of implementing the claims, and other equivalent features and acts are intended to be within the scope of the claims.

[0054] It will be understood that the benefits and advantages described above may relate to one embodiment or to several embodiments. The embodiments are not limited to those that solve any or all of the problems described or those that have any or all of the benefits and advantages described. Further, it will be understood that references to "an" or "an" item may refer to one or more of those items.

[0055] The steps of the methods described herein may be performed in any suitable order, or simultaneously where appropriate. Additionally, individual blocks may be deleted from any method without departing from the spirit and scope of the subject matter described herein. Aspects of any of the embodiments described above may be combined with aspects of any of the other embodiments described above to form further embodiments without losing the desired effect.

[0056] As used herein, the term "comprising" is used to mean including the specified methods, blocks, or elements, but not including such blocks or elements in an exclusive list, and the methods or apparatus may include additional blocks or elements.

[0057] It will be understood that the above description is given by way of example only, and that various modifications may be made by those skilled in the art. The above specification, examples, and data provide a complete description of the structure and use of the exemplary embodiments. Although various embodiments have been described above with a certain degree of particularity, or with reference to one or more individual embodiments, those skilled in the art may make many modifications to the disclosed embodiments without departing from the spirit or scope of the present specification. [Explanation of symbols]

[0058] 101 qubits 102 qubits 103 QCR 104 QCR 201 qubits 202 qubits 203 qubits 204 qubits 301 Ancira Qubit 302 Ancillary Qubit 303 qubits 304 QCR 305 QCR 401 Josephson Junction 402 Josephson Junction 403 resonator 404 SIN junction 405 SIN junction 406 Bias voltage source 407 First control signal source 408 Second Control Signal Source 501 Coupler 502 Source 503 Destination 601 Flux Qubit 701 Capacitive Shunt Josephson Junction 901 Coupler Network 1001 Coupler 1201 Common control signal line 1401 Series coupled LC resonator 1402 LC resonator 1403 LC resonator 1404 LC resonator 1601 qubits 1602 qubits 1603 qubits 1604 qubits 1611 Addressing Lines 1612 Addressing Lines 1613 Addressing Lines 1614 Addressing Lines 1621 resonator 1622 resonator 1623 resonator 1624 resonator

Claims

1. 1. An arrangement for coupling to a qubit, comprising: The quantum bit; and other circuit elements controllably coupled to and isolated from the qubits to perform quantum computing operations; a network of resonators between the qubits and the other circuit elements; and Equipped with the network of resonators includes a plurality of resonators, including linear or nonlinear resonators or both; An arrangement wherein at least two of the plurality of resonators have the same circuit topology but different frequency responses.

2. The arrangement of claim 1 , wherein the other circuit element is a quantum circuit refrigerator.

3. The arrangement of claim 1 , wherein the other circuit element is another quantum bit.

4. 4. The arrangement of claim 1 , wherein the network of resonators comprises the plurality of resonators coupled in series between the quantum bit and the other circuit element.

5. 5. The arrangement of claim 4, wherein there are at least six of the resonators coupled in series between the quantum bit and the other circuit element.

6. 6. An arrangement according to claim 4 or 5, wherein each of the resonators comprises a capacitively shunted Josephson junction.

7. 6. The arrangement of claim 4 or 5, wherein each of the resonators comprises a quantum bit.

8. 4. The arrangement of claim 1 , wherein the network of resonators includes at least one series-coupled LC resonator as part of a connection between the quantum bit and the other circuit element, and at least one LC resonator between the connection and ground.

9. 9. The arrangement of claim 8, including three LC resonators between the connection and ground, one of which is coupled between a midpoint of the series-coupled LC resonators and ground.

10. 10. A quantum computing system comprising a plurality of qubits, at least one of which forms part of the arrangement of any one of claims 1 to 9.

11. the plurality of qubits forming an array; Each quantum bit in the array forms part of the arrangement of any one of claims 1 to 7, and the quantum bits in the array together form the other circuit elements.

11. The quantum computing system of claim 10.

12. the qubits in the array are addressable via a grid addressing scheme comprising a grid of addressing lines in at least two different directions through the array, such that combinations of control signals via the grid addressing scheme are configured to selectively define which qubits in the array become coupled together via the network of resonators.

12. The quantum computing system of claim 11.

13. 1. A method for coupling to a qubit, comprising: controllably coupling and decoupling the qubits to and from other circuit elements to perform quantum computing operations; transmitting the controllable coupling through a network of resonators between the qubit and the other circuit element; Including, the network of resonators includes a plurality of resonators, including linear or nonlinear resonators or both; A method wherein at least two of the plurality of resonators have the same circuit topology but different frequency responses.

14. 14. The method of claim 13, wherein the resonator is a static resonator and the controllable coupling and decoupling is achieved by tuning an operating frequency of at least one of the qubits and the other circuit elements.

15. 14. The method of claim 13, wherein among the plurality of resonators there is at least one frequency-tunable resonator, and the controllable coupling and decoupling involves tuning one or more resonant frequencies of such at least one frequency-tunable resonator.

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