LC filter

Abstract

Disclosed herein is an LC filter. The LC filter includes at least one capacitor; and a first inductive element between the at least one capacitor and a reference plane. The first inductive element links the at least one capacitor to the reference plane.

Description

LC FILTERTECHNICAL FIELD

[0001] Aspects of the present disclosure are related to quantum processing systems and more particularly to LC filters for quantum devices.BACKGROUND

[0002] Recent years have seen the development of microwave quantum devices that include both high-quality factor Qi (well exceeding 105for bare resonators at the single photon level) microwave resonating elements and broadband control. These two aspects can compete with each other, leading to a degradation of the resonating element performance, in particular Qi that can be brought down well below 103to 104.SUMMARY

[0003] According to a first embodiment of the present disclosure, there is provided an LC filter, comprising: at least one capacitor; and a first inductive element between the at least one capacitor and a reference plane, wherein the first inductive element links the at least one capacitor to the reference plane.

[0004] In some embodiments, the at least one capacitor comprises one or more first electrodes and one or more second electrodes, and the first inductive element is connected to at least one of the one or more first electrodes or at least one of the one or more second electrodes. The at least one capacitor may be an interdigitated capacitor comprising N fingers in the first capacitor electrodes and M fingers in the second capacitor electrodes. The N fingers may extend from a signal trace and the M fingers may extend from a reference plane. Further, the interdigitated capacitor may include fingers in the range of 1-1000 and more preferably in the range of 20-100.

[0005] In some embodiments, the first inductive element has a straight, spiral or meandering geometry. Further, the first inductive element may be created by cutting away a portion of a connection between the M fingers and the reference plane and leaving a stripof reference plane material that acts as the first inductive element linking the M fingers and the reference plane.

[0006] Further, the strip may have a width of less than 10pm and more preferably may have a width of approximately 0.2pm-5pm.

[0007] In some embodiments, the first inductive element is created by cutting away a portion of a connection between the M fingers and the reference plane, thereby leaving a strip of reference plane material connecting one or more inductors that act as the first inductive element linking M fingers to the reference plane.

[0008] The LC filter further includes a second inductive element connected between the at least one capacitor and a signal port that facilitates connection between the LC filter and external circuitry, the signal port being one of a micro-bump or a bond pad.

[0009] In some embodiments, the LC filter further includes at least a third inductive element, connected to the at least one of the one or more first electrodes or at least one of the one or more second electrodes.

[0010] The first, second and / or third inductive elements may be made of a high kinetic inductance superconducting material. The superconducting material may be at least one of NbTiN, NbN, TiN, WSi, MoRe, or GrAl, with a thickness between 2nm and lOOnm, with a sheet kinetic inductance, Lk less than 10,000pH / sq or more preferably less than 200pH / sq. Further still, the at least one capacitor may be made of the same material as any one of the first, second or third inductive elements.

[0011] The LC filter forms a band-pass filter with a notch response at a particular frequency range. The frequency range may be varied by adjusting a number of fingers of the interdigitated capacitor or by varying the geometry of the first inductive element and the position of the first inductive element with respect to the capacitor and reference plane. Further, the frequency range may be varied by adjusting the width and / or shape of the first inductive element between the M fingers and the reference plane.

[0012] The LC filter in some embodiments may be connected to a control line of a qubit node comprising a plurality of qubits at one end and at least one superconducting quantum device at the other end.

[0013] In still some other embodiments, the at least one capacitor or the first inductive element of the LC filter is coupled to a first electronic component having a first operatingfrequency in a quantum device including a second electronic component having a second operating frequency. In such embodiments, the LC filter has a notch response including high attenuation at the second operating frequency and low attenuation at or below the first operating frequency.

[0014] According to another aspect of the present disclosure there is provided a quantum processing system comprising: at least two qubit nodes, each node comprising a plurality of qubits, and a plurality of control lines for controlling operation of the plurality of qubits, the qubit nodes having an operating frequency range; at least one resonator connecting the at least two qubit nodes, the at least one resonator operating at a resonator frequency; and the LC filter of the first aspect connected in at least one control line of the at least two qubit nodes; wherein the LC filter operates to attenuate signals at the resonator frequency and permit signals at the qubits operating frequency range.

[0015] Further aspects of the present invention and further embodiments of the aspects described in the preceding paragraphs will become apparent from the following description, given by way of example and with reference to the accompanying drawings.BRIEF DESCRIPTION OF DRAWINGS

[0016] Features and advantages of the present invention will become apparent from the following description of embodiments thereof, by way of example only, with reference to the accompanying drawings, in which:

[0017] Fig. 1 is an example of a resonating quantum device capacitively coupled to a control line.

[0018] Fig. 2 is an example of a resonating quantum device capacitively coupled to a control line equipped with an LC filter that protects the performance of the device as the losses K are reduced.

[0019] Fig. 3 is an example of a conventional superconducting LC low-pass filter.

[0020] Fig. 4 is a plot of the transmission through a conventional superconducting LC low-pass filter, showing the inability to achieve large cut-off and large attenuation.

[0021] Fig. 5 shows an example of the superconducting microwave filter according to some aspects of the disclosure.

[0022] Fig. 6 is a plot of the transmission through an LC filter according to aspects of the disclosure with and without the inductive path to ground.

[0023] Fig. 7 is a plot showing the experimentally measured transmission through three example filters according to some aspects of the present disclosure.

[0024] Fig. 8 is a plot of the transmission spectrum of a filter for different weak link widths WWL.

[0025] Fig. 9 is a plot of simulation data comparing the response of an LC filter and an LCL filter.

[0026] Fig. 10 is a schematic circuit with an LCL filter with an inductive path to ground.

[0027] Fig. 11A is a top view of another example of a superconducting microwave filter according to some aspects of the present disclosure.

[0028] Fig. 1 IB is a cross-section view of the superconducting microwave filter of Fig. 11 A.

[0029] Fig. 12A is another example of a superconducting micro wave filter according to some aspects of the present disclosure.

[0030] Fig. 12B is a plot of the transmission spectrum of the filter of Fig. 12A for different positions of a first inductor.

[0031] Fig. 13 is a schematic view of an example quantum processing unit connecting two quantum dot arrays with the LC filter according to aspects of the present disclosure.DETAILED DESCRIPTIONOverview

[0032] Fig. 1 shows an example resonating quantum device 102 capacitively coupled to a control line 104 (e.g., a control line associated with a quantum processor).

[0033] Significant progress has been made, with the demonstration of the strong coupling regime between qubits (e.g., of the quantum processor) and microwave photons (e.g., of the resonating quantum device 102). In this regime, the exchange of energy between the qubits and the microwave photons is faster than the energy loss processes,allowing for coherent and efficient transfer of quantum information achieved on a variety of semiconducting spin qubit platforms.

[0034] One key challenge that has been identified towards high-fidelity operations is to improve the intrinsic quality factor Qi of the resonating quantum device 102, which is primarily limited by the parasitic leakage of photons via a multitude of control lines 204 required to operate quantum devices such as quantum processors. This microwave leakage is further exacerbated by the high impedance resonating quantum devices 102 (e.g., resonators) (in the ~kQ range) that are employed to achieve larger spin-photon coupling strengths between the qubits and photons. These impedances can reach a few thousand Ohms using high kinetic inductance materials.

[0035] Amongst possible solutions to mitigate these microwave losses, the control lines 104 can be equipped with low-pass LC filters directly patterned on the same chip as the device being controlled by the control lines 104. This arrangement is shown in Fig. 2. As can be seen in this figure, an LC filter 202 is placed on the control line 104. Fig. 3 shows an example of the LC low-pass filter 202. Filter 202 includes at least one inductor (L) 302. The inductor 302 is coupled to a signal port (e.g., a micro-bump or a bond pad) that facilitates electrical connection between the filter and external circuitry.

[0036] In some embodiments, filter 202 also includes an interdigitated capacitor (IDC) 304 connected to the inductor 302. An IDC is a type of capacitor structure where the capacitor plates are arranged in a closely spaced alternating pattern, resembling the interlocking fingers of two hands. This arrangement increases the surface area available for capacitance within a compact area, thereby enhancing the capacitance density per unit area. The IDC 304 includes N metal electrodes (or fingers) extending from the signal trace 306 and the fully connected ground plane 308, interleaved with each other over finger length Lfto increase the effective surface area and thus the capacitance per unit area.

[0037] An example two-element low-pass LC filter 300 is modelled to obtain the frequency response of the transmission parameter S21 for a range of filter series inductance (L) (x-axis) and shunt capacitor (C) values (y-axis) as shown in Fig. 4. Fig. 4 also shows the corresponding cut-off frequency (contours 402) and attenuation at a typical resonator frequency f = 5GHz (contour lines 404). The cut-off frequency is defined for a 3dB insertion loss. A trade-off can be observed between the attenuation at a typical resonator frequency of 5GHz, and the cutoff frequency. In general, the attenuation may be increasedby implementing large nominal L and C values. However, it is challenging to generate large planar capacitance above 10F due to their large footprint, which introduces parasitic resonances and degrades attenuation. Therefore, to attain high attenuation at the resonator frequency, large inductors are typically used in such filters. However, the large inductance compromises the cut-off frequency, often resulting in cut-off frequencies below 200MHz, which is insufficient for high-fidelity qubit control.

[0038] This detrimental effect gets worse when using high kinetic inductance Lk films, which are necessary to enhance the spin -photon coupling strength. Conversely, filters that have higher cut-off frequencies typically provide limited attenuation at the resonator frequency, compromising the resonator quality factor.

[0039] Accordingly, conventional low pass LC filter designs have struggled to simultaneously achieve both high attenuation at the resonator frequency and a high cut-off frequency.

[0040] This observation has spurred the development of LC filter prototypes that go beyond the two-element low-pass LC model. An anti-resonance can be obtained using the impedance mismatch on the inductor, resulting in a notch response with a state of the art ~60dB attenuation at the target resonator frequency. However, despite an improved cutoff between 0.5 Ghz and 1GHz, this existing notch filter still relies on a sizeable inductor L around 80nH.

[0041] A five element Chebyshev type II filter composed of two inductors and three parallel plate capacitors was also recently designed. It provides over 70dB of isolation while maintaining cutoffs exceeding 1GHz, at the expense of multi-layer fabrication and enhanced footprint. Accordingly, it appears that all criteria (low L for large cut-off, large attenuation around 5GHz, simple fabrication and low L / low C for small footprint) haven’t been met to date.

[0042] Aspects of the present disclosure provide a new filter design that addresses one or more of these limitations. In particular, the filter disclosed herein simultaneously achieves high attenuation at a target resonator frequency and a high cutoff frequency suitable for fast qubit control in quantum devices. The filter is a two-dimensional band stop LC filter that is engineered with a weak inductive path to ground within the capacitor structure of the filter. This inductive path to ground causes the filter to behave like a small LC filter at low frequencies resulting in high cutoff frequency (e.g., well above 1GHz), butbecome strongly reflective at higher frequencies where it achieves high attenuation at the target resonator frequency.

[0043] In some embodiments, the geometry of the filter is based on a novel interdigitated capacitor design with an inductive element between the main ground plane and the fingers of the inter-digitated capacitor, which creates a notch anti-resonance response (where the photons are reflected instead of being absorbed) at the resonator frequency without the need of a large inductor or capacitor. The presently disclosed filter design is compatible with high kinetic inductance materials required for high-impedance resonators and can be fabricated in a single superconducting thin-film deposition and etching step, facilitating integration in QPUs.In other embodiments, the filter includes a parallel plate capacitor made of two superconducting layers (a bottom layer and a top layer) separated by a dielectric layer such as SiO2, SiN, amorphous Si, or a vacuum gap.The LC filter

[0044] Fig. 5 shows an example of the LC band stop filter 500 according to some aspects of the present disclosure. The filter 500 protects control lines 104 from microwave leakage from resonators of microwave quantum devices 102 and hence preserves a high- quality factor for the resonator. Importantly, the LC filter 500 also has a high-cutoff value above 1GHz, which is necessary for good qubit control in quantum processors, for example.

[0045] Filter 500 includes at least one inductive element (or inductor, L) 502. Inductor 502 has a width WL and a length 11 - where the subscript L denotes the width (w) / length (1) for the inductor. The inductor 502 is coupled to a signal port (e.g., a micro-bump or a bond pad) that facilitates electrical connection between the filter 500 and external circuitry.

[0046] Filter 500 also includes an interdigitated capacitor (IDC) 504. The IDC 504 includes N metal electrodes (or fingers) extending from the signal trace 506 and M metal electrodes extending from a reference plane (or ground plane) 508, interleaved with each other over finger length Lf to increase the effective surface area and thus the capacitance per unit area. The finger length Lf may range from 10pm to 100pm. In some examples, IDC 504 comprises a top row of fingers and a bottom row of fingers. The top row of fingers comprises z fingers and the bottom row of fingers comprises j fingers. Where z and j arepositive integers. In some examples, the top and bottom row of fingers may have the same number of fingers and in other embodiments, they may have different number of fingers.

[0047] Inset 510 shows a zoomed-in portion of the IDC 504. In particular, the N fingers extending from the signal trace 506 have a width wi and the M fingers extending from the reference plane 508 have a width W2, respectively. Adjacent fingers (i.e., the fingers extending from the signal trace and the fingers extending from the reference / ground plane) are separated by a distance si. A finger extending from the ground plane 508 is separated from the signal plane 506 by a distance S2 and a finger extending from the signal trace is separated from the ground plane 508 by a distance S3. The parameters si, S2, S3, wi and W2 are typically in the range of 0.5pm-5pm. In some embodiments, the signal plane 506 and ground plane 508 are galvanically isolated. This enables voltage biasing via electrodes connected to the IDC signal trace of width WST.

[0048] Typically, the M fingers extending from the ground plane are homogeneously connected to the surrounding ground plane 512. In the present filter, however, most of this connection is cutaway - see cutaway portion 516 in Fig. 5, such that there is an inductive path to ground bridged by a strip 514 of width WWL. The range of width WWL is between 0.2pm and 5pm. This creates a strong resonance at the resonator frequency for its protection and preserves the cut-off well above 1GHz for qubit operations.

[0049] The strip is an inductive element. In some embodiments, the inductive element may be a nanowire with a particular geometry, such as a straight, spiral or meandering geometry. Further, the inductive element may be made of a high kinetic inductance superconducting material such as NbTiN, NbN, TiN, WSi, MoRe, GrAl, with a thickness between 2nm and lOOnm, with a sheet kinetic inductance, Lk of less than lOOOpH / sq and in some embodiments with a sheet kinetic inductance, Lk of less than 200pH / sq.

[0050] The capacitance and inductance values of filter 500 can be engineered to be relatively low (e.g. C < 0.5pF, L < lOnH), in contrast to previous designs that relied on large inductors. This allows the filter 500 to maintain a high cut-off frequency, typically above 1GHz, while still providing strong attenuation (e.g. > 50dB) at the resonator frequency.

[0051] Filter 500 can be fabricated in a single superconducting thin-film deposition and etching step, using high kinetic inductance materials compatible with the high- impedance resonators required for strong spin-photon coupling. This simplicity offabrication can facilitate the integration of multiple filters in a modular spin qubit processor architecture.

[0052] Fig. 6 is a plot 600 showing the attenuation of a conventional LC filter 202 (without the inductive path to ground) and of filter 500 (circuit illustrated by 706) (with the inductive path to ground). The x-axis of the plot 600 shows the frequency in GHz and the y-axis shows the attenuation in dB. Response 604 corresponds to the conventional LC filter 202. As seen in this plot, with a typical LC filter 202, the response 604 is relatively smooth and the attenuation increases slightly as frequency increases. Response 608 corresponds to the filter 500, which introduces a small inductance Lp (of approximately 5nH) within the capacitor. As seen from plot 600, filter 500 achieves a strong notch in the response 608 at approximately 5GHz (which is the resonator frequency). For each filter 202 and 500, the inductance (L) and capacitance (C) values are 8.5nH and 0.2pF, respectively. As can be seen, response 608 is substantially the same as response 604 except for the notch at 5GHz. Accordingly, filter 500 simultaneously achieves both low attenuation at frequencies in the range of OGHz-lGHz (response is substantially flat) and high attenuation at approximately 5GHz.

[0053] It should be noted that while filter 500 has been described as providing low attenuation around 1GHz and high attenuation around 5GHz, the frequency at which high attenuation occurs can be adjusted. The specific geometry of the IDC 504, such as the number, length, and width of the interdigitated fingers, can be tuned to control the frequency of the notch response. This provides flexibility in targeting the filter 500 to the resonator frequency of interest. Additionally, the weak inductive link to ground can be adjusted by varying the width of the connecting strip 514, further enabling frequency tuning.

[0054] It will be appreciated that while filter 500 has been described with respect to a resonator, the filter 500 is applicable to any suitable system for controlling a notch response. For example, filter 500 can be coupled to two different electronic components each with their own operating frequency to prevent leakage from one electronic component affecting the other component. In such embodiments, the filter 500 can be adjusted, for example, to allow for low attenuation of the frequency of the first electronic component while simultaneously allowing high attenuation of the frequency of the second electronic component.

[0055] In order to configure filter 500 for a given application, parameters of the IDC 504 and the weak link can be controlled.Results

[0056] To experimentally establish that filter 500 is driven by a controlled inductance element embedded in the capacitor, three example filters using sheet kinetic inductance Lk= 65pH / sq film were fabricated and tested. The only difference between the three example filters is the number of fingers in IDC 504. The first filter has 61 fingers, the second filter has 81 fingers, and the third filter has 101 filters.

[0057] In the design flow, large cut-off frequencies using ABCD matrices were targeted which provide the initial capacitor and inductor specifications. An ABCD matrix represents the transmission matrix of the filter. The capacitor and inductor specifications in combination with the sheet kinetic inductances, are used to inform the creation of representative circuit layouts.

[0058] Finite-element electromagnetic simulations (calculating high-frequency transmission matrices) are then used to characterise the nontrivial wideband behaviour of each of the example fabricated filters. Fig. 7 is a plot 700 showing the experimentally measured transmission through three example filters according to aspects of the present disclosure at 4.2K. On the x-axis is the frequency in GHz and on the y-axis is the transmission in decibels. Dashed lines 702, 704 and 706 show the experimental transmission for the filter with 61, 81 and 101 fingers, respectively. The experimental data is in good agreement with the Sonnet numerical simulations (dashed lines) using Lk = 65pH / sq. The cut-off frequency for all three filters is well above 1GHz.

[0059] The frequency at which the notch appears can be controlled using the geometry of the IDC 604. It can be observed from Fig. 7 that the notch frequency varies from approximately 3.8GHz for the filter with 101 fingers to 6.2GHz for the filter with 61 fingers. This indicates that decreasing the number of fingers increases the notch frequency.

[0060] Fig. 8 is a plot 800 of the transmission spectrum of a filter for different weak link widths WWL. On the x-axis is the frequency in GHz and on the y-axis is the transmission in decibels. The notch frequency varies from 4GHz to 8GHz when the weak link width WWL increases from 1pm to 3 pm as shown by plots 802, 804, and 806.

[0061] Fig. 9 is a plot of simulation data comparing the response of an LC filter and an LCL filter, where the LCL filter comprises one more superconducting inductive elementon the signal trace. This results in the capacitor (and the superconducting weak inductive link to ground) to be sandwiched between two superconducting inductive elements. The x-axis shows frequency in GHz and the y-axis shows transmission in decibels. It can be observed that the attenuation may be further enhanced to ~80dB through upgrading to a 3- stage LCL filter (data line 902) compared to an LC filter (data line 904). Further, the notch is widened, enabling 60dB isolation over a 100MHz band in which the resonator frequency may be placed, and 40dB isolation over a 1GHz band.

[0062] Fig. 10 shows a schematic circuit diagram showing an LCL filter 1000. The nominal capacitance and inductance values are low (C < O.lpF, L < lOnH), resulting in high cutoff frequencies of lGHz-2GHz, exceeding nanowire inductor filter cutoffs by an order of magnitude. In the latter case, the gate filter could be engineered to also serve as a Purcell filter. The footprint is low, ~ 200 *300pm, and when converted into an LCL fdter, the length of the additional inductor may be leveraged to place the larger IDC structures further from the resonator, for fan-out.Alternate embodiments

[0063] Fig. 11 shows another example LC filter according to aspects of the present disclosure. In particular, Fig. 11A is a top view of the example LC filter 1100 and Fig. 1 IB is a cross section view of the example LC filter 1100.

[0064] In this embodiment, the capacitor is a parallel plate capacitor made of two superconducting layers (a bottom layer 1104 and a top layer 1106) separated by a dielectric layer 1108. The dielectric layer 1108 may be made of a suitable material such as SiOi, SiN, or amorphous Si. In some embodiments, the dielectric layer 1108, may be a vacuum gap-10065] The top layer 1106 carries the capacitor top plate 1110, the reference ground plane 1112, and a first inductor (LI). The bottom layer 1104 carries the signal trace and a second inductor (L2). The first inductor, LI, galvanically connects these two elements - i.e., inductor LI connects the top plate of the capacitor to the reference ground plane 1112 in the top layer 1106.

[0066] The inductor LI can be patterned for example as a meander nano wire as shown in Fig. 11 A or as a straight nanowire.

[0067] The performance of this LC filter 1100 according to this novel geometry remains identical to that of the LC filter 500, with an expected resonance of the LC filter around 5GHz and a large cut-off frequency above 1GHz.

[0068] In another embodiment, instead of a narrow strip line 514, with a width WWL around 0.5 to 2pm, defining the inductor LI, the strip line may have a much wider width WWL > 5pm. In this embodiment, the strip line does not define the inductor LI. Instead, the inductor LI can be defined as a single meander or straight nano wire between the wider strip line and the reference ground plane.

[0069] Fig. 12A depicts an example of this variation of the LC filter 1200. As can be seen in this example, the strip 1202 is much wider than the strip 516 of LC filter 500. Further, the LI inductor is defined as a meandering or straight nanowire 1204 between the reference ground plane 1206 and the strip 1202.

[0070] The position of the LI inductor (d) along the capacitor (L) can be used to tune the LC filter resonant frequency around 5GHz, while maintaining a high cut-off frequency above 1GHz. This is depicted in the chart of Fig. 12B with two different positions of the inductor LI. When the position of the inductor LI is such that the d-L / L = 0 (see response 1210), the notch response of the filter is about 50dB and when the position of the inductor LI is such that d-L / L = 0.5 (see response 1212), the notch response of the filter is more pronounced.An example qubit system

[0071] This section describes the implementation of the LC filter with a large-scale quantum processor.

[0072] Achieving a large-scale quantum processor requires architectures with thousands of qubits or more with the ability to maintain performance when scaling up. In the context of semiconducting spin qubits, one challenge with achieving such large-scale processors relates to the density of quantum dots / donors on a processor chip. It is known that exchange interactions between qubits decay exponentially with quantum dot / donor separation, meaning that the quantum dots / donors need to be closely and precisely placed (e.g., just tens to hundreds of nanometres apart). In such a two-dimensional qubit array, it becomes extremely difficult to include gates, necessary for control and readout, to quantum dots / donors in the centre of the array. Furthermore, such a dense packing of quantumdots / donors and control electronics implies a rate of heat dissipation that is currently incompatible with cryogenic temperatures necessary for qubit coherence.

[0073] One approach to address these challenges involves integrating multiple qubit nodes into a quantum computing processor. Each node contains a limited number of quantum dots or donors along with their respective circuitry. These nodes can be interconnected via suitable interconnect technology, reducing overall density while enabling quantum computation across nodes. In some interconnect techniques, one or more qubits of one node are linked with one or more qubits of another node.

[0074] Fig. 13 is a schematic view of an example quantum processor unit (QPU) 1300 that includes two interconnected qubit nodes 1302 - nodes 1302A and 1302B. It will be appreciated that although Fig. 13 illustrates two nodes, in an actual implementation the QPU 1300 may have many more nodes. In general, the number of nodes utilized for a given QPU 1300 may depend on the application, the number of qubits located in each node and / or the computational requirements of the QPU 1300.

[0075] Each node 1302 includes a plurality of qubits 1303 arranged in a two- or three- dimensional array. The number of qubits 1303 located in each node 1302 depends on several factors such as the distance between qubits, the number of control lines and / or gates that can be accommodated on the node to address each qubit in the node 1302, and the heat dissipated by the control circuitry. In some examples, the nodes 1302 are small enough such that control lines 1304 (including a gate) located on the chip surface or within the silicon substrate can address each individual qubit 1303, and the qubits are close enough together for exchange interactions (i.e., at a length scale on the order of 10nm-20nm). In the example shown in Fig. 13, each node 1302 includes four qubits 1303 arranged in a two- dimensional array. It will be appreciated that node 1302A may have a different number of qubits compared to node 1302B. Further, the arrangement of the qubits in the various nodes 1302 may vary.

[0076] The nodes 1302 can be separated from each other by approximately 100pm- 1mm. Further, the nodes 1302 can be connected to each other by one or more interconnect means. In some examples, the nodes may be connected via one or more resonators, such as superconducting microwave resonators, forming a circuit quantum electrodynamic (cQED) architecture. A cQED resonator is a specialized microwave circuit that is usedhere to couple spin qubits to the electric field of microwave photons circulating within the resonator, enabling long-range qubit-qubit interactions mediated by the resonator.

[0077] Coupling between donor quantum dots and the resonators can be achieved through charge dipole coupling and a spin-orbit mechanism. This occurs when the qubit's charge state interacts with the electric field component of microwave photons in the resonator, which happens when their energy levels match the resonant frequency of the photons. This alignment allows the resonator's oscillating electric field to impact the charge distribution within the quantum dots, facilitating coherent exchange of quantum information.

[0078] As shown in Fig. 13, a resonator 1304 may connect the pair of nodes 1302. In one example, the resonator 1304 is coupled to one qubit in each of the pair of nodes 1302. In this example, qubit 1303 A in node 1302A is coupled with qubit 13O3B in node 1302B via the resonator 1304. In another example, the resonator 1304 is connected to one or more electrodes 1306. As the resonator 1304 can mediate two-qubit gate operations, quantum information can be transferred between the qubit nodes via the resonator 1304, allowing for connectivity that is critical to implement useful quantum algorithms in QPU 1300.

[0079] In Fig. 13, the qubits that are coupled to the resonator 1304 on each node 1302 (i.e., qubit 1303 A and qubit 13O3B) may be any suitable type of qubit. In one example, the qubits coupled to the resonator 1304 are fabricated as donor qubits. In one example qubit 13O3A and qubit 13O3B are phosphorus donor quantum dots, for example, 2P quantum dots. The other qubits on node 1302 may also be 2P donor dots, however this is not essential. In some examples, the qubits that are not coupled to the resonator 1304 may be any other type of qubits such as single donor qubits or gate-controlled qubits, superconducting qubits or topological qubits without departing from the scope of the present embodiment. Further, the qubits 1303 on each node 1302 may be coupled to their nearest neighbours via an exchange coupling.

[0080] The resonator 1304 may be made of a thin (e.g., a few nanometers in width), high-kinetic-inductance superconducting material. Examples of high-kinetic inductance materials include nitrides (e.g. NbN, NbTiN, TiN), silicides (e.g., WSi), or GrAl. In one example, the resonator 1304 is a X / 2 resonator so that an electric field anti-node is located at the donor qubits 1303 A and 13O3B maximizing coupling to its charge dipole. Theresonator 1304 can also serve as a reservoir from which a single electron is loaded onto the qubit 1303 A or 13O3B, at a time scale far slower than the resonance frequency.

[0081] A key challenge in implementing cQED resonators with qubits arises from the small physical size of the qubit devices. The proximity of the qubit control lines (e.g., 1306) to the high-impedance resonators (e.g., 1304) results in parasitic capacitive coupling. Parasitic capacitive coupling refers to the capacitance that forms between different components or structures in an electronic circuit or device. As discussed previously, these parasitic capacitances provide a leakage pathway for the microwave photons circulating in the resonator 1304. This leakage can significantly degrade the quality factor Q of the resonator 1304 which is a critical parameter for achieving high-fidelity quantum interconnects between distant spin qubits (where Q, is a measure of the efficiency and effectiveness of a resonator in storing and transferring energy).

[0082] To mitigate these problems, according to aspects of the present disclosure, as shown in Fig. 13, each of the qubit control lines 1306 is equipped with the LC filter 500, 1100 or 1200. In other embodiments, one or more of the control lines 1306 in each qubit node 1302 may be equipped with the LC filter 500, 1100 or 1200. In yet other embodiments, a subset of the qubit control lines 1306 in any qubit node 1302 in the quantum processing unit 1300 may be equipped with the LC filter 500, 1100, or 1200.

[0083] It will be appreciated that while Fig. 13 shows two connected qubit nodes, embodiments may include a plurality of connected qubit nodes without departing from the scope of the present disclosure.

[0084] The methods and the quantum processor architectures described herein uses quantum mechanics to perform computation. The processors, for example, may be used for a range of applications and provide enhanced computation performance, these applications include encryption and decryption of information, advanced chemistry simulation, optimization, machine learning, pattern recognition, anomaly detection, financial analysis and validation amongst others.

[0085] It will be appreciated by persons skilled in the art that numerous variations and / or modifications may be made to the invention as shown in the specific embodiments without departing from the spirit or scope of the invention as broadly described. The present embodiments are, therefore, to be considered in all respects as illustrative and not restrictive.

[0086] As used herein, except where the context requires otherwise, the term "comprise" and variations of the term, such as "comprising", "comprises" and "comprised", are not intended to exclude further additives, components, integers or steps.

Claims

CLAIMS1. An LC filter, comprising: at least one capacitor; and a first inductive element between the at least one capacitor and a reference plane, wherein the first inductive element links the at least one capacitor to the reference plane.

2. The LC filter of claim 1, wherein the at least one capacitor comprises one or more first electrodes and one or more second electrodes, and the first inductive element is connected to at least one of the one or more first electrodes or at least one of the one or more second electrodes.

3. The LC filter of claim 1, wherein the first inductive element has a straight, spiral or meandering geometry.

4. The LC filter of claim 2 or claim 3, wherein the at least one capacitor is an interdigitated capacitor comprising N fingers in the one or more first electrodes and M fingers in the one or more second electrodes.

5. The LC filter of claim 4, wherein the interdigitated capacitor comprises fingers in the range of 1-1000 and more preferably in the range of 20-100.

6. The LC filter of claim 4 or claim 5, wherein the N fingers extend from a signal trace and the M fingers extend from a reference plane.

7. The LC filter of any one of claims 4 to 6, wherein the first inductive element is created by cutting away a portion of a connection between the M fingers and the reference plane, thereby leaving a strip of reference plan material that acts as the first inductive element linking the M fingers and the reference plane.

8. The LC filter of claim 7, wherein the strip has a width of less than 10pm, and more preferably a width between 0.2pm and 5.0pm.

9. The LC filter of any one of claims 4 to 6, wherein the first inductive element is created by cutting away a portion of a connection between the M fingers and the reference plane, thereby leaving a strip of reference plane material connecting one or more inductors that act as the first inductive element linking M fingers to the reference plane.

10. The LC filter of any one of the preceding claims, further comprising a second inductive element connected between the at least one capacitor and a signal port that facilitates connection between the LC filter and external circuitry.

11. The LC filter of any one of claims 2 to 10, further comprising at least a third inductive element, connected to the at least one of the one or more first electrodes or the at least one of the one or more second electrodes.

12. The LC filter of any one of the preceding claims, wherein the first, second and / or third inductive elements are made of a high kinetic inductance superconducting material.

13. The LC filter of claim 12, wherein the superconducting material is at least one of NbTiN, NbN, TiN, WSi, MoRe, or GrAl, with a thickness between 2nm and lOOnm, with a sheet kinetic inductance of less than lOOOpH / sq and more preferably with a sheet kinetic inductance of less than 200pH / sq.

14. The LC filter of any one of the preceding claims, wherein the at least one capacitor is made of a high kinetic inductance superconducting material.

15. The LC filter of any one of the preceding claims, further forming a low-pass filter with a notch response at a particular frequency range.

16. The LC filter of claim 15, wherein the particular frequency range is adjustable by varying the geometry and / or position of the first inductive element with respect to the at least one capacitor and the reference plane.

17. The LC filter of claim 15 or claim 16, wherein the particular frequency range is varied by adjusting a number of fingers of the interdigitated capacitor.

18. The LC filter of any one of claims 15 to 17, wherein the particular frequency range is varied by adjusting the width and / or shape of the first inductive element between the M fingers and the reference plane.

19. The LC filter of any one of the preceding claims, wherein a cut-off frequency is larger than 100MHz, preferably larger than 1GHz, for broadband control purposes.

20. The LC filter of any one of the preceding claims, connected to a control line of a qubit node comprising a plurality of qubits at one end and at least one superconducting quantum device at the other end.

21. The LC filter of any one of the preceding claims, wherein the at least one capacitor or the first inductive element is coupled to a first electronic component having a first operating frequency in a quantum device including a second electronic component having a second operating frequency; and wherein the LC filter has a notch response including high attenuation at the second operating frequency and low attenuation at or below the first operating frequency.

22. A quantum processing system comprising:at least two qubit nodes, each node comprising a plurality of qubits, and a plurality of control lines for controlling operation of the plurality of qubits, the qubit nodes having an operating frequency range; at least one resonator connecting the at least two qubit nodes, the at least one resonator operating at a resonator frequency; and the LC filter of any one of claims 1 to 21 connected in at least one control line of the at least two qubit nodes; wherein the LC filter operates to attenuate signals at the resonator frequency and permit signals at the qubits operating frequency range.

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