Cryogenic device

Abstract

A cryogenic device comprises N + 1 stages, wherein N is an integer greater than 0. The temperature on each stage increases incrementally with increasing stage number, wherein stage 0 has a lowest temperature and stage N has a highest temperature. The device comprises at least one signal line leading at least from a stage n + 1 to a stage n, wherein the signal line comprises a signal attenuator on stage n. The signal attenuator is a signal coupler, which signal coupler splits an incoming signal into an attenuated signal and a residual signal. The residual signal is led back from stage n to at least stage n + 1.

Description

[0001] Cryogenic Device

[0002] FIELD OF THE INVENTION

[0003] The present invention relates to a cryogenic device according to the preamble of claim 1 as well as to a use of a signal coupler as a signal attenuator in such a device, according to claim 32.

[0004] BACKGROUND OF THE INVENTION

[0005] In modem quantum computing setups, hundreds or even thousands of microwave lines are needed to control the qubits of a quantum processor in a cryogenic environment. In a typical cabling, radio frequency attenuators need to be inserted at different temperature stages of a dilution refrigerator in the mentioned control lines for signal conditioning. Their main function is to reduce the thermal noise floor (Johnson-Nyquist noise) in each microwave line by attenuating the (in- band) noise and unavoidably also the signal propagating from a higher (warmer) temperature stage. The related dissipation power, mainly coming from the highly amplified signal that is converted into heat, brings a remarkable thermal load at the physical location where these attenuators are installed in the dilution refrigerator. A major limiting factor for the scalability of such cryogenic systems is thus the cooling power at each stage, which should not exceed the heat generated. Krinner et al. (EPJ Quantum Technology 2019, 6(2)) have provided a comprehensive study of the design principles for the wiring of such a cryogenic setup, in order to minimize active and passive heat loads and properly manage the heat budget. Passive heat load is due to heat flow from higher temperature stages to lower temperature stages, conducted through the installed cables. Active heat load arises due to the dissipation (Joule heating) of applied signals in attenuators and in the cables themselves. The cooling power decreases by orders of magnitude with lower temperature stages in a dilution refrigerator. The lower the temperatures, the lower is thus the cooling power of the system. Due to finite heat conductivity it is unavoidable that the heating will increase the Johnson-Nyquist noise generated in each line to a level which is higher than it would be according to the temperature stage of the dilution refrigerator. This effect worsens in stages closer to zero Kelvin where the temperature gradients and the noise power level approach zero.

[0006] It is therefore a problem underlying the present invention to overcome the aforementioned shortcomings in the prior art. In particular, it is a problem underlying the present invention to provide a cryogenic infrastructure for quantum measure- ments, such as quantum computing, with improved heat management.

[0007] In particular, the present invention shall allow for installation of a higher number of signal lines in the setup, for instance to increase the number of qubits in a quantum computer. Furthermore, thermal noise generated in the lower temperature stages, especially close to zero kelvin, shall be reduced. SUMMARY OF THE INVENTION

[0008] The present invention relates to a cryogenic device comprising N + 1 stages, wherein N is an integer greater than 0. The temperature on each stage increases incrementally with increasing stage number, wherein stage 0 has a lowest temperature and stage N has a highest temperature. The device comprises at least one signal line leading at least from a stage n + 1 to a stage n. The signal line comprises a signal attenuator on stage n. The signal attenuator is a signal coupler. The signal coupler splits an incoming signal into an attenuated signal and a residual signal. The residual signal is led back from stage n to at least stage n + 1.

[0009] According to the present invention, the amount of signal corresponding to the needed attenuation is thus coupled out of the signal line and the residual signal is sent back to a higher temperature stage with typically higher cooling power (such as in the case of a dilution refrigerator). This leads to a lower heat load at lower temperature stages, which may allow to increase the number of signal lines and help to lower the thermal noise generated in the lower temperature stages, especially such close to zero Kelvin (e.g. 10 mK, 100 mK).

[0010] Resistive signal attenuators convert the dissipated power into heat at the location where they are installed. With the proposed distributed design of attenuator and coupler, the location of heat generation and the location of the signal attenuation can be separated. This gives the advantage to place the heat sources to temperature stages with sufficient cooling power and enables scalability towards an in- creased number of signal lines at same cooling power. Furthermore, lower thermal noise levels can be achieved, as the proposed device will operate at lower temperature, since no heating occurs by attenuating the initial signal levels.

[0011] The at least one signal line can lead from a stage n + i to stage n, wherein i is an integer between 1 and N + 1 - n. Typically, the at least one signal line leads from stage N + 1 to stage n, with stage N + 1 being the stage with the highest temperature, which is often room temperature. This allows placing the signal generating and receiving components, such as frequency synthesizers and spectrum analyzers, outside the thermal isolation of the device.

[0012] The residual signal can be led back from stage n to a stage n + j, wherein j is an integer between 1 and N + 1 - n. In principle, it would be ideal to lead the residual signal back to one of the highest stages, such as stage N + 1 or stage N, as in case of a dilution refrigerator, the cooling power is the highest at those stages, or even an external cooling would be possible. However, leading the residual signal over many stages increases the number of signal lines, which leads to an increase of passive heat load at the lower stages, which is not desirable. A balance between those factors thus has to be found. Usually, good results can be achieved, if j equals 1 , 2 or 3.

[0013] The attenuated signal can be led further to at least a stage n - 1 , wherein n is greater than zero. More particularly, the attenuated signal can be led further to a stage n - k, wherein k in an integer between 1 and n. Usually the attenuated signal is led to stage 0, in which case k would be equal to n. To avoid any misunderstanding, this would not exclude, that the signal is further attenuated a stages lower than stage n, for instance with a further signal coupler, as explained herein below.

[0014] The coupling factor of the signal coupler can be -1 to -80 dB, preferably -3 to -60 dB, more preferably -10 to -40 dB, such as -10 dB or -20 dB.

[0015] In practice the coupling factor does typically not exceed -3 dB, since more than this would result in more coupled power than residual power. Nevertheless, in certain applications, this might well be the case.

[0016] The signal coupler can be a directional coupler. Directional couplers are passive devices used mostly in the field of radio technology. They couple a defined amount of the electromagnetic power in a transmission line to a port enabling the signal to be used in another circuit. An essential feature of directional couplers is that they only couple power flowing in one direction. By way of example, power entering the input port is coupled to the coupled port, but not to the so-called isolated port. Power entering the output port is coupled to the isolated port, but not to the coupled port. Directional couplers have a number of advantages in cryogenic applications. In particular, they can be realized of superconductive materials, meaning that their active heat load can essentially be eliminated at low temperatures (typically below 10 K, see further below). Furthermore, they do not comprise magnetic components (as opposed to isolators und circulators), which might disturb quantum experiments, such as the qubits of a quantum processor. A further advantage of directional couplers is that the inner conductors with typically much higher thermal conductivity than the insulating material, which are difficult to thermalize at the individual temperature levels in coaxial cables, are interrupted, thus avoiding a direct thermal bridge from room temperature to the lowest temperature level.

[0017] Directional couplers are most frequently constructed from two coupled transmission lines set close enough together, such that energy passing through one is coupled to the other. This technique is favored at microwave frequencies, which are commonly used for quantum experiments. In this context, the directional coupler can have a planar design, such as stripline or microstrip. The planar design can be a rigid or a flexible one.

[0018] A stripline is a transverse electromagnetic (TEM) transmission line medium, which is a form of planar transmission line. A stripline circuit uses a flat strip of metal which is sandwiched between two parallel ground planes. The insulating material of the substrate forms a dielectric. The width of the strip, the thickness of the substrate and the relative permittivity of the substrate determine the characteristic impedance of the strip which is a transmission line. To prevent the propagation of unwanted modes, the two ground planes must be shorted together. This is commonly achieved by a row of vias running parallel to the strip on each side.

[0019] A microstrip is a type of planar electromagnetic transmission line, which can be fabricated with any technology where a conductor is separated from a ground plane by a dielectric layer known as substrate. Microwave components such as antennas, couplers, filters, power dividers etc. can be formed from microstrip, with the entire device existing as the pattern of metallization on the substrate.

[0020] Stripline or microstrip (generally PCB I Flex-PCB) are both very suitable for a device according to the present invention, because they allow several couplers to be accommodated in parallel in a small space. In addition, the directional couplers and other required elements (such as short and / or 50 Q load) can be easily implemented and, in case of a Flex-PCB, even be combined in one piece with the signal lines, replacing the coaxial cables.

[0021] Multiple other realization of directional couplers exist and could be used, e.g. integrated devices based on ceramic, glass or any other substrates, suspended stripline versions with center conductors positioned in air / vacuum. The directional coupler can also be built in a waveguide design.

[0022] The incoming signal can be fed at an input port into the directional coupler. The coupled signal can be taken at a coupled port out of the directional coupler. The residual signal can be taken at a transmitted port out of the directional coupler.

[0023] The residual signal can be led back to at least stage n + 1 by a separate signal line. In cases where a directional coupler is used, the separate signal line is then usually connected to the transmitted port of the directional coupler. Such a layout has the advantage that is relatively simple and that the entire residual signal can be dissipated at a higher temperature level. However, the number of signal lines is increased, which - as mentioned before - is not desirable due to an increase of passive heat load at the lower stages. Alternatively, the residual signal can be reflected by a reflective element to be fed back into the same signal line.

[0024] In cases where a directional coupler is used, the reflective element is then usually connected to the transmitted port of the directional coupler. Such a layout has the advantage that the same signal line can be used for leading the signal to stage n and for leading the residual signal back to at least a stage n + 1 . An increase of passive heat load at the lower stages is thus avoided. However, when a directional coupler is used, this comes at the prize that small fraction of the reflected residual signal is coupled out of the line when passing the coupler for a second time, to leave at the isolated port. One possibility is to dissipate this fraction at stage n, however increasing active heat load.

[0025] The reflective element can be implemented as an open signal line end or as a short.

[0026] The residual signal can be dissipated at stage n + j by a dissipating element. The dissipating element can be a resistive element, also referred to as load, such as a matched load or a broadband load.

[0027] The device according to the present invention can further comprise a circulator or an isolator to path cumulated energy to further higher temperature stages. In the present context, a circulator is a passive, non-reciprocal three- or four-port device that only allows a microwave or radio-frequency (RF) signal to exit through the port directly after the one it entered. The circulator or isolator have the further purpose of protecting the RF source from the reflected power and to provide a clean 50 Q termination, in order to avoid multiple reflections. If the RF source already has the appropriate properties, an isolator or circulator is not necessary.

[0028] The residual signal can be reflected by the reflective element at the transmitted port of the directional coupler to be fed back into the directional coupler and thus the same signal line. In such a setup, the coupled signal can be fed at an isolated port out of the directional coupler.

[0029] The at least one signal line can be selected from the group consisting of a coaxial line, a stripline, a microstrip or a waveguide.

[0030] In case of a coaxial line, the signal line can have a diameter of 2.2 mm or less, preferably 1.2 mm or less, for instance 0.86 mm. Using smaller diameter cables is generally beneficial, to reduce the passive heat load, which scales with the square of the diameter, whereas the attenuation in the cable scales approximately linearly.

[0031] The signal line can for instance be made of stainless steel or a Copper-Nickel alloy (cupronickel). These materials have a relatively high signal attenuation, which is desired, but comes at a price of a high active heat load at a given stage.

[0032] The signal line typically has a length per stage of 5-40 cm, in particular 10-25 cm.

[0033] The at least one signal line can be at least partially superconductive. This has the advantage that the active heat load of the signal line is eliminated in the parts where the line is superconductive. Furthermore, superconductive materials usually have a relatively low thermal conductivity, which reduces the passive heat load at lower stages, caused by the signal line. This effect is increased by the fact that a superconductive signal line can be implemented with an even smaller diameter, as essentially no resistive losses occur, which are the main reason to increase diameter of microwave lines.

[0034] A superconductive signal line can for instance be made of Nb-Ti. Niobium-tita- nium (Nb-Ti) is an alloy of niobium and titanium, used industrially as a Type II superconductor wire, typically for superconducting magnets, normally as Nb-Ti fibres in an aluminium or copper matrix. Its critical temperature is about 10 K. Nb- Ti alloys are notable for their easy workability and affordability, distinguishing them from other superconducting materials. Nb-Ti has the further advantage that it remains superconducting even at high magnetic field strengths. Pure niobium loses its superconducting properties at higher magnetic field strengths. However, such field strengths do usually not occur in devices according to the present invention, pure niobium is an alternative.

[0035] Also lead can be used as a superconductor, but has disadvantages since it cannot be soldered and exposed to higher temperatures as in extrusion during cable production.

[0036] Two or more signal lines can be combined together in one or more cable tree(s). N can be selected form the group consisting of 1 , 2, 3, 4, 5, 6, 7, 8, 9 and 10. A typical dilution refrigerator for instance has a total of five or six stages, including the room temperature stage, meaning that N would be equal to 4 or 5.

[0037] In cases wherein N is at least 2, the signal line can comprise a cascade of signal attenuators. The cascade of signal attenuators can comprise at least two signal attenuators at individual stages. In particular, the cascade of signal attenuators can comprise at least two signal couplers at individual stages.

[0038] The signal line can comprise at least one further element selected from the group consisting of a resistive signal attenuator, a low pass filter, a band pass filter and an infrared filter.

[0039] Preferably, the cooling power on a given stage is greater than the total heat load resulting on this stage by at least a factor of 1 .2, more preferably at least a factor of 1.5, even more preferably at least a factor of 2, even still more preferably at least a factor of 3.

[0040] The temperature at stage 0 can be less than 100 mK, preferably less than 50 mK, more preferably less than 20 mK. Such temperatures are preferred for conducting solid-state based quantum experiments, such as solid-state based quantum computing.

[0041] The device can further comprise a dilution refrigerator and optionally additionally at least one pulse tube refrigerator. A dilution refrigerator is a cryogenic device that provides continuous cooling to temperatures as low as 2 mK, with no moving parts in the low-temperature region. The cooling power can for instance be provided by the heat of mixing helium-3 and helium-4 isotopes.

[0042] The at least one signal line can be suitable for transmission of an electromagnetic wave with a frequency in a range of 1 -100 GHz, preferably 2-20 GHz, more preferably 3-10 GHz.

[0043] The device can further comprise at stage 0 a solid-state based quantum device, in particular a superconducting quantum device, such as a superconducting quantum processor. The quantum processor can comprise at least 10, preferably at least 102, more preferably at least 103, even more preferably at least 104, even still more preferably at least 105qubits.

[0044] Superconducting quantum computing is a branch of solid state quantum computing that implements superconducting electronic circuits using superconducting qubits as artificial atoms, or quantum dots. For superconducting qubits, the two logic states are the ground state and the excited state, denoted |g) and |e) respectively. Various models of quantum computation exist, but the most popular models incorporate concepts of qubits and quantum gates (or gate-based superconducting quantum computing).

[0045] A qubit is a generalization of a bit (a system with two possible states) capable of occupying a quantum superposition of both states. A quantum gate, on the other hand, is a generalization of a logic gate describing the transformation of one or more qubits, once a gate is applied given their initial state. Physical implementation of qubits and gates is challenging for the same reason that quantum phenomena are difficult to observe in everyday life given the minute scale on which they occur. One approach to achieving quantum computers is by implementing superconductors, whereby quantum effects are macroscopically observable, though at the price of extremely low operation temperatures.

[0046] For a superconducting quantum processor, the at least one signal line can be selected from a drive line and a flux line.

[0047] Drive lines are used for controlling the quantum states of the qubits, typically with a microwave tone, realizing single-qubit gates, and for probing the frequency shift of readout resonators. To reduce thermal population of qubits, and frequency shifts of the qubits due to their dispersive interaction with a readout resonator, the number of thermal noise photons in the drive lines arriving at stage 0 is typically required to be well below the single photon level in both cases. More precisely, to guarantee a noise photon number on the 10’3level, a total attenuation of about 60 dB is typically required. At the same time, the bandwidth of the drive lines is required to be large enough to cover the typical frequency ranges of qubits (4-6 GHz) and of readout resonators (4-8 GHz).

[0048] Flux lines are used for implementing two-qubit gates, which are based on the dynamical flux tunability of the transition frequency of a qubit or of a separate coupling subcircuit. In addition, qubit frequency variations, occurring due to imperfections in the fabrication of so-called Josephson junctions, can be compensated. In an embodiment of the present invention, each qubit is accessed by a dedicated set of control lines, including at least per-qubit dedicated drive lines and flux lines. The number of drive lines and RF flux lines in the setup would thus correspond to the number of qubits.

[0049] However, it is also possible that multiple qubits are accessed by a given set of control lines, such as by frequency separation, or tuning out of different qubits, or even by accessing a many-qubit system or subsystem.

[0050] A further aspect of the present invention relates to a quantum computer, comprising a device as described herein above. Yet another aspect of the present invention relates to a use of a signal coupler as a signal attenuator in a device as described herein above.

[0051] It is to be understood that both the foregoing general description and the following detailed description present embodiments are intended to provide an overview or framework for understanding the nature and character of the disclosure. The accompanying drawings are included to provide a further understanding and are incorporated into and constitute a part of this specification. The drawings illustrate various embodiments, and together with the description serve to explain the principles and operation of the concepts disclosed.

[0052] BRIEF DESCRIPTION OF THE DRAWINGS

[0053] The herein described invention will be more fully understood from the detailed description given herein below and the accompanying drawings, which should not be considered limiting to the invention described in the appended claims. The drawings are showing:

[0054] Fig. 1 Schematic view of the wiring in a cryogenic device according to the prior art;

[0055] Fig. 2 Conventional notation symbol of a directional coupler (according to the prior art);

[0056] Fig. 3a Implementation of a directional coupler as a stripline (according to the prior art);

[0057] Fig. 3b Implementation of a directional coupler as a stripline (according to an aspect of the present invention);

[0058] Fig. 4 Schematic view of the wiring in a cryogenic device according to a first embodiment of the present invention;

[0059] Fig. 5 Schematic view of the wiring in a cryogenic device according to a second embodiment of the present invention;

[0060] Fig. 6 Schematic view of the wiring in a cryogenic device according to a third embodiment of the present invention;

[0061] Fig. 7 Schematic view of the wiring in a cryogenic device according to a fourth embodiment of the present invention; Fig. 8 Schematic view of the wiring in a cryogenic device according to a fifth embodiment of the present invention;

[0062] Fig. 9 Graph showing a comparison of the dissipated power in a drive line at each stage of a cryogenic device according to the prior art and in two embodiments according to the present invention for stainless steel signal lines;

[0063] Fig. 10 Graph showing a comparison of the dissipated power in a drive line at each stage of a cryogenic device according to the prior art and in two embodiments according to the present invention for stainless steel and Nb-Ti signal lines.

[0064] DESCRIPTION OF THE EMBODIMENTS

[0065] Reference will now be made in detail to certain embodiments, examples of which are illustrated in the accompanying drawings, in which some, but not all features are shown. Indeed, embodiments disclosed herein may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will satisfy applicable legal requirements. Whenever possible, like reference numbers will be used to refer to like components or parts.

[0066] Figure 1 shows the wiring of the drive and flux lines in a dilution refrigerator for quantum experiments, as proposed by Krinner et al. (EPJ Quantum Technology 2019, 6(2), Section 3.2). For ease of understanding, only one drive line and one flux line are displayed.

[0067] As apparent, three resistive attenuators (loads; Ld) of -20 dB are installed at each of stages 0, 1 and 3, resulting in a total attenuation of -60 dB. The flux lines have a total attenuation of -20 dB, which is realized by a single resistive load (Ld) on stage 3. To these total attenuations comes an additional attenuation of ca. -9 dB, which sums up in the RF cables from stage 5 to stage 0.

[0068] This is assumed to be sufficient to reduce the thermal noise photon number on stage 0 to an acceptable level. Table 1 shows the specifications of the commercially available dilution refrigera- tor used (Bluefors XLD400; N = 4).

[0069] Figure 2 shows the symbol generally used for a directional coupler. The symbol may have the coupling factor in dB marked on or next to it. Directional couplers generally have four ports. Port P1 is the input port where power is applied. Port P3 is the coupled port where a portion of the power applied to port P1 appears. Port P2 is the transmitted port where the power from port P1 is outputted, less the portion that went to port P3. Since directional couplers are frequently symmetrical, there also exists port P4, the isolated port. A portion of the power applied to port P2 will be coupled to port P4.

[0070] Figure 3a shows the realization of a quarter-wavelength (A / 4) directional coupler as a stripline, as known in the prior art. The two parallel ground planes are omitted for ease of view. The power on the coupled line 2 flows in the opposite direction to the power on the main line 1 , hence the port arrangement is not the same as shown in Fig. 2, but the numbering remains the same. The main line 1 is the section between ports P1 and P2 and the coupled line 2 is the section between ports P3 and P4.

[0071] Figure 3b shows the realization of a directional coupler as a stripline, according to an aspect of the present invention. The two parallel ground planes are omitted for ease of view. The power entering the input port P1 is passing through the main line 1 and reflected by reflective element 3, which is implemented as a short between the main line and the two parallel ground planes. As mentioned before, in a stripline directional coupler, the power on the coupled line 2 flows in the opposite direction to the power on the main line 1 . The reflected power on the main line 1 is thus coupled into the coupled line 2 to leave the directional coupler at the isolated port P4. The incoming power in the main line 1 is coupled into the coupled line 2 to be dissipated at termination 4, which is typically a load of 50 Q. The proposed layout thus represents a particularly efficient implementation of a directional coupler in a stripline, which can even be included in a flat ribbon cable, without the need of discrete construction elements and optimized cable routing. This is particularly advantageous, if a high number of signal lines is used, such as several hundreds or thousands in quantum computing applications. As mentioned before, although the port arrangement is not the same as shown in Fig. 2, the numbering and nomenclature remains the same.

[0072] Figure 4 shows the wiring of the drive and flux lines in a first embodiment of the present invention. For ease of understanding, only one drive line and one flux line are displayed. As apparent, power introduced into the drive and flux lines passes resistive attenuators (loads; Ld) of -20 dB installed at stage 3 for both lines, just like in the wiring shown in Figure 1 . Since at stage 3 the active heat load has been found to be negligibly small compared to the passive heat load and cooling power, no adaptation of the layout is considered necessary there.

[0073] However, the resistive attenuators on stages 0 and 1 have been replaced by directional couplers with a coupling factor of -20 dB each. The signal coming from stage 2 enters the directional coupler on stage 1 through the input port. The signal leaving the coupled port is further passed to stage 0 (see following paragraph). The signal leaving the transmitted port is led back to stage 2 by a separate signal line, where it is dissipated with a load. The isolated port is connected to a load as well, or to a reflective element.

[0074] The signal coming from stage 1 enters the directional coupler on stage 0 through the input port. The signal leaving the coupled port is further passed to the sample, for instance a quantum processor. The signal leaving the transmitted port is led back to stage 1 by a separate signal line, where it is dissipated with a load. The isolated port is connected to the load or reflective element. By this setup, the active heat loads on stages 0 and 1 can be significantly reduced, while the thermal photon number remains essentially at the same level.

[0075] The symbol and port arrangement used for the directional couplers in Figure 4 and all following figures is the conventional one shown in Figure 2. It is understood that the actual cable routing can be different in reality, for instance if the directional couples are implemented in a planar design, such as a stripline (see Fig. 3a and Fig. 3b) or a microstrip. Cable loops, which are apparent in the figures, might thus not exist in reality.

[0076] Figure 5 shows the wiring of the drive and flux lines in a second embodiment of the present invention, similar to the wiring according to Figure 4.

[0077] As apparent, the transmitted port of the directional coupler on stage 1 is connected to a reflective element. The reflected power is thus sent back through the directional coupler and therefore for the greatest part of it back to higher stages, in particular to stage 3, where it is dissipated by the resistive load. The signal leaving the directional coupler at the coupled port is further passed to stage 0 (see following paragraph). The isolated port of the directional coupler on stage 1 is connected to a load.

[0078] The signal coming from stage 1 enters the directional coupler on stage 0 through the input port. The signal leaving the coupled port is further passed to the sample, for instance a quantum processor. The transmitted port of the directional coupler on stage 1 also connected to a reflective element. The reflected power is thus sent back through the directional coupler and therefore for the greatest part of it back to stage 1 , where it is dissipated by the respective load. The isolated port of the directional coupler on stage 0 is connected to a load or a reflective element.

[0079] By this arrangement, the active heat loads on stages 0 and 1 can be significantly reduced, while the thermal photon number remains essentially at the same level. Since the number of signal lines between individual stages is not increased, also the passive heat load is not increased.

[0080] Figure 6 shows the wiring of the drive and flux lines in a third embodiment of the present invention, similar to the wiring according to Figure 5.

[0081] As apparent, the wiring of the coupled and isolated ports has been exchanged for both directional couplers on stages 0 and 1 . The incoming signal at stage 1 is thus reflected by the reflective element at the transmitted port, before it is sent back through the directional coupler to leave at the isolated port and be further passed to stage 0. The same applies to stage 0, with the exception that the signal leaving isolated port is further passed to the sample, for instance a quantum processor.

[0082] This setup has the advantage that it is particularly suitable for implementation of the directional couplers as a planar design, such as stripline or microstrip, where the arrangement of the coupled and isolated ports is opposite to the notation shown in Fig. 2 (cf. Fig. 3).

[0083] Figure 7 shows the wiring of the drive and flux lines in a fourth embodiment of the present invention, similar to the wiring according to Figure 5. As apparent, the load on stage 3 has been removed and the coupling factor of both directional couplers on stages 1 and 0 has been reduced to -30 dB. In order to dissipate the residual signal, which is reflected from stages 1 and 0, a circulator with a load is foreseen a stage 5, which is the room temperature stage. Instead of a circulator and load, also an isolator may be used.

[0084] Figure 8 shows the wiring of the drive and flux lines in a fifth embodiment of the present invention, similar to the wiring according to Figure 7.

[0085] As apparent, the directional coupler on stage 1 has been further removed and the coupling factor of the remaining directional coupler on stage 0 has been reduced to -60 dB. The fully unattenuated signal is this directly sent to stage 0 and only the fraction of it, which is required and corresponds to the appropriate thermal noise level, is coupled into the sample. The remaining signal is reflected back to room temperature stage 5 and dissipated there by the arrangement of circulator and load.

[0086] This setup significantly reduces the number of devices and connections. Furthermore, the entire signal attenuation is realized on the lowest temperature stage 0, which in principle allows to achieve a minimal thermal noise photon number.

[0087] Figure 9 shows the calculated dissipated power in a single drive line at each stage of the dilution refrigerator according to Table 1 (Bluefors XLD400; N = 4) for three different wirings. For all three configurations, stainless steel (SS) cables were assumed to be used. The parameters of the calculation correspond to those used by Krinner et al. (EPJ Quantum Technology 2019, 6(2), Section 5.1 ). They thus refer to the application of a continuous microwave tone at 5 GHz and a power of 16 dBm, corresponding to a signal level of -52.5 dBm at stage 0.

[0088] Temperature-dependent thermal conductivities and attenuations of the cables were selected such that the calculated heat outputs matched with Krinner et al. (comparison with Fig. 8). The attenuators were then replaced with the circuits described here and the heat outputs were calculated on this basis. The properties and lengths of the cables were not changed for this purpose.

[0089] - Graph A: Wiring of drive line as proposed by Krinner et al. (EPJ Quantum Technology 2019, 6(2), Section 3.2; cf. Figure 1);

[0090] - Graph B: Wiring of drive line according to first embodiment of present invention (cf. Figure 4);

[0091] - Graph C: Wiring of drive line according to second embodiment of present invention (cf. Figure 5).

[0092] As apparent, the dissipated power, and therefore also the active heat load caused by the drive line, is very similar between the different wirings for stages 4 to 2. However, a significant reduction is achieved for stages 1 and 0, which are most sensitive to thermal noise and have the least cooling power.

[0093] Table 2 shows the material of the cables, attenuation and dissipated power at each of the stages.

[0094] SS = Stainless Steel

[0095] Figure 10 shows the calculated dissipated power in a single drive line at each stage of the dilution refrigerator according to Table 1 (Bluefors XLD400; N = 4) for three different wirings. For all three configurations, stainless steel (SS) cables were assumed to be used between stages 5, 4 and 3 and superconductive Nio- bium-Titanium cables between stages 3, 2, 1 and 0. The parameters of the calculation correspond to those used by Krinner et al. (EPJ Quantum Technology 2019, 6(2), Section 5.1 ). They thus refer to the application of a continuous microwave tone at 5 GHz and a power of 16 dBm, corresponding to a signal level of ca. -52.5 dBm at stage 0. In order to account for the reduced dissipation of the superconductive cables, loads of -21 dB were chosen instead of -20 dB. The thermal conductivity of the Nb-Ti cables was assumed to be identical to those of the stainless steel cables. Only the electrical losses were reduced to -0.5 dB / m.

[0096] Graph A: Wiring of drive line as proposed by Krinner et al. (EPJ Quantum

[0097] Technology 2019, 6(2), Section 3.2; cf. Figure 1);

[0098] - Graph B: Wiring of drive line according to first embodiment of present invention (cf. Figure 4);

[0099] - Graph C: Wiring of drive line according to second embodiment of present invention (cf. Figure 5). As apparent, the dissipated power, and therefore also the active heat load caused by the drive line, is similar between the different wirings for stages 4 to 2, although at stage 2 a higher power can be observed for Graph B. However, a substantial reduction of more than one order of magnitude is achieved for stages 1 and 0, which are most sensitive to thermal noise.

[0100] Table 2 shows the material of the cables, attenuation and dissipated power at each of the stages.

[0101] SS = Stainless Steel; Nb-Ti = Niobium-Titanium

[0102] The words used in the specification are words of description rather than limitation, and it is understood that various changes may be made without departing from the spirit and scope of the invention.

[0103] LIST OF DESIGNATIONS

[0104] 1 Main Line

[0105] 2 Coupled Line 3 Reflective Element 3 (Short)

[0106] 4 Termination (Load)

[0107] P1 Input Port P2 Transmitted Port

[0108] P3 Coupled Port

[0109] P4 Isolated Port

[0110] LIST OF ABBREVIATIONS Ld Load

[0111] Rfl Reflective Element

[0112] DR Drive Line

[0113] FLX Flux Line

Claims

PATENT CLAIMS1 . Cryogenic device comprising N + 1 stages, wherein N is an integer greater than 0, wherein the temperature on each stage increases incrementally with increasing stage number, wherein stage 0 has a lowest temperature and stage N has a highest temperature, wherein the device comprises at least one signal line leading at least from a stage n + 1 to a stage n, wherein the signal line comprises a signal attenuator on stage n, characterized in that the signal attenuator is a signal coupler, which signal coupler splits an incoming signal into an attenuated signal and a residual signal, wherein the residual signal is led back from stage n to at least stage n + 1.

2. The device according to claim 1 , wherein the at least one signal line leads from a stage n + i to stage n, wherein i is an integer between 1 and N + 1 - n.

3. The device according to one of claims 1 or 2, wherein the residual signal is led back from stage n to a stage n + j, wherein j is an integer between 1 and N + 1 - n.

4. The device according to one of claims 1 to 3, wherein the attenuated signal is led further to at least a stage n - 1 , wherein n is greater than zero.

5. The device according to claim 4, wherein the attenuated signal is led further to a stage n - k, wherein k in an integer between 1 and n.

6. The device according to claim one of claims 1 to 5, wherein the coupling factor of the signal coupler is -1 to -80 dB, preferably -3 to -60 dB, more preferably -10 to -40 dB, such as -10 dB or -20 dB.

7. The device according to claim one of claims 1 to 6, wherein the signal coupler is a directional coupler.

8. The device according to claim 7, wherein the directional coupler has a planar design, such as stripline or microstrip.

9. The device according to one of claims 7 or 8, wherein the incoming signal is fed at an input port into the directional coupler.

10. The device according to one of claims 7 to 9, wherein the coupled signal is fed at a coupled port out of the directional coupler.11 . The device according to one of claims 7 to 10, wherein the residual signal is fed at a transmitted port out of the directional coupler.

12. The device according one of claims 1 to 11 , wherein the residual signal is led back to at least stage n + 1 by a separate signal line.

13. The device according to one of claims 1 to 12, wherein the residual signal is reflected by a reflective element to be fed back into the same signal line.

14. The device according to claim 13, wherein the residual signal is reflected by the reflective element at the transmitted port of the directional coupler to be fed back into the directional coupler and thus the same signal line.

15. The device according to claim 14, wherein the coupled signal is fed at an isolated port out of the directional coupler.

16. The device according one of claims 1 to 15, wherein the residual signal dissipated at stage n + j by a dissipating element.

17. The device according to one of claims 1 to 16, wherein the at least one signal line is selected from the group consisting of a coaxial line, a stripline, a microstrip or a waveguide.

18. The device according to one of claims 1 to 17, wherein the at least one signal line is at least partially superconductive.

19. The device according to one of claims 1 to 18, wherein N is selected form the group consisting of 1 , 2, 3, 4, 5, 6, 7, 8, 9 and 10.

20. The device according to one of claims 1 to 18, wherein N is at least 2 and the signal line comprises a cascade of signal attenuators.21 . The device according to claim 20, wherein the cascade of signal attenuators comprises at least two signal attenuators at individual stages.

22. The device according to one of claims 20 or 21 , wherein the cascade of signal attenuators comprises at least two signal couplers at individual stages.

23. The device according to one of claims 1 to 22, wherein the signal line comprises at least one further element selected from the group consisting of a resistive signal attenuator, a low pass filter, a band pass filter and an infrared filter.

24. The device according to one of claims 1 to 23, wherein the cooling power on a given stage is greater than the total heat load resulting on this stage by at least a factor of 1 .2, preferably at least a factor of 1 .5, more preferably at least a factor of 2, even more preferably at least a factor of 3.

25. The device according to claim one of claims 1 to 24, wherein the temperature at stage 0 is less than 100 mK, preferably less than 50 mK, more preferably less than 20 mK.

26. The device according to one of claims 1 to 25, further comprising a dilution refrigerator and optionally additionally at least one pulse tube refrigerator.

27. The device according to claim one of claims 1 to 26, wherein the at least one signal line is suitable for transmission of an electromagnetic wave with a frequency in a range of 1 -100 GHz, preferably 2-20 GHz, more preferably 3-10 GHz.

28. The device according to claim one of claims 1 to 27, further comprising at stage 0 a solid-state based quantum device, in particular a superconducting quantum device, such as a superconducting quantum processor.

29. The device according to claim 28, wherein the quantum processor com- prises at least 10, preferably at least 102, more preferably at least 103, even more preferably at least 104, even still more preferably at least 105qubits.

30. The device according to one of claims 28 or 29, wherein the at least one signal line is selected from a drive line and a flux line.31 . Quantum computer, comprising a device according to claim one of claims 1 to 30.

32. Use of a signal coupler as a signal attenuator in a device according to claim one of claims 1 to 30.

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