Apparatuses for reduction of thermal noise at cryogenic temperatures

Abstract

According to an aspect, there is provided a quantum circuit assembly. The quantum circuit assembly comprises a quantum device configured to be controllable via a control signal received via a control signal input of the quantum device. Moreover, the quantum circuit assembly comprises an attenuator circuit having an input for receiving the control signal and an output connected to the control signal input of the quantum device. The attenuator circuit comprises a reactive element for reflecting or guiding a part of the control signal away from the quantum device at a frequency band of the control signal. The reactive element is a reactive circuit component or a reactive circuit.

Description

APPARATUSES FOR REDUCTION OF THERMAE NOISE AT CRYOGENICTEMPERATURESTECHNICAL FIELD

[0001] Various example embodiments relate to quantum devices and, more specifically, solutions for driving quantum devices.BACKGROUND

[0002] A quantum-technological device (or simply a quantum device) is a physical system that utilizes quantum mechanical principles such as superposition, entanglement, and quantum tunnelling to perform computations, process information, or execute specialized tasks beyond the capabilities of classical (i.e., non-quantum) devices. One example of a quantum device is a quantum processing unit (QPU). Quantum devices are typically very sensitive to noise especially at and close to their operational frequency or frequencies. Quantum devices are commonly driven by signals that are generated at elevated temperatures and travel to the quantum device via cables or other transmission lines. However, all transmission lines suffer from Johnson-Nyquist noise (equally called thermal noise), even if perfectly impedance-matched. This is problematic since if the thermal noise photons, emitted by the dissipative element matching to the characteristic impedance of the transmission line, reach the quantum device, they may excite the quantum device or disturb it in some other way. For example, if the device is a QPU, noise photons at qubit frequency cause bit- flip errors and noise photons at other frequencies lead to phase-flip errors.SUMMARY

[0003] According to an aspect, there is provided the subject matter of the independent claims. Embodiments are defined in the dependent claims.

[0004] According to a first aspect, there is provided a quantum circuit assembly, comprising:a quantum device configured to be controllable via a control signal received via a control signal input of the quantum device; and an attenuator circuit having an input for receiving the control signal and an output connected to the control signal input of the quantum device, wherein the attenuator circuit comprises a reactive element for reflecting or guiding a part of the control signal away from the quantum device at a frequency band of the control signal, wherein the reactive element is a reactive circuit component or a reactive circuit.

[0005] According to a second aspect, there is provided a tunable on-chip filter for a drive line of a qubit, comprising: a transmission line comprising a first end for receiving a control signal of the drive line, a second end being terminated with an open circuit, a short circuit or a termination impedance, a first section for coupling to the qubit and a second section arranged between the first section and the second end; and one or more superconductive quantum interference devices, SQUIDs, integrated into the second section of the transmission line, wherein the one or more SQUIDs, acting as one or more tunable inductors, are configured to be coupled inductively to a fastflux line for adjusting tuning of the one or more SQUIDs; or one or more Josephson field-effect transistors, JoFETs, integrated into the second section of the transmission line, wherein the one or more JoFETs are configured to operate as one or more tunable inductors.

[0006] According to a third aspect, there is provided a tunable on-chip filter for a drive line of a qubit, comprising: a transmission line comprising a first end for receiving a control signal of the drive line, a first section for coupling to the qubit and a second end; and one or more Josephson field-effect transistors, JoFETs, connected between the second end of the transmission line and the ground, wherein an effective length of the transmission line is controllable via one or more voltages applied to one or more gates of the one or more JoFETs.

[0007] One or more examples of implementations are set forth in more detail in the accompanying drawings and the description below. Other features will be apparent from the description and drawings, and from the claims.BRIEF DESCRIPTION OF THE DRAWINGS

[0008] FIGs. 1 to 9 illustrate quantum circuit assemblies for driving a quantum device according to some embodiments;

[0009] FIGs. 10 to 12 illustrate tunable filters according to some embodiments; and

[0010] FIGs. 13A & 13B illustrate, respectively, a system comprising, on the right, a quantum circuit assembly according to an embodiment based on using a directional coupler as an attenuator and, on the left, a reference quantum circuit assembly based on a purely resistive attenuator and measurement results associated with said two quantum circuit assemblies.DETAIEED DESCRIPTION OF SOME EMBODIMENTS

[0011] In the following, the term “cryogenic temperature” may be defined as a temperature smaller than 123 K (-150 °C). However, in the context of embodiments, the cryogenic temperatures may be considerable smaller than this limit (e.g., smaller than 1 K).

[0012] In the following, the term “qubit frequency” refers to a frequency defined by the energy difference between the two computational states of the qubit. In other words, the qubit frequency qubitis defined aswhere E1and Eoare, respectively, energies of the excited state 11) and the ground state |0), and h is the Planck’s constant. The qubit frequency is the frequency of the radio signal for driving the qubit from 10) to | 1). The qubit frequency may be dependent on qubit biasing (e.g., qubit biasing voltage). In other cases, the qubit frequency may be fixed (i.e., non- tunable). The qubit frequency may be equally called a qubit resonance frequency.

[0013] In the following, the term “sweet spot of a qubit” refers to an optimal operating point of a (tunable) qubit in terms of minimizing sensitivity to noise and maximizing coherence time. Namely, the sweet spot corresponds typically to a biasing (e.g., a biasing voltage) that minimizes sensitivity to noise and maximizes coherence time.

[0014] Quantum devices (equally called quantum-technological devices) such as quantum processing units (QPUs) are very sensitive to noise especially at and close to their operation frequency. Quantum devices are typically driven by signals that are generated at elevated temperatures (that is, temperatures elevated relative to cryogenic temperatures at which the quantum devices are operated) and travel to the quantum device via cables (e.g., coaxial cables) or other transmission lines (e.g., co-planar waveguides). However, all transmission lines suffer from Johnson-Nyquist noise (equally called thermal noise), even if perfectly impedance-matched. This is problematic since if the thermal noise photons, emitted by the dissipative element matching to the characteristic impedance of the transmission line, reach the quantum device, they may cause unwanted excitations and disturbances to the quantum device. For example, if the device is a QPU, noise photons at the qubit frequency (i.e., at the frequency defined by the energy difference between the two computational states of the qubits of the QPU) cause bit- flip errors and noise photons at other frequencies lead to phase-flip errors. Typically, these noise photons are absorbed to resistive attenuators at the qubit frequency and filtered away at frequencies far from the qubit frequency. However, since signal powers in the order of tens of picowatts and above are required at the qubit to drive it at high fidelity, the cryogenic attenuators at the qubit temperature tend to heat up. Consequently, the attenuators themselves start to emit thermal photons owing to their Johnson-Nyquist spectrum. These thermal photons are harmful for the operation of the quantum device.

[0015] Let us assume that the quantum device driven by the noisy signal needs a power of Pdevto be driven as desired. Let us also assume that one needs to lower the power level of the noise by a factor of A » 1 at the temperature of the quantum device before the signal reaches the quantum device. Here, A is a power reduction factor (or equally attenuation), that is, a ratio of input power to output power. In the case of a single attenuator, the power heating the attenuator Patt(i.e., input power of the attenuator) is defined as Patt= dPdev, where, as described above, A is a power reduction factor and Pdevis the power reaching the quantum device. One may then solve the temperature of the attenuator Tattfrom the equation Patt=^att( ato To)Tatt, where Gattis a total thermal conductance of the attenuator to the phonon bath at To, including electron-phonon coupling, photonic heat conduction and electron diffusion of heat according to the Wiedemann-Franz law. Under most circumstances, the electron-phonon thermal conductance Ge-pis the dominant term of the total thermal conductance Gatt, but since it is directly proportional to the fourth power oftemperature To, the heating of the attenuator from any power Patt> 10 pW x A can significantly heat up the attenuator at millikelvin temperatures.

[0016] The aforementioned problem may be solved by using a tree of multiple attenuators (i.e., a set of attenuators arranged in a tree structure), instead of a single attenuator. More specifically, a tree of attenuators refers to a hierarchical or branched arrangement of multiple attenuators, where the signal is progressively attenuated through multiple stages. The total attenuation of the attenuator tree may be written as ]”[ / < -dfc, where Akis the power reduction factor associated with k-th attenuator. With this method, the last attenuator is heated up only by the power Plast att« ast^dev which may, for example, be only twice or four times the signal power at the quantum device. In practice however, such an attenuator tree may become very long since the first attenuator is still heated up to an elevated temperature and the noise photons from it need to be absorbed before reaching the device. Furthermore, if the attenuators in the tree are placed close to each other to save space at the cryogenic temperatures, the bulk of the tree may heat up, thus also heating the last attenuator.

[0017] The embodiments are directed to various solutions to the above described technical problems. The embodiments are based on the observation that the signal-to-noise ratio (SNR) for the (control) signal directed to the quantum device operated at the cryogenic temperature does not increase when an attenuator is applied to said signal since the attenuator attenuates both the signal and the noise with the same factor A. In fact, since the attenuator itself also adds some noise photons on top of the signal, the SNR actually decreases slightly owing to the use of attenuators. Thus, instead of using resistive attenuators that are plagued by Johnson-Nyquist noise as described above, the embodiments employ at least one reactive element to block the thermal photons. Some embodiments introduce various additional elements in addition to said at least one reactive element to further reduce the amount of thermal noise reaching the quantum device as will be described in detail below.

[0018] FIG. 1 illustrates one simplistic embodiment of the concept discussed in the previous paragraph. Namely, FIG. 1 shows a quantum circuit assembly 100 comprising an attenuator circuit 110 and a quantum device 101.

[0019] The quantum device 101 may be any physical system that utilizes quantum mechanical principles to perform computations, process information, and / or execute specialized tasks beyond the capabilities of classical non-quantum devices. The quantumdevice 101 may be pure quantum device or a hybrid quantum device (comprising both quantum and classical processing functions). For example, quantum device 101 may be, for example, a QPU (or other quantum computing device), a circuit-quantum-electrodynamical (circuit-QED) device, a quantum-dot device, a qubit circuit, a quantum sensor circuit, a quantum simulator circuit, or a quantum communication device. This definition may apply also to further embodiments of the quantum circuit assembly comprising a quantum device.

[0020] The quantum device 101 is configured to be controllable via a control signal received via a control signal input of the quantum device 101. The control signal has a certain frequency band of operation. Said frequency band may be a radio frequency (RF) band (e.g., a micro wave frequency band). In general, radio frequencies are defined as electromagnetic frequencies within the range from 20 kHz to 300 GHz while micro wave frequencies are defined as electromagnetic frequencies within the range from 300 MHz and 300 GHz. Thus, said frequency band may be within one or both of said ranges. The control signal may be, for example, a drive or driving signal applied to the quantum device 101 (via said control signal input) to manipulate the quantum state of at least one qubit (being, e.g., superconducting qubits) of the quantum device 101.

[0021] The attenuator circuit 110 has an input (or an input terminal or port) for receiving the control signal (e.g., via a transmission line such as a coaxial cable) and an output (or an output terminal or port) connected to the control signal input of the quantum device 110. In the illustrated embodiment, the attenuator circuit 110 comprises a reactive element 111 connected with the quantum device 101. In FIG. 1, i denotes reactance of the reactive element 111. Said reactive element 111 may be selected or configured so as to enable reflecting or guiding a part of the control signal away from the quantum device 101 at the frequency band of the control signal (while the rest of the control signal is let through to the quantum device 101). The reactive element 111 may be a reactive circuit component (e.g., an inductor or a capacitor) or a reactive circuit. The reactive circuit may comprise one or more reactive circuit component such as one or more inductors (optionally including one or more pairs of mutually coupled inductors) and / or one or more capacitors. The reactive element 111 may be substantially purely reactive (i.e., it may not contain a substantial resistive component). Because photons are reflected, not absorbed, by such as reactive element 111, the reactive element 111 does not heat up and, thus, does not generate excess thermal noise. Thus, in its simplest form, the attenuator circuit 110 does not comprise any resistive elements (e.g., resistors) at the device temperature and the reactance added in theimmediate vicinity of the quantum device 101 reflects noise photons back to the same cable where they came from.

[0022] In some embodiments where the reactive element 111 is the reactive circuit, the reactive circuit 111 may be further configured to filter out noise photons outside of the frequency band of the control signal. Here, the attenuation caused by the reactive circuit 102 outside of the frequency band of the control signal may be larger compared to attenuation caused by the reactive circuit 111 within the frequency band of the control signal. In other words, within the frequency band of the control signal, a significant part of the control signal may still propagate to the quantum device 101 while the noise photons outside of the frequency band of the control signal may be filtered out more substantially.

[0023] As an alternative to the embodiment discussed in the previous paragraph, the attenuator circuit 110 may comprise a (separate) bandpass filter for filtering out noise photons outside of the frequency band of the control signal. The passband of the bandpass filter may correspond substantially to the frequency band of the control signal. The bandpass filter may be, for example, an LC filter.

[0024] In some embodiments, the reactive element 111 may be a directional coupler arranged so that an input port of the directional coupler is used for receiving the control signal and a coupled port of the directional coupler is used for outputting the control signal towards the quantum device 101, as will be discussed in detail in connection with FIGs. 2 & 3.

[0025] The attenuator circuit 110 may be connected to the quantum device 101 via a transmission line 102. The transmission line 102 may be a cable such as a (cryogenic) coaxial cable. Alternatively, the transmission line 102 may be a strip line, a coplanar waveguide or a triaxial waveguide. The length of the transmission line 102 should preferable be kept electrically small (i.e., small relative to the effective wavelength inside the transmission line 102) to avoid resonances in the transmission line 102. At least in some embodiments, the length of the transmission line 102 may be smaller than or equal to 3ATL / 4 (or even smaller than or equal to ATL / 4), where ATLis a central wavelength of the frequency band of the control signal within the transmission line. For example, the length of the transmission line 102 may be equal to ATL / 4, ATL / 2 or 3ATL / 4. The transmission line 102 (or specifically conducting parts thereof) may comprise a superconducting material such as niobium, niobium-titanium (NbTi) or aluminum.

[0026] The quantum circuit assembly 100 may be operated at a cryogenic temperature Ti. Said cryogenic temperature may be, for example, smaller than or equal to 30 mK. Said cryogenic temperature may be achieved, for example, using a cryostat comprising a dilution refrigerator.

[0027] FIGs. 2 & 3 illustrate two special cases of the quantum circuit assembly 100 where the reactive element 111 is specifically a directional coupler 211, 311. In FIGs. 2 & 3, the elements 201, 202 & 301, 302 may correspond to elements 101, 102 of FIG. 1 and are, thus, not discussed here for brevity. Moreover, the operating temperature 7^ of the quantum circuit assembly 200 & 300 may be defined as described in connection with FIG. 1.

[0028] FIGs. 2 & 3 illustrate two alternatives for using a directional coupler for guiding a part of the control signal away from the quantum device 101 at the frequency band of the control signal (while the rest of the control signal is let through to the quantum device 101). Thus, in these embodiments, the attenuation circuit 210, 310 comprises (or consists of) the directional coupler 211, 311. The directional coupler 211, 311 may be any conventional directional coupler. The directional coupler 211, 311 may be, for example, constructed from two coupled transmission lines (acting effectively as mutually coupled inductors) set close enough together such that energy passing through one is coupled to the other (though other designs, e.g., ones based on waveguides may also be employed). According to a general definition of a directional coupler, the directional coupler 211, 311 comprises four ports: an input port (top-left port in FIGs. 2 & 3), a transmitted port (bottom-left port in FIGs. 2 & 3), a coupled port (bottom-right port in FIGs. 2 & 3) and an isolated port (bottom-left port in FIGs. 2 & 3). In both of FIGs. 2 & 3, the directional coupler 211, 311 is arranged such that the input and coupled ports of the directional coupler 211, 311 serve as the input and output ports of attenuator circuit 210, 310 while the transmitted and isolated ports are terminated with matched loads 221, 222, 321, 322 ZL(being typically 50 Q loads). Thus, the directional coupler 210, 310 is used for attenuating the control signal by a coupling factor of the directional coupler (e.g., 10 dB or 20 dB). The isolated port may be specifically terminated with the matched load at the operating temperature 7^ .

[0029] The difference between FIGs. 2 & 3 lies in how the transmitted port is terminated. Referring to FIG. 2, the transmitted port of the directional coupler 211 is terminated, similar to the isolated port, with the matched load 221 at the operating temperature T1. On the hand, in FIG. 3, the transmitted port of the directional coupler 311 isterminated with the matched load 321 at a higher temperature T2compared to the operating temperature 7^ . Said higher temperature may be, for example, a higher cryogenic temperature or a non-cryogenic temperature such as room temperature. In this case, the transmitted port may, in practice, be connected to a transmission line 323 that is terminated, at said higher temperature T2, with the matched load 321.

[0030] In some alternative embodiments (not shown in FIG. 3), the transmitted port of the directional coupler 311 may be connected to a plurality of resistive elements (e.g., resistive circuit components or resistors) at respective plurality of temperatures. The plurality of resistive elements may be connected in series. Last of the plurality of resistive elements may be a matched load. The plurality of temperatures associated with the plurality of resistive elements may increase when moving farther from the directional coupler 311. One example of this type of embodiment is discussed in connection with FIG. 13 A.

[0031] Any of the further embodiments discussed below may optionally employ a directional coupler, using either of the configurations of FIGs. 2 & 3, as the reactive element. In embodiments where two reactive elements are provided, one or both of these reactive elements may correspond to directional couplers using either of the configurations of FIGs. 2 & 3.

[0032] FIG. 4 illustrates another embodiment of a quantum circuit assembly 400 for reducing thermal noise at a quantum device 401. The quantum circuit assembly 400 corresponds to a variation of the quantum circuit assembly of FIG. 1. Namely, the elements 401, 402, 411 may correspond to elements 101, 102, 111 of FIG. 1 and are, thus, not discussed here for brevity. Moreover, the operating temperature 7^ of the quantum circuit assembly 400 may be defined as described in connection with FIG. 1. It should, however, be noted that the values of some of the aforementioned elements may be different in the embodiments corresponding to FIG. 4 compared to embodiments corresponding to FIG. 1 due to the introduction of the additional element 412.

[0033] Use of a purely reactive element for redirecting power away from the sensitive quantum device as discussed in connection with FIG. 1 without causing the thermal noise to couple to the quantum device in an undesirable way may be challenging in practice. Namely, it may not always be possible to arrange a relatively large reactive element (e.g., an inductor or capacitor) very close to the quantum device. In other words, a distance between said relatively large reactive element and the quantum device may not always be electricallysmall (i.e., small relative to the operational wavelength of the control signal) due to practical concerns. In such cases, the inputted control signal may form standing waves between the reactive element and the quantum device. If a frequency of these standing waves happens to be close to any of the resonance frequencies of the quantum device, they may be able to excite these resonance frequencies of the quantum device and, thus, have a detrimental effect on the operation of the quantum device. To overcome this problem, the attenuator circuit 410 of FIG. 4 comprises, in addition to the reactive element 111, a resistive element 412 (being, e.g., a resistive circuit component, a resistor or a resistive circuit) arranged between the reactive element 411 and the quantum device 401 (or specifically between the reactive element 411 and the transmission line 402 connecting the quantum device 401). Namely, a first terminal of the resistive element 412 is connected to the reactive element 411 (namely, to the output of the reactive element 411 facing the quantum device 401) and a second terminal of the resistive element is connected to the ground. The resistive element 412 ensures that any resonances occurring between the reactive element 411 and the quantum device 401 are extinguished.

[0034] It should be noted that the heating power of the resistive element 412 is essentially equal to the input power Pdevof the quantum device 401 since the resistive element 412 is not used for attenuating the signal going to the quantum device 401. Therefore, this embodiment is superior both to the solution where only a single (resistive) attenuator is employed as well as the solution where a (resistive) attenuator tree is employed.

[0035] The resistive element 412 may be impedance-matched to the transmission line 402 at the frequency band of the control signal (or at least at some frequencies of the frequency band). In other words, the resistance of the resistive element 412 may be equal to the characteristic impedance of the transmission line (being, e.g., 50 ).

[0036] FIG. 5 illustrates another embodiment of a quantum circuit assembly 500 for reducing thermal noise at a quantum device 501. The quantum circuit assembly 500 corresponds to a variation of the quantum circuit assemblies of FIGs. 1 & 2. The elements 501, 502, 511 may correspond to elements 101, 102, 111 of FIG. 1 and the element 512 may correspond to element 412 of FIG. 4 and are, thus, not discussed here for brevity. Moreover, the operating temperature of the quantum circuit assembly 500 may be defined as described in connection with FIG. 1. It should, however, be noted that the values of some of the aforementioned elements may be different in the embodiments corresponding to FIG. 5compared to embodiments corresponding to any of FIGs. 1 to 4 due to the introduction of the additional element 513.

[0037] In FIG. 5, the attenuator circuit 510 comprises a first reactive element 511 and a second reactive element 513. The first reactive element 511 is arranged, similar to the quantum circuit assembly 200 of FIG. 2, to precede the resistive element 512 while the second reactive element 513 is arranged to follow the resistive element 512. In other words, the second reactive element 513 is arranged between an input of the attenuator circuit 510 and a first terminal (i.e., the non-grounded terminal) of the resistive element 512 and the transmission line 502, and the second reactive element 513 is arranged between a first terminal of the resistive element 512 and the transmission line 502. Similar to as described in connection with FIG. 1 for the first reactive element 111, the second reactive element 513 may be a second reactive circuit component or a second reactive circuit. In general, the first and second reactive elements 511, 513 may be defined as described in connection with FIG. 1 for the reactive element 111.

[0038] In some embodiments, the attenuation d2caused by the second reactive element 513 may be smaller than the attenuation A1caused by the first reactive element 511 at the frequency band of the control signal, that is, d2may be (much) smaller than A1(but still larger than one) at the frequency band of the control signal. In other words, a reflection coefficient (i.e., Si l parameter) at the first reactive element 511 at the frequency band of the control signal is larger compared to the reflection coefficient at the second reactive element 513 at the frequency band of the control signal. This provides benefit that less power will be dissipated in the resistive element 512 and, hence, the resistive element 512 heats up less and exhibits lower noise.

[0039] In some embodiments based on either of the quantum circuit assemblies 400, 500 of FIGs. 4 & 5, an engineered electromagnetic environment may be employed in place of the resistive element 412, 512 to induce even lower amount of thermal noise than possible using a low-temperature resistive element. Such an engineered environment may be, for example, a quantum-circuit refrigerator. Said quantum-circuit refrigerator may be impedance-matched to the transmission line 402, 502 at the frequency band of the control signal, similar to the resistive element 412, 512.

[0040] FIG. 6 illustrates another embodiment of a quantum circuit assembly 600 for reducing thermal noise at a quantum device 601. The quantum circuit assembly 600 buildsupon the previous quantum circuit assemblies of FIGs. 1 to 3. The elements 601, 602, 611 may correspond to elements 101, 102, 111 of FIG. 1, the element 612 may correspond to element 412 of FIG. 4 and the element 613 may correspond to element 513 of FIG. 5. These elements are, thus, not discussed here for brevity. Moreover, the operating temperature of the quantum circuit assembly 600 may be defined as described in connection with FIG. 1. It should, however, be noted that the values of some of the aforementioned elements may be different in the embodiments corresponding to FIG. 6 compared to embodiments corresponding to FIGs. 1 to 5 due to the introduction of the additional element 614 to 616.

[0041] In the quantum circuit assembly 600 of FIG. 6, first and second resistive elements 612, 614 and corresponding first and second three-port circulators 615, 616 have been introduced in order to extinguish even the aforementioned heating power Pdevof the resistive element 612. Namely, the first and second three-port circulators are arranged between the first and second reactive elements 611 in series via first and second ports of the first and second three-port circulators 615, 616. Each of the first and second three-port circulators 615, 616 is configured such that a signal entering the first port will exit (only) through the second port, a signal entering the second port will exit (only) through a third port, and a signal entering a third port will exit (only) through the first port. Moreover, the first and second resistive elements 612, 614 have, each, a first terminal connected to a third port of one of the first and second three-port circulators 615, 616 and a second terminal connected to the ground.

[0042] In FIG. 6, the heating power Pdevis absorbed by the first resistive element 612 before going to the second resistive element 614. Here, the second resistive element 614 may be considered the primary resistive element, that is, the resistive element where the thermal radiation is subject to the quantum device 601. In this case, there is no direct heating from the signal to the primary resistive element 614. The primary resistive element is only heated up by photonic heat conduction. Thus, it will be very well thermalized to the transmission line 602.

[0043] While FIG. 6 shows specifically two grounded resistive elements 612, 614 and two three-port circulators 615, 616, a quantum circuit assembly according to an embodiment may, in general, comprise one or more grounded resistive elements and one or more three- port circulators arranged in an analogous manner to the example of FIG. 6. Namely, the one or more three-port circulators may be arranged between the first and second reactiveelements 611, 613 (or more generally between the first reactive element 611 and the output of the attenuator circuit 610 facing the quantum device 601) in series via first and second ports of the one or more three-port circulators, wherein each of the one or more three-port circulators is configured such that a signal entering the first port will exit (only) through the second port, a signal entering the second port will exit (only) through a third port, and a signal entering a third port will exit (only) through the first port. Moreover, the one or more grounded resistive elements may be connected, respectively, to the one or more third ports of the one or more three-port circulators (that is, the first terminals of the one or more resistive element may be connected to said one or more third ports while the second terminals are grounded). In some alternative embodiments, the second reactive element 613 may be omitted (i.e., replaced with a short circuit). Additionally or alternatively, in some embodiments, a three-port circulator may be omitted from one or more junctions connecting to resistive elements (similar to as shown in FIG. 7).

[0044] In some embodiments (not shown in FIG. 6), at least one bandpass filter may be provided between a plurality of three-port circulators to reduce the photonic heat conduction. For example, such a bandpass filter may be provided between each pair of adjacent three-port circulators of the attenuator circuit or between at least some of them. For example, in the case of the quantum circuit assembly 600 of FIG. 6, a single bandpass filter configured to filter said photonic heat conduction could be introduced between the first and second three-port circulators 615, 616. The at least one bandpass filter may have a passband corresponding to or at least comprising a frequency band of the control signal.

[0045] FIG. 7 illustrates another embodiment of a quantum circuit assembly 700 for reducing thermal noise at a quantum device 701. The quantum circuit assembly 700 builds upon the previous quantum circuit assemblies of FIGs. 1 to 5 and is, specifically, an alternative to the quantum circuit assembly 600 of FIG. 6. The elements 701, 702, 711 may correspond to elements 101, 102, 111 of FIG. 1 , the element 712 may correspond to element 412 of FIG. 4 and the element 713 may correspond to element 513 of FIG. 5. These elements are, thus, not discussed here for brevity. Moreover, the operating temperature 7^ of the quantum circuit assembly 700 may be defined as described in connection with FIG. 1. It should, however, be noted that the values of some of the aforementioned elements may be different in the embodiments corresponding to FIG. 7 compared to embodiments corresponding to FIGs. 1 to 5 due to the introduction of the additional element 712 to 714, 715.

[0046] The quantum circuit assembly 700 corresponds to a large extent to the quantum circuit assembly 600 of FIG. 6 and, thus, any of the features and definitions provided in connection with FIG. 7 may apply, mutatis mutandis, also here. While, in the quantum circuit assembly 600 of FIG. 6, first and second resistive elements 612, 614 and corresponding first and second three-port circulators 615, 616 were provided, in the quantum circuit assembly 700, first and second resistive elements 712, 714 and a single three-port circulator 715 is provided. The three-port circulator 715 is connected between the first reactive element 711 and the quantum device 701 via first and second ports of the three-port circulator 715. Moreover, a third port of the three-port circulator 715 is connected to the first resistive element 712, which is grounded. Here, the three-port circulator 715 is configured such that a signal entering the first port will exit (only) through the second port, a signal entering the second port will exit (only) through a third port, and a signal entering a third port will exit (only) through the first port. The second resistive element 714, which is also grounded, is connected to the second port of the three-port circulator 715 (and to the second reactive element 713). Thus, in summary, the difference compared to FIG. 6 is that no circulator is provided for connecting to the primary resistive element 714.

[0047] Similar to as described in connection with FIG. 6, the quantum circuit assembly 700 (or specifically the attenuator circuit 710 thereof) may be generalized to cover different numbers of resistive elements 712, 714 and three-port circulators 715. Namely, in more general embodiments, the attenuator circuit may comprise one or more three-port circulators arranged between the first and second reactive elements in series via first and second ports of the one or more three-port circulators, where each of the one or more three- port circulators is configured such that a signal entering the first port will exit through the second port, a signal entering the second port will exit through a third port, and a signal entering a third port will exit through the first port. Moreover, the attenuator circuit may comprise a plurality of grounded resistive elements comprising one or more grounded resistive elements connected, respectively, to the one or more third ports of the one or more three-port circulators and a grounded resistive element connected to the second port of a three-port circulator closest to the quantum device. In some embodiments, the second reactive element 713 may be omitted (i.e., replaced with a short circuit).

[0048] In some alternative embodiments (not shown in FIG. 7), the three-port circulator 715 may be arranged so that its first port is connected to the element 711, 712, itssecond port is connected to the second reactive element 713 (or directly to the transmission line 702) and its third port is connected to the second resistive element 714.

[0049] FIG. 8 illustrates a further embodiment of a quantum circuit assembly 800 for further reducing thermal noise at a quantum device 801. The quantum circuit assembly 800 builds upon the previous quantum circuit assembly 500 of FIG. 5. The elements 801, 802, 810, 811, 812, 813 may correspond to elements 501, 502, 510, 511, 512, 513 of FIG. 5 and are, thus, not discussed here for brevity. It should, however, be noted that the values of some of the aforementioned elements may be different in the embodiments corresponding to FIG. 8 compared to embodiments corresponding to FIG. 5 due to the introduction of the additional element 820 to 822.

[0050] Referring to FIG. 8, the quantum circuit assembly 800 comprises, in addition to the elements 801, 802, 810, 811, 812, 813 corresponding to elements 501, 502, 510, 511, 512, 513 of the quantum circuit assembly 500 of FIG. 5, a secondary attenuator circuit 820 connected to an input of the (primary) attenuator circuit 810 (i.e., preceding the attenuator circuit 810). In general, the secondary attenuator circuit 820 may be defined to correspond to any circuit topology described above for the (primary) attenuator circuit. In the specific embodiment of FIG. 8, the secondary attenuator circuit 820 comprises a secondary reactive element 821 (having a reactance) and a secondary grounded resistive element 822 (having a resistance) connected to the secondary reactive element. Here, the secondary reactive element 821 may be a secondary reactive circuit component or a secondary reactive circuit, similar to as described for the reactive element 111 in connection with FIG. 1.

[0051] The secondary attenuator circuit 820 has a different operational temperature compared to the (primary) attenuator circuit 810, the transmission line 802 and the quantum device 801. Namely, while the (primary) attenuator circuit 810, the transmission line 802 and the quantum device 801 may be operated at a cryogenic temperature Ti (being, e.g., smaller than or equal to 30 mK), the secondary attenuator circuit may be operated at an elevated temperature Tz (i.e., at a temperature Tz higher than Ti). This serves to further reduce the heat load resulting from the control signal. In other words, during operation of the quantum circuit assembly 800, there may be provided means for cooling the quantum device 801 and the attenuator circuit 810 (and the transmission line 802) to a first cryogenic temperature Ti and the secondary attenuator circuit 820 to a second cryogenic temperature Tz higher than the first cryogenic temperature Ti. Said means for the cooling may comprise,for example, a cryostat comprising a multi-stage cryogenic cooling system based, e.g., on dilution refrigerators. For example, a Bluefors XLD dilution refrigeration measurement system may be used for the cooling.

[0052] In some embodiments, the secondary reactive element 821, being a reactive circuit, may also be configured to filter out noise photons outside of the frequency band of the control signal at the second temperature T2. In such embodiments, the attenuation caused by the secondary reactive circuit outside of the frequency band of the control signal may, optionally, be larger compared to attenuation caused by the secondary reactive circuit within the frequency band of the control signal.

[0053] Alternatively, the secondary attenuator circuit 820 may further comprise a second bandpass filter configured to filter out noise photons outside of the frequency band of the control signal at the second temperature T2.

[0054] FIG. 9 illustrates a system comprising multiple quantum circuit assemblies 903, 933 controllable or drivable via the same control (or driving) signal. Referring to FIG. 9, the system 900 comprises n quantum circuit assemblies 903, 933, where n is an integer larger than or equal to 2. In FIG. 9, the n quantum circuit assemblies 903, 933 are based on the embodiment of FIG. 1, that is, each of the n quantum circuit assemblies 903, 933 comprises an attenuator circuit 910, 940 comprising a reactive element 911, 941 (being, e.g., a reactive circuit component or a reactive circuit), a quantum device 901, 931 and a transmission line 902, 932 connecting the attenuator circuit 910, 940 and the quantum device 901, 931.

[0055] Additionally, the n quantum circuit assemblies 903, 933 comprises a plurality of matching circuits (MCs) connecting adjacent quantum circuit assemblies 903, 933 to each other so as to enable use of the same control signal for driving the plurality of quantum circuit assemblies. In other words, each quantum circuit assembly 903, 933 of the n quantum circuit assemblies 903, 933 comprises a matching circuit 904, 934 having at least a first terminal (or port) for receiving the control signal (either directly or via one or more other matching circuits), a second terminal (or port) for outputting the control signal to an adjacent matching circuit or, in the case of the last matching circuit 933 in the chain of n connected matching circuit 903, 933, to a matched load and a third terminal (or port) for outputting the control signal towards a quantum device 901, 931 of the quantum circuit assembly 903, 933. Each matching circuit 904, 934 of a quantum circuit assembly 903, 933 may be defined soas to allow the control signal to propagate both to the quantum device 901 , 931 of the present quantum circuit assembly 903, 933 and to the adjacent quantum circuit assembly 903, 933 (unless the quantum circuit assembly is the last quantum circuit assembly 933 in the chain) while preventing interference between adjacent quantum circuit assemblies 903, 933. As mentioned above, the second terminal of the last matching circuit 933 in the chain of n connected matching circuit 903, 933 (being the last to receive the control signal) may be connected to a matched load (e.g., a 50 Q load). Similar to as discussed in connection with FIG. 3, the matched load 950 may be at a higher temperature T2compared to the operating temperature 7^ of the n quantum devices 901, 931. Said higher temperature may be, for example, a higher cryogenic temperature or a non-cryogenic temperature such as room temperature. In this case, the transmitted port may, in practice, be connected to a transmission line 951 (e.g., a coaxial cable) that is terminated, at said higher temperature T2, with the matched load 950.

[0056] In some alternative embodiments, the matched load 950 may be at the operating temperature Tr. In such embodiments, the matched load 950 may form a part of the matching circuit 934, that is, the last matching circuit 934 may have only a first terminal for receiving the control signal via one or more other matching circuits and a second terminal for outputting the control signal towards a quantum device of the quantum circuit assembly.

[0057] In general, the n quantum circuit assemblies 903, 933 may be based on any of the quantum circuit assemblies discussed in connection with any of FIGs. 1 to 8. These alternative embodiments may still include the n matching circuits 904, 934 (preceding the attenuator circuit 910, 940) and the load impedance 950 (connected to the last matching circuit 934).

[0058] In some embodiments, the concept of FIG. 9 may be employed for driving a plurality of ports of a single quantum device, instead of a plurality of quantum devices 901, 931. Alternatively, the concept of FIG. 9 may be employed for driving a plurality of ports of a plurality of quantum devices where each quantum device comprises one or more ports for receiving the control signal. The number of said one or more ports may be the same for all quantum devices or different for at least some of the plurality of quantum devices.

[0059] The embodiments discussed in connection with FIG. 9 provide the benefit of being able to reduce the number of RF (or micro wave) sources and cables crossing different temperatures, and the thermal load on the cryostat due to the drive power (i.e., powerassociated with the control or drive signal) since a large fraction of the power created at room temperature can be used to drive the quantum devices or a single multi-port quantum device without reducing the SNR of the drive.

[0060] In some embodiments, any of the attenuator circuits 110, 210, 310, 410, 510, 610, 710, 810, 903, 933 as discussed above may be configured to reflect or guide at least 10%, optionally at least 50% or at least 90%, of the control signal away from the quantum device.

[0061] According to some embodiments, there is provided a method comprising using an attenuator circuit 110, 210, 310, 410, 510, 610, 710 as discussed above for attenuation of a control signal (e.g., a drive signal) before it is fed to a quantum device.

[0062] According to some embodiments, there is provided a method comprising using attenuator circuits 810, 820 as discussed above for attenuation of a control signal (e.g., a drive signal) before it is fed to a quantum device.

[0063] According to some embodiments, there is provided a method comprising using n attenuator circuits 903, 933 as discussed above for attenuation of a control signal (e.g., a drive signal) before it is fed to n quantum devices, to n ports of a single quantum device or to n ports of m quantum devices, where n is a positive integer larger than one and m is a positive integer larger than one and smaller than n.

[0064] Optimal quantum processors for practical applications require fast control, long decay times, low power dissipation, and efficient qubit reset mechanisms. However, current qubit control techniques often lead to compromises in these key properties. To achieve fast control with low drive power, the qubit must be strongly coupled to the control line, which leads to decreased qubit decay times and susceptibility to thermal noise from the drive line.

[0065] To overcome or at least alleviate these problems, some embodiments are directed to a tunable on-chip filter enabling fast control with significantly improved decay times and without increasing heat load. Namely, the tunable on-chip filter may decouple a quantum device at a band of frequencies from the drive line. This property can be used to fully remove the energy decay and suppress the dephasing of the state of the quantum device. The use of a tunable filter, instead of a non-tunable filter, is beneficial as designing an integrated circuit (IC) comprising a non-tunable filter while still providing a high fabricationyield is challenging since the filter frequency needs to be designed and fabricated, in that case, to exactly match the qubit frequency at the qubit sweet spot. In other words, the filter needs to be designed and manufactured so that its stopband matches the qubit frequency at the qubit sweet spot. We solve this problem with the tunability of the filter, i.e., the qubit frequency can be fixed and still we can tune the filter stopband exactly to the qubit frequency without adding new decay channels to the qubit. As a side effect of the tunability of the filter and by adding a fast frequency tuning to the filter, this scenario facilitates efficient qubit reset to the ground state (by shifting the filter stopband away from the qubit frequency), which may rival the performance of established methods.

[0066] FIG. 10 illustrates system 1000 (being, e.g., a quantum integrated circuit) according to embodiments. The system 1000 may form a part of a QPU or other quantum device. The system 1000 comprises a drive line 1004 (i.e., a transmission line for feeding the control or drive signal), a qubit 1001 coupled to the drive line 1004 and a tunable (on- chip) filter 1010 integrated directly into the drive line 1004. Thus, the drive line 1004 (or at least a part thereof) may be considered a part of the tunable filter 1010.

[0067] According to a general definition, the qubit 1001 is a fundamental unit of quantum information, analogous to a classical bit, but capable of existing in a superposition of quantum states. It can be described as a quantum two-level system, where the logical states |0) and |1) correspond to distinct quantum states of the system. The state of the qubit can be represented as a coherent superposition of these basis states, defined by the wavefunction | ip) = a | 0) + / ? | 1), where a and / ? are complex probability amplitudes satisfying \a\2+ | / ?|2= 1 . The qubit 1001 may be, for example, a transmon qubit (sometimes called just a transmon). In other embodiments, the qubit 1001 may be a flux qubit, a phase qubit, a fluxonium qubit, an unimon qubit, a quarton qubit, a zero-pi qubit, a trimon qubit, a quantum dot qubit, a gatemon qubit, a donor qubit, a resonator qubit, a majorana qubit or a dual rail qubit. The qubit 1001 may be coupled to the drive line 1004 either capacitively or inductively. The qubit 1001 may be a fixed-frequency qubit. Thus, the tuning of the system 1000 may be performed only via the tunable filter 1010 (not via biasing of the qubit 1001).

[0068] The tunable filter 1010 may be a bandstop filter. The tunable filter 1010 comprises a transmission line 1004 (i.e., the drive line or a part thereof) having a first end for receiving the control signal of the drive line 1004 and a second end being terminatedwith a termination 1005. In the simplistic presentation of FIG. 1, the first end is connected to an RF voltage source 1003 supplying the control signal. Said termination 1005 may be an open circuit, a short circuit or a (finite) termination impedance. Moreover, the transmission line 1004 comprises at least a first section 1006 for coupling to the qubit 1001 and a second section 1007 arranged between the first section 1006 and the second end (having said termination 1005). The first section 1006 may be either capacitively or inductively coupled to the qubit 1001. In some (but not all) embodiments, the first section 1006 may be the only section for coupling to the qubit 1001. The transmission line 1004 may be, for example, a coplanar waveguide. Alternatively, the transmission line 1004 may be a strip line, a coaxial cable or a triaxial waveguide. The transmission line 1004 may be made of a superconducting material such as niobium, tantalum or aluminum.

[0069] In some alternative embodiments (not shown in FIG. 10), the transmission line 1004 may comprise a third section for coupling to the qubit 1001 (in addition to the coupling provided by the first section 1006). In other words, the transmission line 1004 may be coupled to the qubit 1001 via two separate sections (that is, via the first section 1006 and the third section). The coupling of the third section to qubit 1001 may be capacitive or inductive. The third section may be arranged between the first section 1006 and the termination 1005. The first and third sections may be non-contiguous (i.e., separated by at least one further section of the drive line 1004). To enable this, the transmission line 1004 may comprise, between the first section 1006 and the termination 1005, a 180° turn so as to allow the transmission line 1004 to travel past the qubit 1001 a second time.

[0070] A tunable element 1002 is integrated into the second section 1007. The tunable element 1002 is configured to enable tuning of the filter stopband. The tunable element 1002 (and, thus, also the tunable filter 1010 as a whole) may have a plurality of tuning settings corresponding, respectively, to a plurality of (adjacent) filter stopbands. In some embodiments, at least some of said plurality of filter stopbands may be partially overlapping. The tunable filter 1010 may be configured to have a tunable stopband around a qubit frequency of the qubit 1001. In other words, at least one stopband achieved with respective at least one of a plurality of tuning settings of the tunable filter 1010 may comprise the qubit frequency. This enables tuning of the system 1000 without having to rely on optimizing biasing to reach the sweet spot of the qubit 1001. As mentioned above, the qubit 1001 may, in fact, have fixed qubit frequency here, i.e., it may be non-tunable via biasing. The tunable element 1002 may enable tuning of, for example, an effective length (i.e., an electricallength) of the transmission line 1004. This, in turn, leads to frequency tuning of the filter response. The tunable filter 1010 may, thus, enable full decoupling of the qubit 1001 from the drive line 1004 at the qubit frequency, while permitting strong signal interactions at subharmonic frequencies (i.e., at at least some frequencies smaller than the qubit frequency such as at one third of the qubit frequency and surrounding frequencies). This unique capability enables efficient control of the qubit state (e.g., enabling fast resetting of the qubit 1001 by tuning the filter stop band outside the qubit resonance), while allowing significantly longer decay times. Thus, use of the tunable filter 1010 according to embodiments may lead to higher gate and initialization fidelity in quantum devices (e.g., QPUs).

[0071] Said tunable element 1002 may comprise, for example, at least one superconducting quantum interference device (SQUID). Said at least one SQUID may be connected, e.g., in series with each other. Each SQUID may act here effectively as a tunable inductor. These embodiments are described in further detail in connection with FIG. 12. Any of the features and definitions provided in connection with FIG. 12 may apply also here.

[0072] In some other embodiments, said tunable element 1102 may comprise, for example, at least one Josephson field effect transistor (JoFET). Each JoFET may also be configured to act, in this embodiment, as a tunable inductor.

[0073] In some embodiments, the system 1000 (being, e.g., a quantum integrated circuit) may be operated at a cryogenic temperature Ti. Said cryogenic temperature may be, for example, smaller than or equal to 60 mK but preferably smaller than or equal to 30 mK. Said cryogenic temperature may be achieved, for example, using a cryostat comprising a dilution refrigerator.

[0074] In some embodiments, the length of the transmission line 1004 from the first section 1006 (e.g., from the part farthest from the termination 1005 or from a center of the first section 1006) to the termination 1005 may be Aq / 4, where Aqis a wavelength of a mode in the drive line 1004 at a qubit frequency. In other words, the tunable filter 1010 may correspond to a tunable quarter-wave filter (i.e., a quarter-wave filter where the stopband of the quarter- wave filter may be finetuned via the tunable element 1002). This may apply especially when the termination 1005 corresponds to an open circuit (or to a sufficiently high finite impedance), assuming that the drive line 1004 is coupled to the qubit 1001 only via the first section 1006 as depicted in FIG. 10. In such a case when the tunable element is shorted, the open-end creates a boundary condition for the voltage along the transmissionline, resulting in a voltage anti-node at the open-end and a node at the qubit location when operating at the resonance frequency of the qubit (i.e., at the qubit frequency). Consequently, this configuration enforces net-zero voltage amplitude for the qubit 1001, effectively decoupling the qubit 1001 from the drive line 1004 at the qubit frequency. However, at the subharmonic frequency, the voltage profile at the qubit 1001 is close to its maximum, thereby establishing a strong coupling between the qubit 1001 and the drive line 1004.

[0075] In other embodiments, the length of the transmission line 1004 from the first section 1006 e.g., from the part farthest from the termination 1005 or from a center of the first section 1006) to the termination 1005 may be Aq / 2, where Aqis a wavelength of a mode in the drive line 1004 at a qubit frequency. In other words, the tunable filter 1010 may correspond to a tunable half-wave filter (i.e., a half-wave filter where the stopband of the half- wave filter may be finetuned via the tunable element 1002). This may apply especially when the termination 1005 corresponds to a short circuit (or to a sufficiently low finite impedance), assuming that the drive line 1004 is coupled to the qubit 1001 only via the first section 1006 as depicted in FIG. 10 (not also via the aforementioned third section). Similar benefits are achieved in this case as described in previous paragraph for the quarter-wave filter terminated with an open circuit.

[0076] In some embodiments (namely, ones where the drive line 1004 does not comprise said third section for coupling to the qubit 1001), the length of the transmission line 1004 from the first section 1006 (e.g., from the part of the first section 1006 farthest from the termination 1005 or from a center of the first section 1006) to the termination 1005 (i.e., to the second end) may be an integer multiple of Aq / 4 (i.e., one of Aq / 4 , Aq / 2, 3Aq / 4, Aq, 5Aq / 4, ...). The length of the transmission line 1004 may be selected so as to have a voltage zero at the qubit locations (i.e., at the first section 1006). Thus, if said integer multiple of Aq / 4 is odd, the termination 1005 may be an open circuit (or a large finite impedance). If the integer multiple of Aq / 4 is even, the termination 1005 may be a short circuit (or a small finite impedance).

[0077] In some embodiments where the drive line 1004 comprises said third section for coupling to the qubit 1001, the length of the transmission line 1004 from the first section 1006 (e.g., from the part of the first section 1006 farthest from the termination 1005 or from a center of the first section 1006) to the termination 1005 (i.e., to the second end) or to the third section (e.g., to the part of the third section closest to the termination 1005 or to a centerof the third section) may be an integer multiple of Aq / 2 (i.e., one of Aq / 2,q, 3q / 2, ...). In some embodiments, the integer multiple may be odd (i.e., one ofAq / 2, 3Aq / 2, 5Aq / 2 ...). This corresponds (substantially) to a case where equal but opposite voltages exist at the qubit locations (i.e., at the first and third sections 1006).

[0078] FIG. 11 illustrates an alternative system 1100 (being, e.g., a quantum integrated circuit) according to embodiments. The system 1100 may form a part of a QPU or other quantum device. Similar to FIG. 10, the system 1100 comprises a drive line 1104 (i.e., a transmission line for feeding the control or drive signal), a qubit 1101 coupled to the drive line 1104 (capacitively or inductively) and a tunable (on-chip) filter 1110 integrated directly into the drive line 1104. Thus, the drive line 1104 (or at least a part thereof) may be considered a part of the tunable filter 1110. The tunable filter 1110 may be a bandstop filter. The qubit 1101 may be defined as described in connection with the qubit 1001 of FIG. 10. The qubit 1101 may be a fixed- frequency qubit (that is, the tuning of the system 1100 is performed only via the tunable filter 1110).

[0079] In contrast to the system of FIG. 10, in the system 1100 of FIG. 11, a tunable element 1102 is used for terminating the drive line 1104 (i.e., not integrated into a middle section of the drive line 1104). In other words, the tunable filter 1110 comprises a transmission line 1104 (i.e., the drive line of a part thereof) comprising a first end for receiving a control signal of the drive line, a first section 1106 for coupling to the qubit 1101 and a second end onto which a tunable element 1102 is integrated or connected. The first section 1106 may be either capacitively or inductively coupled to the qubit 1101. The transmission line 1104 may be, for example, a coplanar waveguide. Alternatively, the transmission line 1104 may be a strip line, a coaxial cable or a triaxial waveguide. The transmission line 1104 may be made of a superconducting material such as niobium, tantalum or aluminum.

[0080] Said tunable element 1102 may be connected between the second end of the transmission line 1104 and the ground. The tunable element 1102 is configured to enable tuning of the filter stopband. The tunable element 1102 (and, thus, also the tunable filter 1110 as a whole) may have a plurality of tuning settings corresponding, respectively, to a plurality of (adjacent) filter stopbands. In some embodiments, at least some of said plurality of filter stopbands may be partially overlapping. The tunable filter 1110 may be configured to have a tunable stopband around a qubit frequency. In other words, at least one stopbandachieved with respective at least one of the plurality of tuning settings of the tunable filter 1110 may comprise the qubit frequency. This enables tuning of the system 1100 without having to rely on optimizing biasing to reach the sweet spot of the qubit 1101. As mentioned above, the qubit 1101 may, in fact, have fixed qubit frequency here, i.e., it may be non- tunable via biasing). The tunable element 1102 may enable tuning of, for example, an effective length (i.e., an electrical length) of the transmission line 1104. This, in turn, leads to frequency tuning of the filter response (e.g., tuning of the filter stopband). Said tuning may enable full decoupling of the qubit 1101 from the drive line 1104 at the resonance frequency of the qubit 1101 (i.e., at the qubit frequency), while permitting strong signal interactions at subharmonic frequencies such as one third of the qubit frequency. This unique capability enables efficient control of the qubit state, while allowing significantly longer decay times.

[0081] In some embodiments, said tunable element 1102 may comprise, for example, at least one Josephson field effect transistor (JoFET). An effective length (i.e., an electrical length) of the transmission line 1104 may be controllable via at least one voltage applied to the at least one JoFET 1102. In some embodiments, each JoFET may correspond here to one bit of information that controls the effective length of the transmission line 1104. For example, 10 JoFETs would give 1024 different length possibilities to choose from. The at least one JoFET may act here effectively as a switch.

[0082] In some embodiments, the tunable element 1102 may comprise n capacitors and n JoFETs connecting, respectively, the n capacitors to the ground, where n is an integer larger than or equal to one. In other words, the n capacitors are connected in series, respectively, with the n JoFETs (i.e., each capacitor is connected in series with a single JoFET). A total effective capacitance associated with the one or more capacitors (i.e., total effective capacitance of the tunable element 1102) is controllable via one or more voltages applied to one or more gates of the one or more JoFETs. This may be interpreted as effectively tuning the electrical length of the transmission line 1104. The n capacitors may have capacitance values Ck= C0 / 2kwith k = 1, 2, ... , n. Thus, the total capacitance of the n capacitors may be Ctot= X / < Ckbk= Cob / 2n. Here, Cois a chosen constant capacitance and b is an integer with the binary representation b = (1b2... bn). The values of bkare determined by whether the JoFET connecting the capacitance Ckto ground is conducting (bk= 1) of not conducting (bk= 0).

[0083] In some alternative embodiments (not shown in FIG. 11), the transmission line 1104 may comprise a third section for coupling to the qubit 1101 (in addition to the coupling provided by the first section 1106). In other words, the transmission line 1104 may be coupled to the qubit 1101 via two separate sections (that is, via the first section 1106 and the third section). The coupling of the third section to qubit 1101 may be capacitive or inductive. The third section may be arranged between the first second 1106 and the tunable element 1102. The first and third sections may be non-contiguous (i.e., separated by at least one further section of the drive line 1104). To enable this, the transmission line 1104 may comprise, between the first section 1106 and the tunable element 1102, a 180° turn so as to allow the transmission line 1104 to travel past the qubit 1101 a second time.

[0084] In some embodiments, the length of the transmission line 1104 from the first section 1106 (e.g., from the part of the first section 1106 farthest from the tunable element 1102 or from a center of the first section 1106) to the tunable element 1102 may be substantially Aq / 4, where Aqis a wavelength of a mode in the drive line 1104 at a qubit frequency. In other words, the tunable filter 1110 may correspond to a tunable quarter- wave filter (i.e., a quarter- wave filter where the stopband of the quarter- wave filter may be finetuned via the tunable element 1102). In other embodiments, the length of the transmission line 1104 from the first section 1106 (e.g., from the part farthest from the tunable element 1102 or from a center of the first section 1106) to the tunable element 1102 may be substantially equal to Aq / 2, where Aqis a wavelength of a mode in the drive line 1104 at a qubit frequency. In other words, the tunable filter 1110 may correspond to a halfwave filter (i.e., a half-wave filter where the stopband of the half-wave filter may be finetuned via the tunable element 1102).

[0085] In some embodiments (namely, ones without the aforementioned third section of the drive line 1104 for coupling to the qubit 1101), the length of the transmission line 1104 from the first section 1106 (e.g., from the part of the first section 1106 farthest from the tunable element 1102 or from a center of the first section 1106) to the tunable element 1102 may be (substantially) an integer multiple of Aq / 4 (i.e., one of Aq / 4, Aq / 2, 3Aq / 4, Aq, 5Aq / 4 ...).

[0086] In some embodiments (both where the drive line 1104 comprises or does not comprise said third section for coupling to the qubit 1101), the length of the transmission line 1104 from the first section 1106 (e.g., from the part of the first section 1106 farthestfrom the tunable element 1102 or from a center of the first section 1106) to the tunable element 1102 (i.e., to the second end) or to the third section (e.g., to the part of the third section closest to the tunable element 1102 or to a center of the third section) may be (substantially) an integer multiple of Aq / 2 (i.e., one of Aq / 2 , Aq, 3Aq / 2, ...). In some embodiments, the integer multiple may be odd. This corresponds (substantially) to a case where equal but opposite voltages exist at the qubit locations (i.e., at the first and third sections 1106).

[0087] In some embodiments, the system 1100 (being, e.g., a quantum integrated circuit) may be operated at a cryogenic temperature Ti. Said cryogenic temperature may be, for example, smaller than or equal to 60 mK, preferably smaller than or equal to 30 mK. Said cryogenic temperature may be achieved, for example, using a cryostat comprising a dilution refrigerator.

[0088] FIG. 12 illustrates one detailed implementation of the system 1000 of FIG. 10 according to some embodiments. Thus, any of the features and definition provided in connection with FIG. 10 may apply, mutatis mutandis, also here.

[0089] Similar to FIG. 10, the system 1200 comprises a drive line 1204 (here, a coplanar waveguide for feeding the control or drive signal), a qubit 1201 coupled to the drive line 1204 and a tunable (on-chip) filter 1210 integrated directly into the drive line 1204. Specifically, the drive line 1204 comprises a first section 1206 (capacitively) coupled to the qubit 1201 and a second section 1207 into which SQUIDs 1202 (acting as tuning elements) are integrated. The drive line 1204 has a first end 1208 for receiving the control (or drive or driving) signal of the drive line 1204 and a second end 1205 being terminated with an open circuit (though, in other embodiments, some alternative termination such as a short circuit or a finite impedance may be employed). The drive line 1204 may be, for example, a coplanar waveguide. The drive line 1204 may be made of a superconducting material such as niobium, tantalum or aluminum.

[0090] In the example of FIG. 12, the drive line 1204 further comprises a first meander line section 1211 between the first section 1206 and the second section 1207 and a second meander line section 1212 between the second section 1207 and the second end 1205. A meander line section may be defined, in general, as a section (of a transmission line) having a serpentine or zigzag pattern. These meander line sections 1211, 1212 serve to increase the length of the drive line 1204 (e.g., to achieve certain resonant length) in a way whichminimizes the area taken up by the drive line 1204. In some embodiments, none or only one of the meander line sections 1211, 1212 may be implemented. In some embodiments, one or more meander line sections similar to the meander line sections 1211, 1212 may be implemented in the drive line 1104 of FIG. 11 (e.g., between the first section 1106 and the tunable element 1102).

[0091] As mentioned above, in FIG. 12, the tunable element of the tunable filter 1210 is a set of SQUIDs 1202 arranged in series (sometimes called a SQUID array). Specifically, 5 SQUIDs 1202 are employed in the example of FIG. 12 though, in other embodiments, one or more SQUIDs may be employed. Each of the SQUIDs 1202 acts effectively as a tunable inductor. By using multiple SQUIDs 1202 in series, the tunability may be extended compared to using a single SQUID.

[0092] According to general definition, a SQUID is a very sensitive magnetometer used to measure extremely weak magnetic fields using a superconducting loop containing two Josephson junctions arranged in parallel (or a single Josephson junction). This loop design gives the SQUID a unique property: its inductance can be adjusted by applying an external magnetic field. The SQUIDs 1202 may be specifically direct current (DC) SQUID, that is, the SQUIDs 1202 may comprise, each, a superconducting loop containing two parallel Josephson junction and being excitable using a DC or low-frequency signal. The superconducting loops of the SQUIDs 1202 may be made, for example, from niobium.

[0093] Said excitation signal is receivable by the SQUIDs 1202 via a fast flux line 1203 (being, e.g., a coplanar waveguide). Namely, the DC current of the fast flux line 1203 (or specifically the associated static magnetic field) may be used for biasing the SQUIDs 1202. The fast flux line 1203 is used for carrying a current that creates a magnetic field, which then induces a flux in the superconducting loops of the SQUIDs 1202 via mutual inductance. Thus, by changing the amplitude and / or frequency of the current in the fast flux line 1203, the flux induced in the SQUIDs 1202 can be controlled. The change in the induced flux, in turn, directly affects an inductance of the SQUIDs 1202. Thus, tuning of the tunable filter 1210 (or specifically stopband thereof) is enabled (e.g., to better match the qubit frequency of the qubit 1201).

[0094] In FIG. 12, the qubit 1201 is specifically a transmon (i.e., a transmission line shunted plasma oscillation qubit). A transmon is a type of superconducting charge qubit (i.e., a qubit whose basis states are charge states and which is capable of superconduction). Acharge state is state which represents the presence or absence of excess Cooper pairs of electrons on a superconducting island. According to a general definition, a charge qubit (equally called a Cooper-pair box) is formed by a (tiny) superconducting island coupled by a Josephson junction to a superconducting reservoir. Thus, the (charge) state of the charge qubit is determined by the number of Cooper pairs that have tunneled across the Josephson junction. The quantum superposition of charge states can be achieved by tuning the gate voltage that controls the chemical potential of the superconducting island. In a transmon, two superconductors of the Josephson junction of the charge qubit are also (capacitively) shunted in order to decrease the sensitivity to charge noise, while maintaining a sufficient anharmonicity for selective qubit control. Thus, a transmon is essentially a modified Cooperpair box with a Josephson junction shunted by a capacitor (e.g., a parallel-plate capacitor). This shunt capacitor may have, for example, a cross-like shape, as shown in FIG. 12. This type of transmon is sometimes called an x-mon.

[0095] The transmon 1201 is capacitively coupled to readout circuitry 1230 configured to enable reading out a quantum state of the transmon 1201 without disturbing the transmon 1201. Namely, transmon 1201 is capacitively coupled to a horseshoe capacitor 1231 of the readout circuitry 1230 arranged to partially surround the transmon 1201. The readout circuitry 1230 comprises, in addition to said horseshoe capacitor 1231, a readout resonator 1232 acting as a frequency-dependent probe for the quantum state of the transmon 1201 and a readout line 1233 (i.e., a transmission line such as a coplanar waveguide) capacitively coupled to the readout resonator 1232. The readout line 1233 is used for delivering a probe signal to the readout resonator 1232 and collecting the reflected / transmitted signal. The readout circuitry 1230 may be connected, via the readout line 1233, to readout signal processing circuitry (not shown in FIG. 12) for processing the readout signal at room temperature (or other non-cryogenic temperature). When the quantum state of the transmon 1201 shifts, the resonance frequency of the resonator is shifted by a certain value enabling state discrimination.

[0096] It should be noted that the embodiments are not limited to using the specific, somewhat simplistic readout circuitry 1230 as depicted in FIG. 12. Any other conventional qubit (or transmon) readout circuitry may also be used in connection with embodiments.

[0097] FIGs. 13A & 13B illustrate, respectively, a system comprising, on the right, an exemplary implementation 1300 of the quantum circuit assembly 300 of FIG. 3 based onusing a directional coupler as a reactive element of an attenuator circuit and, on the left, a reference quantum circuit assembly based on a purely resistive attenuator circuit and measurement results associated with said two quantum circuit assemblies. Namely, FIG. 13B shows the normalized dephasing time (unitless) as a function of excitation power at 2 GHz in dBm. The dephasing time is normalized to a dephasing time obtained when the power of the thermal noise signal is extremely low (i.e., when the thermal noise photons minimally disturb the quantum state).

[0098] Referring to the right-side of FIG. 13 A, the quantum circuit assembly 1300 has a drive line input D4 connected via a first resistive element 1302 at temperature 700 mK and a second resistive element 1303 at temperature 100 mK to an input port of a directional coupler 1311. The directional coupler is operating at temperature 10 mK. The coupled port of the directional coupler 1311 is connected to a qubit 1301, the isolated port of the directional coupler is connected to matched load (i.e., 50 load) at 10 mK temperature and the transmitted port of the directional coupler 1311 is connected via a third resistive element 1305 at temperature 100 mK and a fourth resistive element 1304 at temperature 700 mK to an output E4. The output E4 is terminated with a 50 matched load at room temperature. The first, second, third and fourth resistive elements 1302-1305 cause, respectively, attenuation of 10 dB, 20 dB, 10 dB and 20 dB.

[0099] Referring to the left-side of FIG. 13 A, the reference quantum circuit assembly 1320 has a drive line input DI connected via a first resistive element 1321 at temperature 700 mK, a second resistive element 1322 at temperature 100 mK and a third resistive element 1323 at temperature 10 mK to a qubit 1301. The first, second and third resistive elements 1321-1323 cause, respectively, attenuation of 10 dB, 20 dB and 20 dB.

[0100] To evaluate the impact of heating noise, an additional 2 GHz tone (sufficiently detuned from the qubit frequencies to avoid direct disturbances) to both drive line inputs DI and D4. In the D4 configuration, excess power dissipates in higher temperature stages, as indicated by the E4 line. FIG. 13B shows the measured dephasing time of four qubits on the same chip, with the applied excitation power (at room temperature) on the horizontal axis. The data reveals that, for the conventional line (dotted lines: Q1 D1, Q2 D1, Q3 D1, Q4 D1), the dephasing time decreases by an average of 30 % as the power increases to 10 dBm. In contrast, the implementation according to an embodiment (solid lines: Q1 D4, Q2 D4, Q3 D4, Q4 D4) maintains constant dephasing time up to 10 dBm.

[0101] Reference throughout this specification to one embodiment or an embodiment means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present solution. Thus, appearances of the phrases “in one embodiment” or “in an embodiment” in various places throughout this specification are not necessarily all referring to the same embodiment.

[0102] As used herein, a plurality of items, structural elements, compositional elements, and / or materials may be presented in a common list for convenience. However, these lists should be construed as though each member of the list is individually identified as a separate and unique member. Thus, no individual member of such list should be construed as a de facto equivalent of any other member of the same list solely based on their presentation in a common group without indications to the contrary. In addition, various embodiments and example of the present solution may be referred to herein along with alternatives for the various components thereof. It is understood that such embodiments, examples, and alternatives are not to be construed as de facto equivalents of one another, but are to be considered as separate and autonomous representations of the present solution.

[0103] Even though embodiments have been described above with reference to examples according to the accompanying drawings, it is clear that the embodiments are not restricted thereto but can be modified in several ways within the scope of the appended claims. Therefore, all words and expressions should be interpreted broadly and they are intended to illustrate, not to restrict, the embodiment. It will be obvious to a person skilled in the art that, as technology advances, the inventive concept can be implemented in various ways. Further, it is clear to a person skilled in the art that the described embodiments may, but are not required to, be combined with other embodiments in various ways.INDUSTRIAL APPLICABILITY

[0104] At least some embodiments find industrial application in quantum devices and, more specifically, solutions for driving quantum devices.

Claims

CLAIMS1. A quantum circuit assembly, comprising: a quantum device configured to be controllable via a control signal received via a control signal input of the quantum device; and an attenuator circuit having an input for receiving the control signal and an output connected to the control signal input of the quantum device, wherein the attenuator circuit comprises a reactive element for reflecting or guiding a part of the control signal away from the quantum device at a frequency band of the control signal, wherein the reactive element is a reactive circuit component or a reactive circuit.

2. The quantum circuit assembly of claim 1, wherein the attenuator circuit is configured to reflect or guide at least 10%, optionally at least 50% or at least 90%, of the control signal away from the quantum device.

3. The quantum circuit assembly of claim 1 or 2, wherein the attenuator circuit comprises: the reactive element being the reactive circuit component; and a first bandpass filter configured to filter out noise photons outside of the frequency band of the control signal, or wherein the attenuator circuit comprises the reactive element being the reactive circuit being further configured to filter out noise photons outside of the frequency band of the control signal, attenuation caused by the reactive circuit outside of the frequency band of the control signal being larger compared to attenuation caused by the reactive circuit within the frequency band of the control signal.

4. The quantum circuit assembly according to any of claims 1 to 3, further comprising: a transmission line connecting the output of the attenuator circuit to the control signal input of the quantum device.

5. The quantum circuit assembly of claim 4, wherein a length of the transmission line is smaller than or equal to 3ATL / 4, ATLbeing a central wavelength of the frequency band of the control signal within the transmission line.

6. The quantum circuit assembly according to any preceding claim, wherein the attenuator circuit further comprises: a resistive element arranged between the reactive element and the output of the attenuator circuit, wherein a first terminal of the resistive element is connected to the reactive element and a second terminal of the resistive element is connected to the ground.

7. The quantum circuit assembly of claim 4 or 5, wherein the attenuator circuit further comprises: a resistive element arranged between the reactive element and the output of the attenuator circuit, wherein a first terminal of the resistive element is connected to the reactive element and a second terminal of the resistive element is connected to the ground, the resistive element being impedance-matched to the transmission line at the frequency band of the control signal.

8. The quantum circuit assembly of claim 6 or 7, wherein the reactive element is a first reactive element, and the attenuator circuit further comprises: a second reactive element arranged between the first terminal of the resistive element and the output of the attenuator circuit, wherein the second reactive element is a second reactive circuit component or a second reactive circuit.

9. The quantum circuit assembly of any of claims 1 to 5, wherein the the attenuator circuit further comprises: one or more three-port circulators arranged in series between the first reactive element and the output of the attenuator circuit via first and second ports of the one or more three-port circulators, each of the one or more three-port circulators being configured such that a signal entering the first port will exit through the second port, a signal entering the second port will exit through a third port, and a signal entering a third port will exit through the first port; and one or more grounded resistive elements connected, respectively, to the one or more third ports of the one or more three-port circulators.

10. The quantum circuit assembly of any of claims 1 to 5, wherein the reactive circuit component is a first reactive element, and the attenuator circuit further comprises: a second reactive element arranged between the first reactive element and the output of the attenuator circuit, wherein the second reactive element is a second reactive circuit component or a second reactive circuit; one or more three-port circulators arranged in series between the first and second reactive elements via first and second ports of the one or more three-port circulators, each of the one or more three-port circulators being configured such that a signal entering the first port will exit through the second port, a signal entering the second port will exit through a third port, and a signal entering a third port will exit through the first port; and one or more grounded resistive elements connected, respectively, to the one or more third ports of the one or more three-port circulators.

11. The quantum circuit assembly of claim 9 or 10, wherein the one or more three- port circulators comprise a plurality of three-port circulators, and the attenuator circuit further comprises: at least one bandpass filter arranged between the plurality of three-port circulators.

12. The quantum circuit assembly of claim 4 or 5, wherein the attenuator circuit further comprises: a quantum-circuit refrigerator arranged between the reactive element and the output of the attenuator circuit, wherein the quantum-circuit refrigerator is impedance-matched to the transmission line at the frequency band of the control signal.

13. The quantum circuit assembly according to any preceding claim, wherein the reactive element comprises a directional coupler, the input and the output of the reactive element corresponding, respectively, to an input port and a coupled port of the directional coupler, and an isolated port and a transmitting port of the directional coupler being both terminated with matched loads.

14. The quantum circuit assembly according to any preceding claim, wherein the quantum device is a circuit-quantum-electrodynamical device, quantum-dot device, qubitcircuit, quantum sensor circuit, quantum simulator circuit, quantum communication device, or a quantum processing unit, QPU.

15. A system comprising: a plurality of quantum circuit assemblies according to any preceding claim comprising a plurality of attenuator circuits and either a respective plurality of quantum devices connected to the plurality of attenuator circuits or one or more quantum devices comprising a respective plurality of ports connected to the plurality of attenuator circuits; and a plurality of matching circuits connecting adjacent quantum circuit assemblies to each other so as to enable use of the same control signal for driving the plurality of quantum devices or the one or more quantum devices.

16. A system comprising: the quantum circuit assembly according to any preceding claim, wherein the quantum circuit assembly further comprises a secondary attenuator circuit connected to an input of the attenuator circuit, the secondary attenuator circuit comprising:- a secondary reactive element, wherein the secondary reactive element is a secondary reactive circuit component or a secondary reactive circuit, and- a secondary grounded resistive element connected to the secondary reactive element; and means for cooling the quantum device and the attenuator circuit to a first cryogenic temperature and the secondary attenuator circuit to a second cryogenic temperature higher than the first cryogenic temperature.

17. The system of claim 16, wherein the first cryogenic temperature is smaller than or equal to 30 mK.

18. The system of claim 16 or 17, wherein the secondary attenuator circuit comprises: the secondary reactive element being the secondary reactive circuit component; and a second bandpass filter configured to filter out noise photons outside of the frequency band of the control signal at the second temperature, or.wherein the secondary attenuator circuit comprises the secondary reactive element being the secondary reactive circuit, the secondary reactive circuit being further configured to filter out noise photons outside of the frequency band of the control signal, attenuation caused by the secondary reactive circuit outside of the frequency band of the control signal being larger compared to attenuation caused by the secondary reactive circuit within the frequency band of the control signal.

19. A tunable on-chip filter for a drive line of a qubit, the tunable on-chip filter comprising: a transmission line comprising a first end for receiving a control signal of the drive line, a second end being terminated with an open circuit, a short circuit or a termination impedance, a first section for coupling to the qubit and a second section arranged between the first section and the second end; and one or more superconductive quantum interference devices, SQUIDs, integrated into the second section of the transmission line, wherein the one or more SQUIDs, acting as one or more tunable inductors, are configured to be coupled inductively to a fast-flux line for adjusting tuning of the one or more SQUIDs; or one or more Josephson field-effect transistors, JoFETs, integrated into the second section of the transmission line, wherein the one or more JoFETs are configured to operate as one or more tunable inductors.

20. The tunable on-chip filter of claim 19, wherein the transmission line comprises: a first meander line section between the first section and the second section; and / or a second meander line section between the second section and the second end.

21. The tunable on-chip filter of claim 19 or 20, wherein the one or more SQUIDs comprise a plurality of SQUIDs arranged in series.

22. A tunable on-chip filter for a drive line of a qubit, the tunable on-chip filter comprising: a transmission line comprising a first end for receiving a control signal of the drive line, a first section for coupling to the qubit and a second end; and one or more Josephson field-effect transistors, JoFETs, connected between the second end of the transmission line and the ground, wherein an effective length of thetransmission line is controllable via one or more voltages applied to one or more gates of the one or more JoFETs.

23. The tunable on-chip filter of claim 22, further comprising: one or more capacitors connected in series, respectively, with the one or more JoFETs.

24. The tunable on-chip filter according to any of claims 19 to 23, wherein the first section is configured to enable inductive and / or capacitive coupling to the qubit.

25. The tunable on-chip filter according to any of claims 19 to 24, wherein the transmission line is a coplanar waveguide, a strip line, a coaxial cable, or a triaxial waveguide.

26. The tunable on-chip filter according to any of claims 19 to 25, wherein the transmission line further comprises a third section for coupling to the qubit, the third section being arranged between the first section and the second end.

27. The tunable on-chip filter of claim 26, wherein a length of the transmission line from the first section to the third section is substantially equal to an odd integer multiple of Aq / 2, with Aqbeing a wavelength of a mode in the drive line at a qubit frequency.

28. The tunable on-chip filter according to any of claims 19 to 25, wherein a length of the transmission line from the first section to the second end is substantially equal to an integer multiple of Aq / 4, with Aqbeing a wavelength of a mode in the drive line at a qubit frequency.

29. A quantum integrated circuit comprising: the tunable on-chip filter according to any of claims 19 to 25; and the qubit coupled to the first section of the tunable on-chip filter.

30. The quantum integrated circuit of claim 29, wherein the qubit is a transmon, a fluxonium, a phase qubit, a unimon qubit, a majorana qubit, or a quantum-dot qubit.

31. The quantum integrated circuit of claim 29 or 30, further comprising: readout circuitry coupled to the qubit.

32. The quantum integrated circuit according to any of claims 29 to 31 , wherein the tunable on-chip filter is configured to have a tunable stopband around a qubit frequency of the qubit.

Images