Transmission lines in superconducting circuits

Abstract

The present disclosure describes a device comprising a superconducting circuit and a circuit connector for coupling the superconducting circuit to an external circuit. The superconducting circuit comprises a circuit resonator and a transmission line coupled between the circuit connector and the circuit resonator. The length of the transmission line is such that substantially zero current passes between the circuit connector and the transmission line when a drive signal is applied to the circuit resonator via the transmission line.

Description

Technical Field

[0001] The present disclosure relates to superconducting circuits, and particularly to a superconducting circuit including a resonant circuit element. The present disclosure further relates to a transmission line connecting a resonant circuit element to an external circuit.

Background Art

[0002] Elements exhibiting electrical resonance are commonly used in superconducting circuits, for example, to implement qubits in quantum computers. Such a circuit resonator may be, for example, a conventional quarter-wavelength or half-wavelength transmission line resonator, or may consist of capacitive and inductive components coupled to a Josephson junction.

[0003] A circuit resonator generally has a known target frequency that can be determined when the circuit is designed. When a superconducting circuit including a circuit resonator is operated, a drive signal generated in an external circuit can be transmitted to the resonator via a transmission line in the superconducting circuit. If the drive signal frequency matches the known resonance frequency of the circuit resonator, the signal sets the resonator to an operating state.

[0004] Circuit resonators belonging to the same superconducting circuit should preferably operate independently of each other in most applications. Therefore, in many cases it is necessary to assign a separate transmission line to each circuit resonator. Then, its operation is ideally unaffected by drive signals transmitted to other resonators in the same superconducting circuit.

[0005] Superconducting circuits with dedicated transmission lines for individual qubits are known from the prior art. A common problem with such circuits is that the strong electric field that the drive signal generates in each line causes large crosstalk between the transmission lines.

Summary of the Invention

[0006] The object of this disclosure is to provide a device for mitigating the crosstalk problem in superconducting circuits in a simple manner. The object of this disclosure is achieved by a configuration characterized by the description of the independent claim. Preferred embodiments of this disclosure are disclosed in the dependent claims.

[0007] This disclosure is based on the idea of ​​selecting the length of the transmission line in such a way that the electric field surrounding the transmission line decreases rapidly with distance from the transmission line. The advantage of the configuration of this disclosure is that the drive signal can be effectively supplied to the desired resonator without affecting other resonators in the same superconducting circuit. [Brief explanation of the drawing]

[0008] In the following, this disclosure will be described in more detail by preferred embodiments with reference to the accompanying drawings.

[0009] [Figure 1a] Examples of devices equipped with superconducting circuits are given. [Figure 1b] An example of a cross-section of a coplanar waveguide is shown. [Figure 1c] An example of a capacitively coupled open transmission line is given. [Figure 1d] An example of an inductively coupled short-circuit transmission line is given. [Figure 2] Examples include circuit boards, retaining structures, and superconducting circuits. [Modes for carrying out the invention]

[0010] This disclosure describes a device comprising a superconducting circuit and a circuit connector that couples the superconducting circuit to an external circuit. The superconducting circuit comprises a circuit resonator having a target resonant frequency. The superconducting circuit also comprises a transmission line having a first end and a second end. The first end of the transmission line is coupled to the circuit resonator, and the second end of the transmission line is coupled to the circuit connector. In other words, the superconducting circuit comprises a circuit resonator, a circuit connector, and a transmission line coupled between the circuit resonator and the circuit connector.

[0011] Figure 1a schematically illustrates a device with a superconducting circuit. The device is illustrated in the xy-plane, which may be called the device plane or horizontal plane. The z-direction, which may also be called the vertical direction, is perpendicular to the xy-plane. The terms “horizontal” and “vertical” as used herein simply refer to a plane and a direction perpendicular to that plane. They do not suggest anything about how the device should be oriented in use or during manufacturing.

[0012] The device in Figure 1a comprises a first circuit resonator 121 and a second circuit resonator 122. The circuit resonators described herein may be, for example, qubits. Alternatively, they may be any other type of high-frequency circuit resonator that can be implemented in a superconducting circuit.

[0013] The superconducting circuit is constructed on a circuit board 112, which may be, for example, a silicon substrate. The circuit board 112 may be attached to a retaining structure 111, which provides structural support and includes electrical connections to external circuits. The configuration illustrated in Figure 1a is only one possibility. Many other configurations and shapes are also possible for connecting external circuits to the superconducting circuit. A gap 113 may separate the circuit board 112 from the retaining structure 111.

[0014] The circuit board 112 may be coated with a superconducting layer (not otherwise illustrated in Figure 1a). The superconducting circuit is formed within the superconducting layer. The superconducting layer may be, for example, a layer of Nb, Al, TiN, NbN, NbTiN, or Ta. The device includes circuit connectors 141-142 that couple the superconducting circuit to an external circuit 17. These circuit connectors may be located on a retaining structure 111 that is at least partially adjacent to the circuit board 112, for example, as illustrated in Figure 1a. Alternatively, they may be located on several other device parts adjacent to the circuit board 112.

[0015] The superconducting circuit in Figure 1a comprises a first transmission line 18 having a first end 181 and a second end 182. The first end 181 of the first transmission line 18 is capacitively coupled to a first circuit resonator 121, and the second end 182 of the first transmission line is coupled to a first circuit connector 141 using an electrical connector. Here, capacitive coupling means that although there is no direct electrical contact because the transmission line is electrically isolated from the resonator by a separator, the first end of the transmission line is close enough to the resonator to electrically interact with it through the separator.

[0016] The electrical connectors presented in this disclosure may include, for example, wire bonds 15, or any other electrical connections that directly connect a second end of a transmission line to a circuit connector. The superconducting circuit may also include, for example, electrode regions 13 to which each transmission line terminates, where the electrode regions 13 and wire bonds 15 together may form an electrical connector that directly connects the transmission lines to a circuit connector. The device may also include additional wires 151 which can be used to set a portion of the superconducting layer on the surface of the circuit board to ground potential by connecting it to a ground region on a retaining structure 111.

[0017] The superconducting circuit in Figure 1a also includes a second transmission line 19 having a first end 191 and a second end 192. The first end 191 of the second transmission line 19 is inductively coupled to a second circuit resonator 122, and the second end 192 of the second transmission line 19 is coupled to a second circuit connector 142 using an electrical connector.

[0018] Figure 1b illustrates an xz cross-section of a coplanar waveguide that can be used as a transmission line. The superconducting layer 10 covers the circuit board 112. The transmission line 18 may be a coplanar waveguide created in the superconducting layer by etching a first waveguide trench 101 and a second waveguide trench 102 into the superconducting layer. Thereafter, the waveguide trenches 101 and 102 form a central conductor 109 in the transmission line. The transmission line may have a characteristic central conductor width W in the horizontal direction, determined by the distance between the waveguide trenches 101 and 102. The gap width S also affects the characteristics of the transmission line. The central conductor width W may be, for example, in the range of 0.1 to 500 μm or 2 to 50 μm. The gap width S may be, for example, in the range of 0.1 to 500 μm or 2 to 50 μm. W and S do not necessarily have to be constant over the entire length of the transmission line. In exemplary embodiments, both W and S may be in the range of 2 to 50 μm at the narrowest part of the transmission line. The height H of the superconducting layer 10 determines the depth of the waveguide trenches 101 and 102. The most important variable in this disclosure is the length of the transmission line, i.e., the distance from its first end to its second end, which will be discussed in more detail below.

[0019] In a superconducting circuit, transmission lines can be capacitively or inductively coupled to a circuit resonator. In Figure 1a, the first transmission line 18 is an open transmission line capacitively coupled to the first circuit resonator 121. Figure 1c illustrates this capacitive coupling in more detail. Figure 1c shows the first end 181 of the first transmission line 18 adjacent to the first circuit resonator 121 (only partially illustrated). An open transmission line is created by joining the first waveguide trench 101 to the second waveguide trench 102. As a result, the central conductor 109 between the first waveguide trench 101 and the second waveguide trench 102 is isolated from the rest of the superconducting layer by these trenches. When a drive signal is delivered to the transmission line, the AC current at the first end 181 of the first transmission line 18 becomes zero. Nevertheless, the high-frequency electromagnetic waves in the first transmission line 18 generate an oscillating current in the first circuit resonator 121 via capacitive interaction. This allows the first circuit resonator 121 to be driven to a resonant state by the drive signal oscillating in the transmission line 18. An open transmission line may also be called an open-ended transmission line.

[0020] In FIG. 1a, the second transmission line 19 is a short-circuited transmission line inductively coupled to the second circuit resonator 122. FIG. 1d illustrates the inductive coupling in more detail. The second transmission line 19 is formed by a third waveguide trench 103 and a fourth waveguide trench 104. The third and fourth waveguide trenches terminate before they reach the second circuit resonator 122, which is only partially illustrated. A center conductor 109 between the third waveguide trench 103 and the fourth waveguide trench 104 is directly connected to a surrounding region of the superconducting layer, which is set to ground potential. When a drive signal is supplied to the transmission line, this short-circuit connection causes the AC current at the first end 191 of the transmission line to reach a maximum value. The current flowing through the first end 191 of the second transmission line 19 induces an alternating current in the second circuit resonator 122. As a result, the second circuit resonator 122 can be driven into a resonant state by the drive signal oscillating on the short-circuited transmission line 19. The short-circuited transmission line may also be referred to as a short-ended transmission line.

[0021] The electric field generated from the transmission line depends on the characteristics of the transmission line and the characteristics of the electrical connectors and circuit connectors through which the drive signal enters the transmission line. Electrical connectors typically need to be implemented with elements having a significantly higher characteristic impedance than that of the transmission line itself. A wire bond is an example of such an element. The higher the AC current driven back and forth through the electrical connector when the drive signal enters the transmission line, the stronger the electric field radiated around the transmission line. As a result, when the current flowing through the electrical connector is minimized, the electric field decreases rapidly with increasing distance from the transmission line. Consequently, when the current is minimized, crosstalk between adjacent transmission lines is also minimized.

[0022] When a high-frequency driving signal is applied to the transmission line, the signal forms a substantially stationary wave on the transmission line, and when a zero-current node of the standing wave coincides with the second end of the transmission line to which the electrical connector is connected, the current flowing through the electrical connector is minimized. From the above analysis of open transmission lines and short-circuited transmission lines, two different solutions can be developed.

[0023] The present disclosure describes a device comprising a superconducting circuit and a circuit connector coupling the superconducting circuit to an external circuit. The superconducting circuit comprises a circuit resonator. The superconducting circuit also comprises a transmission line having a first end and a second end. The first end of the transmission line is coupled to the circuit resonator, and the second end of the transmission line is coupled to the circuit connector. The length of the transmission line is such that when a driving signal is applied to the circuit resonator via the transmission line, the current passing between the circuit connector and the transmission line is substantially zero.

[0024] Embodiment of open transmission line In a first exemplary embodiment, the device comprises a superconducting circuit and a circuit connector coupling the superconducting circuit to an external circuit. The superconducting circuit comprises a circuit resonator having a target resonant frequency. The superconducting circuit also comprises a transmission line having a first end and a second end. The first end of the transmission line is coupled to the circuit resonator, and the second end of the transmission line is coupled to the circuit connector. The transmission line has a characteristic effective speed of light. The transmission line is an open transmission line, the first end of the transmission line is capacitively coupled to the circuit resonator, and the length of the transmission line is (N * L) / 2, where N is a positive integer and L is equal to the effective speed of light divided by the target resonant frequency.

[0025] The effective speed of light depends on the material and geometry of the transmission line. The effective speed of light for a given transmission line can be easily calculated and, to some extent, can also be adjusted by changing the geometry.

[0026] The AC current at the first end 181 of the first transmission line 18 in the open circuit discussed above is zero because the transmission line terminates at this point. The standing wave of this first transmission line indicates the next zero-current point at a distance D1 = L / 2 from the first end 181. If the wavelength is sufficiently long, consecutive zero-current points will occur at distances D2 = L, D3 = 3L / 2, or more generally (N * It arises from L) / 2, where N is a positive integer. N can be, for example, 1, 2, 3, 4, or any other positive integer.

[0027] In other words, the current at the second end 182 of the transmission line can be minimized by making the length of the transmission line equal to a multiple of L / 2. Since the frequency of the drive signal is equal to the target resonant frequency, the wavelength L is calculated by dividing the effective speed of light by the target resonant frequency.

[0028] The transmission line may be a coplanar waveguide. Regardless of whether the transmission line is a coplanar waveguide or not, the transmission line may have a meandering shape.

[0029] The first transmission line does not need to have a straight shape. Figure 2 illustrates a superconducting circuit in which reference numbers 211, 212, 221, 23, 241, 25, 251, 28, 281, and 282 correspond to reference numbers 111, 112, 121, 13, 141, 15, 151, 18, 181, and 182 in Figure 1a, respectively. The illustrated circuit comprises six circuit resonators, each of which is coupled to an external circuit via a transmission line such as 18. Here, each transmission line is still (N * The transmission line has a meandering shape that allows it to be long enough to achieve a length of L) / 2 while being limited to a relatively small area. The length of the transmission line is measured along the transmission line path, in this case along a meandering shape where the transmission line folds back and forth, from its first end to its second end.

[0030] In Figure 2, a square circuit board 212 is placed within a square cavity in the retaining structure 211. Each circuit connector 241 on the retaining structure 211 is coupled to the corresponding transmission line 28 using wire bonds 15. Additional wires 251, located in areas of the retaining structure where no circuit connectors exist, connect the top surface of the circuit board 212 to an electrically grounded area on the retaining structure 211. This allows the superconducting layer on the circuit board 212 to be grounded. Alternatively, other electrical connections may be used to set the layer of superconducting material to ground potential.

[0031] The device illustrated in Figure 2 may also include a side wall 278 and a top cover (not illustrated). The side wall and top cover may define the extent of the vacuum enclosure. The side wall and top cover may be made of copper, for example. The side wall 278 may include a sealed through-hole 277 into which a circuit connector 241 is coupled to an external circuit. The device architecture illustrated in Figure 2 can also be used in the embodiment of the short-circuit transmission line presented below, differing only in the detailed functionality of the transmission line.

[0032] Embodiment of a short-circuit transmission line In a second exemplary embodiment, the device comprises a superconducting circuit and a circuit connector that couples the superconducting circuit to an external circuit. The superconducting circuit includes a circuit resonator having a target resonant frequency. The superconducting circuit also includes a transmission line having a first end and a second end. The first end of the transmission line is coupled to the circuit resonator, and the second end of the transmission line is coupled to the circuit connector. The transmission line has a specific effective velocity of light. The transmission line is a short-circuit transmission line, and the first end of the transmission line is inductively coupled to the circuit resonator. The length of the transmission line is (N * This is approximately equal to (L) / 2 - (L / 4), where N is a positive integer and L is equal to the effective speed of light divided by the target resonant frequency.

[0033] The analysis provided above in the first exemplary embodiment can be applied to this second exemplary embodiment with some modifications. The AC current at the first end 191 of the short-circuited second transmission line 19 discussed above reaches a maximum value IMAX because the first end is connected to ground potential. The standing wave of this first transmission line indicates the next zero current point at a distance D1 = L / 4 = L / 2 - L / 4 from the first end 191. If the wavelength is sufficiently long, consecutive zero current points may be at distances D2 = L / 4, D3 = 3L / 2 - L / 4, or more generally (N * It arises from L) / 2 - (L / 4), where N is a positive integer. N can be, for example, 1, 2, 3, 4, or any other positive integer.

[0034] In other words, the current at the second end 192 of the transmission line is equal to the length of the transmission line (N * It can be minimized by making it equal to (L) / 2 - (L / 4). Since the frequency of the drive signal is equal to the target resonant frequency, the wavelength L is calculated by dividing the effective speed of light by the target resonant frequency.

[0035] Similar to the first example, the first transmission line does not need to have a straight shape. Here, each transmission line is still (N * The transmission line has a meandering shape, as illustrated in Figure 2, which allows it to be long enough to achieve a length of L) / 2-(L / 4) while being limited to a relatively small area. The transmission line may be a coplanar waveguide, and whether or not the transmission line is a coplanar waveguide, the transmission line may have a meandering shape.

Claims

1. A device comprising a superconducting circuit and a circuit connector configured to connect the superconducting circuit to an external circuit, wherein the superconducting circuit is A circuit resonator having a target resonant frequency, A transmission line having a first end and a second end, wherein the first end is coupled to the circuit resonator and the second end is coupled to the circuit connector, The aforementioned transmission line has the specific effective speed of light, The transmission line is an open transmission line, the first end of the transmission line is capacitively coupled to the circuit resonator, and the length of the transmission line is (N * L) / 2 is approximately equal to the value obtained by dividing the effective speed of light by the target resonant frequency, where N is a positive integer and L is equal to the value obtained by dividing the effective speed of light by the target resonant frequency. A device in which the second end of the transmission line is connected to the circuit connector by wire bonding.

2. The device according to claim 1, wherein the transmission line is a coplanar waveguide.

3. The device according to claim 1 or 2, wherein the transmission line has a meandering shape.

4. A device comprising a superconducting circuit and a circuit connector configured to connect the superconducting circuit to an external circuit, wherein the superconducting circuit is A circuit resonator having a target resonant frequency, A transmission line having a first end and a second end, wherein the first end is coupled to the circuit resonator and the second end is coupled to the circuit connector, The aforementioned transmission line has the specific effective speed of light, The transmission line is a short-circuit transmission line, the first end of the transmission line is inductively coupled to the circuit resonator, and the length of the transmission line is (N * This is approximately equal to (L) / 2 - (L / 4), where N is a positive integer and L is equal to the value obtained by dividing the effective speed of light by the target resonant frequency. A device in which the second end of the transmission line is connected to the circuit connector by wire bonding.

5. The device according to claim 4, wherein the transmission line is a coplanar waveguide.

6. The device according to claim 4 or 5, wherein the transmission line has a meandering shape.

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