Josephson junction resistance tuning

Abstract

The invention is in the field of superconducting integrated circuits, in particular methods for fabricating and tuning superconducting integrated circuit elements such as Josephson junctions. The invention includes thermally annealing at least one layer of a Josephson junction with a heated element in order to modify the resistance of the Josephson junction.

Description

[0001] JOSEPHSON JUNCTION RESISTANCE TUNING

[0002] Technical Field

[0003] The invention is in the field of superconducting integrated circuits, in particular methods for fabricating and tuning superconducting integrated circuit elements such as Josephson junctions.

[0004] Background

[0005] Superconducting qubits contain one or multiple Josephson junctions. A Josephson junction comprises two superconducting regions separated by a non-superconducting barrier, usually an electrical insulator.

[0006] The qubit frequency, i.e. the frequency difference between the ground state and first excited state, of a transmon qubit at cryogenic temperatures can be predicted from the normal state resistance of the Josephson junctions, i.e. their electrical resistance measured at room temperature. Consequently, the resistance of the Josephson junction(s) is carefully controlled in order to produce qubits with a desired qubit frequency.

[0007] Fine-grained control over qubit frequencies is required in order to scale up quantum computers, i.e. to increase the number of qubits in a single quantum processing unit. For example, frequency crowding makes it more difficult to address individual qubits as the number of qubits increases - a lack of precise control over qubit frequencies exacerbates the problem. However, even state of the art Josephson junction fabrication processes cannot produce Josephson junctions with the desired precision in their resistance values.

[0008] Prior art methods of modifying qubit frequencies include annealing Josephson junctions using a thermal source such as a laser to modify the resistance of the Josephson junction, for example as described in US 10,340,438 B2 and C. Granata et al, 2008 J. Phys.: Conf. Ser. 97 012110.

[0009] Summary of the Invention

[0010] A first aspect of the invention is a method for modifying the normal state resistance of a Josephson junction. The method comprises thermally annealing the Josephson junction by bringing a heated element in proximity to the Josephson junction and / or a region of the substrate adjacent to the Josephson junction. This method provides a novel way to locally anneal the Josephson junction to tune their resistances individually. This approach is solely based on a thermal effect as it acts on the junction barrier to expedite the oxide aging. Consequently, it leads to a decrease in Josephson junction resistance. The heated element may comprise a tip with a radius of curvature of less than 5 pm, and the tip of the heated element may be brought in proximity to the Josephson junction and / or a region of the substrate adjacent to the Josephson junction.

[0011] The heated element may be a grounded conductive element.

[0012] The method may further comprise imaging the Josephson junction prior to thermally annealing the Josephson junction.

[0013] The method may comprise heating the heated element to at least 100 degrees Celsius.

[0014] The method may further comprise controlling the temperature of the heated element in order to achieve a predetermined change in the normal state resistance of the Josephson junction. Controlling the temperature enables controlled local heating of the Josephson junction, which results in a thermal effect acting on the junction barrier. Consequently, it leads to a change in the Josephson junction resistance.

[0015] Controlling the temperature of the heated element may comprise monitoring or estimating the temperature of the heated element based on one or more of: a temperature sensor measurement and an electrical current applied to a resistive wire within the heated element.

[0016] The method may further comprise: measuring the normal state resistance of the Josephson junction; and determining the parameters relating to the heated element, in particular its temperature and the duration of time for which the heated element is in proximity to the Josephson junction and / or the region of the substrate adjacent to the Josephson junction, required to produce a predetermined change in the normal state resistance of the Josephson junction.

[0017] Bringing the heated element in proximity to the Josephson junction and / or a region of the substrate adjacent to the Josephson junction may comprise scanning the Josephson junction and / or the region of the substrate adjacent the Josephson junction with the heated element.

[0018] Determining the parameters relating to the heated element may further comprise determining the scanning speed of the heated element required to produce a predetermined change in the normal state resistance of the Josephson junction. When fabrication residue is present on the Josephson junction and / or substrate, the method may further comprise removing said fabrication residue from the Josephson junction and / or the region of the substrate with the heated element.

[0019] Removing fabrication residue may be performed simultaneously with thermally annealing the Josephson junction.

[0020] The Josephson junction may comprise a lower superconducting electrode layer disposed on a substrate, an upper superconducting electrode layer, and a non-superconducting barrier layer disposed between the lower superconducting electrode layer and upper superconducting electrode layer, and thermally annealing the Josephson junction may comprise thermally annealing the non-superconducting barrier layer.

[0021] Bringing the heated element in proximity to the Josephson junction may comprise bringing the heated element in proximity to the upper superconducting barrier layer.

[0022] The heated element may be an atomic force microscope tip.

[0023] The method may further comprise placing at least the Josephson junction in an atomic force microscope and bringing the heated element in proximity to the Josephson junction and / or a region of the substrate adjacent to the Josephson junction may comprise bringing the atomic force microscope tip in proximity to the Josephson junction and / or a region of the substrate adjacent to the Josephson junction.

[0024] The Josephson junction may be part of a superconducting qubit, and modifying the normal state resistance of the Josephson junction may modify the frequency of the qubit.

[0025] A second aspect of the invention is a method of manufacturing a qubit. The method comprises: manufacturing a qubit, wherein manufacturing the qubit includes providing at least one Josephson junction on a substrate, and; modifying the qubit frequency by modifying the normal state resistance of the at least one Josephson junction according to the method of any preceding claim.

[0026] Modifying the qubit frequency may comprise increasing the normal state resistance of the Josephson junction thereby decreasing the qubit frequency.

[0027] A third aspect of the invention is an apparatus for modifying the normal state resistance of a Josephson junction. The apparatus comprises: a stage for retaining a substrate on which the Josephson junction is disposed; a heated element configured to heat the Josephson junction and / or a region of the substrate adjacent to the Josephson junction; and a drive system configured to bring the heated element into contact or proximity with the Josephson junction by either moving the heated element or moving the stage.

[0028] The heated element may be configured to be heated to at least 100 degrees Celsius.

[0029] Brief Description of the Drawings

[0030] Figure 1 is a flow chart depicting a method for modifying the normal state resistance of a Josephson junction.

[0031] Figure 2 depicts a first method of thermally annealing a Josephson junction and / or a region of a substrate with a heated element.

[0032] Figure 3 depicts a second method of thermally annealing a Josephson junction and / or a region of a substrate with a heated element.

[0033] Figure 4 depicts a third method of thermally annealing a Josephson junction and / or a region of a substrate with a heated element.

[0034] Detailed Description

[0035] Figure 1 is a flow chart depicting a method 100 for modifying the normal state resistance of a Josephson junction. In this context, “normal state resistance” means the resistance of the Josephson junction at a non-superconducting temperature.

[0036] In the method of the present invention, the normal state resistance of the Josephson junction is modified by thermally annealing the Josephson junction by bringing a heated element in proximity to the Josephson junction and / or the substrate on which the Josephson junction is located. The effect of the exposure to the heated element on the resistance of the Josephson junction persists after the heated element is removed.

[0037] In this context, a heated element is a physical component, e.g. a probe, tip, or bitl, such as an atomic force microscope tip, which is supplied with thermal energy to raise its temperature. The thermal energy may be supplied by any suitable source, for example Joule heating or the thermoelectric effect. The heated element can thus be at a room temperature during part of the steps of the method and does not need to be constantly at a higher temperature during the method steps. For example, the heated element can then have its temperature being raised at a certain moment of the method, such as when it is located in proximity to Josephson junction or substrate that should be heated.

[0038] At step 101 , the Josephson junction is provided on a substrate. The Josephson junction may be manufactured according to any suitable method, for example the “Manhattan” method described in Potts, A., Routley, P.R., Parker, G.J. et al. Novel fabrication methods for submicrometer Josephson junction qubits. Journal of Materials Science: Materials in Electronics 12, 289-293 (2001 )., or the Dolan method described in G. J. Dolan, Offset masks for lift-off photoprocessing, Appl. Phys. Lett. 31 , 337-339 (1977). The Josephson junction in general has a superconductor-insulator-superconductor structure. Some exemplary commonly used superconductors are aluminium, niobium, tantalum or titanium nitride or any combination thereof. The insulator layer is typically a very thin layer of oxide, e.g., aluminium oxide. The substrate may be silicon, sapphire, ceramic or any other material suitable for use as a substrate for superconducting integrated circuits. The Josephson junction may be formed as a component of a superconducting qubit, for example as a transmon qubit as described in Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A, 76(4), 042319 (2007), or a unimon qubit as described in Hyyppa, E., Kundu, S., Chan, C.F. et al. Unimon qubit. Nat Commun 13, 6895 (2022).

[0039] When the Josephson junction is formed as part of a qubit, the Josephson junction’s normal state resistance accounts for almost the entire normal state resistance of the qubit. The qubit frequency, i.e. the transition frequency corresponding to the transition from the qubit ground state to the first excited state, which are typically used to represent computational basis states, varies based on the normal state resistance of the qubit. Therefore, by modifying the normal state resistance of the Josephson junction, the normal state resistance of the qubit can be modified, allowing fine tuning of the qubit frequency. In particular, modifying the qubit frequency may comprise increasing the normal state resistance of the Josephson junction thereby decreasing the qubit frequency.

[0040] Step 101 of providing the Josephson junction may also include placing the entire quantum processing unit inside an annealer in order to cause global thermal annealing, which artificially expedites the oxide aging process. The purpose of this step is to make the oxide to become more stable so that the qubit resistance shows almost no further change for an extended period even when stored in ambient environment.

[0041] After the Josephson junction has been provided, the normal state resistance of the Josephson junction or the normal state resistance of the qubit that the Josephson junction is part of may be measured at step 102. After measuring the normal state resistance of the Josephson junction or qubit, the desired change in the Josephson junction resistance, qubit resistance of qubit frequency can, at step 103, be used to select, i.e. determine, the parameters of the heated element and the exposure of the Josephson junction and / or substrate to the heated element.

[0042] These parameters may include the distance between the heated element and the Josephson junction and / or the region of the substrate to be heated, the temperature of the heated element, the length of time for which the heated element is in proximity with the Josephson junction and / or the region of the substrate, the size of the heated element, and the way in which the heated element is brought into proximity with the Josephson junction and / or the region of the substrate. This list of parameters should not be seen to be limiting. The determination of some of these parameters, such as the distance between the heated element and the Josephson junction and / or the region of the substrate to be heated may also take into account the imagining performed at step 104 describes below.

[0043] The relationship between the parameters mentioned above and the change in the resistance of the Josephson junction vary based on the materials used to manufacture the Josephson junction, the method of manufacturing the Josephson junction, and the size of the Josephson junction, amongst other factors. The relationship between these parameters and the change in the resistance value for a given set of these factors can be readily determined by experiment, by simply measuring the change in resistance produced by different combinations of parameters.

[0044] As an example, in one experiment performed by the inventors, an estimated tip temperature of 120 degrees Celsius, scanning speed of 1 pm / s, scanning area of 3pm x 3pm and scanning time of 15 mins resulted in a normal state resistance increase of approximately 15%. Resistance increases of up to or more than 100% are possible with the method of the present invention, depending on the junction fabrication and treatment parameters.

[0045] During the annealing operation the temperature of the heated element may be controlled by monitoring or estimating the temperature of the heated element based on one or more of: a temperature sensor measurement and an electrical current applied to a resistive wire within the heated element.

[0046] By performing steps 102 and 103, the method 101 can advantageously be adapted to each Josephson junction on a given QPU chip, taking into account small variations in the manufacturing process in order to precisely fine tune the Josephson junction resistance / qubit frequency. However, these steps may not necessarily be performed every time the method 100 is performed. For example, if Josephson junctions are repeatedly produced using the same method each time, the properties of the Josephson junctions may be similar enough that using the same parameters for each Josephson junction provides a sufficiently accurate change in the Josephson junction resistance.

[0047] At step 104 of the method 100, the Josephson junction may be imaged using an atomic force microscope in order to identify the precise location for bringing the heated element into proximity with the Josephson junction and / or substrate. This identification is carried out in step 105. Other imaging techniques, such as electron microscopy may be used instead of atomic force microscopy, but atomic force microscopy may be particularly advantageous where the heated element used to thermally anneal the Josephson junction is the same atomic force microscope tip used to image the Josephson junction and / or substrate. In this case, the tip may be unheated in the imaging step 104 in order to avoid any incidental thermal annealing of the Josephson junction during the imaging step 104.

[0048] Steps 102, 103, 104 and 104 may be performed in any suitable order, for example, for example steps 104 and 105 may be performed in parallel with steps 102 and 103, before steps 102 and 103, or after steps 102 and 103, and are not necessarily directly following each other. Steps 104 and 105 may not necessarily be performed every time the method 100 is performed.

[0049] At step 106, the Josephson junction is thermally annealed by bringing the heated element in proximity to the Josephson junction and / or a region of the substrate on which the Josephson junction is located. Thermally annealing the Josephson junction may include bringing the heated element in proximity to part of the Josephson junction, the whole of the Josephson junction, part of the substrate, part of the Josephson junction and part of the substrate, or the whole of the Josephson junction and part of the substrate. Where the heated element is brought into proximity with part of the substrate, the part of the substrate is preferably adjacent to the Josephson junction, such that thermal energy deposited in the substrate by the heated elements is transferred to the Josephson junction in order to thermally anneal the Josephson junction.

[0050] In this context, “bringing into proximity” means bringing the heated element close enough to the Josephson junction and / or substrate in order for sufficient thermal energy to be transferred from the heated element to the Josephson junction in order to thermally anneal the Josephson junction. Bringing into proximity may therefore include bringing the heated element into direct contact with the Josephson junction and / or substrate, or bringing the heated element in proximity to the Josephson junction and / or substrate without making direct contact. Thermal annealing of the Josephson junction by proximity of the heated element to the Josephson junction and / or substrate results in a local annealing effect. This local annealing has expedites the oxide aging of the junction barrier, which consequently leads in a resistance change of the Josephson junction. In this approach, the resistance change is solely due to the thermal effect of the local annealing on the Josephson junction.

[0051] Thermal annealing of the Josephson junction by proximity of the heated element to the Josephson junction and / or substrate leads to an increase in the normal state resistance of the Josephson junction. The magnitude of the change in the normal state resistance depends on the amount of thermal energy transferred to the Josephson junction from the heated elements and therefore depends on, amongst other factors, the distance between the heated element and the Josephson junction and / or substrate, the temperature of the heated elements, the length of time for which the heated element is in proximity with the Josephson junction and / or substrate, the size of the heated element, and the way in which the heated element is brought into proximity with the Josephson junction and / or substrate. By controlling some or all of these factors, and optionally other factors, the magnitude of the resistance change can be controlled.

[0052] Furthermore, the use of a heated element for thermally annealing the Josephson junction may have an added benefit compared to thermal annealing by electromagnetic radiation in that the heated element can remove residual material from the process used to manufacture the Josephson junction or other unwanted matter. This is particularly useful where the Josephson junction is used as part of a superconducting qubit, as the presence of residual material or other unwanted matter on the surface of the Josephson junction can lead to decreased qubit relaxation and coherence times, in particular the relaxation and decoherence times also commonly referred to as Ti and T2. The effect of removing residual material and other unwanted matter from the surface of the Josephson junction and / or substrate is most pronounced when the heated element is brought into contact with the Josephson junction and / or substrate.

[0053] In some embodiments, the heated element is a heated atomic force microscope tip. However, the present invention is not limited to use atomic force microscope tips. It will be understood that except where atomic force microscopy is explicitly used, other heated elements may be used.

[0054] The heated element may be conductive and grounded, or heavily doped, in order to avoid electrostatic discharge damaging the Josephson junction or other sensitive components formed on the same wafer.

[0055] The heated element may be heated to 100 degrees Celsius or more. Step 107 includes cleaning fabrication residues from the surface of the Josephson junction and / or a region of a substrate on which the Josephson junction is formed using the heated element. This may be done by scanning the Josephson junction and / or the region of the substrate with the heated element. This is particularly useful where the Josephson junction is used as part of a superconducting qubit, as the presence of residual material or other unwanted matter on the surface of the Josephson junction can lead to decreased qubit coherence time, in particular the decoherence time also commonly referred to as T2. The effect of removing residual material and other unwanted matter from the surface of the Josephson junction and / or substrate is most pronounced when the heated element is brought into contact with the Josephson junction and / or substrate. Step 107 may be performed after the annealing step 106, as shown in Figure 1 , or may be performed before the annealing step 106.

[0056] Figure 2 depicts a first method of modifying the normal state resistance of the Josephson junction by thermally annealing the Josephson junction by bringing a heated element in proximity to the Josephson junction and / or a region of the substrate adjacent to the Josephson junction.

[0057] The Josephson junction 200 depicted in Figure 2 is a generic Josephson junction formed by a process as described in Potts, A., Routley, P.R., Parker, G.J. et al. :”Novel fabrication methods for submicrometer Josephson junction qubits”, Journal of Materials Science: Materials in Electronics 12, 289-293 (2001 ). However, the present invention is not limited to use with Josephson junctions of a particular form or method of manufacture provided that the Josephson junction 200 and / or adjacent substrate can be brought into proximity with a heated element in order to thermally anneal the Josephson junction 200. The Josephson junction 200 is formed on a substrate 201 and is made up of a base electrode 202, dielectric layer 203, and counter electrode 204. However, further layers can also be part of the Josephson junction 200. For example, each layer mentioned above can be made of a combination of layers.

[0058] The electrical properties of the Josephson junction 200, such as its normal state resistance, are determined by the properties of the overlapping regions of base electrode 202, dielectric layer 203 and counter electrode 204. In some contexts, the term “Josephson junction” may be understood to mean only the overlapping regions of the base electrode 202, dielectric layer 203 and counter electrode 204, but in the present context the term “Josephson junction” should be understood to mean the overlapping regions of the base electrode 202, dielectric layer 203, and counter electrode 204 as well as adjacent parts of the base electrode 203 and counter electrode 204. In this context, “adjacent” may mean the parts of the base electrode 203, and counter electrode 204 close enough to overlapping regions of the base electrode 203, dielectric layer 203, and counter electrode 204 such that when they are irradiated with the electron beam in accordance with the present method a change in the normal state resistance of the Josephson junction 200 is observed.

[0059] In the example of Figure 2, the heated element 205 is brought into proximity with the upper surface of the counter electrode 204. In this context, “upper” means distal to the substrate 201. The heated element 205 may include a tip 206 that is proximate to the Josephson junction 200 and / or substrate 201 . The tip 206 may have a radius of curvature of less than 5 pm. The drawing of Figure 2 is not to scale. In practice the radius of curvature of the tip 206 may be as large or larger than the upper surface of the counter electrode 204.

[0060] Where the radius of curvature of the of tip 206 is smaller than the upper surface of the counter electrode 204, the tip 206 may be scanned across the Josephson junction 200 and / or substrate 201 in order to expose more of the Josephson junction 200 to the thermal energy of the heated element 205. An example scanning pattern 207 is shown in Figure 2, but this specific scanning pattern should not be seen as limiting on the invention. Other scanning patterns may also be used. Furthermore, while the scanning pattern 207 is shown entirely within the overlapping regions of the base electrode 202, dielectric layer 203, and counter electrode 204, other scanning patterns may be used that extend partially or even wholly outside of the overlapping region.

[0061] Figure 3 shows an alternative example to that depicted in Figure 2 in which the tip 206 of the heated element 205 is repeatedly brought into proximity at different points 307 on the upper surface of the counter electrode 204. Such action may be referred to as “tapping” as opposed to the continuous scanning shown in Figure 2. While Figure 3 shows the points 307 only within the overlapping regions of the base electrode 202, dielectric layer 203, and counter electrode 204, other points may be used on both the Josephson junction 200 and / or a region of the substrate 201 adjacent to the Josephson junction 200.

[0062] Figure 4 shows a further alternative example to that depicted in Figures 2 and 3 where the tip 206 is brought into proximity with a single point 407 on the upper surface of the counter electrode 204 of the Josephson junction 200. This way of bringing the tip 206 into proximity with the Josephson junction 200 may be useful when the size of the tip 206 (or radius of curvature of the tip 206) is similar or larger than the size of the Josephson junction 200.

[0063] According to the invention, the use of a heated element 206, in particular a tip 206, being brought into proximity to the Josephson junction and / or to a region of the substrate adjacent to the Josephson junction enables local heating of the Josephson junction and / or a region of the substrate adjacent to the Josephson junction. Each of the different techniques depicted in Figures 2 to 4 may be used alone in order to carry out thermal annealing of a Josephson junction, or any combination of some or all of the techniques may be used. Furthermore, the examples shown in Figures 2 to 4 should not be considered to be limiting and other ways of bringing a heated element into proximity with a Josephson and / or substrate may be used in the present invention.

[0064] The method for modifying the normal state resistance of a Josephson junction described above may be part of a larger method of manufacturing a qubit. As explained above, increasing the normal state resistance of the Josephson junction decreases the frequency of the qubit including the Josephson junction. As such, a method of manufacturing a qubit, may include first manufacturing the qubit, which includes the Josephson junctions and subsequently modifying the qubit frequency by modifying the normal state resistance of the at least one Josephson junction using to the method described above.

[0065] The method for modifying the normal state resistance may be performed using a specific apparatus or device for modifying the normal state resistance of a Josephson junction. Such an apparatus may include a stage for retaining a substrate on which the Josephson junction is disposed, a heated element configured to heat the Josephson junction and / or a region of the substrate adjacent to the Josephson junction and a drive system configured to bring the heated element into contact or proximity with the Josephson junction by either moving the heated element or moving the stage. The apparatus may be a modified atomic force microscope or a different, dedicated device.

Claims

Claims1 . A method (100) for modifying the normal state resistance of a Josephson junction (200), the method (100) comprising:- thermally annealing the Josephson junction (200) by bringing a heated element (205) in proximity to the Josephson junction (200) and / or a region of the substrate (201 ) adjacent to the Josephson junction (200).

2. The method (100) of claim 1 , wherein the heated element (205) comprises a tip (206) with a radius of curvature of less than 5 pm, and wherein the tip (206) of the heated element (205) is brought in proximity to the Josephson junction (200) and / or a region of the substrate (201 ) adjacent to the Josephson junction (200).

3. The method (100) of claim 1 or 2, wherein the heated element (205) is a grounded conductive element.

4. The method (100) of any preceding claim, wherein the method (100) further comprises imaging the Josephson junction (200) prior to thermally annealing the Josephson junction (200).

5. The method (100) of any preceding claim, wherein the method (100) comprises heating the heated element (205) to at least 100 degrees Celsius.

6. The method (100) of any preceding claim, wherein the method (100) further comprises controlling the temperature of the heated element (205) in order to achieve a predetermined change in the normal state resistance of the Josephson junction (200).

7. The method (100) of claim 6, wherein controlling the temperature of the heated element (205) comprises monitoring or estimating the temperature of the heated element (205) based on one or more of: a temperature sensor measurement and an electrical current applied to a resistive wire within the heated element (205).

8. The method (100) of any preceding claim9, wherein the method (100) further comprises:- measuring the normal state resistance of the Josephson junction (200); and- determining the parameters relating to the heated element (205), in particular its temperature and the duration of time for which the heated element (205) is in proximity to the Josephson junction (200) and / or the region of the substrate (201 ) adjacent to the Josephson junction (200), required to produce a predetermined change in the normal state resistance of the Josephson junction (200).

9. The method (100) of any preceding claim, wherein bringing the heated element (205) in proximity to the Josephson junction (200) and / or a region of the substrate (201 ) adjacent to the Josephson junction (200) comprises scanning the Josephson junction (200) and / or the region of the substrate (201 ) adjacent the Josephson junction (200) with the heated element (205).

10. The method (100) of claim 9, wherein determining the parameters relating to the heated element (205) further comprises the scanning speed of the heated element (205) required to produce a predetermined change in the normal state resistance of the Josephson junction (200).11 . The method (100) of claim 9 or 10, wherein when fabrication residue is present on the Josephson junction (200) and / or substrate (201 ), the method (100) further comprises removing said fabrication residue from the Josephson junction (200) and / or the region of the substrate (201 ) with the heated element (205).

12. The method (100) of claim 11 wherein removing fabrication residue is performed simultaneously with thermally annealing the Josephson junction (200).

13. The method (100) of any preceding claim, wherein the Josephson junction (200) comprises a lower superconducting electrode layer disposed on a substrate (201 ), an upper superconducting electrode layer, and a non-superconducting barrier layer disposed between the lower superconducting electrode layer and upper superconducting electrode layer, and wherein thermally annealing the Josephson junction (200) comprises thermally annealing the non-superconducting barrier layer.

14. The method (100) of claim 13, wherein bringing the heated element (205) in proximity to the Josephson junction (200) comprises bringing the heated element (205) in proximity to the upper superconducting barrier layer.

15. The method (100) of any preceding claim, wherein the heated element (205) is an atomic force microscope tip.

16. The method (100) of claim 15, wherein the method (100) further comprises placing at least the Josephson junction (200) in an atomic force microscope, and wherein bringing the heated element (205) in proximity to the Josephson junction (200) and / or a region of the substrate (201 ) adjacent to the Josephson junction (200) comprises bringing the atomic force microscope tip in proximity to the Josephson junction (200) and / or a region of the substrate (201 ) adjacent to the Josephson junction (200).

17. The method (100) of any preceding claim, wherein the Josephson junction (200) is part of a superconducting qubit, and wherein modifying the normal state resistance of the Josephson junction (200) modifies the frequency of the qubit.

18. A method (100) of manufacturing a qubit, the method (100) comprising manufacturing a qubit, wherein manufacturing the qubit includes providing at least one Josephson junction (200) on a substrate (201 ), and; modifying the qubit frequency by modifying the normal state resistance of the at least one Josephson junction (200) according to the method (100) of any preceding claim.

19. The method (100) of claim 18, wherein modifying the qubit frequency comprises increasing the normal state resistance of the Josephson junction (200) thereby decreasing the qubit frequency.

20. An apparatus for modifying the normal state resistance of a Josephson junction (200), the apparatus comprising:- a stage for retaining a substrate (201 ) on which the Josephson junction (200) is disposed;- a heated element (205) configured to heat the Josephson junction (200) and / or a region of the substrate (201 ) adjacent to the Josephson junction (200); and- a drive system configured to bring the heated element (205) into contact or proximity with the Josephson junction (200) by either moving the heated element (205) or moving the stage.21 . The apparatus of claim 20, wherein the heated element (205) is configured to be heated to at least 100 degrees Celsius.

22.

22. The method (100) according to any one of claims 1 to 19 or the apparatus according to any one of claims 20 or 21 , wherein bringing the heated element (205) in proximity to the Josephson junction (200) and / or the region of the substrate (201 ) adjacent to the Josephson junction (200) comprises bringing the heated element (205) close enough to the Josephson junction (200) and / or the region of the substrate (201 ) in order for sufficient thermal energy to be transferred from the heated element (205) to the Josephson junction (200) to thermally anneal the Josephson junction (200).

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