Josephson travelling wave parametric amplifier and method for obtaining the same

Abstract

Disclosed is a Josephson travelling wave parametric amplifier (JTWPA) comprising a conductive layer, a dielectric layer, and a plurality of Josephson junctions, wherein each Josephson junction (210) comprises a pair of electrodes (211, 212) that extend towards each other to define an area of overlap, wherein at least one electrode (211) of one or more of the pairs of electrodes comprises a first lengthwise segment (211a) comprising the area of overlap, and a second lengthwise segment (211b), the second lengthwise segment having a width (Db211) larger than a width (Da211) of the first lengthwise segment, whereby the second lengthwise segment having the enlarged width, in conjunction with the conductive layer and the dielectric layer, defines a capacitive structure that at least partially defines a capacitance of the JTWPA, and wherein the first and second lengthwise segments are integrally formed. A method for obtaining the JTWPA and a quantum computing system comprising the JTWPA are also disclosed.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to a Josephson travelling wave parametric amplifier (JTWPA), to a method for obtaining such a JTWPA and to a system comprising such a JTWPA.BACKGROUND

[0002] Josephson travelling wave parametric amplifiers (JTWPAs) are amplifiers capable of amplifying low amplitude signals with high gain and a minimal amount of introduced noise that approximates the quantum limit.

[0003] JTWPAs comprise a plurality of superconducting Josephson junctions that define a transmission line through which an input signal to be amplified propagates. The Josephson junctions may be connected to one another in series or to form a plurality of superconducting quantum interference devices (SQUIDs) or superconducting non-linear asymmetric inductive elements (SNAILs). Each Josephson junction (or alternatively SQUID or SNAIL) functions as a non-linear inductive element that amplifies the input signal based on non-linear interaction with a pump signal, resulting in a transfer of energy from the pump signal to the signal amplification of the input signal. The non-linear inductive elements form a repeating structure of unit cells, with each unit cell comprising a capacitance to ground. In the non-linear inductive elements the input signal interacts with a pump signal, resulting in a transfer of energy from the pump signal to the input signal. This in turn results in amplification of the input signal and the generation of an additional idler signal. The number of Josephson junctions comprised by a JTWPA may be selected with respect to a degree of amplification to be achieved.

[0004] JTWPAs are suitable for amplifying particularly weak signals and find application within e.g. the field of quantum computing. In the field of quantum computing, JWTPAs may be utilised to read out superconducting quantum bits (qubits). The number of Josephson junctions comprised by a JTWPA may be significant, with hundreds or even thousands of Josephson junctions comprised by a transmission line.

[0005] State of the art JTWPAs are susceptible to improvements with respect to miniaturisation. Miniaturisation is an important factor in the design of JTWPAs for various reasons.

[0006] On the one hand, an increased degree of miniaturisation decreases the physical dimensions and footprint of a JTWPA. This facilitates integration of JTWPAs into larger systems with limited space and comprising various additional components. JTWPAs are an essential component for high performance quantum computing and the miniaturisation of these is one of the key challenges for scaling up to the high qubit count systems required for fault tolerant quantum computation.

[0007] On the other hand, a JTWPA with an increased degree of miniaturisation comprises a reduced amount of material that makes up the JTWPA. JTWPAs must be cooled to temperatures close to absolute zero, typically in the order of millikelvins, prior to operation. A miniaturised JTWPA having a decreased amount of material may thus be cooled more efficiently and at a faster rate, while using less capacity of a cryostat.

[0008] A further important factor in the design of JTWPAs relates to their manufacturing cycle time and manufacturing yield. Manufacturing cycle time refers to the amount of time required to fabricate one or a batch of JTWPAs, whereas manufacturing yield may refer to the number of non-defective units that is obtained when a batch of JTWPAs or alternatively JTWPA components is fabricated. Evidently, it is desirable to have a short manufacturing cycle time and a high manufacturing yield when fabricating JTWPAs or JTWPA components. It will be appreciated that this is particularly relevant within the field of quantum computing, which is currently characterised by a trend towards more complex hardware comprising ever increasing numbers of components. This results in correspondingly increased manufacturing cycle times and decreased manufacturing yields. It is therefore desirable to provide a JTWPA that facilitates fabrication techniques or methods resulting in an improved manufacturing cycle time and / or an improved manufacturing yield.

[0009] Reference is made here to CN 117294258 A (UNIVERSITY OF SCIENCE AND TECHNOLOGY OF CHINA; HEFEI NATIONAL LABARATORY) 26 December 2023 (26.12.2023), which is acknowledged as closest prior-art. CN 117294258 discloses a traveling wave parameter amplifier and a fabrication method thereof. The traveling wave parameter amplifier comprises a substrate, a grounded first superconducting metal layer and a multitude of microstrip wire cores, each adapted to be connected to respective ends of neighbouring Josephson junctions. CN 117294258 A furthermore discloses that this device can be fabricated by a fabrication method that involves individually connecting each of the microstrip wire cores to each electrode of neighbouring Josephson junctions. Recalling that JTWPAs comprise substantial numbers of Josephson junctions, the device known from CN 117294258 is therefore obtained through a convoluted fabrication method that falls short in terms of cycle time and yield.

[0010] In stark contrast to the traveling wave parameter amplifier known from CN 117294258 A, the JTWPA according to the present disclosure does not comprise connectable microstrip wire cores of the above described type, but instead comprises Josephson junctions with electrodes having first lengthwise segments and second lengthwise segments that are integrally formed, for example by a means of a single iteration of an angled evaporation fabrication technique. The first lengthwise segments comprise areas of overlap between electrodes forming Josephson junctions, whereas the second lengthwise segments comprise respective widths that are increased relative to the widths of the first lengthwise segments. In conjunction with a conductive layer and a dielectric layer, the second lengthwise segments having the enlarged width define capacitive structures that at least partially define a characteristic impedance of the JTWPA.

[0011] Advantageously, the JTWPA according to the present disclosure may be fabricated very efficiently in a minimal number of fabrication steps and an improved manufacturing cycle time. A transmission line of the herein disclosed JTWPA may be finalised immediately when the electrodes of the Josephson junctions are formed, thereby completely avoiding the additional fabrication steps of forming connections between each of the electrodes of each of the Josephson junctions and neighbouring microstrip wire cores, as is known from CN 117294258 A.

[0012] The objective of the present disclosure is to provide a JTWPA with which one or more, or possibly even others, of the disadvantages of JTWPAs known from the prior art is / are obviated or abated.SUMMARY

[0013] The above stated object of the present disclosure is achieved with a Josephson travelling wave parametric amplifier (JTWPA) in accordance with a first general aspect of the present invention, the JTWPA comprising a conductive layer, a dielectric layer, and a plurality of Josephson junctions comprised by a transmission line, wherein each Josephson junction comprises a pair of electrodes that extend towards each other to define an area of overlap, wherein at least one electrode of one or more of the pairs of electrodes comprises a first lengthwise segment comprising the area of overlap, and a second lengthwise segment opposite the first lengthwise segment, wherein the second lengthwise segment of said at least one electrode comprises a width (which alternatively may be referred to as a "diameter") extending orthogonal to a lengthwise direction of the electrode and substantially parallel to the conductive layer, said width being larger than a width of the first lengthwise segment, whereby the second lengthwise segment having the enlarged width, in conjunction with the conductive layer and the dielectric layer, defines a capacitive structure that at least partially defines a capacitance of the JTWPA.

[0014] The inventors of the JTWPA according to the present invention realised that by selectively increasing a width within at least a certain lengthwise segment of an electrode in a specified direction, a specified capacitance to ground of the transmission line may be achieved for each Josephson junction or unit cell. In this way, a characteristic impedance of the JTWPA may be achieved without the inclusion of additional discrete capacitor components, or at least with a reduced amount of such discrete capacitor components.

[0015] The capacitance to ground of consecutive Josephson junctions is an important design criterion of the JTWPA as a whole. This capacitance to ground must comprise a value such that satisfies a wave equation describing a signal propagating through the transmission line. In a JTWPA according to the present invention, the required capacitance to ground is achieved entirely by leveraging the intrinsic capacitance of electrode(s) of one or more Josephson junctions, by designing the shape of said electrode accordingly. This renders the inclusion of additional discrete capacitors (e.g. parallel plate capacitors and the like) to be superfluous, which may thus be omitted. The result is that a JTWPA is obtained with a decreased physical footprint and increased degree of miniaturisation, which is moreover well suited to be fabricated in a highly efficient manner with reduced cycle time and in increased fabrication yield.

[0016] In a preferred embodiment of a JTWPA according to the present invention, the plurality of Josephson junctions is arranged in a meandering arrangement pattern, wherein turns of the meandering arrangement pattern are defined by respective first lengthwise segments comprising the area of overlap of neighbouring electrode pairs of consecutive Josephson junctions.

[0017] The JWTPA according to the present invention having one or more electrodes with an increased width may moreover be advantageously arranged in a space efficient meandering pattern. In such a meandering pattern, the transmission line extends in a zig-zagging pattern with parallelly extending lengthwise segments and turns connecting the lengthwise segments. The above described configuration of electrodes of Josephson junctions facilitates easy and space efficient arrangement of the transmission line in such a meandering pattern on the limited surface area of a substrate.

[0018] In further preferred embodiments of a JTWPA according to the present invention, the meandering pattern of the plurality Josephson junctions comprise a first substructure, comprising a first Josephson junction comprising a first electrode and a second electrode, a second Josephson junction comprising the second electrode and a third electrode, wherein the second electrode is interposed between the first electrode and the third electrode, a third Josephson junction comprising the third electrode and a fourth electrode, wherein the third electrode is interposed between the second electrode and the fourth electrode, and a fourth Josephson junction comprising the fourth electrode and a fifth electrode, wherein the fourth electrode is interposed between the between the third electrode and the fifth electrode, wherein the first electrode, the third electrode and the fifth electrode extend parallel to one another in a first direction, and the second electrode and the fourth electrode extend parallel to one another in a second direction.

[0019] The above described first substructure is particularly suitable for implementing the aforementioned lengthwise segments of the meandering transmission line. Consecutive electrodes are arranged in U-shaped formations each forming two Josephson junctions, wherein said U-shaped formations are arranged mirrored to one another to achieve a highly space efficient arrangement.

[0020] In further preferred embodiments of a JTWPA according to the present invention, the meandering pattern of the plurality Josephson junctions comprises a second substructure, comprising a fifth Josephson junction comprising a sixth electrode and a seventh electrode, a sixth Josephson junction comprising the seventh electrode and an eight electrode, a seventh Josephson junction comprising the eight electrode and a nineth electrode, and an eight Josephson junction comprising the nineth electrode and a tenth electrode, wherein the sixth electrode, the eight electrode and the tenth electrode extend substantially parallel to one another in a third direction, and the seventh electrode and the nineth electrode extend substantially parallel to one another in fourth direction.

[0021] The here above described second substructure is particularly suitable to implement turns in the meandering pattern of the transmission line, likewise in a space efficient manner with an increased number of Josephson junctions per unit of length of the transmission line.

[0022] In further preferred embodiments of a JTWPA according to the present invention, the first lengthwise segment and the second lengthwise of the at least one electrode segment are integrally formed.

[0023] In further preferred embodiments of a JTWPA according to the present invention, the first lengthwise segment and the second lengthwise segment are formed in a single iteration of a fabrication technique, preferably a single iteration of an angled evaporation fabrication technique.

[0024] The JTWPA according to the present invention and disclosure is not, as explained here above, dependent on the inclusion of additional parallel plate capacitors and the like. Instead, the entirety of the required capacitance to ground is achieved by means of the electrodes themselves, which are designed to achieve the required capacitance to ground to thereby achieve the corresponding characteristic impedance. All electrodes are substantially identical and during fabrication of the JTWPA may be formed integrally using the same fabrication technique (e.g. angled evaporation). This entails that the entire transmission line of the JTWPA may be obtained using only this fabrication technique, without requiring additional fabrication techniques to fabricate e.g. additional capacitors to achieve the required capacitance to ground. As such, in these embodiments the JTWPA may be fabricated in a manner that is highly efficient with reduced manufacturing cycling time and increased manufacturing yield.

[0025] In further preferred embodiments of a JTWPA according to the present invention, the second lengthwise segment comprises a shape that is substantially circular or polygonal with a plurality of equally dimensioned sides.

[0026] In further preferred embodiments of a JTWPA according to the present invention, a first contour of the second lengthwise segment, when viewed in a first deposition direction of the fabrication technique, corresponds to a second contour of the second lengthwise segment, when viewed in a second deposition direction of the fabrication technique, and / or the second lengthwise segment exhibits rotational symmetry with respect to the first deposition direction and the second deposition direction of the fabrication technique.

[0027] In further preferred embodiments of a JTWPA according to the present invention, the second lengthwise segment comprises a substantially square shape.

[0028] In embodiments wherein the JTWPA according to present invention is formed using angled evaporation as a fabrication technique, the transmission line of the JTWPA is formed by depositing conductive material from a crucible from a plurality of different deposition directions. Because angled evaporation is dependent on shadows cast by a resist to selectively deposit conductive material on specific surfaces, where the conductive material deposited is in principle determined by the orientation of the crucible relative to the work piece. This entails that it is preferable to design the second segment having the enlarged width in such a way, that said enlarged width remains consistent regardless of the deposition orientation used when performing consecutive angled evaporation iterations.

[0029] The above may be achieved by designing the second lengthwise segment of the at least one electrode to comprise a substantially circular shape. A substantially circular shape comprises the advantage that respective second lengthwise segments comprise similar surface areas regardless of the angled evaporation deposition direction that is used. Similar results may be achieved by designing the second lengthwise segment of the at least one electrode to comprise a polygonal shape having equally dimensioned sides, as long as said polygonal shape is oriented adequately in consideration of the angled evaporation deposition directions. Both second lengthwise segments comprising a substantially circular shape and second lengthwise segments comprising polygonal shape having equally dimensioned sides oriented in consideration of the angled evaporation deposition directions may be said to exhibit rotational symmetry with respect to each of these angled evaporation directions. Typically, two different angled evaporation directions are utilised that differ from one another by 90 degrees.

[0030] In further preferred embodiments of a JTWPA according to the present invention, the second lengthwise segment having the substantially square shape is oriented such that a diagonal of the second lengthwise segment coincides with a lengthwise direction of the at least one electrode.

[0031] In embodiments wherein the JTWPA is fabricated using angled evaporation with two different angled evaporation directions at 90 degrees, it is particularly advantageous to design the second lengthwise segment to comprise the substantially square shape. In these embodiments, second lengthwise segments of consecutive electrodes may be obtained having very consistent physical dimensions, regardless of the deposition direction that is used for that particular angled evaporation iteration. This is because for square shapes, the shadows cast by the resists are particularly well predictable, even more so than for substantially circular shapes and other polygonal shape with equally dimensioned sides.

[0032] In further preferred embodiments of a JTWPA according to the present invention, the diagonal of the second lengthwise segment furthermore coincides with a horizontal vector component of at least one of the first deposition direction and the second deposition direction of the fabrication technique.

[0033] In further preferred embodiments of a JTWPA according to the present invention, the second lengthwise segment comprises a surface area of 3 µm² to 1000 µm², more preferably of 6 µm² to 600 µm², most preferably of 10 µm² to 150 µm².

[0034] In further preferred embodiments of a JTWPA according to the present invention, one or both of a capacitance and an inductance of the transmission line is periodically modulated, whereby the impedance of the transmission line is periodically modulated, such that a phase matching stopband is defined in a dispersion relationship of the transmission line.

[0035] [effect]In these embodiments, phase matching between an input signal to be amplified and a pump signal may be achieved by periodically modulating impedance of the transmission line. In these embodiments, additional phase matching structures otherwise included in the transmission line of the JTWPA, such as discrete phase matching resonators, may be reduced in number or even entirely obviated. Reducing the number of phase matching resonators or excluding them entirely results in a yet further improved degree of miniaturisation.

[0036] In further preferred embodiments of a JTWPA according to the present invention, the inductance of the transmission line is periodically modulated by periodic modulation of respective widths of first lengthwise segments of consecutive electrodes, such that electrode pairs constituting consecutive Josephson junctions comprise periodically modulating areas of overlap.

[0037] In further preferred embodiments of a JTWPA according to the present invention, the capacitance of the transmission line is periodically modulated by periodic modulation of respective widths of the second lengthwise segments of consecutive electrodes forming the plurality of Josephson junctions constituting the transmission line.

[0038] The above stated object of the present disclosure is moreover achieved with a quantum computing system in accordance with a second general aspect of the present invention, said quantum computing system comprising at least a quantum processing unit (QPU) comprising at least one measurement object, and at least one JTWPA in accordance with the present disclosure.

[0039] The above stated object of the present disclosure is moreover achieved with a method for obtaining a JTWPA in accordance with a third general aspect of the present invention, the method comprising: providing a layer stack comprising a substrate, a conductive layer, a dielectric layer and a resist, subjecting the layer stack to an exposure process followed by a development process, to thereby remove the resist at areas corresponding to respective Josephson junctions to be formed, forming a plurality of Josephson junctions each comprising a pair of electrodes that extend towards each other to define an area of overlap, forming at least one electrode of one or more of the pairs of electrodes to comprise: a first lengthwise segment comprising an area of overlap with a neighbouring electrode, and a second lengthwise segment opposite the first lengthwise segment, wherein said second lengthwise segment is formed to comprise a width extending orthogonal to a lengthwise direction of the electrode and substantially parallel to the conductive layer, said width being larger than a width of the first lengthwise segment.

[0040] In a preferred embodiment of the method in accordance with the present invention, the step of forming the plurality of Josephson junctions comprises: forming the plurality of Josephson junctions in a meandering arrangement pattern, wherein turns of the meandering arrangement pattern are defined by respective first lengthwise segments comprising the area of overlap with a neighbouring electrode of consecutive Josephson junctions, wherein the meandering arrangement pattern is preferably formed to comprise a first substructure, comprising a first Josephson junction comprising a first electrode and a second electrode, and a second Josephson junction comprising the second electrode and a third electrode, wherein the second electrode is interposed between the first electrode and the third electrode, wherein the first and third electrode extend parallel to one another in a first meandering direction of the meandering pattern, and the second electrode extends in a second meandering direction of the meandering pattern perpendicular to the first meandering direction, and wherein consecutive first substructures are arranged mirrored along a heartline of the first substructure.

[0041] In a further preferred embodiments of the method in accordance with the present invention, the meandering arrangement pattern is formed to comprise a second substructures, comprising a third Josephson junction comprising a fourth electrode and a fifth electrode, a fourth Josephson junction comprising the fifth electrode and a sixth electrode, a fifth Josephson junction comprising the sixth electrode and a seventh electrode, and a sixth Josephson junction comprising the seventh electrode and an eight electrode, wherein the fourth electrode, the sixth electrode and the eight electrode extend parallel to one another in the first meandering direction, and wherein the fifth electrode and the seventh electrode extend parallel to one another in the second meandering direction of the meandering pattern.

[0042] In a further preferred embodiments of the method in accordance with the present invention, the first lengthwise segment and the second lengthwise of the at least one electrode segment are integrally formed, preferably in a single iteration of a fabrication technique, more preferably a single iteration of an angled evaporation fabrication technique.

[0043] In a further preferred embodiments of the method in accordance with the present invention, the second lengthwise segment is formed to comprise a substantially square shape, wherein said substantially square shape is preferably oriented such that a diagonal of the second lengthwise segment coincides with a lengthwise direction of the at least one electrode.BRIEF DESCRIPTION OF THE DRAWING

[0044] The present invention will be elucidated here below with reference to the drawing, in which:

[0045] Fig. 1 schematically depicts an electronic circuit of a JTWPA that may correspond to some embodiments of the present invention;

[0046] Fig. 2 shows a top-down view of an exemplary embodiment of a part of a transmission line comprised by the JTWPA of Fig. 1 in accordance with the present disclosure;

[0047] Fig. 3A, Fig. 3B and Fig. 3C illustrate an example of successive steps of a method for obtaining a JTWPA in accordance with the present disclosure;

[0048] Fig. 4A and Fig. 4B respectively show sectional views of alternative embodiments of the transmission line of Fig. 2 to Fig. 3C;

[0049] Fig. 5A schematically depicts a transmission line of the JTWPA in accordance with preferred embodiments of the present invention;

[0050] Fig. 5B shows a microscopic view of a first part of the transmission line of Fig. 5A;

[0051] Fig. 5C shows a microscopic view of a second part of the transmission line of Fig. 5A;

[0052] Fig. 6A shows a top-down view of a further exemplary embodiment of a part of a transmission line comprised by the JTWPA in accordance with the present disclosure;

[0053] Fig. 6B shows a schematic depiction of an electronic circuit of the embodiment of Fig. 6A; and

[0054] Fig. 7 schematically depicts an exemplary embodiment of a system in accordance with certain embodiments of the present invention.DETAILED DESCRIPTION

[0055] Fig. 1 schematically depicts an electronic circuit of a Josephson travelling wave parametric amplifier (JTWPA) 100 according to an exemplary embodiment of the present invention. The JTWPA 100 may be cooled to a cryogenic temperature where it exhibits superconductivity to amplify microwave signals.

[0056] The JTWPA 100 comprise a transmission line 103 through which an input signal to be amplified propagates. In the exemplary embodiment of Fig. 1, the transmission line 103 comprises a plurality of Josephson junctions 110, 120, 130 connected in series to define the transmission line 103. It will be appreciated that the transmission line 103 may alternatively comprise superconducting quantum interference devices (SQUIDs) and / or superconducting non-linear asymmetric inductive elements (SNAILs), both of which likewise comprise Josephson junctions. Each Josephson junction 110, 120, 130 functions as a non-linear inductive element capable of amplifying an input signal based on non-linear interacting with a pump signal, to thereby achieve parametric amplification of the input signal. The JTWPA 100 may achieve parametric amplification based on a four-wave mixing or three-wave mixing principle. In the case of four-wave mixing, four photons are involved in the amplification process in which two pump signal photons are combined into a signal having the frequency of the input signal, and an idler signal photon. Similarly, three-wave mixing involves the interaction of three photons.

[0057] In accordance with certain embodiments, the transmission line 103 may comprise a microstrip, an inverted microstrip or a stripline geometry. Possible geometries of the transmission line 103 in accordance with various embodiments of the present invention will be further elucidated here below with reference to Fig. 4A and Fig. 4B.

[0058] The transmission line 103 is periodically shunted to an electrical ground connection 105 via a plurality of capacitor structures 111, 112, 113 to achieve a characteristic impedance JTWPA 100. Το prevent unwanted reflections of signals, the capacitance of each of the ground capacitors 133 of is selected such that the JTWPA 100 comprises a predefined impedance of e.g. 50 Ω.

[0059] While the transmission line 103 of the JTWPA 100 may be shunted to the electrical ground connection 105 at every Josephson junction 110, 120, 130 as is depicted in Fig. 1, the present disclosure is not limited thereto.

[0060] Wave mixing-based amplification is a phase dependent process that requires a phase difference between the input signal and the pump signal to be zero or at least close to zero. However, the input signal and the pump signal experience a negative phase shift as they propagate through the transmission line 103. To counteract this relative phase shift and ensure phase matching of the pump signal and the input signal at each of the Josephson junctions 110, 120, 130, certain embodiments of the JTWPA 100 furthermore comprise one or more phase matching phase matching resonators 107 that are periodically connected the transmission line 103 via a capacitor 104. The phase matching resonator 107 in Fig. 1 comprises a resonator capacitor 108 and a resonator inductor 106. To ensure adequate phase matching, the phase matching resonator 107 may be configured to define a phase matching stopband with respect to a specific frequency of the input signal propagating through the transmission line 103.

[0061] It is noted that the phase matching resonator 107 is merely an optional feature that may be excluded from the JTWPA 100, in accordance with certain preferred embodiments of the present invention. In these embodiments, phase matching may be achieved by alternative means. An example of these embodiments will be discussed here below with reference to Fig. 6A and Fig. 6B.

[0062] It will be appreciated that the JTWPA 100 may comprise additional components other than the components shown in Fig. 1 and described hereabove. In particular, in certain embodiments the JTWPA 100 may comprise additional capacitors and Josephson junctions 110, 120, 130. It will moreover be appreciated that the number of capacitors and Josephson junctions 110, 120, 130 comprised JTWPA 100 may vary depending on the required specifications of the JTWPA 100. For example, the number of Josephson junctions 110, 120, 130 may be selected in consideration of a degree of amplification that is to be achieved. In accordance with certain embodiments, the number of Josephson junctions 110, 120, 130 comprised by the JTWPA 100 may be several hundred, several thousand or more.

[0063] It will also be appreciated that, while all of the Josephson junctions 110, 120, 130 in Fig. 1 are connected in series to define the transmission 103, the present disclosure is not limited thereto. The transmission line 103 may alternatively comprise e.g. SQUIDs, SNAILs and possibly other devices comprising Josephson junctions.

[0064] The JTWPA 100 may exhibit an enhanced degree of miniaturisation at least on account of the manner through which the capacitor structures 111, 112, 113 are physically implemented. This is elucidated with reference to Fig. 2 and Fig. 3A to Fig. 3C.Fig. 2 shows a top-down view of a physical implementation of (a part of) a JTWPA 200, in accordance with the present invention and disclosure. Fig. 3A to Fig. 3C illustrate a method for obtaining or fabricating a JTWPA 300 in accordance with the present invention. The JTWPA 300 of Fig. 3A-C and the JTWPA 200 of Fig. 2 each correspond to the JTWPA 100 of Fig. 1.

[0065] The JTWPA 200 of Fig. 2 comprises a plurality of Josephson junctions 210, of which one is depicted in Fig. 2. The Josephson junction 210 is formed by a pair of a first electrode 211 and a second electrode 212. The first electrode 211 and a second electrode 212 extend towards one another to define an area of overlap indicated by the dashed encirclement in Fig. 2. Electrode 211 and electrode 212 moreover each comprise a respective free end 211', 212' beyond the area of overlap. The area of overlap comprises a weak link between the first electrode 211 and the second electrode 212 of non-conductive material forming a tunnel junction that facilitates wave-mixing based amplification, as described here above.

[0066] In accordance with certain embodiments of the present invention, the first electrode 211 and the second electrode 212 may comprise aluminium. In such embodiments, the weak link interposed between the first electrode 211 and the second electrode 212 at the area of overlap may comprise aluminium oxide. The skilled person will nevertheless appreciate that the first and second electrodes 211, 212 may comprise alternative materials that exhibit superconducting properties at cryogenic temperatures.

[0067] The Josephson junction 210 formed by the first electrode 211 and the second electrode 212 are arranged on a dielectric layer 208 that is comprised by a layer stack. The layer stack moreover comprises at least one grounded conductive layer 307 and a substrate 309 (see Fig. 3A). Possible configurations of the layer stack within the scope of the present disclosure will be elucidated here below with reference to Fig. 3A to Fig. 3C and Fig. 4A and Fig. 4B. In Fig. 2, only the dielectric layer 208 is visible.

[0068] The first and electrodes 211, 212 constituting the pair of electrodes forming the Josephson junction 210 each moreover comprise a respective first lengthwise segment 211a, 212a and a second lengthwise segment 211b, 212b. The first lengthwise segment 211a of the first electrode 211 and the first lengthwise segment 212a of the second electrode 212 each comprise the area of overlap defining the Josephson junction 210. The size or surface area of the area of overlap is an important characteristic of the Josephson junction 210, because it defines the critical current I of the Josephson junction 210, which in turn is selected in consideration of the input signal (e.g. a signal emitted by a superconducting qubit) to be amplified. As such, the respective widths D211a, D212a of the first lengthwise segment 211a, 212a are in practice fixed with respect of the application of the JTWPA 200, 300. As can be discerned from Fig. 2, this size or surface area of the area of overlap is effectively defined by the respective widths D211a, D212a of the first lengthwise segment 211a, 212a of the first and second electrodes 211, 212.

[0069] Each of the first and second electrodes 211, 212 moreover comprises a respective second lengthwise segment 211b, 212b different from the respective first lengthwise segments 211a, 212a. The respective second lengthwise segments 211b, 212b are each arranged opposite the first lengthwise segment 211a, 212a on their respective electrodes 211, 212.

[0070] The widths D211a, D212a and D211b, D2126 of, respectively, the first lengthwise segments 211a, 212a and the second lengthwise segments 211b, 212b may alternatively be referred to as "diameters" D211a, D212a, D211b and D212b.

[0071] As can be discerned from Fig. 2 in conjunction with Fig. 3A, the respective enlarged widths D211b, D212b, each extend orthogonal to respective lengthwise directions of the first and second electrodes 211, 212; and substantially parallel to the conductive layer 307. It is noted that in the top-down view of Fig. 2, the conductive layer 307 is arranged underneath the dielectric layer 208.

[0072] The first electrode 211 and the second electrode 212 are conductors and therefore exhibit an intrinsic capacitance when arranged in the vicinity of other conductors and separated by a dielectric. In accordance with the present invention, the respective enlarged widths D211b, D212b of the second lengthwise segments 211b, 212b are dimensioned such that the second lengthwise segments 211b, 212b form capacitive structures with the conductive layer 307 disposed underneath the dielectric layer 208, 308. In other words, according to the present invention the intrinsic capacitances of the first electrode 211 and second electrode 212 are leveraged to implement the capacitor structures 111, 112, 113 shown in the electrical circuit of Fig. 1, by forming the first and second electrodes 211, 212 to comprise said enlarged width.

[0073] The here above described configuration of the first and second electrodes 211, 212 renders the inclusion of additional discrete capacitors, such as additional (parallel plate) capacitors and capacitors comprising return conductors as found in coplanar waveguides, to be redundant. Such additional discrete capacitors thus do not need to be included for achieving a characteristic impedance of the JTWPA 200, which is typically 50 Ω. The JTWPA 200 may therefore be formed with smaller dimensions and with an increased degree of miniaturisation.

[0074] In Fig. 2, the second lengthwise segments 211b, 212b of the first and second electrodes 211, 212 have their respective widths D2116, D2126 enlarged and the second lengthwise segments 211b, 212b each comprise a substantially square shape. It will be appreciated that the present disclosure is not limited thereto and that the second lengthwise segments 211b, 212b may alternatively comprise e.g. circular shapes and polygonal shapes that preferably comprise equally dimensioned sides.

[0075] In embodiments wherein the JTWPA 200 including the at least one Josephson junction 210 is fabricated using angled evaporation or a comparable fabrication technique, certain shapes of the second lengthwise segments 211b, 212b result in better fabrication results than others. A preferred method for fabricating a JTWPA 100, 200 based on angled evaporation or comparable fabrication techniques is elucidated here below with reference to Fig. 3A to 3C.

[0076] Regardless of their shape, the second lengthwise segments 211b, 212b may comprise enlarged widths D211b, D2126 such that their respective surface areas comprise 3 µm² to 1000 µm², more preferably 6 µm² to 600 µm², most preferably 10 µm² to 150 µm².

[0077] Fig. 3A shows a perspective view of a workpiece 300 that is subjected to a method in accordance with the present disclosure to thereby obtain the JTWPA 200 of Fig. 2.

[0078] The workpiece 300 constitutes (part of) a TWPA and comprises a substrate layer 309, a conductive or electrical ground layer 307 arranged on the substrate layer 309 and a dielectric layer 308 arranged on the conductive layer 307 opposite the substrate layer 309. A photoresist 306 is arranged on the dielectric layer 308 opposite the conductive layer 307.

[0079] In a method for obtaining a JTWPA 100, 200 in accordance with certain embodiments of the present invention, the photoresist 306 of the workpiece 300 is subjected to an exposure process followed by a development process to etch a predefined pattern in the photoresist 306, exposing the dielectric layer 308 underneath. From Fig. 3A it can be discerned that the etched pattern comprises two elongate patterns that intersect with one another and are formed by selectively removing the material of the photoresist 306. The elongate patterns both comprise a respective narrowed section 311a', 312a' and a respective enlarged section 311b', 312b'.

[0080] Fig. 3B shows the workpiece 300 of Fig. 3A in a state following the state of the workpiece 300 depicted in Fig. 3A.

[0081] In Fig. 3A, the first electrode 311 has been formed within the elongate pattern including narrowed section 311a' and enlarged section 311b'. Here, the first lengthwise segment 31 la of the first electrode 311 is formed in the narrowed section 311a' and its second lengthwise segment 311b is formed in the enlarged section 311b' of the etched pattern. The first electrode 311 is formed using angled evaporation. Angled evaporation, and substantially similar or comparable fabrication techniques involving deposition of evaporated metal at an angle, may also be referred to as the Niemeyer-Dolan technique, shadow evaporation, angular evaporation and tri-angle deposition.

[0082] Angled evaporation involves conductive material (e.g. vaporised aluminium) being deposited onto the workpiece 300 from a crucible (not shown) from a disposition direction at an angle relative to the workpiece 300, to thereby form the first electrode 311. In Fig. 3B, the angled evaporation deposition direction is indicated by the arrow at the righthanded side of the figure.

[0083] When conductive material is deposited onto the workpiece 300 from the deposition direction depicted in Fig. 3B, the dielectric layer 308 within the narrowed section 311a' is entirely covered by the deposited conductive material. In contrast, the enlarged section 311b' is only partially covered by the deposited conductive material, leaving a small area 399 of the dielectric layer 308 along the edge of the enlarged section 311b' exposed. At this partial circumferential area 399 of the enlarged section 311b', the conductive material is blocked by the photoresist 306 before it can reach the dielectric layer 308. In other words, the photoresists 306 casts a 'shadow' in this area 399.

[0084] It is noted that in Fig. 3A, no deposited conductive material is present within the second elongate pattern other than within where its narrowed section 312a' overlaps with the narrowed section 31la' of the elongate pattern, the deposition of conductive material here being blocked by the photoresist 306.

[0085] The conductive material deposited onto the workpiece 300 using angled evaporation may be vaporised aluminium or any other suitable material that exhibits superconducting properties at cryogenic temperatures.

[0086] Following the deposition of conductive material illustrated in Fig. 3A, an oxidation layer (not shown) may be formed on the deposited conductive material. For example, a layer of aluminium oxide may be formed on the deposited conductive material by briefly introducing oxygen into an enclosure in which the workpiece 300 is contained and which is otherwise kept hermetically sealed from its environment. Aluminium oxide may constitute the weak link at the area of overlap between the first electrode 211 and the second electrode 212 forming the Josephson junction 210 in Fig. 2.

[0087] Fig. 3C shows the workpiece 300 of Fig. 3A and Fig. 3B in a state following the state of the workpiece depicted in Fig. 3B. The workpiece 300 may have been rotated relative to a crucible (not shown) prior to the state depicted in Fig. 3C.

[0088] In Fig. 3C, the workpiece 300 has been subjected to a second iteration of the angled evaporation technique to thereby form the second electrode 312. The deposition direction is indicated by the arrows on the lefthanded side of this figure. The second electrode comprises a first lengthwise segment 312a formed in the narrowed section 312a' of the elongate pattern and a second lengthwise segment 312b formed in the enlarged section 312b' of the elongate pattern.

[0089] Similar to what is described here above with reference to Fig. 3B, the deposited conductive material covers the entire surface area of dielectric layer 308 within the narrowed section 312a', and only partially covers dielectric layer 308 within the enlarged section 312b' due to a shadow being cast in a peripheral area of the enlarged section 312b' by the photoresist 306. The now formed respective first lengthwise segments 31la and 311b now overlap with one another to form the area of overlap defining the Josephson junction 310. Again, no conductive material is deposited in an area 399' at the periphery of the enlarged section 312b', due to the photoresist 306 casting a shadow in this area 399'.

[0090] After completion of the fabrication step depicted in Fig. 3C, the photoresist 306 may be removed from the workpiece 300 along with any build-ups of excess deposited conductive material, to thereafter obtain the JTWPA 200 depicted of Fig. 2.

[0091] It will be appreciated that Fig. 3A to Fig. 3C merely depict the fabrication of a single Josephson junction 310 among a plurality of Josephson junctions comprised by a JTWPA 100, 200 in accordance with the present disclosure and invention. In practical implementations of the depicted method, multitudes of first electrodes 311 may be formed in a single angled evaporation deposition iteration and further multitudes of second electrodes 312 may be formed in a single second angled evaporation deposition iteration. As such, the many Josephson junctions 110, 120, 130, 210 comprised by the JTWPA 100, 200 may be fabricated very efficiently in a minimal number of fabrication steps and with a reduced manufacturing cycle time. With no subsequent fabrication steps required to form further components (e.g. parallel plate capacitors, interdigitated capacitors, and the like) to achieve the characteristic impedance of the transmission line 103, the transmission line 103 may be finalised immediately when all the Josephson junctions 310 are formed. A JTWPA 100, 200 in accordance with the present disclosure thus not only exhibits a high degree of miniaturisation due to the absence of additional capacitors, but is also particularly well suited to be fabricated using a highly efficient fabrication method, that in principle conducted exclusively using angled evaporation or comparable fabrication techniques, without requiring additional fabrication steps to form said additional capacitors.

[0092] From Fig. 3B and Fig. 3C, it can be discerned that the formed second lengthwise segments 211b, 212b each comprise a surface area that is smaller than a width or surface area of the enlarged sections 311b', 312b' in which they are respectively formed. As is explained here above, this results from the casting of shadows by the photoresist 306 within areas 399, 399', which is inherent to angled evaporation and other comparable fabrication techniques.

[0093] The enlarged sections 311b', 312b' etched into the photoresist 306 must therefore be designed and dimensioned to take the casting of shadows by the photoresist 306 into account, such that the successively formed second lengthwise segments 311b, 312b each comprise a substantially identical width D311b, D3126 resulting in respective surface areas matching a desired capacitance, regardless of the angled evaporation direction used to form them. Said desired capacitance in part determines the characteristic impedance (typically 50 2) of the JTWPA to prevent reflections of signals entering and leaving the JTWPA.

[0094] One possible shape for the enlarged sections 311b', 312b' that theoretically matches the above stated criteria is a substantially circular shape. A substantially circular shape for the enlarged sections 311b', 312b' comprises the advantage that the formed enlarged section 311b', 312b' at least theoretically always comprises a substantially identical width and surface area, regardless of which angled evaporation deposition direction is used and the angle between them. Substantially circular shapes for the enlarged sections 311b', 312b' moreover comprise the advantage that, regardless of the angle between the angled evaporation deposition direction, the obtained enlarged sections 311b', 312b' are always substantially identical, at least in theory.

[0095] Notwithstanding the above, consistency between second lengthwise segments 311b, 312b of respective electrodes 311, 312 may also be achieved with polygonal shapes having equally dimensioned sides. Such polygonal shapes must, however, be oriented in consideration of both of the angled evaporation deposition directions that are utilised. More specifically, these polygonal shapes must be oriented such that they exhibit rotational symmetry with respect to the first angled evaporation disposition direction (see Fig. 3B, the arrows on the righthanded side of the figure) and the second angled evaporation disposition direction (see Fig. 3C, the arrows on the lefthanded side of the figure).

[0096] Second lengthwise segments 311b, 312b comprising substantially circular shapes likewise exhibit rotational symmetry with respect to the first angled evaporation disposition direction and the second angled evaporation disposition direction, regardless of the angle between these different disposition directions. Nevertheless, substantially circular shapes have been found to result in a reduced consistency of the second lengthwise segments 311b, 312b relative to polygonal shapes (e.g. square shapes). Presumably, this results from the fact that circular shapes comprise curved edges, for which it is difficult to predict how shadows will be cast during an angled evaporation fabrication process.

[0097] In accordance with certain embodiments of the present invention, a first contour of the second lengthwise segment 311b, 312b of the at least one electrode 311, 312, when viewed in a first deposition direction (e.g. as indicated the arrows by the arrows at the righthanded side of Fig. 3B) of the angled evaporation fabrication technique, corresponds to a second contour of the second lengthwise segment 311b, 312b, when viewed in a second deposition direction (e.g. as indicated by the arrows at the lefthanded side of Fig. 3B) of the angled evaporation fabrication technique.

[0098] In practice, the angle between the first angled evaporation disposition direction and the second angled evaporation disposition direction is typically 90 degrees. When said angle is 90 degrees, it is particularly advantageous for the lengthwise segments 311b, 312b to comprise a substantially square shape, which is the case for the embodiments in the appended drawing. In said depicted embodiments, the substantially square lengthwise segments 311b, 312b are moreover oriented such that their diagonal coincides with the lengthwise directions of the at least one electrode 311, 312.

[0099] In accordance with more preferred embodiments, the diagonal of the second lengthwise segments 311b, 312b furthermore coincides with a horizontal vector component of at least one of the first (angled evaporation) deposition direction and the second (angled evaporation) deposition direction of the (angled evaporation) fabrication technique.

[00100] Fig. 2 and Fig. 3A to Fig. 3C depict an embodiment wherein the JTWPA 200 or workpiece 300 exhibits what may be referred to as a microstrip geometry. The present disclosure is, however, not limited thereto and Fig. 4A and Fig. 4B respectively depict alternative geometries.

[00101] With the method according to the present invention illustrated in Fig. 3A to Fig. 3B based on angled evaporation, the first lengthwise segment 311a and the second lengthwise segment 311b of the first electrode 311 are preferably integrally formed. Likewise, the first lengthwise segment 312a and the second lengthwise segment 312b of the second electrode 312 are preferably integrally formed.

[00102] Fig. 4A depicts a cross section of an alternative embodiment of the JTWPA 100, 200, 300 of the foregoing figures comprising an alternative geometry. The geometry of the embodiment depicted in Fig. 4B may be referred to as an inverse microstrip geometry that differs from the geometry of the foregoing figures in that the conductive layer 407 is arranged on top of the dielectric layer 408 and the substrate 409. In the embodiment of Fig. 4A, the dielectric layer 408 is interposed between the conductive layer 407 and the substrate 409. The dielectric layer 408 moreover encloses an electrode 412, which is effectively embedded within the dielectric layer 408. The electrode 412 may correspond to either the first electrode 211, 311 or the second electrode 212, 312 of the foregoing figures.

[00103] Fig. 4B depicts a cross section of a further alternative embodiment comprising a stripline geometry. In Fig. 4B, a first conductive layer 407' and a second conductive layer 407" are arranged on either side of the dielectric layer 408. The conductor 412', which may correspond to either the electrode 211, 311 or the second electrode 212, 312 of the foregoing figures, is embedded within the dielectric layer 408.

[00104] In accordance with various embodiments, the conductive layer may extend underneath or above each one of the plurality of Josephson junctions. In these embodiments, the single conductive layer may form capacitive structures with each second lengthwise segments having the enlarged widths, and the conductive layer is preferably electrically grounded. Furthermore, in these embodiments the JTWPA may be free capacitive structures that are not arranged underneath or above the Josephson junctions or its transmission but laterally thereof, whether they be planar shunt capacitors or parallel plate capacitors.

[00105] Fig. 5 shows a schematic depiction of a transmission line 503 corresponding to the transmission line in Fig. 1. The transmission line 503 comprises a plurality of Josephson junctions 210 corresponding to the embodiment depicted in Fig. 2. The number of Josephson junctions 210 may be selected in consideration of a required degree of amplification of an input signal. As such, the number of Josephson junctions included in the transmission line 503 may be several hundred or several thousand.

[00106] The transmission line 503 of. Fig. 5A is arranged in a pattern that optimises the number of Josephson junctions per unit of surface area. As such, the transmission line 503 is arranged in an alternating or zig-zagging pattern, comprising longitudinal sections 551 of the transmission line 503 alternating with turn sections 562, after which the transmission line has made a 180 degree turn. While it is conceivable that other meandering patterns (e.g. circular) may be utilised, a transmission line 103 comprising Josephson junctions according to the present invention is particularly well suited to implement the meandering pattern of the transmission line 503 of Fig. 5A. This will be made apparent with reference to Fig. 5B and Fig. 5C, which respectively depict microscopic views 551', 562' of the longitudinal sections 551 and the turn sections 562.

[00107] Fig. 5B shows a microscopic view of one of the longitudinal sections 550 of the transmission line 503 of Fig. 5A. From Fig. 5B, it can be discerned that consecutive electrodes 511, 512, 513, 514, 515 form a first substructure 551' that encompasses consecutive Josephson junctions 510, 520, 530, 540.

[00108] The first substructure 551' comprises a first Josephson junction 510 that with a first electrode 511 and a second electrode 512, that overlap form the first Josephson junction 510. The second electrode 512 and a third electrode 513 overlap to define a second Josephson junction 520, with the second electrode 512 being arranged between the first electrode 511 and the third electrode 513. The third electrode 513 overlaps with a fourth electrode 514 to define a third Josephson junction 530. Here, the third electrode 513 is arranged between the second electrode 512 and the fourth electrode 514. The fourth electrode 514 extends towards a fourth Josephson junction 540, which is formed by the fourth electrode 514 overlapping with a fifth electrode 515.

[00109] The first substructure 551', comprising the consecutive electrodes 511, 512, 513, 514, 515 overlapping to form the consecutive Josephson junctions 510, 520, 530, 540, may thus be considered to exhibit a U-like shape; with a plurality of these first substructures 551' arranged sequentially mirrored along opposing sides of the dashed heartline 588 in Fig. 5B, forming the longitudinal sections 551 of the transmission line 503.

[00110] In certain embodiments, the first electrode, the third electrode 513 and the fifth electrode 515 all extend lengthwise parallel to one another in a single first meandering direction coinciding with a diagonal direction of the substantially square shaped second lengthwise segments of each of the first, third and fifth electrodes 511, 513, 515. In these embodiments, said first direction meandering may moreover coincide with a horizontal vector component of a first deposition direction of the angled evaporation fabrication technique.

[00111] Likewise, it can be discerned from Fig. 5B that the second electrode 512 and the fourth electrode 514 also extend parallel to one another in a second meandering direction. In embodiments wherein the deposition directions of the angled evaporation fabrication technique intersect one another at 90 degrees, the second meandering direction may be perpendicular to the aforementioned first meandering direction. This second meandering direction preferably coincides with a horizontal vector component of a second deposition direction of the angled evaporation fabrication technique, and with diagonal directions of the respective substantially square shaped second lengthwise segments of both of the second electrode 512 and the fourth electrode 514. Consequently, the first substructure 551' of Fig. 5A is easily fabricated using the fabrication method described here above with reference to Fig. 3A to Fig. 3C.

[00112] The first electrode 511 and the fifth electrode may be arranged at an offset in the first meandering direction. The first electrode 511 and the third electrode 513 may be arranged at an offset in the second meandering direction. The third electrode and the fifth electrode 515 may be arranged at an offset in the second meandering direction. The second electrode 512 and the fourth electrode 514 may be arranged at an offset in the first meandering direction.

[00113] The longitudinal sections 551 of Fig. 5A are preferably connected to one another via turn sections 562. Fig. 5C shows a microscopic view of a turn section 562, which will be referred to as a second substructure 562' of the transmission line 503.

[00114] Fig. 5C shows that said second substructure 560' comprises a fifth Josephson junction 550 with a sixth electrode 516 and a seventh electrode 517 that overlap one another to define the fifth Josephson junction 550. The seventh electrode 517 moreover overlaps with an eight electrode 518 to form the sixth Josephson junction 560. The second substructure 560' moreover comprises a seventh Josephson 570 junction having the eight electrode 518 overlapping with a nineth electrode 519. Lastly, the second substructure 560' comprises an eight Josephson junction 580 where the nineth electrode 519 overlaps with a tenth electrode 521.

[00115] In Fig. 5C, the seventh electrode 517 and the nineth electrode 519 extend substantially parallel to one another in a third direction. In embodiments wherein the transmission line 503 comprises both the here above described first substructure 551' and the second substructure 562', this third direction may be the first direction referred to in relation to Fig. 5B.

[00116] Likewise, in Fig. 5C the sixth electrode 516, the eight electrode 518 and the tenth electrode 521 extend substantially parallel to one another in a fourth direction. The fourth direction may be substantially perpendicular to the third direction of Fig. 5B. In embodiments wherein the transmission line 503 comprises both the first substructure 551' and the second substructure 560', the fourth direction may correspond to the second direction of referred to in relation to Fig. 5B.

[00117] Fig. 6A and Fig. 6B show a transmission line 603 of a JTWPA in accordance with additional embodiments of the present invention. The embodiment depicted in Fig. 6A and Fig. 6B comprises additional measures for achieving phase matching between the input signal to be amplified and the pump signal. As such, in these embodiments the one or more phase matching resonators 107 (see Fig. 1) may be reduced or even omitted entirely.

[00118] As explained here above with reference to Fig. 1, the impedance of the transmission line 103 is predefined to prevent unwanted reflections, and typically comprises 50 Ω. In the embodiment of Fig. 6A and 6B, the impedance of the transmission line 603 is periodically modulated, e.g. from 48 Ω to 52 Ω, to thereby engineer a phase matching stopband in the dispersion relation of the transmission line. As such, phase matching between the input signal to be amplified and the pump signal may be achieved without using a discrete phase matching resonator 107, as is the case in the embodiment of Fig. 1.

[00119] The impedance of the transmission line 603 may be periodically modulated by periodically modulating one or both of the capacitance and inductance (or critical current) of each Josephson junction 610, 620, 630. In the exemplary embodiment of Fig. 6A and Fig. 6B, both of the capacitance and the inductance are periodically modulated.

[00120] In Fig. 6B, the capacitance of the second lengthwise segments 611b, 612b, 613b of the consecutive electrodes 611, 612, 613 is represented by the respective symbol sizes of capacitors C611b, C612b, C613b. From Fig. 6B, it can be discerned that the second lengthwise segments 611b of electrode 611 comprises a capacitance C6116 that is larger than a capacitance C6126 of second lengthwise segments 612b of electrode 612. Similarly, the second lengthwise segments 612b of electrode 612 comprises a capacitance C6126 that is larger than a capacitance C6136 of second lengthwise segments 613b of electrode 613. In other words, in the embodiment of Fig. 6B the capacitance of consecutive electrodes 611, 612, 613, 614 periodically modulated by periodic modulation of respective widths D611b, D612b, D613b, D614b of the second lengthwise segments 611b, 612b, 613b, 614b of consecutive electrodes 611, 612, 613, 614 forming the plurality of Josephson junctions 610, 620, 630 constituting the transmission line 603.

[00121] The inductance of Josephson junctions 610, 620, 630 is inversely proportional to their respective areas of overlap and their respective critical currents. In Fig. 6B, the symbol size of the Josephson junctions 610, 620, 630 represents their respective critical currents. Thus, from Fig. 6B it can be discerned that Josephson junction 610 comprises a larger critical current than neighbouring Josephson junction 620 and a correspondingly smaller inductance than neighbouring Josephson junction 620. Josephson junction 620 in turn comprises a larger critical current and smaller inductance than neighbouring Josephson junction 630.

[00122] Referring now to Fig. 6A, the partially shown transmission line 603 comprises a plurality of electrodes 611, 612, 613, 614 that collectively form three Josephson junctions 610, 620, 630 among additional Josephson junctions of the transmission line 603. Each electrode 611, 612, 613, 614 comprises a respective second lengthwise segment 611b, 612b, 613b, 614b with a respective enlarged width D6116, D612b, D613b, D614b.

[00123] The embodiment of Fig. 6A differs from e.g. the embodiment depicted in Fig. 2 with respect to the relative dimensions of the respective widths D6116, D612b, D613b, D6146 of the second lengthwise segments 611b, 612b, 613b, 614b of consecutive electrodes 611, 612, 613, 614. From Fig. 6A, it can be discerned that the widths D6116 of the second lengthwise segment 611b of electrode 611 is larger than the width D6126 of the second lengthwise segment 612b of electrode 612. Similarly, said width D6126 of the second lengthwise segment 612b of electrode 612 is larger than the width D6136 of the second lengthwise segment 613b of electrode 613. The second lengthwise segment 614b of electrode 614 comprises a width D6146 larger than the width D6136 of the second lengthwise segment 613b of the electrode 613.The second lengthwise segments 611b, 612b, 613b, 614b of consecutive electrodes 611, 612, 613, 614 thus exhibit variance with respect to their respective enlarged width D6116, D612b, D613b, D6146. The varying widths D611b, D612b, D613b, D614b of consecutive electrodes 611, 612, 613, 614 modulate periodically, wherein the respective widths D6116, D612b, D613b, D614b of second lengthwise segments 611b, 612b, 613b, 614b of consecutive electrodes 611, 612, 613, 614 incrementally increase and incrementally decrease along the length of the transmission line 603. As depicted in Fig. 6B, this results in the period modulation of the respective capacitances C611b, C612b, C613b of the second lengthwise segments 611b, 612b, 613b. The periodic modulation of the respective widths D611b, D612b, D613b, D614b of the second lengthwise segments 611b, 612b, 613b, 614b, and consequently the capacitances C611b, C612b, C613b, follow a sinusoidal course having a first period.

[00124] Referring again to Fig. 6A, the consecutive first lengthwise segments 611a, 612a, 612a', 613a, 613a', 614a of consecutive electrodes 611, 612, 613, 614 likewise exhibit variance with respect to their widths D611a, D612a, D613a, D614a. Specifically, electrode 611 comprises a first lengthwise segment 611a having a width D611a equal to the width D612a of the first lengthwise segment 612a of electrode 612; and larger than the respective widths D612a' and D613a of the respective first lengthwise segments 612a', 613a of electrodes 612 and 613. Similarly, the respective widths D612a and D613a of the first lengthwise segments 612a' and 613a may be equal to one another and each larger than the respective widths D613a' and D614a of the first lengthwise segments 613a', 614a.

[00125] Hence, the respective areas of overlap of the consecutive Josephson junctions 610, 620, 630 likewise exhibit variance with respect to their respective sizes. Specifically, Josephson junction 610 comprises a larger area of overlap than Josephson junction 620, which in turn comprises a larger area of overlap than Josephson junction 630. The variance in respective areas of overlap of consecutive Josephson junctions 610, 620, 630 may likewise follow a sinusoidal course, having a second period.

[00126] Because the critical current of each Josephson junction 610, 620, 630 is inversely proportional to their respective area of overlap, Josephson junction 610 comprises a critical current larger than Josephson junction 620, which in turn comprises a critical current larger than Josephson junction 630. Because the inductance of Josephson junctions 610, 620, 630 is inversely related to their respective areas of overlap and critical currents, Josephson junction 610 comprises a smaller inductance than Josephson junction 620, which in turn comprises a smaller inductance to Josephson junction 630.

[00127] The respective overlaps (see the dashed encirclements in Fig. 6A) of consecutive Josephson junctions 610, 620, 630 are defined by the respective first lengthwise segments 611a, 612a, 612a', 613a, 613a', 614a constituting said overlaps.

[00128] In other words, in the embodiment of Fig. 6A and Fig. 6B the inductance of the transmission line 603 is periodically modulated by periodic modulation of respective widths D611a, D612a, D612a', D613a, D613a', D614a of first lengthwise segments 611a, 612a, 612a', 613a, 613a', 614a of the consecutive electrodes 611, 612, 613, 614, such that electrode pairs constituting consecutive Josephson junctions 610, 620, 630 comprise periodically modulating areas of overlap (indicated by the dashed line encirclements in Fig. 6B).

[00129] Periodic modulation of the impedance of the transmission line 603 may thus be achieved by periodically modulating the capacitance, the inductance, or both the capacitance and the inductance of electrodes 611, 612, 613, that form the Josephson junctions 610, 620, 630 constituting the transmission line 603. The impedance of the transmission line is periodically modulated to define a phase matching stopband in the dispersion relationship of the transmission line 603, i.e. a frequency band at which signals are absorbed and dissipation of energy occurs. This phase matching stopband matches a frequency of the pump signal used in the parametric amplification of the input signal to be amplified, causing the pump signal to acquire a positive phase shift. Careful control of the pump signal frequency and pump power results in this positive phase shift cancelling out the aforementioned negative phase shift, thereby achieving the phase matching required for amplification of the signal tone.

[00130] It will be appreciated that in the embodiment of Fig. 6A and Fig. 6B, the inclusion of discrete phase matching resonators 107 (see Fig. 1) may be redundant. Instead, adequate phase matching may be achieved with the incrementally varying widths of the first lengthwise segments 611a, 612a, 613a and the second lengthwise segments 611b, 612b, 613b of the consecutive electrodes 611, 612, 613. A JTWPA in accordance with the embodiment of Fig. 6A and Fig. 6B may therefore exhibit an enhanced degree of miniaturisation and can moreover be fabricated using the efficient fabrication process as described here above with reference to Fig. 3A to Fig. 3B. This efficient fabrication process may not include additional steps for fabricating discrete phase matching resonators 107.

[00131] With no subsequent fabrication steps required to form further components (e.g. the phase marching resonator 107 of Fig. 1, and the like) to achieve the characteristic impedance of the JTWPA, the transmission line 603 may be finalised immediately when all the Josephson junctions 610, 620, 630 are formed. A JTWPA in accordance with the embodiment of Fig. 6 therefore not only exhibits a high degree of miniaturisation due to the absence of additional phase matching resonators, but is moreover particularly well suited to be fabricated using a highly efficient fabrication method, that may in principle be conducted exclusively using angled evaporation or comparable fabrication techniques, without requiring additional fabrication steps to form said additional phase matching resonators.

[00132] The aforementioned first and second periods may be determined with respect to various other parameters of the of the JTWPA and / or the input signal to be amplified. The skilled person is aware that these periods may be determined by solving the relevant wave equations, e.g. using specialised simulation software, or the like.

[00133] Fig. 7 schematically depicts an exemplary embodiment of a system 780 in accordance with a further aspect of the present disclosure and invention. In the exemplary embodiment of Fig. 7, the system 780 is (part of) a quantum computing system. However, the present disclosure is not limited thereto and it will be appreciated that it is entirely conceivable that the system 780 is of an alternative nature. The system 780 may, for example, constitute an astronomical measurement system for measuring weak astronomical signals.

[00134] Notwithstanding the above, the system 780 of Fig. 7 comprises a measurement object 710 embodied by a qubit 710. More than one qubit 710 may be present within the system 780, of which only one is shown in Fig. 7. In embodiments of the system 780 that are not quantum computing systems, the measurement object 710 may be constituted by e.g. a detector configured to detect cosmic microwave background, or the like.

[00135] The qubit 710 may emit a signal representing a quantum state of the qubit 780 and is connected to a JTWPA 700 via an isolator 740 and a directional coupler 760. Said signal emitted by the qubit 710 constitutes the input signal in the description here above with reference to the foregoing figures. The isolator 740 is included to prevent any back-action stemming from additional components from reaching the qubit 710, which is extremely sensitive and is therefore preferably protected.

[00136] The pump signal is generated by a wave generator 720 connected to the directional coupler 760 via a plurality of attenuators 730, 730', 730'". The directional coupler 760 feeds the input signal from the qubit 710 to the JTWPA 700 together with a pump signal via an input (not shown). Alternatively, two inputs may be present for separately feeding the input signal and the pump signal into the JTWPA 700. In such embodiments, the directional coupler 760 may be integrated within a housing of the JTWPA 700.

[00137] Upon reaching the JTWPA 700, the input signal is amplified based on the pump signal as described here above with reference to the foregoing figures. The JTWPA 700 of Fig. 7 is equivalent to the JTWPA 200 of Fig. 2.

[00138] At its other end, the JTWPA 700 is connected to an output 790 via first and second high-electron-mobility transistors 782, 784, a high / low pass filter 770, and first and second isolators 742, 744. The output 790 may be constituted by a digitiser or the like. The first high-electron-mobility transistors (HEMT) 782 and second HEMT 784 are included in the system 780 to further amplify the input signal, because the JTWPA 700 by itself may not produce sufficient gain to facilitate a readout of the amplified input signal. First and second isolators 742, 744 are included to prevent noise generated by the first and second HEMTs 782, 784 from reaching the JTWPA 700 and / or the qubit 710. The low / high pass filter 770 filters out the pump signal, which may simplify readout of the amplified input signal by means of digitiser 790.

[00139] With reference to Fig. 2, in certain embodiments of a JTWPA in accordance with the present disclosure the second lengthwise segments 211b, 212b having the relatively enlarged width D211b, D212b may alternatively or additionally be arranged at the free ends 211', 212' of their respective electrodes 211, 212.

[00140] Disclosed is furthermore a Josephson travelling wave parametric amplifier (JTWPA) in accordance with the following clauses.

[00141] Clause 1: a Josephson travelling wave parametric amplifier, JTWPA, comprising: a conductive layer; a dielectric layer; and a plurality of Josephson junctions comprised by a transmission line, wherein each Josephson junction comprises a pair of electrodes that extend towards each other to define an area of overlap, wherein at least one electrode of one or more of the pairs of electrodes comprises: a first lengthwise segment comprising at least the area of overlap; and a second lengthwise segment opposite the first lengthwise segment, wherein the second lengthwise segment of said at least one electrode comprises a width (extending orthogonal to a lengthwise direction of the electrode and substantially parallel to the conductive layer), said width being larger than a width of the first lengthwise segment, whereby the second lengthwise segment having the enlarged width, in conjunction with the conductive layer and the dielectric layer, defines a capacitive structure that at least partially defines a characteristic impedance of the JTWPA.

[00142] Clause 2: the JTWPA of clause 1, wherein the plurality of Josephson junctions is arranged in a meandering arrangement pattern, wherein turns of the meandering arrangement pattern are defined by respective first lengthwise segments comprising the area of overlap of neighbouring electrode pairs of consecutive Josephson junctions.

[00143] Clause 3: the JTWPA of clause 2, wherein the meandering pattern of the plurality Josephson junctions comprise a first substructure, comprising: a first Josephson junction comprising a first electrode and a second electrode; a second Josephson junction comprising the second electrode and a third electrode, wherein the second electrode is interposed between the first electrode and the third electrode; a third Josephson junction comprising the third electrode and a fourth electrode, wherein the third electrode is interposed between the second electrode and the fourth electrode; and a fourth Josephson junction comprising the fourth electrode and a fifth electrode, wherein the fourth electrode is interposed between the between the third electrode and the fifth electrode; wherein the first electrode, the third electrode and the fifth electrode extend parallel to one another in a first direction; and the second electrode and the fourth electrode extend parallel to one another in a second direction.

[00144] Clause 4: the JTWPA of clause 2 or 3, wherein the meandering pattern of the plurality Josephson junctions comprises a second substructure, comprising: a fifth Josephson junction comprising a sixth electrode and a seventh electrode; a sixth Josephson junction comprising the seventh electrode and an eight electrode; a seventh Josephson junction comprising the eight electrode and a nineth electrode; and an eight Josephson junction comprising the nineth electrode and a tenth electrode, wherein the sixth electrode, the eight electrode and the tenth electrode extend substantially parallel to one another in a third direction, and the seventh electrode and the nineth electrode extend substantially parallel to one another in fourth direction.

[00145] Clause 5: the JTWPA of any one of the foregoing clauses, wherein the first lengthwise segment and the second lengthwise of the at least one electrode segment are integrally formed.

[00146] Clause 6: the JTWPA of clause 5, wherein the first lengthwise segment and the second lengthwise segment are formed in a single iteration of a fabrication technique, preferably a single iteration of an angled evaporation fabrication technique.

[00147] Clause 7: the JTWPA of clause 6, wherein the second lengthwise segment comprises a shape that is substantially circular or polygonal with a plurality of equally dimensioned sides.

[00148] Clause 8: the JTWPA of clause 6 or 7, wherein a first contour of the second lengthwise segment, when viewed in a first deposition direction of the fabrication technique, corresponds to a second contour of the second lengthwise segment, when viewed in a second deposition direction of the fabrication technique; and / or wherein the second lengthwise segment exhibits rotational symmetry with respect to the first deposition direction and the second deposition direction of the fabrication technique.

[00149] Clause 9: the JTWPA of clause 8, wherein the second lengthwise segment comprises a substantially square shape.

[00150] Clause 10: the JTWPA of clause 9, wherein the second lengthwise segment having the square shape is oriented such that a diagonal of the second lengthwise segment coincides with a lengthwise direction of the at least one electrode.

[00151] Clause 11: the JTWPA of clause 10, wherein the diagonal of the second lengthwise segment furthermore coincides with a horizontal vector component of at least one of the first deposition direction and the second deposition direction of the fabrication technique.

[00152] Clause 12: the JTWPA of any one of the foregoing clauses, wherein the second lengthwise segment comprises a surface area of 3 µm² to 1000 µm², more preferably of 6 µm² to 600 µm², most preferably of 10 µm² to 150 µm².

[00153] Clause 13: the JTWPA of any one of the foregoing clauses, wherein one or both of a capacitance and an inductance of the transmission line is periodically modulated, whereby the impedance of the transmission line is periodically modulated, such that a phase matching stopband is defined in a dispersion relationship of the transmission line.

[00154] Clause 14: the JTWPA of clause 13, wherein the inductance of the transmission line is periodically modulated by periodic modulation of respective widths of first lengthwise segments of consecutive electrodes, such that electrode pairs constituting consecutive Josephson junctions comprise periodically modulating areas of overlap.

[00155] Clause 15: the JTWPA of clause 13 or 14, wherein the capacitance of the transmission line is periodically modulated by periodic modulation of respective widths of the second lengthwise segments of consecutive electrodes forming the plurality of Josephson junctions constituting the transmission line.

[00156] Disclosed is furthermore a quantum computing system in accordance with the following clause.

[00157] Clause 16: a quantum computing system, comprising at least: at least one measurement object, such as a quantum bit, qubit; and at least one JTWPA according to any one of the foregoing clauses.

[00158] Disclosed is furthermore a Josephson travelling wave parametric amplifier (JTWPA) in accordance with the following clauses.

[00159] Clause 17: a method for obtaining a JTWPA, comprising: providing a layer stack comprising a substrate, a conductive layer, a dielectric layer and a resist, subjecting the layer stack to an exposure process followed by a development process, to thereby remove the resist at areas corresponding to respective Josephson junctions to be formed, forming a plurality of Josephson junctions each comprising a pair of electrodes that extend towards each other to define an area of overlap, wherein the method further comprises: forming at least one electrode of one or more of the pairs of electrodes to comprise: a first lengthwise segment comprising an area of overlap with a neighbouring electrode; and a second lengthwise segment opposite the first lengthwise segment, wherein said second lengthwise segment is formed to comprise a width extending orthogonal to a lengthwise direction of the electrode and substantially parallel to the conductive layer, said width being larger than a width of the first lengthwise segment.

[00160] Clause 18: the method of clause 17, wherein the step of forming the plurality of Josephson junctions comprises: forming the plurality of Josephson junctions in a meandering arrangement pattern, wherein turns of the meandering arrangement pattern are defined by respective first lengthwise segments comprising the area of overlap with a neighbouring electrode of consecutive Josephson junctions, wherein the meandering arrangement pattern is preferably formed to comprise a first substructure, comprising: a first Josephson junction comprising a first electrode and a second electrode; and a second Josephson junction comprising the second electrode and a third electrode, wherein the second electrode is interposed between the first electrode and the third electrode, wherein the first and third electrode extend parallel to one another in a first meandering direction of the meandering pattern, and the second electrode extends in a second meandering direction of the meandering pattern perpendicular to the first meandering direction, wherein consecutive first substructures are arranged mirrored along a heartline of the first substructure.

[00161] Clause 19: the method of clause 18, wherein the meandering arrangement pattern is formed to comprise a second substructure, comprising: a third Josephson junction comprising a fourth electrode and a fifth electrode; a fourth Josephson junction comprising the fifth electrode and a sixth electrode; a fifth Josephson junction comprising the sixth electrode and a seventh electrode; and a sixth Josephson junction comprising the seventh electrode and an eight electrode, wherein the fourth electrode, the sixth electrode and the eight electrode extend parallel to one another in the first meandering direction, and wherein the fifth electrode and the seventh electrode extend parallel to one another in the second meandering direction of the meandering pattern.

[00162] Clause 20: the method of any one of the foregoing clauses 17-19, wherein the first lengthwise segment and the second lengthwise of the at least one electrode segment are integrally formed, preferably in a single iteration of a fabrication technique, more preferably a single iteration of an angled evaporation fabrication technique.

[00163] Clause 21: the method of clause 20, wherein the second lengthwise segment is formed to comprise a shape that is substantially circular or polygonal with a plurality of equally dimensioned sides, wherein the second lengthwise segment is formed to exhibit rotational symmetry with respect to a first deposition direction and a second deposition direction of an angled evaporation fabrication technique.

[00164] It will be appreciated that the scope of the sought after protection is not limited to any one of the above described embodiments of the disclosed method and quantum computing circuitry apparatus. The skilled person will acknowledge that various components and features of the described embodiments can be combined with one another or otherwise modified. The scope of the sought after protection is therefore not limited to any one of the above listed practical applications or embodiments, but is defined solely by the features stated in the claims and, at least in certain jurisdictions, their equivalents.

Claims

1. A Josephson travelling wave parametric amplifier, JTWPA, comprising:a conductive layer;a dielectric layer; anda plurality of Josephson junctions comprised by a transmission line, wherein each Josephson junction comprises a pair of electrodes that extend towards each other to define an area of overlap,wherein at least one electrode of one or more of the pairs of electrodes comprises:a first lengthwise segment comprising at least the area of overlap; anda second lengthwise segment opposite the first lengthwise segment,wherein the second lengthwise segment of said at least one electrode comprises a width larger than a width of the first lengthwise segment, whereby the second lengthwise segment having the enlarged width, in conjunction with the conductive layer and the dielectric layer, defines a capacitive structure that at least partially defines a characteristic impedance of the JTWPA, andwherein the first lengthwise segment and the second lengthwise of the at least one electrode segment are integrally formed.

2. The JTWPA of claim 1, wherein the plurality of Josephson junctions is arranged in a meandering arrangement pattern, wherein turns of the meandering arrangement pattern are defined by respective first lengthwise segments comprising the area of overlap of neighbouring electrode pairs of consecutive Josephson junctions.

3. The JTWPA of claim 2, wherein the meandering pattern of the plurality Josephson junctions comprise a first substructure, comprising:a first Josephson junction comprising a first electrode and a second electrode;a second Josephson junction comprising the second electrode and a third electrode, wherein the second electrode is interposed between the first electrode and the third electrode;a third Josephson junction comprising the third electrode and a fourth electrode, wherein the third electrode is interposed between the second electrode and the fourth electrode; anda fourth Josephson junction comprising the fourth electrode and a fifth electrode, wherein the fourth electrode is interposed between the between the third electrode and the fifth electrode;wherein the first electrode, the third electrode and the fifth electrode extend parallel to one another in a first direction; andthe second electrode and the fourth electrode extend parallel to one another in a second direction.

4. The JTWPA of claim 2 or 3, wherein the meandering pattern of the plurality Josephson junctions comprises a second substructure, comprising:a fifth Josephson junction comprising a sixth electrode and a seventh electrode;a sixth Josephson junction comprising the seventh electrode and an eight electrode;a seventh Josephson junction comprising the eight electrode and a nineth electrode; andan eight Josephson junction comprising the nineth electrode and a tenth electrode,wherein the sixth electrode, the eight electrode and the tenth electrode extend substantially parallel to one another in a third direction, andthe seventh electrode and the nineth electrode extend substantially parallel to one another in fourth direction.

5. The JTWPA of any one of the foregoing claims, wherein the first lengthwise segment and the second lengthwise segment are formed in a single iteration of a fabrication technique, preferably a single iteration of an angled evaporation fabrication technique.

6. The JTWPA of claim 5, wherein the second lengthwise segment comprises a shape that is substantially circular or polygonal with a plurality of equally dimensioned sides.

7. The JTWPA of claim 5 or 6, whereina first contour of the second lengthwise segment, when viewed in a first deposition direction of the fabrication technique, corresponds to a second contour of the second lengthwise segment, when viewed in a second deposition direction of the fabrication technique; and / orwherein the second lengthwise segment exhibits rotational symmetry with respect to the first deposition direction and the second deposition direction of the fabrication technique.

8. The JTWPA of claim 7, wherein the second lengthwise segment comprises a substantially square shape.

9. The JTWPA of claim 8, wherein the second lengthwise segment having the square shape is oriented such that a diagonal of the second lengthwise segment coincides with a lengthwise direction of the at least one electrode.

10. The JTWPA of claim 9, wherein the diagonal of the second lengthwise segment furthermore coincides with a horizontal vector component of at least one of the first deposition direction and the second deposition direction of the fabrication technique.

11. The JTWPA of any one of the foregoing claims, wherein the second lengthwise segment comprises a surface area of 3 µm² to 1000 µm², more preferably of 6 µm² to 600 µm², most preferably of 10 µm2 to 150 µm².

12. The JTWPA of any one of the foregoing claims, wherein one or both of a capacitance and an inductance of the transmission line is periodically modulated, whereby the impedance of the transmission line is periodically modulated, such that a phase matching stopband is defined in a dispersion relationship of the transmission line.

13. The JTWPA of claim 12, wherein the inductance of the transmission line is periodically modulated by periodic modulation of respective widths of first lengthwise segments of consecutive electrodes, such that electrode pairs constituting consecutive Josephson junctions comprise periodically modulating areas of overlap.

14. The JTWPA of claim 12 or 13, wherein the capacitance of the transmission line is periodically modulated by periodic modulation of respective widths of the second lengthwise segments of consecutive electrodes forming the plurality of Josephson junctions constituting the transmission line.

15. A quantum computing system, comprising at least:- at least one measurement object, such as a quantum bit, qubit; and- at least one JTWPA according to any one of the foregoing claims.

16. Method for obtaining a JTWPA, comprising:providing a layer stack comprising a substrate, a conductive layer, a dielectric layer and a resist,subjecting the layer stack to an exposure process followed by a development process, to thereby remove the resist at areas corresponding to respective Josephson junctions to be formed,forming a plurality of Josephson junctions each comprising a pair of electrodes that extend towards each other to define an area of overlap;wherein the method further comprises,forming at least one electrode of one or more of the pairs of electrodes to comprise:a first lengthwise segment comprising an area of overlap with a neighbouring electrode; anda second lengthwise segment opposite the first lengthwise segment, wherein said second lengthwise segment is formed to comprise a width larger than a width of the first lengthwise segment.

17. The method of claim 16, wherein the step of forming the plurality of Josephson junctions comprises:forming the plurality of Josephson junctions in a meandering arrangement pattern, wherein turns of the meandering arrangement pattern are defined by respective first lengthwise segments comprising the area of overlap with a neighbouring electrode of consecutive Josephson junctions,wherein the meandering arrangement pattern is preferably formed to comprise a first substructure, comprising:a first Josephson junction comprising a first electrode and a second electrode; anda second Josephson junction comprising the second electrode and a third electrode,wherein the second electrode is interposed between the first electrode and the third electrode,wherein the first and third electrode extend parallel to one another in a first meandering direction of the meandering pattern, and the second electrode extends in a second meandering direction of the meandering pattern perpendicular to the first meandering direction,wherein consecutive first substructures are arranged mirrored along a heartline of the first substructure.

18. The method of claim 17, wherein the meandering arrangement pattern is formed to comprise a second substructure, comprising:a third Josephson junction comprising a fourth electrode and a fifth electrode;a fourth Josephson junction comprising the fifth electrode and a sixth electrode;a fifth Josephson junction comprising the sixth electrode and a seventh electrode; anda sixth Josephson junction comprising the seventh electrode and an eight electrode,wherein the fourth electrode, the sixth electrode and the eight electrode extend parallel to one another in the first meandering direction, andwherein the fifth electrode and the seventh electrode extend parallel to one another in the second meandering direction of the meandering pattern.

19. The method of any one of the foregoing claims 16 - 18, wherein the first lengthwise segment and the second lengthwise of the at least one electrode segment are integrally formed, preferably in a single iteration of a fabrication technique, more preferably a single iteration of an angled evaporation fabrication technique.

20. The method of claim 19, wherein the second lengthwise segment is formed to comprise a shape that is substantially circular or polygonal with a plurality of equally dimensioned sides,wherein the second lengthwise segment is formed to exhibit rotational symmetry with respect to a first deposition direction and a second deposition direction of an angled evaporation fabrication technique.

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