High-temperature superconducting quantum bit with disorder-induced tunnel barrier

Abstract

The invention relates to high temperature superconducting qubits with disorder induced tunnel barriers. A superconducting qubit circuit and a method of forming a superconducting qubit are disclosed herein. A superconducting qubit circuit includes a superconducting qubit, where the superconducting qubit includes a tunnel junction in a superconducting material having a critical temperature above 1.2 K. The tunnel junction is formed from a disorder-induced tunnel barrier, where the disorder results from spatial crystal defects in the superconducting material.

Description

Technical Field

[0001] The present invention belongs to the field of quantum computing. Specifically, the present invention relates to a superconducting qubit circuit having a superconducting qubit including a tunnel junction, and a method of forming a superconducting qubit including a tunnel junction. Background Art

[0002] A quantum computer can solve certain classes of problems faster than a classical computer. This is achieved by using qubits (i.e., quantum mechanical two-level systems that can assume a quantum mechanical superposition of two states (“0” and “1”)) instead of classical bits, which can only be in either of the two states.

[0003] Challenges in implementing a quantum computer involve the implementation and manipulation of qubits. A promising approach is to use qubits based on tunnel junctions, such as Josephson junctions in (or between) superconductors. Cryogenic superconductors (e.g., elemental superconductors such as aluminum (Al)) have been used to form Josephson junctions and qubits with coherence times approaching one millisecond. In the urgent pursuit of emerging quantum technologies, technologies based on aluminum-based Josephson junctions and qubits have successfully demonstrated quantum supremacy and produced the first generation of commercial quantum computers.

[0004] However, despite the high quality and performance of Al Josephson junctions based on cryogenic superconductors and generally all qubit devices, they have some inherent limitations due to the relatively low quality factor of the Josephson junction (the quality factor or characteristic voltage of the junction can be defined as the product of its critical current and the value of the normal state resistance) and the low critical temperature and small superconducting gap of aluminum (i.e., approximately 1.2 K and approximately 50 GHz / 0.2 meV, respectively), which affect the dynamics of Al Josephson junctions and qubit devices and generally require an operating temperature in the low mK range. Additionally, due to the inherent superconducting properties of Al (such as the small superconducting gap), Al Josephson junctions are strongly affected by magnetic fields. The low operating temperature in particular poses significant technical challenges and costs to the operation of quantum computers including qubits based on cryogenic superconductors, such as the need to use a dilution refrigerator to cool the entire quantum processor and its components, including qubits and Josephson junctions. In addition to the need for a low operating temperature, the read and write frequencies of qubits including cryogenic superconductor Josephson junctions may also be limited. The same problems of qubits based on cryogenic superconductors also apply to the case of using such qubits in other quantum devices such as quantum sensors.

[0005] Although superconducting materials with a higher critical temperature and / or a larger superconducting energy gap compared to aluminum have been known for a long time, such materials typically pose other challenges, e.g., challenges regarding the fabrication of Josephson junctions in such materials and, in particular, challenges regarding the suitability of such devices for qubits. Summary of the Invention

[0006] Accordingly, an object of the present invention is to improve superconducting qubits to provide a higher operating temperature, a higher read and / or write frequency, an improved critical current, an improved quality factor, improved noise characteristics, an improved critical magnetic field, and / or a reduced sensitivity to magnetic fields.

[0007] This object is achieved by a superconducting qubit circuit having a superconducting qubit including a tunnel junction according to claim 1 and a method of forming a superconducting qubit including a tunnel junction according to claim 10. Embodiments of the present invention are detailed in the dependent claims.

[0008] According to a first aspect of the present invention, there is provided a superconducting qubit circuit including a superconducting qubit. The superconducting qubit includes a tunnel junction in a superconducting material having a critical temperature above 1.2 K. The tunnel junction is formed by a disorder-induced tunnel barrier, wherein the disorder is generated by spatial crystalline defects in the superconducting material.

[0009] In the context of the present disclosure, a qubit may represent a quantum mechanical two-level system, particularly a quantum mechanical two-level system suitable for quantum information processing. In some embodiments, the quantum mechanical two-level system may be an effective two-level system, i.e., in addition to the two levels (referred to as the "ground state" and the "excited state" respectively), one or more additional levels or states may be included, however, the one or more additional levels or states may be detuned or spaced far enough apart to avoid filling such states. A superconducting qubit may represent a qubit formed at least in part by a superconducting material (i.e., a material that exhibits vanishing resistance below a critical temperature), e.g., including one or more superconducting structures such as one or more superconducting islands, one or more superconducting electrodes, one or more superconducting contacts, and / or one or more superconducting wires or leads.

[0010] In the context of the present disclosure, a tunnel junction may refer, for example, to a junction, connection, or link between two (or more) structures, particularly superconducting structures, through which particles and / or quasiparticles, particularly Cooper pairs, can tunnel (e.g., from one of the two or more structures to another of the two or more structures). In other words, a tunnel junction may be formed by a tunnel barrier (e.g., including the tunnel barrier) separating the two or more structures. The tunnel junction may thus form a weak link between the two or more structures. The tunnel junction may in particular be a Josephson junction (JJ), e.g., a superconductor-insulator-superconductor Josephson junction (S-I-S), a superconductor-normal conductor-superconductor Josephson junction (S-N-S), a Josephson junction formed by a physical constriction (e.g., a point contact) between superconductors (S-c-S), or a combination thereof. The tunnel junction may be arranged, for example, between two superconducting structures (such as islands, electrodes, contacts, and / or wires) (e.g., connecting the two superconducting structures), particularly between a superconducting island and a larger superconducting reservoir (e.g., a superconducting structure much larger than the superconducting island, such as a reference electrode, e.g., a ground electrode / contact (e.g., a ground plane)). As used herein, a superconducting island may refer, for example, to a superconducting structure that has no (strong) superconducting link or connection to other superconducting structures. For example, the superconducting island may be electrically isolated from other superconducting structures except (preferably) one or more weak links, such as tunnel junctions. The tunnel junction may include a physical constriction, e.g., may have a smaller cross-sectional area than the superconducting structures coupled via the tunnel junction, preferably a much smaller cross-sectional area than theirs (e.g., less than 50% of it, in some examples less than 30% of it, and in one example less than 10% of it). In some examples, a superconducting qubit circuit, particularly a superconducting qubit, may include a plurality of tunnel junctions in a superconducting material, e.g., a pair of tunnel junctions (e.g., as part of a SQUID).

[0011] A superconducting qubit (hereinafter also simply referred to as a qubit) includes a superconducting material (e.g., formed in and / or by a superconducting material) in which a tunnel junction is formed. The term "superconducting material" as used herein may refer to a material that becomes superconducting below a corresponding critical temperature, i.e., exhibits vanishing resistance and / or expulsion of a magnetic field below the critical temperature. The qubit includes a superconducting material having a critical temperature higher than 1.2 K (i.e., a critical temperature higher than that of aluminum). Such a superconducting material may also be referred to herein as a "high-temperature superconducting material" or a "high-temperature superconductor", but does not imply any limitation on the material used (except for the aforementioned critical temperature). In particular, such materials are not limited to cuprate superconductors and / or superconductors having a critical temperature higher than the boiling point of liquid nitrogen ("high-temperature superconductors").

[0012] Superconducting materials can have a critical temperature of at least 1.5 K, in some examples at least 2.0 K, preferably at least 4.2 K (the boiling point of liquid helium), in some examples at least 5 K, most preferably at least 10 K, in one example at least 15 K, and in one example at least 20 K. The superconducting material can, for example, have a critical temperature between 4.2 K and 200 K, in some examples between 4.2 K and 50 K, in one example between 5 K and 30 K, and in one example between 10 K and 20 K.

[0013] Superconducting materials can have a superconducting energy gap larger than that of aluminum (0.2 meV). The superconducting material can, for example, have a superconducting energy gap greater than 0.3 meV, in some examples at least 0.5 meV, preferably at least 1.0 meV, in some examples at least 1.5 meV, most preferably at least 2.0 meV, in one example at least 2.5 meV, and in another example at least 3.0 meV.

[0014] Superconducting qubit circuits can be used for (i.e., can be suitable or configured for) operation at an operating temperature of at least 1.0 K, preferably at least 1.5 K, most preferably at least 2.0 K, in one example at least 3.0 K and in one example at least 4.2 K. The operating temperature can be achieved, for example, by appropriately selecting one or more superconducting materials (e.g., nitride-based superconductors) and their critical temperatures, substrate materials (e.g., silicon, sapphire, or MgO), and the parameters of the qubits and tunnel junctions (such as their shape and / or physical dimensions (e.g., the cross-sectional area and / or length of the tunnel junction), the normal state resistance of the tunnel junction, the total capacitance and / or critical current, and / or the energy spacing, Josephson energy, and / or charging energy of the qubit), as detailed below, for example. The (maximum) operating temperature of the qubit circuit can be limited, for example, by the thermal excitation of the qubit (e.g., excitation to an excited state or other higher energy states of the qubit) and / or quasiparticle excitations in the superconducting material, both of which can disrupt coherence. For example, the energy spacing of the qubit, and / or the superconducting energy gap and / or critical temperature of the superconducting material can be selected such that one or both of the energy spacing and the superconducting energy gap are less than, preferably significantly less than, the thermal energy k O associated with the operating temperature T B T O (e.g., less than 50% of it, in some examples less than 30% of it, in one example less than 10% of it, and in one example less than 5% of it). Additionally or alternatively, the sensitivity of the qubit to quasiparticle tunneling and / or charge fluctuations through the tunnel barrier can be reduced (e.g., by appropriately selecting the ratio E J of the Josephson energy E C to the charging energy E J / EC For example, as described in detail below), the coherence and / or maximum operating temperature of the qubit can be improved by reducing the sensitivity of the qubit to environmental noise (e.g., magnetic field and / or charge noise), and / or by reducing dielectric losses (e.g., through an appropriate combination of superconducting and substrate materials). The improved coherence time can translate into a higher maximum temperature because the qubit can maintain its quantum state for a longer time before thermal excitation destroys the quantum state.

[0015] The superconducting material of the qubit can be a single material (e.g., a single metal or alloy), or can be a hybrid or composite material comprising a plurality of different materials (e.g., a combination of different metals and / or alloys), such as a first structure of a first material (e.g., on a first side of a tunnel junction) and a second structure of a second material (e.g., on a second side of the tunnel junction opposite the first side), wherein each of said materials is a superconducting material having a critical temperature above 1.2 K. The superconducting material of the qubit can be or include type-I superconductors and / or type-II superconductors. The superconducting material of the qubit can be or include s-wave superconductors and / or d-wave superconductors.

[0016] The superconducting material can for example be or include nitride-based superconductors, such as one or more of niobium titanium nitride (NbTiN), niobium nitride (NbN), and titanium nitride (TiN). Additionally or alternatively, the superconducting material can for example be or include one or more of yttrium barium copper oxide (YBCO), magnesium diboride (MgB2), bismuth strontium calcium copper oxide (BSCCO), and iron-based superconductors, particularly iron-pnictide superconductors. In one example, the superconducting material is or includes NbTiN, e.g., Nb x Ti 1-x N, where x can for example be between 0.4 and 0.8, in some examples between 0.5 and 0.7, and in one example between 0.6 and 0.65. For example, these materials have a critical temperature and / or superconducting energy gap within the aforementioned ranges.

[0017] The tunnel junction of the qubit (which may also be simply referred to as a junction below) is formed by a tunnel barrier induced by disorder in the superconducting material. As used herein, the term "disorder" can for example refer to a random or substantially random deviation from its ideal structure and / or composition within the superconducting material (e.g., a deviation from its ideal crystal structure in the absence of any impurities). While weak disorder generally does not affect superconductivity, stronger disorder can cause breakdown of the superconducting state and may for example lead to a superconductor-to-metal or superconductor-to-insulator transition. For example, this can occur when the disorder is so strong that the mean free path becomes comparable (e.g., of the same order of magnitude) to the Fermi wavelength. Thus, the disorder region can create a tunnel barrier within the superconducting material, thereby forming a tunnel junction.

[0018] Disorder is generated by spatial crystalline defects in the superconducting material. In the context of the present disclosure, "spatial crystalline defects" can, for example, refer to spatial deviations, dislocations, or interruptions within the crystal structure of the superconducting material. For example, lattice positions or sites within the ideal crystal structure of the superconducting material are not occupied by atoms (e.g., vacancy defects) and / or atoms are arranged at positions different from the lattice positions in the ideal crystalline structure of the superconducting material (e.g., shifted from the lattice positions in the ideal crystal structure of the superconducting material) (e.g., interstitial defects). Thus, spatial crystalline defects should be distinguished from impurity-based disorder or crystalline defects such as substitutional defects, where impurity atoms (which should not be in the superconducting material) occupy regular lattice positions in the ideal crystal structure (e.g., due to ion implantation, as used in, for example, US11,538,977B2). Thus, spatial crystalline defects can also be referred to herein as "non-impurity crystalline defects" or "dislocations". Although impurities may (and typically do) exist in the superconducting material at least to some extent, according to the present invention, spatial crystalline defects are the main form of disorder in the tunnel barriers of superconducting qubits. Spatial crystalline defects can in particular be the form of disorder that ultimately leads to the breakdown of superconductivity in the tunnel barrier and can thus also be referred to as "spatial-crystalline-defect-induced tunnel barrier" or simply "dislocation-induced tunnel barrier". In other words, the amount of impurities present in the tunnel barrier can be lower than, preferably significantly lower than, the threshold required for the breakdown of superconductivity. For example, the mean free path between impurities can be at least one order of magnitude smaller (e.g., less than 10% of it), preferably at least two orders of magnitude smaller (e.g., less than 1% of it), than the Fermi wavelength in the superconducting material. In some examples, the ratio of the amount (e.g., number or density) of impurities (e.g., substitutional defects) to the amount of non-impurity crystalline defects can be less than 0.5, preferably less than 0.2, most preferably less than 0.1, less than 0.05 in some examples, less than 0.02 in one example, and less than 0.01 in one example. Spatial crystalline defects can be or include point defects (e.g., at a single lattice position, such as a single vacancy defect, a single interstitial defect, or a Frenkel defect or pair), line defects (e.g., edge dislocations or screw dislocations), planar defects, or combinations thereof. The disorder-induced tunnel barrier can offer the advantage of having no interface between different materials (such as in an Al / AlO / Al junction) and / or allowing the tunnel barriers / junctions to be placed closer to each other. For example, this can be particularly advantageous for fluxonium qubits and for demonstrating a flux focusing effect in magnetic field measurements.

[0019] In a preferred embodiment, the spatial crystalline defects in the tunnel barrier are created by irradiating with ions, in particular silicon ions and / or inert gas ions (e.g., helium ions and / or neon ions), for example using the method according to the second aspect of the invention described below. The spatial crystalline defects in the tunnel barrier can be created in particular by irradiating with a focused ion beam (e.g., a focused ion beam of inert gas ions and / or silicon ions), as detailed below. For a superconducting material of a given thickness (e.g., film thickness), the energy of the ions can be selected such that the ions penetrate the superconducting material (e.g., into the underlying substrate), preferably without or with only minimal lateral diffusion (e.g., the diameter of the focused ion beam does not increase significantly). The kinetic energy of the ions deposited into the superconducting material can cause the creation of defects, for example by local displacement of atoms. The invention is not intended to be limited to any particular mechanism for creating spatial crystalline defects and is not bound by any particular theory. For example, disorder can be introduced by one or both of the following two mechanisms: 1) Ions can remove (e.g., knock out) atoms from the lattice, thereby creating vacancies and / or surface roughness (e.g., visible in a cross-sectional image), and 2) Ions can displace atoms, causing them to move from their original or native positions in the lattice, and the displaced atoms (which may not be completely removed from the superconducting material) become defects within the lattice (which may also include the resulting vacancies). When the ions penetrate the superconducting material (and thus do not remain therein), the irradiation may not (or only to a small extent) create impurities in the superconducting material. However, some impurities may already be present in the superconducting material prior to irradiation (e.g., due to deposition of the superconducting material), and some of these impurities may also be displaced by the ions. The high ionization potential and / or high kinetic energy of the ions (e.g., helium and / or neon ions) can also cause most impurity atoms or contaminants on, for example, the sample surface and / or in the equipment used for irradiation (e.g., a focused ion beam system and / or an ion microscope) to be ionized early in the process, without forming a significant portion of the ions (e.g., ion beam) that irradiate (e.g., penetrate) the sample.

[0020] Preferably, the tunnel barrier does not contain alumina. In other words, the tunnel barrier (and in some examples, the entire tunnel junction, e.g., also including the portion of the superconducting material adjacent to the tunnel barrier) may not contain a stoichiometrically relevant amount of alumina. For example, the alumina content in the tunnel barrier and / or the tunnel junction can be less than 10 -3 and preferably less than 10 -4 and most preferably less than 10 -5 . In some examples, the tunnel barrier and / or the tunnel junction may be free of aluminum (i.e., any form of aluminum including the element aluminum). For example, the aluminum content in the tunnel barrier and / or the tunnel junction can be less than 10 -3 and preferably less than 10 -4 and most preferably less than 10-5 。

[0021] The cross-sectional area of the tunnel barrier can be less than 3.0·10 4 nm 2 , preferably less than 2.0·10 4 nm 2 , most preferably less than 1.5·10 4 nm 2 , less than 1.0·10 in some examples 4 nm 2 , less than 5·10 in some examples 3 nm 2 , less than 3·10 in some examples 3 nm 2 , less than 2·10 in some examples 3 nm 2 , less than 1·10 in some examples 3 nm 2 , and less than 5·10 in one example 2 nm 2 . The cross-sectional area of the tunnel barrier can be measured transversely across the tunnel barrier, for example, in a plane perpendicular to the direction of current flow through the tunnel barrier. The cross-sectional area can be, for example, an important parameter affecting quantities such as the critical current, normal-state resistance, and / or capacitance of a tunnel junction, and these quantities can determine the quality of the tunnel junction and the entire superconducting qubit, especially their suitability for quantum information processing.

[0022] The length ("width") of the tunnel barrier can be between 0.5 nm and 50 nm, preferably between 1 nm and 25 nm, between 2 nm and 20 nm in some examples, and most preferably between 5 nm and 15 nm. Additionally or alternatively, the length of the tunnel barrier can be, for example, on the same order of magnitude as one or both of the superconducting coherence length and the penetration depth of the superconducting material (e.g., between 0.2 times and 20 times thereof, between 0.5 times and 10 times thereof in some examples, and between 2 times and 6 times thereof in one example). The length of the tunnel barrier can be measured longitudinally across the tunnel barrier, for example, parallel to the direction of current flow through the tunnel barrier. Such short / thin tunnel barriers can be produced, for example, by using focused ion beam irradiation, as described below, for example. Using such short / thin tunnel barriers can allow for strong tunnel coupling across the tunnel junction, even for superconducting materials with short coherence lengths, such as NbTiN (about 2.5 nm) or NbN (about 5 nm), which can be advantageous in other respects, such as improving the energy confinement and / or reducing energy losses within the superconducting qubit circuit, especially its readout circuit.

[0023] The normal-state resistance R of the tunnel junction Ncan be at least 100 Ω, preferably at least 200 Ω, most preferably at least 300 Ω, in some examples at least 400 Ω, and in one example at least 500 Ω. The normal state resistance of the tunnel junction can be, for example, between 100 Ω and 2 kΩ, in some examples between 200 Ω and 1 kΩ, and in one example between 300 Ω and 500 Ω. Additionally or alternatively, the total capacitance of a superconducting qubit (e.g., a superconducting island coupled via a tunnel junction) is at least 10 fF, preferably at least 20 fF, most preferably at least 50 fF. The total capacitance of the superconducting qubit can be, for example, between 10 fF and 1000 fF, in some examples between 20 fF and 500 fF, in one example between 40 fF and 200 fF, and in one example between 50 fF and 100 fF. The total capacitance C ∑ (which may also be referred to as its self-capacitance) can, for example, include the intrinsic capacitance C J of the tunnel junction, and optionally includes one or more additional capacitances in parallel with the tunnel junction, in particular additional shunt capacitances C 0 (e.g., to ground) and / or gate capacitances C g , e.g., C ∑ = C J + C 0 + C g . The normal state resistance of the tunnel junction and the total capacitance of the superconducting qubit can, for example, determine the properties of the superconducting qubit, such as the energy gap, its anharmonicity, and / or its sensitivity to charge noise, as detailed below, for example.

[0024] Additionally or alternatively, the critical current of the tunnel junction can be less than 1.0 μA, preferably less than 0.5 μA, in some examples less than 0.3 μA, most preferably less than 0.2 μA, in one example less than 0.1 μA, and in one example less than 0.05 μA. The critical current of the tunnel junction can be, for example, between 1 nA and 1.0 μA, in some examples between 5 nA and 0.5 μA, and in one example between 10 nA and 0.1 μA. Although it will result in a reduction in the quality factor / characteristic voltage of the tunnel junction, the low critical current can be beneficial for maintaining an appropriate degree of anharmonicity of the qubit (to obtain a well-isolated effective two-level system), while also suppressing charge noise, for example, as detailed below, and can allow for the implementation of high-frequency qubits with large energy gaps (e.g., at least 10 GHz, preferably at least 20 GHz). Nevertheless, in order to achieve the desired quality factor, the normal state resistance can be adjusted (e.g., increased) accordingly. As described in the previously known isolated / single-disorder-based tunnel junctions, such as A. Ruhtinas and I. J. Maasilta, arXiv:2303.17348v1 [cond-mat.supr-con], have significantly larger critical currents (and cross-sectional areas and smaller normal state resistances), making them unsuitable for superconducting qubits, especially high-frequency superconducting qubits.

[0025] In a preferred embodiment, the superconducting qubit is a charge qubit, e.g., a Cooper pair box. The fundamental state of the superconducting qubit can be, for example, the charge state of a superconducting island coupled (e.g., coupled to a larger reservoir, such as a larger superconducting contact, electrode, or wire, especially a grounded contact or electrode) via a tunnel junction. The superconducting qubit can in particular be a SQUID-based charge qubit, i.e., a charge qubit including a superconducting quantum interference device (SQUID) formed by two or more tunnel junctions in a superconducting loop. The SQUID-based charge qubit can, for example, achieve flux tuning of the qubit by adjusting the magnetic flux through the SQUID (e.g., the magnetic flux through the superconducting loop), e.g., to tune the Josephson energy of the tunnel junction. In other examples, the superconducting qubit can also be a different type of qubit, such as a phase qubit, a flux qubit, or a combination of two or more of a charge qubit, a phase qubit, and a flux qubit.

[0026] Preferably, the Josephson energy E J and the charging energy E C of the superconducting qubit (which can be, for example, a charge qubit as described above) have a ratio of E J / E CBetween 20 and 2000, in some examples between 50 and 1000, in some examples between 100 and 1000, preferably between 200 and 600, and in one example between 300 and 500. The Josephson energy can be, for example, the energy associated with the tunneling process across a tunnel junction (e.g., of Cooper pairs), which can be proportional to the critical current I C of the tunnel junction, E J = Φ 0 I C / (2π), where Φ 0 represents the magnetic flux quantum and can determine the energy stored in the tunnel junction when current passes through the tunnel junction. The charging energy E C can be, for example, the energy associated with charging a superconducting qubit (e.g., a superconducting island coupled via a tunnel junction), for example by adding Cooper pairs. The charging energy E C can depend on the total capacitance C ∑ of the qubit and can be given, for example, by E C = e 2 / (2C ∑ ), where e represents the elementary charge. The ratio E J / E C within the aforementioned range can, for example, allow reducing the sensitivity of the qubit to charge noise while maintaining a sufficient degree of anharmonicity. In some examples, the qubit can be embodied as a transmon qubit (e.g., a charge qubit including a tunnel junction and an additional shunt capacitance in parallel, e.g., as described in J. Koch et al., Phys. Rev. A 76, 042319 (2007) or its variants). The qubit can in particular be embodied as an Xmon qubit (e.g., as described in R. Barends et al., Phys. Rev. Lett. 111, 080502 (2013) or its variants). In other examples, the qubit can be, for example, a Gatemon qubit.

[0027] The energy gap of a superconducting qubit can be, for example, between 1 GHz and 500 GHz, in some examples between 5 GHz and 200 GHz, preferably between 10 GHz and 100 GHz, and most preferably between 20 GHz and 50 GHz. As used herein, the energy gap can refer, for example, to the energy difference between the ground state and the excited state of a two-level (or effectively two-level) system forming the superconducting qubit. Such a large energy gap can be achieved, for example, by the large superconducting energy gap of the superconducting material and can, for example, allow for high operation frequencies (e.g., read and / or write frequencies).

[0028] In some embodiments, in addition to superconducting qubits, the superconducting qubit circuit may further include one or more additional elements. In other examples, the claimed superconducting qubit circuit may consist only of superconducting qubits. Some or all of the elements of the superconducting qubit circuit may be formed of a superconducting material, preferably the same superconducting material as the superconducting qubit (e.g., including or consisting of the superconducting material). Additionally, the superconducting qubit circuit may further include one or more normal conducting elements and / or structures and / or one or more insulating elements and / or structures.

[0029] The superconducting qubit circuit may include, for example, a readout electrode and / or a readout circuit for reading out the state of the superconducting qubit (which may include and / or be coupled to the readout electrode), a control electrode for manipulating the state of the superconducting qubit, and one or more of the flux bias lines for adjusting the energy gap of the superconducting qubit. The control line may be included in and / or coupled to the control circuit for manipulating the state of the superconducting qubit, where, in some examples, the control circuit may also be part of the superconducting qubit circuit or, alternatively, may be provided as a separate unit. The flux bias line may be included in and / or coupled to the flux bias circuit for adjusting the energy gap of the superconducting qubit, where, in some examples, the flux bias circuit may also be part of the superconducting qubit circuit or, alternatively, may be provided as a separate unit. The readout electrode and / or the control electrode may be (e.g., capacitively) coupled to the superconducting qubit, particularly its superconducting island. The flux bias line may be configured to generate a magnetic field at the superconducting qubit (e.g., when a current is applied to the flux bias line), particularly a magnetic field passing through the SQUID loop of the qubit. For this purpose, the flux bias line may be, for example, inductively coupled to the superconducting qubit.

[0030] In some examples, the superconducting material of the qubit may be a superconducting film (e.g., formed or deposited as a superconducting film or layer). The superconducting material may be, for example, a superconducting film with a thickness less than 0.5 μm, preferably less than 0.2 μm, in some examples less than 100 nm, in one example less than 50 nm, and in one example less than 25 nm. The superconducting film may be disposed on a substrate, particularly an insulating substrate. The superconducting film may include one or more layers. The superconducting material may particularly be a superconducting thin film. As used herein, the term "thin film" may refer, for example, to a film having a thickness low enough such that one or more properties related to superconductivity within the film (e.g., critical temperature) are different from the corresponding properties of the bulk material. In such a case, the critical temperature of the superconducting material as used herein may refer to the critical temperature of the film (rather than the critical temperature of the bulk material).

[0031] The tunnel junction and one or more, preferably all, of the readout line, readout circuit, control line, and flux bias line (as well as optional control circuitry and / or flux bias circuitry) are made of the same superconducting material (i.e., the high-temperature superconducting material of the qubit in which the tunnel junction is formed) (e.g., comprising said same superconducting material and / or consisting of said same superconducting material). The one or more, preferably all, of the tunnel junction and the readout line, readout circuit, control line, and flux bias line (as well as optional control circuitry and / or flux bias circuitry) can in particular be made of the same superconducting material film, e.g., by patterning the superconducting material film to form the corresponding circuit elements.

[0032] In some examples, the superconducting qubit circuit can include multiple qubits, e.g., (but not limited to) at least 2 qubits, in some examples at least 4 qubits, in some examples at least 8 qubits, in some examples at least 16 qubits, in one example at least 64 qubits, and in one example at least 128 qubits. However, the present invention is not limited to any particular number of qubits, and the superconducting qubit circuit can include any number of qubits. Each of said qubits can be embodied as described above, for example. Additionally or alternatively, the superconducting qubit circuit can include one or more quantum gates (quantum logic gates), each of which can act on one or more qubits, preferably on two or more qubits. In some examples, the superconducting qubit circuit can be or include a quantum processor, or can be used in a quantum processor (and in some examples, for use in a part of a quantum processor). Additionally or alternatively, the superconducting qubit circuit can be or include a quantum sensor, or can be used in a quantum sensor (and in some examples, for use in a part of a quantum sensor). In some examples, the superconducting qubit circuit can be embodied as or disposed on and / or in a chip or chip package.

[0033] According to a second aspect of the present invention, a method of forming a superconducting qubit including a tunnel junction is provided. The method includes forming a superconducting structure of the superconducting qubit, the superconducting structure being formed of a superconducting material having a critical temperature above 1.2 K. The method further includes forming a tunnel junction by generating a disorder-induced tunnel barrier in the superconducting structure, wherein the tunnel barrier is generated by introducing spatial crystal defects into the superconducting material.

[0034] Superconducting qubits, tunnel junctions, superconducting materials, tunnel barriers, and / or spatial crystal defects can, for example, be embodied and / or formed as in any of the superconducting qubit circuits according to the first aspect of the present invention described herein, i.e., can have or include some or all of the features of the corresponding elements of the superconducting qubit circuit according to the first aspect disclosed herein. The method according to the second aspect can be used to form the superconducting qubit circuit according to the first aspect or a part thereof, in particular its superconducting qubit. The execution of the method is not limited to a specific order. As long as technically feasible, the method can be executed in any order, and its steps can also be executed at least partially simultaneously. For example, spatial crystal defects can be introduced into the superconducting material before, during, and / or after the formation of the superconducting structure.

[0035] The superconducting structure of the qubit can be, for example, or include one or more superconducting islands and / or one or more superconducting reservoirs, as described above, for example. Tunnel junctions can be formed to couple the (multiple) superconducting islands to the (multiple) superconducting reservoirs, for example to provide a weak link therebetween. In some examples, multiple tunnel junctions can be formed, for example a pair of tunnel junctions (e.g., for forming a SQUID). Additionally or alternatively, the superconducting structure can be or include one or more other structures, such as one or more superconducting electrodes, one or more superconducting contacts, and / or one or more superconducting wires or leads. The superconducting structure can be composed of (e.g., formed solely of) high-temperature superconducting materials or include high-temperature superconducting materials (e.g., formed of high-temperature superconducting materials, etc.).

[0036] To form a tunnel junction, a disorder-induced tunnel barrier is created in the superconducting structure, where the tunnel barrier can be created before, during, and / or after the formation of the superconducting structure. The tunnel barrier is created by introducing spatial crystal defects into the superconducting material, i.e., is the "spatial crystal defect-induced tunnel barrier" or "dislocation-induced tunnel barrier" as described above. This can include introducing such defects to a certain extent (e.g., in number and / or density) to cause breakdown of superconductivity in the superconducting material, for example to cause a superconductor-to-insulator transition or a superconductor-to-normal conductor transition (e.g., superconductor-to-metal transition). In some examples, forming a tunnel junction can also include forming a physical constriction, for example within or adjacent to the superconducting structure of the qubit. The tunnel barrier can be created in the physical constriction.

[0037] Spatial crystal defects in superconducting materials can be introduced, for example, by irradiating the superconducting materials, in particular with high-energy irradiation (e.g., with particles having an energy of at least 1 keV, preferably at least 5 keV, in some examples at least 10 keV, in one example at least 20 keV, in one example at least 30 keV, and in one example at least 40 keV). For example, the particle energy can be selected based on the thickness of the superconducting material (e.g., film thickness) and / or the length of the tunnel barrier. For example, for a superconducting material with a larger thickness (e.g., for tuning the kinetic inductance and / or increasing the critical temperature), a higher particle energy can be used compared to a superconducting material with a smaller thickness. The irradiation can be or include electromagnetic irradiation (e.g., by X-ray and / or gamma irradiation) and / or irradiation by massive particles such as electrons and / or ions, for example, using a focused electron beam and / or a focused ion beam. The irradiation can be directed irradiation, for example, using a focused beam. Preferably, the irradiation is maskless, i.e., the superconducting material is irradiated without a mask being arranged on the superconducting material to block the irradiation. Additionally or alternatively, spatial crystal defects can also be introduced during the formation (e.g., deposition, growth, and / or patterning) of the superconducting material.

[0038] The irradiation for introducing spatial crystal defects can be adapted to the superconducting material and / or superconducting structure used, in particular one or more of its physical dimensions, such as the length of the tunnel barrier and / or the thickness of the superconducting structure / material (e.g., film thickness). To this end, irradiation parameters such as the type of irradiation (e.g., electromagnetic irradiation versus ion irradiation), the type of irradiation particles (e.g., the type of ions used), the particle energy (e.g., acceleration voltage and / or wavelength), the dose, the fluence (e.g., intensity and / or ion beam current), and / or the dwell time can be adapted to the superconducting material and / or superconducting structure used (e.g., selected based on the superconducting material and / or superconducting structure used). Preferably, the irradiation is adapted to allow the irradiation to penetrate the superconducting material and / or superconducting structure, for example, into the substrate below the superconducting material and superconducting structure respectively, preferably without or with only minimal lateral diffusion.

[0039] In a preferred embodiment, spatial crystal defects are introduced into the superconducting material by irradiating the superconducting material with inert gas ions, in particular helium ions. Additionally or alternatively, silicon ions and / or other inert gas ions, such as neon ions, can also be used.

[0040] Spatial crystalline defects in superconducting materials can be introduced by irradiation using a focused ion beam, in particular a focused ion beam of inert gas ions and / or silicon ions (e.g., a focused helium ion beam and / or a focused neon ion beam). Using a focused ion beam can facilitate the targeted and well-controlled introduction of spatial crystalline defects in certain parts or regions of the superconducting material or structure, even on very small length scales, thus allowing for the "direct writing" of disorder-induced tunnel barriers in the superconducting structure. The spot size of the focused ion beam at the superconducting material can be, for example, below 20 nm, in some examples below 10 nm, preferably below 5 nm, most preferably below 2 nm, in one example below 1 nm, and in one example below 500 pm. The spot size can be, for example, between 100 pm and 5 nm, in some examples between 200 pm and 2 nm, and in some examples between 400 pm and 1.2 nm.

[0041] The superconducting material can be irradiated, for example, with ions, in particular inert gas ions (such as helium ions and / or neon ions and / or silicon ions), at a dose between 10 16 ions / cm 2 and 10 22 ions / cm 2 , preferably between 10 17 ions / cm 2 and 10 21 ions / cm 2 , most preferably between 10 18 ions / cm 2 and 10 20 ions / cm 2 , and in one example between 5·10 18 ions / cm 2 and 5·10 19 ions / cm 2 . For example, the dose can be selected based on the amount of disorder, in particular the amount of spatial crystalline defects to be introduced into the superconducting material, based on the thickness of the superconducting material (e.g., the height of the tunnel barrier), and / or based on the superconducting material used (e.g., nitride-based superconductors may require a much larger dose (e.g., a dose two orders of magnitude larger) than, for example, YBCO to suppress superconductivity). This can enable precise control of the properties, in particular the electrical properties of the tunnel barrier (e.g., the resistivity of the tunnel barrier) (e.g., to form an insulating or metallic tunnel barrier).

[0042] The superconducting material can be arranged on a substrate, in particular an insulating substrate. The superconducting material can be irradiated through its surface exposed from the substrate (e.g., facing away from the substrate), for example, in a direction perpendicular to the surface. The kinetic energy of the ions (e.g., inert gas ions) can be selected so that the ions penetrate the superconducting material into the substrate, for example, so that at least 80%, preferably at least 90%, most preferably at least 95%, at least 98% in some examples, at least 99% in one example, at least 99.9% in one example, at least 99.99% of the ions penetrate the superconducting material into the substrate. This can allow (mainly) the introduction of spatial crystal defects rather than impurities (in contrast to, for example, ion implantation into superconducting materials). The kinetic energy of the ions can, for example, be at least 5 keV, at least 10 keV in some examples, at least 20 keV in one example, and at least 30 keV in one example. Preferably, the ions penetrate the superconducting material with no or minimal lateral diffusion, for example, such that the lateral extent (e.g., width or diameter) of the irradiated region or point (e.g., the lateral extent of the focused ion beam) is substantially unchanged over the thickness of the superconducting material, for example, the thickness of the superconducting material changes (e.g., increases) by less than a factor of two, preferably less than a factor of 1.5, and in one example less than a factor of 1.2. This can ensure uniform disordered regions throughout the superconducting material, maintain the superconducting properties of the rest of the superconducting material, achieve low dynamic inductance, and / or allow for reproducible production of tunnel junctions with desired parameters (e.g., desired junction length, desired critical current, and / or desired normal-state resistance).

[0043] The technique for forming the superconducting structure is not particularly limited and may be or include any technique known in the art for forming a superconducting structure. Forming the superconducting structure may include depositing a superconducting material and / or patterning a superconducting material. The superconducting material may be deposited using one or more deposition techniques known in the art, for example, physical vapor deposition (PVD, such as sputtering, pulsed laser deposition (PLD) and / or electron beam evaporation), chemical vapor deposition (CVD, such as gas-liquid-solid growth, for example, for forming a one-dimensional structure such as a nanowire), atomic layer deposition (ALD), epitaxial growth (e.g., molecular beam epitaxy (MBE)), spin coating, and combinations thereof (e.g., a hybrid method combining two or more of the aforementioned deposition techniques, such as a combination of PLD and MBE). In some examples, the superconducting material may be deposited in a patterned manner, for example, using a suitable mask and / or directional deposition or growth. Additionally or alternatively, the superconducting material can be patterned using one or more patterning techniques known in the art, such as lithography (e.g., electron lithography and / or photolithography), etching (e.g., wet etching, dry etching and / or reactive ion etching) and / or milling (e.g., ion milling).

[0044] In some examples, forming a superconducting structure includes forming (e.g., depositing) a film, in particular a thin film, of a superconducting material. The film may include one or more layers. The film of superconducting material may, for example, be formed to have a thickness as described above for the superconducting qubit circuit according to the first aspect. The thickness of the film may be uniform, that is, the film may be formed as a layer of uniform thickness. Forming a superconducting structure may further include, for example, patterning the film using one or more of the aforementioned patterning techniques to form a superconducting structure.

[0045] The method may further include forming one or more additional structures, for example, one or more additional structures of a superconducting qubit circuit, for example, as detailed above for a superconducting qubit circuit according to the first aspect. The method may, for example, include forming one or more, preferably all, of a readout electrode and / or a readout circuit for reading out the state of a superconducting qubit, a control electrode for manipulating the state of a superconducting qubit, and a flux bias line for adjusting the energy interval of a superconducting qubit. In some examples, the method may also include forming a control circuit for manipulating the state of a superconducting qubit, the control circuit may include and / or be coupled to the control electrode, and / or forming a flux bias circuit for adjusting the energy interval of the superconducting qubit, the flux bias circuit may include and / or be coupled to the flux bias line.

[0046] One or more, preferably all, of the readout electrode, the readout circuit, the control electrode and the flux bias line (and the optional control circuit and / or flux bias circuit) may be formed from the same superconducting material, in particular from the same superconducting material film as the superconducting structure of the superconducting qubit. In particular, the film may be patterned so as to simultaneously form the superconducting structure and one or more, preferably all of the aforementioned structures, for example in a single patterning step or process (e.g., using a common mask and / or a common etching step for all corresponding structures).

[0047] The superconducting qubits of the superconducting qubit circuit according to the first aspect of the invention, and in some examples the entire superconducting qubit circuit according to the first aspect, can be obtained (e.g., obtained or formed, or obtained or formed to have the same structural properties and / or characteristics as obtained or formed) using the method according to the second aspect of the invention according to any one of the embodiments disclosed herein.

[0048] According to a third aspect, the present invention relates to the use of a superconducting qubit circuit according to the first aspect (e.g., a method or process using a superconducting qubit circuit) according to any one of the embodiments disclosed herein, wherein the superconducting qubit circuit operates at an operating temperature of at least 1.0 K, preferably at least 1.5 K, most preferably at least 2.0 K, in one example at least 3.0 K, and in one example at least 4.2 K. For example, the superconducting qubit circuit can be used for quantum information processing (e.g., in a quantum processor and / or a quantum computer) and / or quantum sensing (e.g., in a quantum sensor).

[0049] The superconducting qubit circuit according to the first aspect of the present invention and the method according to the second aspect of the present invention are not limited to high-temperature superconducting materials having a critical temperature higher than 1.2 K, but can also be implemented with any other superconducting material, particularly a superconducting material having a critical temperature of 1.2 K or lower. In addition, the superconducting qubit circuit according to the first aspect of the present invention and the method according to the second aspect of the present invention are not limited to the disorder generated by spatial crystal defects, but additionally or alternatively, can also be implemented using other types of disorder (i.e., any type of disorder-induced tunneling barrier), particularly a specific disorder generated by impurity-based crystal defects. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Hereinafter, a detailed description of the present invention and its exemplary embodiments is given with reference to the accompanying drawings. These figures show the following schematic diagrams:

[0051] Figure 1a and Figure 1b : A top view and a side view of a superconducting qubit circuit according to an example, respectively;

[0052] Figure 2 : A flowchart of a method for forming a superconducting qubit including a tunnel junction according to an example;

[0053] Figure 3a : A top view of a superconducting qubit circuit having a SQUID-based charge qubit according to an example;

[0054] Figure 3b : Figure 3a A close-up top view of the SQUID-based charge qubit of the superconducting qubit circuit of

[0055] Figure 4a : A circuit diagram of a superconducting qubit circuit having a SQUID-based charge qubit, a readout circuit, and a control circuit according to an example;

[0056] Figure 4b : For Figure 4a A circuit diagram of a flux bias circuit of the superconducting qubit circuit of ; and

[0057] Figure 5 :Flowchart of a method for forming a superconducting qubit circuit having a superconducting qubit including a disorder-induced tunneling barrier according to an example. Detailed implementation

[0058] Figure 1a and Figure 1b Schematic diagrams of a superconducting qubit circuit 100 according to a first aspect of the present invention according to an example are depicted in a top view and a side view, respectively. The superconducting qubit circuit 100 (hereinafter simply referred to as the qubit circuit 100) includes a superconducting qubit 102. In this example, the superconducting qubit is formed by a superconducting island 104, and the superconducting island is coupled to a superconducting reservoir (e.g., a larger superconducting electrode or superconducting wire or wire) 106 via a tunnel junction. The tunnel junction (a Josephson junction in this example) is formed by a disorder-induced tunneling barrier 108 disposed between the island 104 and the reservoir 106. The superconducting qubit 102 (hereinafter simply referred to as the qubit 102) (i.e., the island 104, the reservoir 106, and the tunnel barrier 108) is disposed on an insulating substrate 110 (e.g., on an insulating substrate) and is formed of a high-temperature superconducting material having a critical temperature higher than the critical temperature of aluminum (1.2 K) (e.g., including and / or consisting of the high-temperature superconducting material). The high-temperature superconducting material may be, for example, or include NbTiN (T C ≈ 15 K). In other examples, other nitride-based superconductors (such as NbN and / or TiN) may be used, for example, instead of NbTiN (or in addition to NbTiN). Preferably, the high-temperature superconducting material also has a superconducting energy gap higher than that of aluminum (0.2 meV), and the superconducting gap of NbTiN is, for example, about 2.0 meV. In some examples, the superconducting energy gap may be proportional or approximately proportional to the critical temperature. The substrate 110 may include, for example, silicon, sapphire, and / or MgO or consist of them. In some examples, a reference electrode (not shown), such as a ground plane, may be disposed on the bottom surface of the substrate 110, which is opposite to the top surface on which the qubit 102 is disposed. The tunnel barrier 108 and preferably the entire qubit 102 may be aluminum-free, i.e., may not contain any stoichiometrically relevant amounts of elemental aluminum or aluminum compounds, such as aluminum oxide.

[0059] The disorder in the disorder-induced tunneling barrier 108 is generated by spatial crystalline defects in the superconducting material, i.e., by spatial deviations, dislocations, and / or interruptions within the crystal structure of the superconducting material. These defects can include, for example, vacancy defects (unoccupied lattice sites) and / or interstitial defects (e.g., atoms displaced from lattice sites). The density of the spatial crystalline defects causes the tunneling barrier 108 to no longer be in the superconducting state, but rather, for example, in the normal or insulating state, thereby forming a weak link between the island 104 and the reservoir 106. The disorder in the tunneling barrier 108 can be generated, for example, by irradiating (e.g., by using a focused ion beam) with ions, particularly inert gas ions such as helium ions. The disorder in the tunneling barrier 108 can be generated, for example, as detailed below for the method 200 of Figure 2 and / or Figure 5 the method 500 of

[0060] The qubit 102 can be described, for example, at least approximately by a Hamiltonian of the following form (see, for example, J. Koch et al., Phys. Rev. A 76, 042319 (2007))

[0061]

[0062] where E J = Φ 0 I c / (2π) = R Q Δ / (2R N ) represents the Josephson energy of a tunneling junction with a critical current I c , a normal state resistance R N , and a superconducting energy gap Δ (where Φ 0 and R Q are the magnetic flux quantum and the resistance quantum, respectively, and φ is the phase difference across the junction), and where E C = e 2 / 2C ∑ represents the charging energy of the island 104 with a total capacitance C ∑ . The total capacitance of the island 104 can be, for example, the capacitance C J of the tunneling junction and any additional capacitance arranged in parallel therewith (e.g., the gate capacitance C g of a gate (not shown) of the qubit 102 (e.g., for controlling the chemical potential of the island 104) and / or an additional shunt capacitance C 0 (which can also be denoted as C q or C ground ), and the shunt capacitance can be formed, for example, between the island 104 and a reference electrode such as a ground electrode or a plane (e.g., as described below with reference to FIG. 3)). The number of Cooper pairs on the island 104 is represented by and ng is the effective offset charge number.

[0063] The energy gap between the ground state and the first excited state of the qubit 102 can be scaled at least approximately as

[0064]

[0065] where r = E J / E C represents the ratio between the Josephson energy and the charging energy. A smaller ratio r can be associated with a larger anharmonicity of the energy level structure of the qubit 102, such that the ground state and the first excited state form a well-isolated two-level system. On the other hand, a larger ratio r reduces the sensitivity of the qubit 102 to charge noise. The normal state resistance R N (and / or the critical current I c ) and the total capacitance C ∑ of the qubit 102 can be used as tuning parameters for achieving a desired energy gap E 01 and / or a desired ratio r.

[0066] The desired normal state resistance R N (and / or the critical current I c ) and the total capacitance C ∑ of the qubit 102 can be obtained, for example, by correspondingly selecting the physical dimensions and / or shape of the superconducting island 104 and / or the tunnel barrier 108. The tunnel barrier 108 can have, for example, a length L longitudinally through the tunnel barrier 108 (i.e., in the direction from the island 104 to the reservoir 106, e.g., parallel to Figure 1a , Figure 1b the X-axis), a width w transversely through the tunnel barrier 108 (i.e., in a direction perpendicular to the (longitudinal) direction from the island 104 to the reservoir 106 and, e.g., parallel to the surface of the substrate 110, e.g., parallel to Figure 1a the Y-axis), and a height / thickness h vertically through the tunnel barrier 108 (i.e., in a direction perpendicular to the longitudinal direction and the transverse direction and, e.g., perpendicular to the surface of the substrate 110, e.g., parallel to Figure 1b the Z-axis).

[0067] The height h of the tunnel barrier 108 (which can, for example, correspond to the thickness of the superconducting film forming the qubit 102) can be, for example, between 5 nm and 200 nm, preferably between 10 nm and 100 nm, and in some examples between 20 nm and 50 nm. The width w of the tunnel barrier 108 (which can, for example, correspond to the width of the island 104 and / or the reservoir 108, or can be smaller, and in some examples significantly smaller than one or both of the width of the island 104 and the width of the reservoir 108, e.g., to form as Figure 3a, Figure 3b The cross-sectional area of ​​the tunnel barrier 108 (e.g., the product of the width w and the height h in the case where the tunnel barrier 108 has a rectangular cross-section) can be, for example, between 0.5·10 3 nm 2 and 2.0·10 4 nm 2 between 1.0 and 10 3 nm 2 and 1.5·10 4 nm 2 In some examples, between 2.0 and 10 3 nm 2 and 1.0·10 4 nm 2 The length L of the tunnel barrier 108 may be, for example, between 0.5 nm and 50 nm, preferably between 1 nm and 25 nm, and most preferably between 5 nm and 15 nm. The length L of the tunnel barrier 108 may be equal to the coherence length ξ of the superconducting material. 0 On the same order of magnitude (e.g., for NbTiN, ξ 0 ≈2.5nm).

[0068] For example, the physical size and / or shape of the superconducting island 104 and / or the tunnel barrier 108 may be selected such that one or more of the following:

[0069] -Normal state resistance R of the tunnel junction N Between 100Ω and 2kΩ, in some examples between 200Ω and 1kΩ, in one example between 300Ω and 500Ω; and / or

[0070] - The total capacitance C of the superconducting quantum bit 102 ∑ Between 10 fF and 1000 fF, in some examples between 20 fF and 500 fF, in one example between 40 fF and 200 fF, and in one example between 50 fF and 100 fF; and / or

[0071] -The critical current I of the tunnel junction c Between 1 nA and 1.0 μA, in some examples between 5 nA and 0.5 μA, and in one example between 10 nA and 0.1 μA.

[0072] The ratio of Josephson energy to charging energy r = E J / E CFor example, it can be between 100 and 1000, preferably between 200 and 600, and in some examples between 300 and 500, such as 400. This can allow the qubit 102 to be robust against charge noise while still maintaining an appropriate degree of anharmonicity. The Josephson energy E J For example, it can be between 20 GHz and 2 THz, and in some examples between 50 GHz and 500 GHz, and in one example between 100 GHz and 300 GHz. The charging energy E C For example, it can be between 50 MHz and 5 GHz, and in some examples between 0.1 GHz and 1.0 GHz, and in one example between 0.3 GHz and 0.7 GHz. The energy interval E between the ground state and the first excited state of the qubit 102 01 For example, it can be between 10 GHz and 100 GHz, preferably between 20 GHz and 50 GHz, and in one example between 25 GHz and 35 GHz. The energy interval E of the qubit 102 01 And the energy difference E between the first excited state and the second excited state of the qubit 102 12 The detuning between them can be, for example, at least 0.5%, preferably at least 1.0%, most preferably at least 1.5% of the energy interval E 01 And / or can be at least 0.1 GHz, preferably at least 0.2 GHz, most preferably at least 0.4 GHz.

[0073] In some examples, the qubit circuit 100 can be embodied as or arranged on and / or in a chip or chip package (hereinafter simply referred to as a chip). The qubit circuit 100 and / or the chip can include multiple qubits and / or multiple quantum gates. The qubit circuit 100 and / or the chip can, for example, include at least two qubits (e.g., between 2 and 4096 qubits), and in some examples at least 16 qubits (e.g., between 16 and 4096), and in one example at least 64 qubits (e.g., between 64 and 4096 qubits). However, it should be noted that the present invention is not limited to any specific number of qubits, and the qubit circuit 100 and / or the chip can include any number of qubits. In some examples, the qubit circuit 100 and / or the chip or chip package can be a quantum processor and / or a quantum sensor.

[0074] Figure 2FIG. 0 shows a flowchart of a method 200 for forming a superconducting qubit including a tunnel junction according to a second aspect of the present invention. A superconducting qubit circuit (or its qubit) according to the first aspect of the present invention can be formed, for example, using method 200 according to any one of the embodiments described herein, such as any one of superconducting qubit circuits 100, 300, and 400. Hereinafter, Figure 1a , Figure 1b superconducting qubit circuit 100 is used as a non-limiting example for illustrative purposes. Method 200 is not limited to Figure 2 the order of execution implied by the flowchart of

[0075] . As long as technically feasible, method 200 can be executed in any order, and its steps can be performed at least partially simultaneously. For example, a disorder-induced tunnel barrier in the superconducting material generated in step 204 can be generated before, during, and / or after forming the superconducting structure of the superconducting qubit in step 202. Figure 5 Method 200 includes, in step 202, forming a superconducting structure of superconducting qubit 102, such as some or all of superconducting island 104, superconducting reservoir 106, and the region therebetween where tunnel barrier 108 is located. The superconducting structure is formed of a superconducting material having a critical temperature higher than the critical temperature of aluminum (i.e., higher than 1.2 K). The superconducting structure can be formed on a substrate (such as substrate 110), for example, on the substrate, and the substrate can be, for example, an insulating substrate such as a MgO substrate, a silicon substrate, or a sapphire substrate. In one example, the superconducting material is a nitride-based superconductor such as NbTiN, NbN, and / or TiN. The superconducting structure can be formed, for example, by patterned deposition (e.g., using a suitable mask) and / or by deposition of a superconducting film and its subsequent patterning, such as described below for

[0076] method 500.

[0077] Method 200 further includes, in step 204, forming a tunnel junction of the superconducting qubit by generating a disorder-induced tunnel barrier (such as tunnel barrier 108) in the superconducting structure (e.g., in the superconducting structure region disposed between island 104 and reservoir 106). Tunnel barrier 108 is generated by introducing spatial crystal defects into the superconducting material, for example, as described above for superconducting qubit circuit 100.

[0078] The irradiation dose can be selected according to the desired amount of spatial crystal defects, for example, by correspondingly adjusting the intensity of the ion beam and / or the exposure time. The irradiation dose can be selected particularly based on the thickness of the superconducting material (e.g., the height h of the tunnel barrier 108). The superconducting material within the tunnel barrier 108 can be irradiated, for example, at a dose between 10 18 ions / cm 2 and 10 20 ions / cm 2 at a height h between 10 nm and 100 nm, and in some examples at a dose between 5·10 18 ions / cm 2 and 5·10 19 ions / cm 2 at a height h between 20 nm and 50 nm. For example, at a dose of 1.0·10 19 ions / cm 2 at a height h between 30 nm and 40 nm.

[0079] The kinetic energy of the ions can be selected such that the ions do not (at least mainly) stop within the superconducting material / tunnel barrier 108 (e.g., when irradiating along the Figure 1b z - direction), but penetrate the superconducting material / tunnel barrier 108 to reach the substrate 110, for example, to avoid injecting impurities into the superconducting material or at least reducing their quantity. The kinetic energy can also be selected, for example, based on the thickness of the superconducting material / the height h of the tunnel barrier 108. The kinetic energy of the ions can be between 5 keV and 200 keV when the height h is between 10 nm and 100 nm, between 10 keV and 100 keV in some examples when the height h is between 20 nm and 50 nm, and between 20 keV and 40 keV (e.g., 30 keV) in one example when the height h is between 30 nm and 40 nm.

[0080] In addition to steps 202 and 204, method 200 can include other steps, such as coupling the qubit 102 to a readout electrode and / or circuit, a control electrode and / or circuit, and / or a flux bias line and / or circuit, for example, as described below for Figure 5 method 500. In some examples, method 200 can further include connecting the aforementioned circuit elements to an external control and / or readout circuit and / or device, such as a current source, a microwave generator, and / or a network analyzer.

[0081] Figure 3a ,, Figure 3b shows a schematic diagram of a superconducting qubit circuit 300 according to a first aspect of the present invention according to another example. Figure 3a shows a top view of the superconducting qubit circuit 300, whileFigure 3b A close-up top view of the SQUID-based charge qubit 102 of the superconducting qubit circuit 300 is shown.

[0082] The superconducting qubit circuit 300 (abbreviated as qubit circuit 300) is similar to Figure 1a , Figure 1b the superconducting qubit circuit 100 of Figure 2 . The superconducting qubit circuit 300 includes a superconducting qubit 102 (abbreviated as qubit 102) having a pair of tunnel junctions in a high-temperature superconducting material, where the tunnel junctions are formed by disorder-induced tunnel barriers 108A, 108B, and the disorder is generated by spatial crystal defects in the superconducting material. The qubit 102, and in some examples the entire qubit circuit 300, can be formed using the method according to the second aspect of the present invention according to any one of the embodiments disclosed herein (e.g., the method 200 described below and / or Figure 2 Figure 5 the method 500 of

[0083] In Figure 3a , Figure 3b 's example, the qubit 102 is embodied as a SQUID-based charge qubit, i.e., a SQUID-based Xmon qubit (as an example of a transmon qubit). The qubit 102 includes a cross-shaped (or X-shaped) superconducting island 104 and superconducting reservoirs 106, and in this example, the superconducting reservoirs are formed by a reference electrode 302 (such as a grounded electrode or a ground plane surrounding the superconducting island 104). The island 104 is separated from the reference electrode 302 by a (e.g., cross-shaped) gap in which no superconducting material is arranged, but rather, for example, the underlying substrate 110 is exposed, as Figure 3a shown. The substrate 110 can be embodied, for example, as described above for the qubit circuit 100. The island 104 and the reference electrode 302 are weakly coupled via a superconducting quantum interference device (SQUID) 304 formed by a superconducting loop including a pair of tunnel junctions, and each of the pair of tunnel junctions is respectively formed by disorder-induced tunnel barriers 108A and 108B. Each tunnel junction further includes a physical constriction, i.e., a part of the superconducting loop has a reduced cross-sectional area, for example, as Figure 3b shown by a reduced width. The width of the physical constriction can be, for example, less than 10% of the width of the arm of the island 104 to which the SQUID 304 is connected and / or arranged in, preferably less than 5%, most preferably less than 1%, and in some examples less than 0.5%.

[0084] The qubit 102 of the qubit circuit 300 can be at least approximately described by a Hamiltonian of the following form (e.g., see J. Koch et al., Phys. Rev. A 76, 042319 (2007))

[0085]

[0086] where E Ji denotes the Josephson energies of the first / left and second / right tunnel junctions, respectively, and φ i denotes the phase differences across the first / left and second / right tunnel junctions, respectively, and E C denotes the charging energy of the superconducting island 104, denotes the number of Cooper pairs on the island 104, and n g denotes the effective offset charge number. As a result of the magnetic flux quantization along the loop of the SQUID 304, the contribution of the Josephson energy can be adjusted by changing the magnetic flux Φ through the SQUID 304 (i.e., the magnetic flux threading the loop of the SQUID 304). Thereby, the energy levels of the qubit 102, in particular the energy gap between the ground state and the first excited state, can be tuned (flux tuning):

[0087]

[0088] where

[0089]

[0090] and d is a parameter taking into account the critical current asymmetry.

[0091] The parameters and / or physical dimensions of the qubit 102 and the tunnel barriers 108A, 108B can be selected, for example, similarly to those described above for the qubit circuit 100 of Figure 1a , Figure 1b . The total capacitance of the island 104 can be controlled by correspondingly selecting the physical dimensions and / or shape and / or the spacing between the island 104 and the surrounding reference electrodes 302, thereby controlling the charging energy C ∑ . The length of each arm of the cross-shaped island 104 can be, for example, between 10 μm and 2000 μm, in some examples between 20 μm and 500 μm, and in one example between 100 μm and 200 μm. The width of each arm of the cross-shaped island 104 (which can be, for example, equal to the width or diameter of the loop of the SQUID 304) can be, for example, between 2 μm and 200 μm, in some examples between 5 μm and 100 μm, and in one example between 10 μm and 30 μm.

[0092] The qubit circuit 300 further includes a readout electrode 306 for reading out the state of the qubit 102 and a control electrode 308 for manipulating the state of the qubit 302. Both the readout electrode 306 and the control electrode 308 are capacitively coupled to a respective arm of the island 104. The readout electrode 306 may be coupled to and / or included in a readout circuit, for example, a transmission readout circuit having a readout resonator, such as, for example, in the qubit circuit 400 described below Figure 4a , Figure 4b . The control electrode 308 may be coupled to and / or included in a control circuit, for example, similar to the qubit circuit 400 described below Figure 4a , Figure 4b . In some examples, the control circuit may couple the qubit 102 to one or more other qubits and / or one or more quantum gates.

[0093] The qubit circuit 300 also includes a flux bias line 310. The flux bias line 310 may be inductively coupled to the SQUID 304 and / or the qubit 102. The flux bias line 310 may be configured to generate a magnetic field or magnetic flux through the SQUID 304. The magnetic field strength or magnetic flux may be controlled by adjusting the current through the flux bias line 310, for example, for flux tuning of the energy separation of the qubit 102. The flux bias line 310 may be coupled to and / or included in a flux bias circuit, for example, similar to the qubit circuit 400 described below Figure 4a , Figure 4b .

[0094] Figure 3a , Figure 3b . Some or preferably all of the structures shown in (i.e., the qubit 102 with the island 104, the reservoir 106, and the SQUID 304 with the tunnel barriers 108A, 108B, the reference electrode 302, the readout electrode 306, the control electrode 308, and / or the flux bias line 310) may be made of the same high-temperature superconducting material. In one example, the superconducting material is a nitride-based superconductor, such as NbTiN. The corresponding structures may in particular be formed from the same film of the high-temperature superconducting material, which may, for example, be arranged on a substrate 110, similar to that described above for the qubit circuit 100 of Figure 1a , Figure 1b . The corresponding structures may, for example, be formed by patterning the film, for example, as described below for the method 500 of Figure 5 .

[0095] Figure 4a Depicts a circuit diagram of a superconducting qubit circuit 400 according to a first aspect of the present invention according to another example. Figure 4bDepicts a circuit diagram of a flux bias circuit 408 for a superconducting qubit circuit 400 (simply referred to as qubit circuit 400) and / or a flux bias circuit of a superconducting qubit circuit.

[0096] The qubit circuit 400 is similar to Figure 1a 、 Figure 1b qubit circuit 100 of Figure 3a 、 Figure 3b and qubit circuit 300 of. The qubit circuit 400 also includes a SQUID-based superconducting charge qubit 102 (simply referred to as qubit 102), where the SQUID 304 is arranged between the superconducting island 104 and the superconducting reservoir 106 / ground plane 302, readout electrode 306, control electrode 308, and flux bias line 310, all of which can be implemented, for example, as in qubit circuit 100 and / or qubit circuit 300. The island 104 is weakly coupled to the reservoir 106 / ground plane 302 via a pair of tunnel junctions in the SQUID 304. At the same time, the island 104 is also capacitively coupled to the reservoir 106 / ground plane 302 via an additional shunt capacitor C q capacitively, as described above, and the additional shunt capacitor can be customized, for example, by appropriately selecting the physical size and / or shape of the island 104, for example, to achieve a desired ratio E J / E C .

[0097] The readout electrode 306 is included in the readout circuit 402, and the readout electrode is capacitively coupled to the island 104 of the qubit 102 with a readout capacitance (diagnostic capacitance) C d capacitively. The readout circuit 402 is coupled to (and / or includes) a readout line 404, which in this example is embodied as a transmission readout line. The readout circuit 402 includes a diagnostic resonator, which in this example is embodied as a λ / 4 resonator. The readout capacitance C d can determine the coupling strength between the island 304 and the readout electrode 306 / readout circuit 402, for example, the rate at which photons can be exchanged between the qubit 102 and the diagnostic resonator. Therefore, the readout capacitance C d can determine the change χ in the resonator frequency associated with the transition between qubit states, for example, as detailed below. The readout circuit 402 can be inductively coupled to the readout line 404, for example, at the current node of the diagnostic resonator. For example, the readout circuit 402 can be implemented as described by Koch et al., Phys. Rev. A 76, 042319 (2007), R. Barends et al., Phys. Rev. Lett. 111, 080502 (2013), and / or A. Wallraff et al., Nature 431, 162 - 167 (2004).

[0098] Since the qubit 102 is coupled to the readout circuit 402, the resonator frequency of the diagnostic resonator can depend on the state of the qubit 102. A transition between qubit states can change the resonator frequency, for example, by a dispersive shift +χ (or -χ). For example, the coupling strength between the qubit 102 and the resonator can be chosen such that the dispersive shift χ is between 2 and 10 times the resonator linewidth (Q factor), preferably between 3 and 5 times. Additionally or alternatively, the frequency shift x can be, for example, between 0.5 MHz and 100 MHz, preferably between 1 MHz and 10 MHz, and in some examples between 3 MHz and 8 MHz. This can be achieved, for example, by choosing the ratio (voltage divider) β between the readout capacitance C d and the total capacitance C ∑ of the qubit 102, where β can be, for example, between 0.05 and 0.2. In some examples, the dispersive shift can be (at least approximately) scaled as

[0099]

[0100] where represents the root mean square voltage on the resonator associated with one photon (e.g., a microwave photon), e represents the elementary charge, and Δ 0 represents the qubit resonator detuning, see Koch et al., Phys. Rev. A 76, 042319 (2007). The resonator can be detuned from the energy gap of the qubit 102, in particular negatively detuned (such that the resonator frequency is higher than the frequency associated with the energy gap E 01 of the qubit 102). The detuning Δ 0 can be, for example, between 1% and 20% of the energy gap E 01 , preferably between 2% and 15%, most preferably between 5% and 10%, and / or can be between 0.5 GHz and 5 GHz, preferably between 1 GHz and 3 GHz. For example, the value of the readout capacitance C ∑ can be adjusted (especially in relation to the total capacitance C d to adjust the ratio β) to have a desired dispersive shift between the qubit and the resonator at a given detuning. In a preferred embodiment, the qubit circuit 400 operates in a so-called "straddling regime", where 0 < Δ 0 < E C , and in the straddling regime, a larger dispersive shift can be achieved, also see Koch et al., Phys. Rev. A 76, 042319 (2007).

[0101] with the capacitance C cThe control electrode 308 capacitively coupled to the island 104 of the qubit 102 is included in the control circuit 406, which can be used, for example, to manipulate the state of the qubit 102, such as to excite the qubit 102. Additionally or alternatively, the control electrode 308 (or preferably, an additional control electrode capacitively coupled to the left arm of the island 104, not shown for simplicity in Figure 3a and Figure 4a ) can be used to manipulate the state of the qubit 102 by coupling the qubit 102 to one or more other qubits and / or one or more quantum gates (e.g., by capacitively coupling to a quantum bus resonator).

[0102] The qubit circuit 400 can further include a flux bias circuit 408 having a flux bias line 310. The flux bias line 310 can be inductively coupled to the qubit 102, for example, having a mutual inductance M with the SQUID 304, and having a mutual inductance M' with the entire qubit 102 (i.e., the entire circuit including the shunt capacitance C q ). The ratio of the inductances M' and M (i.e., M' / M) can be, for example, between 0.01 and 0.3, preferably between 0.02 and 0.2, and in some examples between 0.05 and 0.15. The inductance M of the SQUID 304 can be, for example, between 0.5 pH and 10 pH, and in some examples between 1.0 pH and 3.0 pH.

[0103] Figure 5 FIG. shows a flowchart of a method 500 for forming a superconducting qubit including a tunnel junction according to a second aspect of the present invention. A superconducting qubit circuit (or its qubit) according to the first aspect of the present invention can be formed, for example, using the method 500 according to any one of the embodiments described herein, such as any one of the superconducting qubit circuits 100, 300, and 400. Hereinafter, the superconducting qubit circuits 300 and 400 are used as non-limiting examples for illustrative purposes. The method 500 is not limited to Figure 5 the execution order implied by the flowchart. As long as technically feasible, the method 500 can be executed in any order, and its steps can be at least partially executed simultaneously. For example, the disorder-induced tunnel barrier generated in step 506 can be generated before, during, and / or after forming the elements of the superconducting qubit circuit in steps 504 and 506.

[0104] The method 500 includes, in step 502, forming a high-temperature superconducting material (e.g., NbTiN, e.g., Nb 0 . 62 Ti 0 . 38A film of N), especially a thin film. The substrate 110 can be an insulating substrate, such as a MgO substrate, preferably a crystalline MgO substrate with a well-defined crystal orientation, for example, a MgO substrate with a cubit (100) orientation. The film can be deposited on the substrate 110, for example, by physical vapor deposition (e.g., pulsed laser deposition). To form the NbTiN film, for example, a NbTi target can be ablated by a laser (e.g., a pulsed infrared laser) in a nitrogen atmosphere, preferably in an ultra-high purity nitrogen atmosphere. The film can be deposited, for example, at a rate between 0.1 nm / min and 10 nm / min, preferably between 0.5 nm / min and 2 nm / min. The film can be deposited with a thickness between 5 nm and 200 nm, preferably between 10 nm and 100 nm, and in one example, between 20 nm and 50 nm. The film can be deposited with a uniform thickness, where the thickness can vary, for example, by less than 20% throughout the film, preferably less than 10%. The critical temperature of NbTiN can vary with the thickness of the film and can be, for example, about 11 K at a thickness of 20 nm, 15 K at a thickness of 50 nm, and 16 K at a thickness of 100 nm.

[0105] In step 504, a mask (e.g., an etching mask) for forming a superconducting structure for forming qubits and / or qubit circuits is formed on the superconducting film. The mask can be used, for example, to form some or all of the elements of the qubit circuit 300 or 400, for example, to form the superconducting island 104, the superconducting reservoir 106, the reference electrode / ground plane 302, the SQUID 304 (including, in some examples, a physical constriction of the tunnel junction), the readout electrode 306, the control electrode 308, and / or the flux bias line 310. In some examples, the mask can also be used to form some or all of the readout circuit 402, the readout line 404, the control circuit 406, and the flux bias circuit 408, at least partially, and in some examples, entirely.

[0106] The mask can be formed, for example, by photolithography, in particular electron beam lithography. A resist (e.g., a positive resist or a negative resist) can be formed on the superconducting film by spin coating. The resist can then be patterned and developed by photolithography. In some examples, different resists can be used to form the mask. For example, a first resist is used to form larger features (e.g., island 104, ground plane 302, readout electrode 306, control electrode 308, and / or flux bias line 310), and a second resist different from the first resist is used to form smaller features (e.g., SQUID 304 having a tunnel junction portion and / or a capacitive element between island 104 and readout electrode 306, control electrode 308, and / or flux bias line 310). The first resist can be, for example, a low-resolution resist configured for a photolithography resolution between 10 nm and 50 nm (e.g., AR-N 7520 electron beam resist from Allresist GmbH), and the second resist can be a high-resolution resist configured for a photolithography resolution between 1 nm and 10 nm (e.g., AR-P6200 electron beam resist from Allresist GmbH).

[0107] In step 506, the superconducting film is patterned using the mask to form superconducting structures of qubits and / or qubit circuits (e.g., the aforementioned elements of qubit circuit 300 or 400). The superconducting film can be patterned, for example, by etching using the mask as an etch mask, in particular reactive ion etching (e.g., in a fluorine plasma). The etching rate can be, for example, between 2 nm / min and 100 nm / min, preferably between 5 nm / min and 30 nm / min. Subsequently, the mask can be removed. In some examples, step 506 can also include polishing of the superconducting film, in particular ion polishing, such as argon ion polishing.

[0108] In step 508, the tunnel junctions of SQUID 304 are formed by generating disorder-induced tunnel barriers 108A, 108B in the superconducting structure / membrane. The tunnel barriers 108A, 108B are generated by introducing spatial crystal defects into the superconducting material, for example, by irradiating with inert gas ions. In this example, the tunnel barriers 108A, 108B are directly written by a focused helium ion beam. For this purpose, a helium ion microscope can be used, where the resolution of the helium ion microscope is preferably lower than 2.0 nm, most preferably between 1.0 nm, for example, between 0.2 nm and 1.0 nm. The helium ions can have a kinetic energy between 20 keV and 40 keV, in some examples between 25 keV and 35 keV, for example 30 keV. The regions of the tunnel barriers 108A, 108B can be, for example, with the dose as described above (e.g., at 5·10 18 ions / cm 2 to 5·1019 ions / cm 2 irradiated with a dose between). For example, the dose can be selected such that the tunnel junction is a superconducting-normal-superconducting (SNS) or superconducting-insulating-superconducting (SIS) tunnel junction. The tunnel barriers 108A, 108B can be formed, for example, to a length between two to six times the coherence length of the superconducting material. For Nb 0 . 62 Ti 0 . 38 N, the coherence length can be, for example, about 2.5 nm.

[0109] The embodiments of the invention disclosed herein are only specific examples for illustrative purposes. The invention can be implemented in various ways and many modifications can be made without changing the underlying basic nature. Therefore, the invention is defined only by the claims as described above.

Claims

1. A superconducting qubit circuit (100, 300, 400) having a superconducting qubit (102), wherein: The superconducting qubit (102) comprises a tunnel junction in a superconducting material having a critical temperature above 1.2 K, the tunnel junction being formed by a disorder-induced tunnel barrier (108, 108A, 108B), wherein the disorder is generated by spatial crystal defects in the superconducting material.

2. The superconducting quantum bit circuit (100, 300, 400) according to claim 1, wherein: The superconducting material has a critical temperature of at least 4.2 K, preferably at least 10 K, and / or wherein the superconducting material has a superconducting energy gap of greater than 0.2 meV, preferably at least 1.0 meV, most preferably at least 2.0 meV.

3. The superconducting quantum bit circuit (100, 300, 400) according to claim 1 or 2, wherein: The superconducting qubit circuit (100, 300, 400) is configured to operate at an operating temperature of at least 1.0K, preferably at least 1.5K, and most preferably at least 2.0K.

4. The superconducting qubit circuit (100, 300, 400) of any one of the preceding claims, wherein: The superconducting material comprises a nitride-based superconductor, in particular one or more of niobium titanium nitride (NbTiN), niobium nitride (NbN) and titanium nitride (TiN), and / or wherein: The superconducting material includes one or more of yttrium barium copper oxide (YBCO), magnesium diboride (MgB2), bismuth strontium calcium copper oxide (BSCCO) and iron-based superconductors.

5. The superconducting qubit circuit (100, 300, 400) of any one of the preceding claims, wherein: The spatial crystal defects in the tunnel barrier (108, 108A, 108B) are produced by irradiation with noble gas ions, in particular helium ions and / or neon ions, preferably by irradiation with a focused ion beam of noble gas ions; and / or The tunnel barrier is free of aluminum oxide, in particular wherein the tunnel junction is free of aluminum.

6. The superconducting qubit circuit (100, 300, 400) of any one of the preceding claims, wherein: The cross-sectional area of ​​the tunnel barrier (108, 108A, 108B) is less than 3.0 . 10 4 nm 2 , preferably less than 2.0 . 10 4 nm 2 , most preferably less than 1.5 . 10 4 nm 2 , and / or where The length (L) of the tunnel barrier (108, 108A, 108B) is between 0.5 nm and 50 nm, preferably between 1 nm and 25 nm, most preferably between 5 nm and 15 nm.

7. The superconducting qubit circuit (100, 300, 400) of any one of the preceding claims, wherein: The normal state resistance of the tunnel junction is at least 100Ω, preferably at least 200Ω, most preferably at least 300Ω; and / or The total capacitance of the superconducting qubit is at least 10 fF, preferably at least 20 fF, most preferably at least 50 fF; and / or The critical current of the tunnel junction is less than 1.0 μA, preferably less than 0.5 μA, and most preferably less than 0.2 μA.

8. The superconducting qubit circuit (100, 300, 400) of any one of the preceding claims, wherein: The superconducting quantum bit (102) is a charge quantum bit, in particular a charge quantum bit based on a SQUID, wherein the Josephson energy E of the charge quantum bit is J With charging energy E C The ratio E J / E C between 50 and 1000, preferably between 200 and 600; and / or The energy interval of the superconducting quantum bit (102) is between 10 GHz and 100 GHz, preferably between 20 GHz and 50 GHz.

9. The superconducting qubit circuit (100, 300, 400) of any of the preceding claims, further comprising one or more of a readout electrode (306) and / or a readout circuit (402, 404) for reading out the state of the superconducting qubit (102), a control electrode (308) for manipulating the state of the superconducting qubit (102), and a flux bias line (310) for adjusting the energy interval of the superconducting qubit (102), in particular wherein: One or more, preferably all, of the tunnel junction and the readout electrode (306), the readout circuit (402, 404), the control electrode (308) and the flux bias line (310) are made of the superconducting material, in particular of the same film of the superconducting material.

10. A method (200, 500) of forming a superconducting qubit (102) comprising a tunnel junction, the method (200, 500) comprising: A superconducting structure (104, 106) forming the superconducting qubit (102), the superconducting structure (104, 106) being formed of a superconducting material having a critical temperature higher than 1.2K; and The tunnel junction is formed by creating a disorder-induced tunnel barrier (108, 108A, 108B) in the superconducting structure (104, 106), the tunnel barrier (108, 108A, 108B) being created by introducing spatial crystal defects into the superconducting material.

11. The method (200, 500) of claim 10, wherein: The spatial crystal defects are introduced into the superconducting material by irradiating the superconducting material with noble gas ions, in particular helium ions and / or neon ions, preferably by irradiating the superconducting material with a focused ion beam of noble gas ions.

12. The method (200, 500) of claim 11, wherein: The superconducting material is 10 17 ions / cm 2 and 10 21 ions / cm 2 Between, preferably 10 18 ions / cm 2 and 10 20 ions / cm 2 and / or wherein the superconducting material is arranged on a substrate (110), and the kinetic energy of the noble gas ions is selected so that the noble gas ions penetrate the superconducting material into the substrate (110).

13. The method (200, 500) of any one of claims 10 to 12, wherein: Forming the superconducting structure (104, 106) comprises forming a film of the superconducting material and patterning the film to form the superconducting structure (104, 106), in particular wherein the method (200, 500) further comprises forming one or more of a readout electrode (306) and / or a readout circuit (402, 404) for reading out the state of the superconducting qubit (102), a control electrode (308) for manipulating the state of the superconducting qubit (102), and a flux bias line (310) for adjusting the energy spacing of the superconducting qubit (102), in particular wherein one or more, preferably all, of the readout line (306), the readout circuit (402, 404), the control line (308) and the flux bias line (310) are formed from the film of the superconducting material.

14. The superconducting quantum bit circuit (100, 300, 400) according to any one of claims 1 to 9, wherein: The superconducting qubit (102) can be obtained using the method (200, 500) according to any one of claims 10 to 13.

15. Use of a superconducting quantum bit circuit (100, 300, 400) as claimed in any one of claims 1 to 9 or claim 14, wherein: The superconducting qubit circuit (100, 300, 400) operates at an operating temperature of at least 1.0K, preferably at least 1.5K, most preferably at least 2.0K.

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