Elevated-temperature superconducting qubits with disorder-induced tunnel barriers

Abstract

To provide a superconducting qubit circuit and a method for forming a superconducting qubit.SOLUTION: A superconducting qubit circuit 100 comprises a superconducting qubit 102. Superconducting structures 104 and 106 formed by the superconducting qubit comprise a tunnel junction in a superconduction material having a critical temperature that exceeds 1.2K. The tunnel junction is formed in disorder-induced tunnel barrier 108, and the disorder is created by a spatial crystallographic defect in the superconducting material.SELECTED DRAWING: Figure 1a

Description

Technical Field

[0001] The present invention relates to the field of quantum computing. In particular, the present invention relates to a superconducting quantum bit circuit having a superconducting quantum bit with a tunnel junction, and a method of forming a superconducting quantum bit with a tunnel junction.

Background Art

[0002] A quantum computer can solve certain classes of problems more quickly than a classical computer. This is achieved by using a quantum mechanical two-level system that can assume a quantum mechanical superposition of two states, instead of a classical bit that can only be in one of two states ("0" and "1").

[0003] Challenges in the implementation of quantum computers relate to the implementation form and operation of quantum bits. A promising approach is to use tunnel junction-based quantum bits, such as Josephson junctions within (or between) superconducting bodies. Cryogenic superconductors, such as elemental superconductors like aluminum (Al), have been used to form Josephson junctions and quantum bits with a coherence time approaching 1 millisecond. In the urgent quest for emerging quantum technologies, Josephson junction-based technologies and aluminum-based quantum bits have successfully demonstrated quantum supremacy and produced the first generation of commercially available quantum computers.

[0004] However, despite their high quality and merits, Al Josephson junctions, and in general all qubit devices based on low-temperature superconductors, have several intrinsic limitations due to the relatively low quality factor of the Josephson junctions (the quality factor or characteristic voltage of the junction can be defined as the product between its critical current and normal state resistance value), as well as the low critical temperature and small superconducting gap of aluminum (i.e., about 1.2 K and about 50 GHz / 0.2 meV, respectively), which affect the dynamics of Al Josephson junctions and qubit devices and typically require an operating temperature in the low mK range. In addition, Al Josephson junctions are strongly affected by magnetic fields due to the intrinsic superconducting properties of Al, such as its small superconducting gap. The low operating temperature causes significant technical challenges and costs, especially in the operation of quantum computers equipped with qubits based on low-temperature superconductors. For example, it requires the use of dilution refrigerators to cool the entire quantum processor, as well as its components including qubits and Josephson junctions. In addition to the need for a low operating temperature, the readout and write frequencies of qubits with low-temperature superconductor Josephson junctions can also be limited. The same problems for qubits based on low-temperature superconductors also apply when such qubits are used in other quantum devices, such as quantum sensors.

[0005] Superconducting materials with a higher critical temperature and / or a larger superconducting energy gap than aluminum have been known for a long time, but such materials often cause other problems, especially regarding the manufacturing of Josephson junctions in such materials and, in particular, the suitability of such devices for use in qubits. SUMMARY OF THE INVENTION

[0006] Accordingly, an object of the present invention is to improve superconducting qubits so as to provide a high operating temperature, a high readout and / or write frequency, an improved critical current, an improved quality factor, an improved noise characteristic, 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 with a tunnel junction according to claim 1, and a method of forming a superconducting qubit with 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 comprising a superconducting qubit. The superconducting qubit comprises a tunnel junction within a superconducting material having a critical temperature above 1.2K. The tunnel junction is formed by a disorder-induced tunnel barrier, and the disorder is created by spatial crystallographic defects within 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), it may include one or more additional levels or states, but such states may be sufficiently detuned or separated so as to avoid populating such states. A superconducting qubit may represent a qubit that is at least partially formed from a superconducting material (i.e., a material that exhibits an electrical resistance that disappears below a critical temperature) (e.g., including or consisting of a superconducting material), and includes, for example, one or more superconducting islands, one or more superconducting electrodes, one or more superconducting contacts, and / or one or more superconducting structures such as one or more superconducting wires or leads.

[0010] In the context of the present disclosure, a tunnel junction may refer to a junction, connection, or linkage 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 (e.g., may comprise) by a tunnel barrier that separates the two or more structures. Thereby, a tunnel junction may form a weak connection between the two or more structures. A tunnel junction may particularly 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 between superconductors (e.g., a point contact) (S-c-S), or a combination thereof. A tunnel junction may be disposed, for example, between two superconducting structures (e.g., a connection), such as an island, an electrode, a contact, and / or a wire, particularly between a superconducting island and a reference electrode, such as a large superconducting reservoir, such as a superconducting structure that is substantially larger than the superconducting island, e.g., a ground electrode / contact (e.g., a ground plane). As used herein, a superconducting island may refer to a superconducting structure that, for example, has no (strong) superconducting connection or connection to other superconducting structures. A superconducting island may be electrically insulated from other superconducting structures, for example, optionally, except for one or more weak connections, such as a tunnel junction. A tunnel junction may comprise a physical constriction and may have, for example, a cross-sectional area that is smaller than the superconducting structures coupled through the tunnel junction, preferably substantially smaller (e.g., less than 50%, in some examples less than 30%, in one example less than 10%). In some examples, a superconducting quantum bit circuit, particularly a superconducting quantum bit, may comprise a plurality of tunnel junctions within a superconducting material, e.g., a pair of tunnel junctions (e.g., as part of a SQUID).

[0011] A superconducting qubit (hereinafter also referred to as a qubit for short) includes a superconducting material in which a tunnel junction is formed (for example, formed within and / or formed from a superconducting material). As used herein, the term "superconducting material" may refer to a material that becomes superconducting, i.e., exhibits zero electrical resistance, below its respective critical temperature and / or emits a magnetic field below its critical temperature. A qubit includes a superconducting material having a critical temperature above 1.2K, 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 with respect to the material used (except for the aforementioned critical temperature). In particular, such materials are not limited to cuprate superconductors and / or superconductors (the "high-temperature superconductors") having a critical temperature above the boiling point of liquid nitrogen.

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

[0013] The superconducting material may have a superconducting energy gap larger than the superconducting energy gap of aluminum (0.2 meV). The superconducting material may have a superconducting energy gap, for example, 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 one example at least 3.0 meV.

[0014] The superconducting quantum bit circuit may be for operating 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 (i.e., it may be suitable to operate or may be configured to operate as such). The described operating temperature can be achieved, for example, by appropriate selection of one or more of the superconducting material (e.g., nitride-based superconductor) and its critical temperature, the substrate material (e.g., silicon, sapphire or MgO), and further its shape and / or physical dimensions (e.g., the cross-sectional area and / or length of the tunnel junction), etc., parameters of the quantum bit and the tunnel junction, the normal state resistance, the total electrostatic capacitance and / or critical current of the tunnel junction, and / or the energy splitting of the quantum bit, the Josephson energy and / or the charging energy, as detailed below. The (maximum) operating temperature of the quantum bit circuit may be limited, for example, by thermal excitation of the quantum bit (e.g., the excited state or other high-energy state of the quantum bit) and / or by quasiparticle excitation in the superconducting material, both of which can disrupt coherence. The energy splitting of the quantum bit and / or the superconducting energy gap, and / or the critical temperature of the superconducting material may be selected such that one or both of the energy splitting and the superconducting energy gap are smaller than, preferably substantially smaller than (e.g., less than 50%, in some examples less than 30%, in one example less than 10%, in one example less than 5%) the thermal energy k O associated with the temperature T B T O . Additionally or alternatively, the coherence and / or maximum operating temperature of the quantum bit can be reduced by reducing the sensitivity of the quantum bit to quasiparticle tunneling and / or charge fluctuations across the tunnel barrier (e.g., as detailed below, the ratio E J of the Josephson energy E C to the charging energy E J / E CBy appropriately selecting (), reducing the sensitivity of the qubit to environmental noise (e.g., magnetic fields and / or charge noise), and / or reducing dielectric losses (e.g., by an appropriate combination of a superconducting material and a substrate material), it may be improved. Since the qubit can maintain its quantum state for a long time before thermal excitation destroys the quantum state, the improvement in coherence time can lead to a high maximum temperature.

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

[0016] The superconducting material is, for example, a nitride-based superconductor, such as one or more of titanium nitride (NbTiN), niobium nitride (NbN), and titanium nitride (TiN), or may include them. Additionally or alternatively, the superconducting material is, for example, 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, or may include them. In one example, the superconducting material is NbTiN, e.g., Nb x Ti 1-x N, where x may be, for example, 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. These materials have, for example, a critical temperature and / or a superconducting energy gap within the ranges described above.

[0017] A tunnel junction of a qubit (hereinafter also referred to as a junction for simplicity) is formed by a tunnel barrier induced by disorder in a superconducting material. As used herein, the term "disorder" may refer to, for example, a random or substantially random deviation within a superconducting material from its ideal structure and / or composition (e.g., from an ideal crystal structure in the absence of impurities). Weak disorder usually does not affect superconductivity, but strong disorder may cause the destruction of the superconducting state, for example, resulting in a superconductor-metal or superconductor-insulator transition. This may occur, for example, when the disorder is strong enough that the mean free path is comparable to the Fermi wavelength (e.g., of the same order of magnitude). Thus, the disorder region can create a tunnel barrier within the superconducting material, thereby forming a tunnel junction.

[0018] This disorder is created by the spatial crystallographic defects of the superconducting material. In the context of the present disclosure, "spatial crystallographic defects" may refer to, for example, spatial deviations, dislocations or interruptions within the crystal structure of the superconducting material. For example, a lattice position or site within the ideal crystal structure of the superconducting material is not occupied by an atom (e.g., a vacancy defect), and / or an atom is arranged at a position different from (e.g., displaced from) the lattice position within the ideal crystal structure of the superconducting material (e.g., an interstitial defect). Thus, spatial crystallographic defects should be distinguished from impurity-based disorder and crystallographic defects such as substitutional defects, and impurity atoms (usually not considered to be within the superconducting material) occupy regular lattice positions in the ideal crystal structure (e.g., as a result of ion implantation as used in U.S. Patent No. 11,538,977). Thus, spatial crystallographic defects may also be referred to herein as "non-impurity crystallographic defects" or "dislocations". Impurities may be present in the superconducting material to at least some extent (usually present), but spatial crystallographic defects are the main form of disorder in the tunnel barrier of the superconducting qubits according to the present invention. Spatial crystallographic defects may in particular be the form of disorder that ultimately contributes to the breakdown of superconductivity in the tunnel barrier, and thus this may also be referred to briefly as "spatial crystallographic defect-induced tunnel barrier" or "dislocation-induced tunnel barrier". In other words, the amount of impurities present in the tunnel barrier may be below, preferably substantially below, the threshold required for superconductivity to degrade. For example, the mean free path between impurities may be at least one order of magnitude smaller than the Fermi wavelength of the superconducting material (e.g., less than 10%), preferably at least two orders of magnitude smaller (e.g., less than 1%). In some examples, the ratio between the amount (e.g., number or density) of impurities (e.g., substitutional defects) and the amount of non-impurity crystallographic defects may be less than 0.5, preferably less than 0.2, most preferably less than 0.1, in some examples less than 0.05, in one example less than 0.02, and in one example less than 0.01.Spatial crystallographic defects can be, or may include, point defects (e.g., a single lattice site, e.g., a single vacancy defect, a single interstitial defect, or a Frenkel defect or pair), line defects (e.g., an edge dislocation or a screw dislocation), planar defects, or combinations thereof. Disorder-induced tunnel barriers can provide the advantage of having no interface between different materials (e.g., in an Al / AlO / Al junction) and / or of being able to bring tunnel barriers / junctions very close to each other. This can be particularly advantageous, for example, for fullerenium qubits and for demonstrating the flux focusing effect in magnetic field measurements.

[0019] In a preferred embodiment, the spatial crystallographic defects in the tunnel barrier are created, for example, by irradiation with ions, in particular silicon ions, and / or noble gas ions such as helium ions and / or neon ions, using the method according to the second aspect of the invention described below. The spatial crystallographic defects within the tunnel barrier are created, in particular, for example, by irradiation with a focused ion beam, for example a focused ion beam of noble gas ions and / or silicon ions, as will be detailed below. For a given thickness (e.g., film thickness) of the superconducting material, the energy of the ions is selected such that the ions penetrate the superconducting material (e.g., into the underlying substrate), preferably without or with minimal lateral spread (e.g., without substantially increasing the diameter of the focused ion beam). The kinetic energy accumulated in the superconducting material by the ions may, for example, result in the creation of defects by local displacement of atoms. While not wishing to limit the present invention to any particular mechanism for creating spatial crystallographic defects and not being bound by any particular theory, disorder may be introduced, for example, by one or both of the following two mechanisms: 1) the ions may remove atoms from the lattice (e.g., knock out), thereby creating vacancies and / or surface roughness (which can be seen, for example, in a cross-sectional image), and 2) the ions may displace atoms, moving them from their original or native positions within the lattice, and the displaced atoms (which cannot be completely removed from the superconducting material) become defects within the lattice (which may also include vacancies created thereby). Since the ions pass through the superconducting material (and thus do not remain within the superconducting material), the irradiation may not create (or only slightly create) impurities within the superconducting material. However, there may already be some impurities present in the superconducting material prior to irradiation (e.g., as a result of the deposition of the superconducting material), and some of them may be displaced by the ions.Due to the high ionization potential of ions (e.g., helium and / or neon ions) and / or their high kinetic energy, for example, on the sample surface and / or within the apparatus used for irradiation (e.g., a focused ion beam system and / or an ion microscope), most impurity atoms or contaminants may be ionized early in the process, resulting in not forming a significant portion of the ions (e.g., an ion beam) that irradiate (e.g., pass through) the sample.

[0020] Preferably, the tunnel barrier does not contain aluminum oxide. In other words, the tunnel barrier (in some examples, the entire tunnel junction may also include a portion of the superconducting material adjacent to the tunnel barrier) may not contain a stoichiometrically significant amount of aluminum oxide. For example, the aluminum oxide content in the tunnel barrier and / or the tunnel junction may be less than 10 -3 less, preferably less than 10 -4 less, most preferably less than 10 -5 and may even be less. In some examples, the tunnel barrier and / or the tunnel junction may not contain aluminum (i.e., any form of aluminum containing elemental aluminum). For example, the aluminum content in the tunnel barrier and / or the tunnel junction may be less than 10 -3 less, preferably less than 10 -4 less, most preferably less than 10 -5 and may even be less.

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

[0022] The length ("width") of the tunnel barrier may be between 0.5 nm and 50 nm, preferably between 1 nm and 25 nm, in some examples between 2 nm and 20 nm, and most preferably between 5 nm and 15 nm. Additionally or alternatively, the length of the tunnel barrier may be on the order of one or both of, for example, the superconducting coherence length and the penetration depth of the superconducting material (e.g., between 0.2 times and 20 times, in some examples between 0.5 times and 10 times, in one example between 2 times and 6 times). The length of the tunnel barrier may be measured longitudinally across the tunnel barrier, for example, parallel to the direction of the current passing through the tunnel barrier. Such short / thin tunnel barriers may be created, for example, by irradiation with a focused ion beam as described below. Using such short / thin tunnel barriers can enable strong tunnel junctions 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 aspects such as improved energy confinement and / or reduced energy loss within superconducting qubit circuits, particularly their readout circuits.

[0023] The normal state resistance R of the tunnel junction Nis at least 100 Ω, preferably at least 200 Ω, most preferably at least 300 Ω, and in some examples at least 400 Ω, and in one example at least 500 Ω. The normal state resistance of the tunnel junction may 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 electrostatic capacitance of the superconducting qubit (e.g., its 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 electrostatic capacitance of the superconducting qubit may 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 electrostatic capacitance C Σ (also referred to as its self-capacitance) of the superconducting qubit, for example, is the sum of the intrinsic capacitance of the tunnel junction C J and, optionally, one or more additional capacitances in parallel with the tunnel junction, in particular an additional parallel capacitance C0 (e.g., grounded), and / or the gate capacitance C g of the superconducting qubit, e.g., C Σ =C J +C0+C g and may include. The normal state resistance of the tunnel junction and the total electrostatic capacitance of the superconducting qubit can determine the characteristics of the superconducting qubit, such as energy splitting, its anharmonicity, and / or its sensitivity to charge noise, as detailed below.

[0024] Additionally or alternatively, the critical current of the tunnel junction may 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 may 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 resulting in a low quality factor / characteristic voltage of the tunnel junction, the low critical current may be advantageous for suppressing charge noise while maintaining an appropriate degree of anharmonicity of the qubit (to obtain a sufficiently isolated effective two-level system), and may enable the implementation of high-frequency qubits with a large energy splitting (e.g., at least 10 GHz, preferably at least 20 GHz). Nevertheless, the normal state resistance may be adjusted (e.g., increased) accordingly to achieve the desired quality factor. For example, previously known isolation / single disorder-based tunnel junctions such as those described by A. Ruhtinas and I. J. Maasilta, arXiv 2303.17348v1 [cond-mat.suprr-con] have substantially large critical currents (and cross-sectional areas and small normal state resistances), making them unsuitable for use in superconducting qubits, particularly high-frequency superconducting qubits.

[0025] In a preferred embodiment, the superconducting qubit is a charge qubit, for example, a Cooper pair box. The ground state of the superconducting qubit may be, for example, the charge state of a superconducting island coupled via a tunnel junction (e.g., to a large superconducting contact, electrode or wire, particularly a large reservoir such as a grounded contact or electrode). The superconducting qubit may in particular be a SQUID-based charge qubit, i.e., a charge qubit comprising a superconducting quantum interference device (SQUID: superconducting quantum interference device) formed by two or more tunnel junctions within a superconducting loop. The SQUID-based charge qubit may, for example, enable flux tuning of the qubit by tuning the flux through the SQUID (e.g., the flux through the superconducting loop) in order to tune the Josephson energy of the tunnel junction. In other examples, the superconducting qubit may also be a different type of qubit, for example, 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 ratio E J of the Josephson energy E C to the charging energy E J / E C of a superconducting qubit (which may be, for example, a charge qubit as described above) is between 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 may be, for example, the energy associated with the tunneling process (e.g., of Cooper pairs) across the tunnel junction, which may be proportional to the critical current I C of the tunnel junction, and E J = φ0I C / (2π), where φ0 represents the magnetic flux quantum and may determine the energy accumulated in the tunnel junction when current passes through the tunnel junction. The charging energy E CIt may be 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 depends on the total capacitance C of the qubit Σ , and for example, E C = e 2 / (2C Σ ), where e represents the elementary charge. The ratio E J / E C within the above range can, for example, enable reduction of the qubit's sensitivity to charge noise while maintaining a sufficient degree of anharmonicity. In some examples, the qubit may be embodied as a transmon qubit (e.g., a charge qubit with a tunnel junction and an additional parallel capacitance in parallel, as described in, for example, J. Koch et al., Phys. Rev. A 76, 042319 (2007), or a variation thereof). The qubit may in particular be embodied as an Xmon qubit (e.g., R. Barends et al., Phys. Rev. Lett. 111, 080502 (2013) or a variation thereof). In other examples, the qubit may be, for example, a Gatemon qubit.

[0027] The energy splitting of the superconducting qubit may 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. The energy splitting used herein may refer to, for example, the energy difference between the ground state and the excited state that forms a two-level (or effective two-level) system of the superconducting qubit. Such a large energy splitting may be enabled, for example, by a large superconducting energy gap of the superconducting material and may enable, for example, a high operating frequency (e.g., readout and / or write frequency).

[0028] In some embodiments, the superconducting quantum bit circuit may comprise one or more additional elements in addition to the superconducting quantum bits, while in other examples, the claimed superconducting quantum bit circuit may consist of only superconducting quantum bits. Some or all of the elements of the superconducting quantum bit circuit may be formed (e.g., include or be composed of) a superconducting material, preferably the same superconducting material as the superconducting quantum bits. Additionally, the superconducting quantum bit circuit may also comprise one or more normal conducting elements and / or structures, and / or one or more insulating elements and / or structures.

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

[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 having a thickness of 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 comprise one or more layers. The superconducting material may particularly be a superconducting thin film. As used herein, the term "thin film" may refer to a film having a thickness that is sufficiently thin such that, for example, one or more properties related to superconductivity within the film, such as the critical temperature, differ from those of the bulk material. In such cases, the critical temperature of the superconducting material as used herein may refer to the critical temperature of the film (rather than that 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 (and optionally, the control circuit and / or flux bias circuit) 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., include and / or are composed of the same superconducting material). The tunnel junction, and one or more, preferably all, of the above-mentioned readout line, readout circuit, control line, and flux bias line (and optionally, the control circuit and / or flux bias circuit) may particularly be made of the same film of superconducting material, for example, by patterning a film of superconducting material to form each circuit element.

[0032] In some examples, a superconducting qubit circuit may include a plurality of qubits, for example (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 a superconducting qubit circuit may comprise any number of qubits. Each of the above qubits may be embodied as described above, for example. Additionally or alternatively, a superconducting qubit circuit may comprise one or more quantum gates (quantum logic gates), each of which may act on one or more qubits, preferably two or more qubits. In some examples, a superconducting qubit circuit may be or comprise a quantum processor, or may be for use in a quantum processor (and in some examples a part thereof). Additionally or alternatively, a superconducting qubit circuit may be or comprise a quantum sensor, or may be for use in a quantum sensor (and in some examples a part of the quantum sensor). In some examples, a superconducting qubit circuit may be embodied or disposed on and / or in a chip or chip package.

[0033] According to a second aspect of the present invention, there is provided a method of forming a superconducting qubit including a tunnel junction. 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 1.2K. The method further includes forming a tunnel junction by creating a randomly induced tunnel barrier within the superconducting structure, the tunnel barrier being created by introducing a spatial crystallographic defect into the superconducting material.

[0034] Superconducting qubits, tunnel junctions, superconducting materials, tunnel barriers, and / or spatial crystallographic defects may be embodied and / or formed, for example, as in a superconducting qubit circuit according to a first aspect of the invention according to any one of the embodiments described herein, i.e., may have or comprise some or all of the characteristics of each element of a superconducting qubit circuit according to the first aspect disclosed herein. The method according to a second aspect may be used to form a 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. If technically feasible, the method may be executed in any order, and its steps may be executed at least partially simultaneously. For example, spatial crystallographic defects may be introduced into the superconducting material before, during, and / or after the formation of the superconducting structure.

[0035] The superconducting structure of a qubit may, for example, as described above, be or comprise one or more superconducting islands and / or one or more superconducting reservoirs, or may be formed to couple superconducting island(s) to superconducting reservoir(s) in order to provide a weak connection therebetween. In some examples, a plurality of tunnel junctions, for example, a pair of tunnel junctions (e.g., to form a SQUID) may be formed. Additionally or alternatively, the superconducting structure may be or comprise one or more other structures such as one or more superconducting electrodes, one or more superconducting contacts, and / or one or more superconducting lines or wires. The superconducting structure may be composed of (e.g., exclusively formed from) a high-temperature superconducting material, or may comprise it (e.g., in particular, be formed from it).

[0036] To form a tunnel junction, a disorder-induced tunnel barrier is created within the superconducting structure, and the tunnel barrier may be created before, during, and / or after the formation of the superconducting structure. The tunnel barrier is created by introducing spatially crystallographic defects into the superconducting material, i.e., the "spatially crystallographic defect-induced tunnel barrier" or "dislocation-induced tunnel barrier" described above. This may include introducing such defects to the extent that they cause a disruption of superconductivity within the superconducting material, e.g., to cause a superconductor-insulator transition, or a superconductor-normal conductor transition (e.g., a superconductor-metal transition) (e.g., in terms of number and / or density). In some examples, forming the tunnel junction may also include forming a physical constriction, e.g., within or at the boundary of the superconducting structure of a qubit. The tunnel barrier may be created at the physical constriction.

[0037] Spatial crystallographic defects in superconducting materials may be introduced, for example, by irradiation of the superconducting material, in particular, high-energy irradiation (for example, using 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, in one example at least 40 keV). The particle energy may be selected, for example, based on the thickness of the superconducting material (for example, film thickness), and / or the length of the tunnel barrier. For example, in the case of a thick superconducting material (for example, to adjust the dynamic inductance and / or increase the critical temperature), higher particle energy may be used than in the case of a thin superconducting material. The irradiation may be electromagnetic irradiation (for example, by X-rays and / or gamma rays), and / or irradiation by a large number of particles such as electrons and / or ions, for example, by a focused electron beam and / or a focused ion beam, or may include them. The irradiation may be, for example, target irradiation using a focused beam. Preferably, the irradiation is mask-free, i.e., the superconducting material is irradiated without a mask being placed thereon to block radiation. Additionally or alternatively, spatial crystallographic defects may also be introduced when forming (for example, depositing, growing, and / or patterning) the superconducting material.

[0038] Irradiation for introducing crystallographic defects in space may be adapted to the superconducting material used and / or to the superconducting structure, in particular to one or more of its physical dimensions, for example the length of the tunnel barrier and / or the thickness of the superconducting structure / material (for example the film thickness). For this purpose, parameters of the irradiation such as the type of radiation (for example electromagnetic radiation versus ionizing radiation), the type of particles of the radiation (for example the type of ions used), the particle energy (for example the acceleration voltage and / or the wavelength), the dose, the fluence (for example the intensity and / or the ion beam current) and / or the residence time may be adapted to the superconducting material and / or the superconducting structure used (for example as selected based thereon). Preferably, the irradiation is adapted such that the irradiation can penetrate the superconducting material and / or the superconducting structure, for example into the substrate under the superconducting material and superconducting structure, preferably with no or minimal lateral spread.

[0039] In a preferred embodiment, the crystallographic defects in space in the superconducting material are introduced by irradiating the superconducting material with noble gas ions, in particular helium ions. Additionally or alternatively, silicon ions and / or other noble gas ions such as, for example, neon ions may also be used.

[0040] Spatial crystallographic defects in superconducting materials may be introduced by irradiation with a focused ion beam, particularly a focused ion beam of noble gas ions and / or silicon ions, such as a focused helium ion beam and / or a focused neon ion beam. The use of a focused ion beam targets the spatial crystallographic defects in a specific part or region of the superconducting material or structure, facilitating a well-controlled introduction even at a very short length scale, and thus enabling the "direct writing" of disorder-induced tunnel barriers within the superconducting structure. The spot size of the focused ion beam in the superconducting material may be, for example, less than 20 nm, in some examples less than 10 nm, preferably less than 5 nm, most preferably less than 2 nm, in one example less than 1 nm, and in one example less than 500 pm. The spot size may 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 may be irradiated with ions, particularly noble gas ions such as helium and / or neon ions, and / or silicon ions, at 10 16 ions / cm 2 ~10 22 ions / cm 2 preferably between 10 17 ions / cm 2 ~10 21 ions / cm 2 most preferably between 10 18 ions / cm 2 ~10 20 ions / cm 2 in one example between 5*10 18 ions / cm 2 ~5*10 19 ions / cm 2It may be irradiated with a dose in between. For example, based on the thickness of the superconducting material (e.g., the height of the tunnel barrier), and / or based on the superconducting material used (for example, nitride-based superconductors may require a significantly larger dose (e.g., a dose two orders of magnitude larger) than, for example, YBCO, to suppress superconductivity), the dose may be selected based on the amount of disorder, in particular, the amount of spatially crystallographic defects introduced into the superconducting material. Thereby, precise control of the properties, in particular the electrical properties of the tunnel barrier, for example, the resistivity of the tunnel barrier (e.g., to form an insulating or metallic tunnel barrier) may be made possible.

[0042] The superconducting material may be disposed on a substrate, particularly an insulating substrate. The superconducting material may be irradiated, for example, in a direction perpendicular to the surface, through its surface exposed from the substrate (e.g., facing away from the substrate). The kinetic energy of the ions (e.g., noble gas ions) is such that the ions penetrate the superconducting material into the substrate, for example, at least 80%, preferably at least 90%, most preferably at least 95%, in some examples at least 98%, in one example 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 may make it possible to introduce (mainly) spatial crystallographic defects rather than impurities (in contrast to, for example, ion implantation into the superconducting material). The kinetic energy of the ions may be, for example, 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. Preferably, the ions penetrate the superconducting material with little or minimal lateral spread (e.g., width or diameter) such that the lateral spread (e.g., width or diameter) of the irradiation region or spot (e.g., the lateral extent of a focused ion beam) does not substantially vary across the thickness of the superconducting material, for example, varying (e.g., increasing) by less than a factor of 2, preferably less than a factor of 1.5, in one example less than a factor of 1.2 across the thickness of the superconducting material. This ensures a uniform disordered region throughout the superconducting material, maintains the superconducting properties of other parts of the superconducting material, enables the realization of low kinetic inductance, and / or enables the reproducible manufacture of tunnel junctions having desired parameters such as a desired junction length, a desired critical current, and / or a desired normal state resistance.

[0043] The technique(s) used to form the superconducting structure is not particularly limited and can be any technique(s) known in the art for forming a superconducting structure or may include the same. Forming the superconducting structure may include depositing and / or patterning a superconducting material. The superconducting material may be deposited using one or more deposition techniques known in the art, such as physical vapor deposition (PVD, e.g., sputtering, pulsed laser deposition (PLD), and / or electron beam evaporation), chemical vapor deposition (CVD, e.g., vapor-liquid-solid growth (VLS) for forming one-dimensional structures such as nanowires), 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 above deposition techniques, e.g., a combination of PLD and MBE). In some examples, the superconducting material may be deposited in a patterned manner using, for example, a suitable mask and / or a targeted deposition or growth. Additionally or alternatively, the superconducting material may 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 of a superconducting material, particularly a thin film. The film may comprise one or more layers. The film of the superconducting material may be formed, for example, with a thickness as described above for a superconducting qubit circuit according to the first aspect. The thickness of the film may be uniform, i.e., the film may be formed as a layer of uniform thickness. Forming a superconducting structure may further include patterning the film to form the superconducting structure using, for example, one or more of the patterning techniques described above.

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

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

[0047] The superconducting qubit of the superconducting qubit circuit according to the first aspect of the present invention, 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 characteristics and / or features as those obtained or formed) using the method according to the second aspect of the present invention according to any one of the embodiments disclosed herein.

[0048] According to a third aspect, the present invention relates to the use (e.g., the method or process of using it) of the superconducting qubit circuit according to the first aspect according to any one of the embodiments disclosed herein, and 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. The superconducting qubit circuit may be used, for example, in quantum information processing (e.g., in a quantum processor and / or a quantum computer), and / or in 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 are not limited to high-temperature superconducting materials having a critical temperature exceeding 1.2 K, and may be implemented with any other superconducting material, particularly a superconducting material having a critical temperature of 1.2 K or less. Further, the superconducting qubit circuit according to the first aspect of the present invention and the method according to the second aspect are not limited to being created by spatial crystallographic defects and being disordered, and additionally or alternatively, may be implemented with other types of disorder (i.e., tunnel barriers induced by any type of disorder), particularly disorder created by impurity-based crystallographic defects.

Brief Description of the Drawings

[0050] Hereinafter, a detailed description of the present invention and a typical embodiment thereof will be given with reference to the drawings. The drawings show the following schematic diagrams.

Fig. 1a

Fig. 1b

Fig. 2

Fig. 3a

Fig. 3b

Fig. 4a

Fig. 4b

Fig. 5

Mode for Carrying Out the Invention

[0051] Figures 1a and 1b respectively show a top view and a side view of a schematic diagram of a superconducting quantum bit circuit 100 according to a first aspect of the present invention by way of an example. The superconducting quantum bit circuit 100 (abbreviated as the quantum bit circuit 100 hereinafter) includes a superconducting quantum bit 102 formed by a superconducting island 104 coupled to a superconducting reservoir 106 (e.g., a large superconducting electrode or a superconducting wire or wire) via a tunnel junction in this example. The tunnel junction, a Josephson junction in this example, is formed by a disorder-induced tunnel barrier 108 disposed between the island 104 and the reservoir 106. The superconducting quantum bit 102 (abbreviated as the quantum bit 102 hereinafter), that is, the island 104, the reservoir 106, and the tunnel barrier 108 are disposed above (e.g., on) an insulating substrate 110 and are formed of (e.g., include, and / or are composed of) a high-temperature superconducting material having a critical temperature exceeding the critical temperature of aluminum (1.2 K). The high-temperature superconducting material is, for example, NbTiN (T C ≈15 K) or may include it. In other examples, other nitride-based superconductors such as NbN and / or TiN may be used instead of (or in addition to) NbTiN. Preferably, the high-temperature superconducting material also has a superconducting energy gap higher than the superconducting energy gap of aluminum (0.2 meV), and the superconducting energy 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 may be composed of them. In some examples, a reference electrode (not shown) such as a ground plate may be disposed on the bottom surface of the substrate 110 on the side opposite to the upper surface where the quantum bit 102 is disposed. The tunnel barrier 108, preferably the entire quantum bit 102, may not contain aluminum, that is, may not contain a stoichiometrically relevant amount of elemental aluminum or an aluminum compound such as aluminum oxide.

[0052] The disorder of the tunnel barrier 108 induced disorderly is created by the spatial crystallographic defects of the superconducting material, i.e., by the spatial deviations, dislocations and / or interruptions within the crystal structure of the superconducting material. These defects may include, for example, vacancy defects (unoccupied lattice points) and / or interstitial lattice defects (e.g., atoms displaced from lattice sites). The density of the spatial crystallographic defects is such that the tunnel barrier 108 is no longer in the superconducting state, for example, in the normal or insulating state, thereby forming a weak connection between the island 104 and the reservoir 106. The disorder of the tunnel barrier 108 may be created, for example, by irradiation with ions, particularly noble gas ions such as helium ions, for example, by irradiation with a focused ion beam. The disorder of the tunnel barrier 108 may be created as detailed, for example, for method 200 of FIG. 2 below, and / or method 500 of FIG. 5.

[0053] The qubit 102 may be described, for example, by a Hamiltonian of the form of at least approximately (e.g., J. Koch et al., Phys. Rev. A 76, 042319 (2007)).

[0054]

Number

[0055] Here, E J = φ0I c / (2π) = R Q Δ / (2R N ) represents the Josephson energy of a tunnel junction having a critical current I c , a normal state resistance R N , and a superconducting energy gap Δ (where φ0 and R Q are the magnetic flux quantum and quantum of resistance, respectively, and φ is the phase difference across the junction), and here, E C = e 2 / 2C Σ represents the charging energy of the island 104 having a total capacitance C Σ The total capacitance of the island 104 is, for example, the capacitance C of the tunnel junctionJ and any additional capacitance arranged in parallel therewith, for example, the gate capacitance C of a gate (not shown) of the qubit 102 (for example, for controlling the chemical potential of the island 104) g and / or an additional shunt capacitance C0 (which may also be denoted as C q or C ground ), may be a sum thereof, which may be formed, for example, between the island 104 and a reference electrode such as a ground electrode or a plane (described below with reference to FIG. 3). The number of Cooper pairs on the island 104 is [Number] represented by, where n g is the number of effective offset charges.

[0056] The energy interval between the ground state and the first excited state of the qubit 102 may scale at least approximately as follows.

[0057] [Number]

[0058] where r = E J / E C represents the ratio between the Josephson and charging energies. A small ratio r may be associated with a large anharmonicity of the energy level structure of the qubit 102 such that the ground state and the first excited state form a well-separated two-level system. On the other hand, the larger the ratio r, the more likely the sensitivity of the qubit 102 to charge noise decreases. The normal state resistance R N (and / or the critical current I c ), and the total capacitance C Σ of the qubit 102 may be used as adjustment parameters to achieve the desired energy interval E 01 and / or the desired ratio r.

[0059] The desired normal state resistance R of the tunnel junctionN (and / or the critical current I c ), and the total capacitance C of the qubit 102 Σ may be obtained, for example, by selecting the physical dimensions and / or shape of the superconducting island 104 and / or the tunnel barrier 108 accordingly. The tunnel barrier 108 may have, for example, a length L across the tunnel barrier 108 in the longitudinal direction (i.e., the direction from the island 104 to the reservoir 106, parallel to the X-axis in FIGS. 1a and 1b, for example), a width w across the tunnel barrier 108 in the transverse direction (i.e., the direction perpendicular to the (longitudinal) direction from the island 104 to the reservoir 106, parallel to the surface of the substrate 110, for example, parallel to the Y-axis in FIG. 1a), and a height / thickness h across the tunnel barrier 108 perpendicularly (i.e., the direction perpendicular to the longitudinal and transverse directions, perpendicular to the surface of the substrate 110, for example, parallel to the Z-axis in FIG. 1b).

[0060] The height h of the tunnel barrier 108 (which may correspond to, for example, the thickness of the superconducting film in which the qubit 102 is formed) may 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 may correspond to, for example, the width of the island 104 and / or the reservoir 108, or in some examples, may be substantially smaller than one or both of the width of the island 104 and the width of the reservoir 108 to form a physical constriction as shown in FIGS. 3a and 3b, for example) may be, for example, between 5 nm and 2000 nm, preferably between 10 nm and 1000 nm, most preferably between 50 nm and 600 nm, and in some examples, between 100 nm and 500 nm. The cross-sectional area of the tunnel barrier 108 (for example, the product of the width w and the height h in the case of a tunnel barrier 108 having a rectangular cross-section) is, for example, 0.5*10 3 nm 2 ~2.0*10 4 nm 2 between, preferably 1.0*10 3 nm 2 ~1.5*10 4 nm 2 between, and in some examples, 2.0*103 nm 2 ~1.0*10 4 nm 2 It may also be between. 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 on the same order of magnitude as the coherence length ξ0 of the superconducting material (for example, ξ0 of NbTiN ≈ 2.5 nm).

[0061] The physical dimensions and / or shape of the superconducting island 104 and / or the tunnel barrier 108 may be selected, for example, as one or more of the following: - The normal state resistance R of the tunnel junction N is 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, and / or - The total electrostatic capacitance C of the superconducting qubit 102 Σ is 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 - The critical current I of the tunnel junction c is 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.

[0062] The ratio r = E of the Josephson energy to the charging energy J / E C is, for example, between 100 and 1000, preferably between 200 and 600, in some examples between 300 and 500, and may be, for example, 400. This makes the qubit 102 robust against charge noise while still maintaining an appropriate degree of anharmonicity. The Josephson energy E J is, for example, between 20 GHz and 2 THz, in some examples between 50 GHz and 500 GHz, and in one example between 100 GHz and 300 GHz. The charging energy E Cmay be, for example, between 50 MHz and 5 GHz, 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 splitting E between the ground state and the first excited state of the qubit 102 01 may be, for example, 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 splitting 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 and the detuning between them may be, for example, at least 0.5% of the energy splitting E 01 , preferably at least 1.0%, most preferably at least 1.5%, and / or at least 0.1 GHz, preferably at least 0.2 GHz, most preferably at least 0.4 GHz.

[0063] In some examples, the qubit circuit 100 may be embodied as a chip or a chip package (hereinafter abbreviated as a chip for simplicity), or may be disposed on and / or within them. The qubit circuit 100 and / or the chip may include a plurality of qubits and / or a plurality of quantum gates. The qubit circuit 100 and / or the chip may include, for example, at least 2 qubits (for example, between 2 and 4096 qubits), in some examples, at least 16 qubits (for example, between 16 and 4096), and in one example, at least 64 qubits (for example, 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 may include any number of qubits. In some examples, the qubit circuit 100 and / or the chip or chip package may be a quantum processor and / or a quantum sensor.

[0064] FIG. 2 shows a flow diagram of a method 200 for forming a superconducting qubit with a tunnel junction according to a second aspect of the present invention by way of example. The method 200 may be used, for example, to form a superconducting qubit circuit (or its qubit) according to a first aspect of the present invention by any one of the embodiments described herein, for example, any one of the superconducting qubit circuits 100, 300, and 400. Hereinafter, the superconducting qubit circuit 100 of FIGS. 1a and 1b will be used as a non-limiting example for illustrative purposes. The method 200 is not limited to the order of execution implied by the flow diagram of FIG. 2. If technically feasible, the method 200 may be executed in any order, and its steps may be executed at least partially simultaneously. For example, the tunnel barrier induced by disorder in the superconducting material created in step 204 may be created before, during, and / or after the formation of the superconducting structure of the superconducting qubit in step 202.

[0065] In step 202, the method 200 includes forming a superconducting structure of the superconducting qubit 102, for example, including part or all of the superconducting island 104, the superconducting reservoir 106, and the region therebetween for the tunnel barrier 108. The superconducting structure is formed of a superconducting material having a critical temperature of aluminum, that is, a critical temperature higher than 1.2K. The superconducting structure may be formed above (e.g., thereon) a substrate, such as a substrate 110 that may be 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 may be formed, for example, by patterned deposition, for example, using a suitable mask, and / or by deposition of a superconducting film and subsequent patterning of the superconducting film, for example, as described below for the method 500 of FIG. 5.

[0066] Method 200 further includes, at step 204, forming a tunnel junction of a superconducting qubit by creating a disorder-induced tunnel barrier, such as tunnel barrier 108, within a superconducting structure, for example, within a region of the superconducting structure disposed between island 104 and reservoir 106. Tunnel barrier 108 is created, for example, by introducing spatial crystallographic defects into the superconducting material as described above for superconducting qubit circuit 100.

[0067] Creating spatial crystallographic defects in the superconducting material may include, for example, irradiating the superconducting material with ions, particularly noble gas ions such as helium ions and / or neon ions. Preferably, a focused ion beam is used, which may provide improved control over the physical dimensions and / or shape of tunnel barrier 108, particularly its length L. The focused ion beam may be generated, for example, by an ion microscope, particularly a helium ion microscope and / or a neon ion microscope.

[0068] The radiation dose may be selected depending on the desired amount of spatial crystallographic defects, for example, by adjusting the intensity of the ion beam and / or the exposure time accordingly. The radiation dose may be selected particularly based on the thickness of the superconducting material, for example, the height h of tunnel barrier 108. The superconducting material within tunnel barrier 108 is, for example, irradiated with a dose between 10 18 ions / cm 2 ~10 20 ions / cm 2 and the height h is between 10 nm and 100 nm. In some examples, at a height h between 20 nm and 50 nm, for example, at a height h of 30 nm - 40 nm, a dose of 1.0*10 18 ions / cm 2 ~5*10 19 ions / cm 2 may be used, and the height h is between 20 nm and 50 nm. For example, at a height h of 30 nm - 40 nm, a dose of 1.0*10 19 ions / cm 2 may be used.

[0069] The kinetic energy of the ions is selected such that the ions reach the substrate 110 through the superconducting material / tunnel barrier 108, rather than (at least mainly) stopping within the superconducting material / tunnel barrier 108 (e.g., when irradiating along the z - direction in FIG. 1b), for example, to avoid injecting impurities into the superconducting material or at least reduce their number. The kinetic energy may 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 may be, for example, between 5 keV and 200 keV when the height h is between 10 nm and 100 nm, in some examples between 10 keV and 100 keV when the height h is between 20 nm and 50 nm, and in one example between 20 keV and 40 keV (e.g., 30 keV) when the height h is between 30 nm and 40 nm.

[0070] In addition to steps 202 and 204, method 200 may include additional 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, as described below for method 500 of FIG. 5, for example. In some examples, method 200 may further include connecting the above - mentioned circuit elements to an external control and / or readout circuit and / or to devices such as a current source, a microwave generator, and / or a network analyzer.

[0071] FIGS. 3a and 3b show schematic diagrams of a superconducting qubit circuit 300 according to a first aspect of the present invention according to another example. FIG. 3a shows a top view of the superconducting qubit circuit 300, and FIG. 3b shows an enlarged top view of the SQUID - based charge qubit 102 of the superconducting qubit circuit 300.

[0072] The superconducting quantum bit circuit 300 (abbreviated as the quantum bit circuit 300) is the same as the superconducting quantum bit circuit 100 in FIGS. 1a and 1b. The superconducting quantum bit circuit 300 includes a superconducting quantum bit 102 (abbreviated as the quantum bit 102) having a pair of tunnel junctions in a high-temperature superconducting material, and the tunnel junctions are formed by disorder-induced tunnel barriers 108A and 108B in which disorder is created by spatial crystallographic defects in the superconducting material. The quantum bit 102, in some examples, the entire quantum bit circuit 300 may be formed using the method according to the second aspect of the present invention according to any one of the embodiments disclosed herein, for example, the method 200 in FIG. 2 and / or the method 500 in FIG. 5 described below.

[0073] In the examples of FIGS. 3a and 3b, the quantum bit 102 is embodied as a SQUID-based charge quantum bit, that is, a SQUID-based Xmon quantum bit (as an example of a transmon qubit). The quantum bit 102 includes a cruciform (or X-shaped) superconducting island 104 and a superconducting reservoir 106 formed by a reference electrode 302 such as a ground electrode or a ground plate surrounding the superconducting island 104 in this example. The island 104 is separated from the reference electrode 302 by a (for example, cruciform) gap, and as shown in FIG. 3a, the superconducting material is not arranged, for example, the underlying substrate 110 is exposed. The substrate 110 may be embodied as described above for the quantum bit circuit 100, for example. The island 104 and the reference electrode 302 are weakly coupled via a superconducting quantum interference device (SQUID) 304 formed by a superconducting loop having a pair of tunnel junctions, each of which is formed by a disorder-induced tunnel barrier 108A and 108B, respectively. Each of the tunnel junctions further includes a physical constriction, that is, a part of the superconducting loop having a reduced cross-sectional area, for example, a reduced width, as shown in FIG. 3b. The width of the physical constriction is, 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, preferably less than 5%, most preferably less than 1%, and in some examples, less than 0.5%.

[0074] The qubit 102 of the qubit circuit 300 may be described, at least approximately, by a Hamiltonian in the form of (e.g., J. Koch et al., Phys. Rev. A 76, 042319 (2007)).

[0075]

Number

[0076] Here, E Ji represents the Josephson energy of the first / left and second / right tunnel junctions, respectively, and φ i represents the phase difference across the first / left and second / right tunnel junctions, respectively, and E C represents the charging energy of the superconducting island 104.

Number

[0077]

Number

[0078] Here,

Number

[0079] The parameters and / or physical dimensions of the quantum bit 102 and the tunnel barriers 108A, 108B may be selected, for example, in the same manner as described above for the quantum bit circuit 100 of FIGS. 1a and 1b. The total electrostatic capacitance of the island 104, and thus the charging energy C Σ may, accordingly, be controlled by selecting the physical dimensions and / or shape of the island 104 and the surrounding reference electrode 302, and / or the spacing therebetween. The length of each arm of the cross-shaped island 104 may 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 may be equal to, for example, the width or diameter of the loop of the SQUID 304) may 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.

[0080] The quantum bit circuit 300 further includes a readout electrode 306 for reading the state of the quantum bit 102 and a control electrode 308 for manipulating the state of the quantum bit 302. Both the readout electrode 306 and the control electrode 308 are capacitively coupled to each of the arms of the island 104. The readout electrode 306 may be coupled to and / or comprise a readout circuit, for example, a transmission readout circuit having a readout resonator, as in the quantum bit circuit 400 of FIGS. 4a and 4b described below. The control electrode 308 may be coupled to and / or comprise a control circuit, for example, in the same manner as the quantum bit circuit 400 of FIGS. 4a and 4b described below. In some examples, the control circuit may couple the quantum bit 102 to one or more other quantum bits and / or to one or more quantum gates.

[0081] The qubit circuit 300 also includes a magnetic flux bias line 310. The magnetic flux bias line 310 may be inductively coupled to the SQUID 304 and / or the qubit 102. The magnetic flux bias line 310 may be configured to generate a magnetic field or magnetic flux passing through the SQUID 304. The magnetic field strength or magnetic flux may be controlled, for example, by adjusting the current passing through the magnetic flux bias line 310 for magnetic flux adjustment of the energy splitting of the qubit 102. The magnetic flux bias line 310 may be coupled to and / or provided with a magnetic flux bias circuit, for example, in the same manner as the qubit circuit 400 shown in FIGS. 4a and 4b described below.

[0082] Part or preferably all of the structures shown in FIGS. 3a and 3b, that is, the qubit 102 having the island 104, the reservoir 106 having the tunnel barriers 108A and 108B, and the SQUID 304, the reference electrode 302, the readout electrode 306, the control electrode 308 and / or the magnetic 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. Each structure may be formed, in particular, from the same film of this high-temperature superconducting material, which may be disposed, for example, on the same substrate 110 as described above for the qubit circuit 100 of FIGS. 1a and 1b. Each structure may be formed, for example, by patterning the film as described below for the method 500 of FIG. 5.

[0083] FIG. 4a shows a circuit diagram of a superconducting qubit circuit 400 according to a first aspect of the present invention according to another example. FIG. 4b shows a circuit diagram of a magnetic flux bias circuit 408 for and / or of the superconducting qubit circuit 400 (abbreviated as the qubit circuit 400).

[0084] The qubit circuit 400 is similar to the qubit circuit 100 of FIGS. 1a and 1b and the qubit circuit 300 of FIGS. 3a and 3b. The qubit circuit 400 also includes a SQUID-based superconducting charge qubit 102 (abbreviated as qubit 102) having a SQUID 304 disposed between a superconducting island 104 and a superconducting reservoir 106 / ground plate 302, a readout electrode 306, a control electrode 308, and a magnetic flux bias line 310, all of which may be embodied, for example, like the qubit circuit 100 and / or the qubit circuit 300. The island 104 is weakly coupled to the reservoir 106 / ground plate 302 via a pair of tunnel junctions within the SQUID 304. In parallel, the island 104 is also capacitively coupled to the reservoir 106 / ground plate 302 via an additional parallel capacitance C q which may be adapted, for example, by appropriately selecting the physical dimensions and / or shape of the island 104 to achieve a desired ratio E J / E C as described above.

[0085] The readout capacitance (diagnostic capacitance) C d capacitively coupled to the island 104 of the qubit 102 by the readout electrode 306 is provided in the readout circuit 402. The readout circuit 402 is coupled to (and / or includes) a readout line 404 embodied as a transmission readout line in this example. The readout circuit 402 includes a diagnostic resonator embodied as a λ / 4 resonator in this example. 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. Thus, the readout capacitance C dFor example, as described in detail below, it is possible to determine a change χ within the resonator frequency related to the transition between qubit states. The readout circuit 402 may be inductively coupled to the readout line 404, for example, at the current node of the diagnostic resonator. The readout circuit 402 may be implemented as described, for example, in 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).

[0086] As a result of the coupling of the qubit 102 to the readout circuit 402, the resonator frequency of the diagnostic resonator may depend on the state of the qubit 102. A transition between qubit states may change the resonator frequency, for example, by a dispersive shift +χ (or -χ). The coupling strength between the qubit 102 and the resonator may be selected such that, for example, the dispersive shift χ is between 2 and 10 times, preferably between 3 and 5 times, the linewidth (Q-factor) of the resonator. Additionally or alternatively, the frequency shift χ may 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 may be achieved, for example, by selecting the ratio (voltage divider) β between the readout capacitance C d and the total capacitance C Σ of the qubit 102, where β may be, for example, between 0.05 and 0.2. In some examples, the dispersive shift may be (at least approximately) scaled as follows.

[0087]

Number

[0088] Here,[[]]

Number

[0089] The control electrode 308 capacitively coupled to the island 104 of qubit 102 by the capacitance C c is provided, for example, within a control circuit 406 that can be used to manipulate the state of qubit 102 in order to excite 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 in FIGS. 3a and 4a for simplicity) may be used to manipulate the state of qubit 102 by coupling qubit 102 to one or more other qubits and / or to one or more quantum gates (e.g., by capacitive coupling to a quantum bus resonator).

[0090] The quantum bit circuit 400 may further include a flux bias circuit 408 having a flux bias line 310. The flux bias line 310 is inductively coupled to the quantum bit 102, for example, by the mutual inductance M with respect to the SQUID 304 and the mutual inductance M' with respect to the entire quantum bit 102 (i.e., the entire circuit including the parallel capacitance C q ). The ratio of the inductances M' and M, i.e., M' / M, may 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 with respect to the SQUID 304 may be, for example, between 0.5 pH and 10 pH, and in some examples, between 1.0 pH and 3.0 pH.

[0091] FIG. 5 shows a flowchart of a method 500 for forming a superconducting quantum bit with a tunnel junction according to a second aspect of the present invention according to another example. The method 500 may be used, for example, to form a superconducting quantum bit circuit (or its quantum bit) according to the first aspect of the present invention by any one of the embodiments described herein, for example, any one of the superconducting quantum bit circuits 100, 300, and 400. Hereinafter, the superconducting quantum bit circuits 300 and 400 are used as non-limiting examples for illustrative purposes. The method 500 is not limited to the execution order implied by the flowchart of FIG. 5. If technically feasible, the method 500 may be executed in any order, and its steps may be executed at least partially simultaneously. For example, the tunnel barrier induced by disorder in the superconducting material created in step 506 may be created before, during, and / or after the formation of the elements of the superconducting quantum bit circuit in steps 504 and 506.

[0092] In step 502 of the method 500, on a substrate such as the substrate 110, for example, NbTiN, for example, Nb 0.62 Ti 0.38Including forming a film of a high-temperature superconducting material such as N, particularly a thin film. The substrate 110 may be an insulating substrate, for example, a MgO substrate, preferably a crystalline MgO substrate having a well-defined crystallographic orientation, for example, a cubic (100) oriented MgO substrate. The film may be deposited on the substrate 110, for example, by physical vapor deposition, for example, pulsed laser deposition. To form the NbTiN film, the NbTi target may be ablated by a laser, for example, a pulsed infrared laser, for example, in a nitrogen atmosphere, preferably in an ultra-high purity nitrogen atmosphere. The film may be deposited, for example, at a rate of 0.1 nm / min to 10 nm / min, preferably 0.5 nm / min to 2 nm / min. The film may 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 may be deposited with a uniform thickness, and the thickness may vary, for example, by less than 20%, preferably less than 10% across the entire film. The critical temperature of NbTiN varies with the thickness of the film and may be, for example, about 11 K for a thickness of 20 nm, 15 K for a thickness of 50 nm, and 16 K for a thickness of 100 nm.

[0093] In step 504, a mask (e.g., an etching mask) for forming the superconducting structure of the qubit and / or the qubit circuit is formed on the superconducting film. The mask may be used, for example, to form some or all of the elements of the qubit circuit 300 or 400, for example, the superconducting island 104, the superconducting reservoir 106, the reference electrode / ground plate 302, the SQUID 304 (in some examples, including 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 may also be used to at least partially, and in some examples, entirely, form some or all of the readout circuit 402, the readout line 404, the control circuit 406, and the flux bias circuit 408.

[0094] The mask may be formed, for example, by lithography, in particular, electron beam lithography. A resist, for example, a positive or negative resist, may be formed on the superconducting film by, for example, spin coating. The resist may then be patterned and developed by lithography. In some examples, different resists are used to form the mask, for example, a first resist for forming large features (e.g., island 104, ground plate 302, readout electrode 306, control electrode 308, and / or flux bias line 310), and a second resist different from the first resist for forming small features (e.g., SQUID 304 having a tunnel junction and / or capacitive element between island 104 and readout electrode 306, control electrode 308, and / or flux bias line 310). The first resist may be, for example, a low-resolution resist configured for lithography resolution between 10 nm and 50 nm (e.g., AR-N 7520 E-Beam resist by Allresist GmbH), and the second resist may be a high-resolution resist configured for lithography resolution between 1 nm and 10 nm (e.g., AR-P 6200 E-Beam resist by Allresist GmbH).

[0095] In step 506, the superconducting film is patterned using a mask to form the superconducting structure of the qubit and / or qubit circuit, such as the above-described elements of qubit circuit 300 or 400. The superconducting film may be patterned, for example, by using the mask as an etching mask and etching, in particular, reactive ion etching (e.g., in a fluorine plasma). The etching rate may be, for example, between 2 nm / min and 100 nm / min, preferably between 5 nm / min and 30 nm / min. The mask may then be removed. In some examples, step 506 may also include milling of the superconducting film, in particular, ion milling such as argon ion milling.

[0096] In step 508, the tunnel junction of SQUID 304 is formed by creating tunnel barriers 108A, 108B induced randomly within the superconducting structure / membrane. The tunnel barriers 108A, 108B are created, for example, by introducing spatial crystallographic defects into the superconducting material by irradiation with noble gas ions, in this example, by direct writing of the tunnel barriers 108A, 108B with a focused helium ion beam. For this purpose, a helium ion microscope may be used, and the resolution of the helium ion microscope is preferably less than 2.0 nm, most preferably between 1.0 nm, for example, between 0.2 nm and 1.0 nm. The helium ions may have a kinetic energy, for example, between 20 keV and 40 keV, in some examples, between 25 keV and 35 keV, for example 30 keV. The area of the tunnel barriers 108A, 108B may be irradiated with a dose, for example, such as the dose described above, for example, 5*10 18 ions / cm 2 ~5*10 19 ions / cm 2 between. The dose may be selected, for example, such that the tunnel junction is a superconducting-normal-superconducting (SNS) or superconducting-insulating-superconducting (SIS) tunnel junction. The tunnel barriers 108A, 108B may be formed, for example, with a length between 2 and 6 times the coherence length of the superconducting material, for example, in Nb 0.62 Ti 0.38 N it may be about 2.5 nm.

[0097] The embodiments of the invention disclosed herein are merely specific examples for illustrative purposes. The present invention can be implemented with many modifications in various ways without changing the underlying basic characteristics. Therefore, the present invention is defined only by the following claims.

Claims

1. A superconducting qubit circuit (100, 300, 400) having a superconducting qubit (102), the superconducting qubit (102) comprising 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), the disorder being created by spatial crystallographic defects in the superconducting material. Superconducting quantum bit circuits (100, 300, 400).

2. the superconducting material has a critical temperature of at least 4.2 K, preferably at least 10 K, and / or the superconducting material has a superconducting energy gap of more than 0.2 meV, preferably at least 1.0 meV, most preferably at least 2.0 meV; 2. The superconducting qubit circuit of claim 1.

3. the superconducting qubit circuit (100, 300, 400) is for operation at an operating temperature of at least 1.0 K, preferably at least 1.5 K, and most preferably at least 2.0 K; 2. The superconducting qubit circuit of claim 1.

4. The superconducting material may include a nitride-based superconductor, in particular one or more of niobium titanium nitride (NbTiN), niobium nitride (NbN), and titanium nitride (TiN), and / or the superconducting material may include one or more of yttrium barium copper oxide (YBCO), magnesium diboride (MgB ２ ), bismuth strontium calcium copper oxide (BSCCO), and iron-based superconductors; 2. The superconducting qubit circuit of claim 1.

5. the spatial crystallographic defects in the tunnel barrier (108, 108A, 108B) have been created 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 does not contain aluminum oxide, in particular the tunnel junction does not contain aluminum; 2. The superconducting qubit circuit of claim 1.

6. The cross-sectional area of ​​the tunnel barrier (108, 108A, 108B) is 3.0*10 ４ nm ２ Less than 2.0*10 ４ nm ２ Less than 1.5*10 ４ nm ２ and / or 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, and most preferably between 5 nm and 15 nm.

7. the normal state resistance of the tunnel junction is at least 100 Ω, preferably at least 200 Ω, most preferably at least 300 Ω; and / or the total capacitance of the superconducting qubits 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; 2. The superconducting qubit circuit of claim 1.

8. The superconducting qubit (102) is a charge qubit, in particular a SQUID-based charge qubit, and the Josephson energy E Ｊ and charging energy E Ｃ Comparison with E Ｊ / E Ｃ is between 50 and 1000, preferably between 200 and 600, and / or The energy splitting of the superconducting qubit (102) is between 10 GHz and 100 GHz, preferably between 20 GHz and 50 GHz; 2. The superconducting qubit circuit of claim 1.

9. a readout electrode (306) and / or readout circuit (402, 404) for reading out the state of the superconducting quantum bit (102), a control electrode (308) for manipulating the state of the superconducting quantum bit (102), and a flux bias line (310) for adjusting the energy division of the superconducting quantum bit (102), in particular, the tunnel junction and one or more of, preferably all of, 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.

2. The superconducting qubit circuit of claim 1.

10. A method (200, 500) of forming a superconducting qubit (102) comprising a tunnel junction, the method (200, 500) comprising: forming a superconducting structure (104, 106) of the superconducting qubit (102), the superconducting structure (104, 106) being formed from a superconducting material having a critical temperature greater than 1.2 K; forming the tunnel junction 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 crystallographic defects into the superconducting material. Method (200,500).

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

12. The superconducting material is 10 １７ ions / cm ２ ~10 ２１ ions / cm ２ Between 10 and 20 １８ ions / cm ２ ~10 ２０ ions / cm ２ and / or the superconducting material is disposed on a substrate (110) and the kinetic energy of the noble gas ions is selected such that the noble gas ions penetrate the superconducting material and enter the substrate (110). The method (200, 500) of claim 11.

13. 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 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 splitting of the superconducting qubit (102), in particular 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. The method (200, 500) of claim 10.

14. The superconducting qubit (102) is obtainable using a method (200, 500) according to any one of claims 10 to 13, 10. The superconducting qubit circuit (100, 300, 400) of any one of claims 1 to 9.

15. Use of a superconducting qubit circuit (100, 300, 400) according to any one of claims 1 to 9, wherein the superconducting qubit circuit (100, 300, 400) operates at an operating temperature of at least 1.0 K, preferably at least 1.5 K, most preferably at least 2.0 K. Use of superconducting qubit circuits (100, 300, 400).

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