Josephson junction annealing method and annealing apparatus

Abstract

Disclosed is a method for forming a superconducting circuitry device, comprising providing at least one Josephson junction formed on a substrate between a first electrical node and a second electrical node, and annealing the at least one Josephson junction by applying an optical beam (340) to the Josephson junction and applying a voltage across the at least one Josephson junction.

Description

JOSEPHSON JUNCTION ANNEALING METHOD AND ANNEALING APPARATUSTECHNICAL FIELD

[0001] The present disclosure relates to the fabrication of superconducting circuitry devices of the type used in superconducting quantum computing. More in particular, the present disclosure relates to methods and apparatuses for adjusting a resonance frequency of one or more Josephson junctions comprised by such a superconducting circuitry device.BACKGROUND

[0002] Quantum computers hold the promise of solving complex problems that are currently infeasible for classical computers. By leveraging principles such as superposition and entanglement, quantum computers can process a vast number of computations simultaneously. This parallelism opens possibilities for breakthroughs in various fields, including cryptography, drug discovery and acceleration of machine learning algorithms.

[0003] Superconducting qubits are integral to the advancement of quantum computing due to their scalability and coherence properties. These qubits rely on superconducting circuits with Josephson junctions that operate at extremely low temperatures, allowing them to exhibit macroscopic quantum mechanical behaviour. Superconducting qubits can furthermore be fabricated using existing semiconductor manufacturing technologies, making them a practical choice for building large-scale quantum processors.

[0004] In superconducting qubits, the transition frequency refers to the energy difference between the qubit's quantum states, specifically the frequency between the ground state |0) and the first excited state | 1). This transition frequency is determined by the design parameters of the superconducting circuit, such as inductance and capacitance, which create a resonant system. The qubit behaves like an anharmonic oscillator, and the quantization of energy levels allows it to function as a two-level system suitable for quantum computing.

[0005] The qubit's transition frequency typically lies in the microwave range and is crucial for its operation and control. By applying microwave pulses at this specific frequency, it is possible to manipulate the qubit's state, performing operations such as quantum gates for computation. Precise knowledge and control of the qubit frequency enable selective addressing of individual qubits in a processor array without disturbing neighbouring qubits. This selectivity reduces crosstalk and enhances gate fidelity, which are vital for maintaining coherence and achieving reliable quantum computation. Additionally, tuning qubit frequencies helps in mitigating errors due to environmental noise and in implementing coupling schemes between qubits for entanglement and more complex operations.

[0006] Fabricating a qubit or Josephson junction having a specific transition frequency nevertheless remains challenging, because even minute variations at the nanoscale inherent to the manufacturing process can lead to substantial frequency shifts. This difficulty in frequency targeting has profoundimplications for the performance of superconducting quantum processors. In a multi -qubit system, it is essential that each qubit operates at a unique frequency to prevent unwanted interactions and crosstalk between qubits. Frequency collisions can cause qubits to unintentionally couple with each other, leading to decoherence and gate errors that undermine the fidelity of quantum operations. As the number of qubits in a processor increases, the complexity of ensuring that all qubits are properly frequency- targeted grows exponentially, complicating scaling efforts.

[0007] The publication entitled “Laser-annealing Josephson junctions for yielding scaled-up superconducting quantum processors” by Hertzberg et al. presents fixed-frequency qubit architectures. To assess scalability, this publication identifies the types of “frequency collisions” that will impair a transmon qubit and cross-resonance gate architecture. Using statistical modeling, the probability of evading all such conditions is computed as a function of qubit frequency precision. It is demonstrated that it is possible to find collision-free lattices.

[0008] The publication entitled “Alternating-bias assisted annealing of amorphous oxide tunnel junctions” by Pappas et al. demonstrates a technique for controllably tuning the electrical properties of aluminum-oxide tunnel junctions. This is accomplished using a low-voltage, alternating-bias applied individually to the tunnel junctions. Transmission electron microscopy shows that the treated junctions are predominantly amorphous, albeit with a more uniform distribution of alumina coordination across the barrier.

[0009] The object of the present disclosure is to provide an annealing method with which one or more of the limitations of the prior-art methods are obviated or abated.SUMMARY

[0010] In accordance with a first aspect of the present disclosure, this object is achieved with the method for forming a Josephson junction. The method comprises providing at least one Josephson junction formed on a substrate between a first electrical node and a second electrical node, and annealing the at least one Josephson junction by applying an optical beam to the Josephson junction, and applying a voltage across the at least one Josephson junction.

[0011] The proposed annealing method may achieve a resistance change of up to 40%, therefore having the ability to correct significant frequency deviations arising from fabrication imperfections. The enhanced annealing range is achieved because the laser heating elevates the temperature of the junction locally, increasing the mobility of atoms within the insulating barrier. This heightened atomic activity makes the junction more responsive to the applied alternating bias voltage, enabling more substantial and controlled modifications to its properties. The synergy between thermal activation and electrical stressing facilitates deeper annealing effects than either method could achieve independently.

[0012] In accordance with preferred embodiments of the method, the voltage is applied across the Joseph junction while the optical beam is applied thereto.

[0013] In accordance with further preferred embodiments of the method, the applied voltage is a DC voltage.

[0014] In accordance with further preferred embodiments of the method, the applied voltage is an alternating DC voltage.

[0015] In accordance with further preferred embodiments of the method, the alternating DC voltage comprises a series of voltage pulses, said pulses preferably having pulse widths of 1.0 millisecond or more.

[0016] In accordance with further preferred embodiments of the method, the alternating DC voltage comprises a, preferably smoothed, square wave form.

[0017] In accordance with further preferred embodiments of the method, the applied voltage comprises 0.88 volts or less, preferably no more than 0.84 volts, more preferably no more than 0.80 volts, and most preferably 0.76 volts or less.

[0018] The proposed method advantageously allows for the usage of relatively low voltages during the annealing process. Applying a voltage to a Josephson junction potentially in a short circuit, resulting in damage to the Josephson junction. Generally, utilising a lower voltage results in a decreased chance of a short circuit occurring and consequently a higher annealing yield.

[0019] In accordance with further preferred embodiments of the method, the method further comprises determining at least one of a resistance and the resonance frequency of the Josephson junction.

[0020] In accordance with further preferred embodiments of the method, the step of applying a voltage across the Josephson junction is reiterated, based at least on the determined resistance and / or the resonance frequency, until a target value of the resistance and / or the resonance frequency is reached.

[0021] In accordance with further preferred embodiments of the method, the step of applying the optical beam to the Josephson junction is performed locally, wherein no more than a fraction of the substrate that comprises the Josephson junction is heated.

[0022] In accordance with further preferred embodiments of the method, the optical beam is a monochromatic optical beam, preferably a laser beam.

[0023] In accordance with further preferred embodiments of the method, the optical beam is applied directly to the Josephson junction.

[0024] In accordance with further preferred embodiments of the method, the optical beam comprises a Gaussian beam profde.

[0025] In accordance with further preferred embodiments of the method, the substrate comprises sapphire.

[0026] In accordance with further preferred embodiments of the method, the substrate comprises silicon.

[0027] In accordance with further preferred embodiments of the method, annealing the at least one Josephson junction causes a negative resonance frequency shift.

[0028] In accordance with a second aspect of the present disclosure, the above object is achieved with a superconducting circuitry device comprising one or more than one Josephson junction, wherein said Josephson junction has been annealed using the method in accordance with any one of the here abovedescribed embodiments.

[0029] In accordance with a preferred embodiment of the superconducting circuitry device, the superconducting circuitry device is one of a quantum processing unit, QPU, with at least one superconducting qubit having the Josephson junction; a travelling wave parametric amplifier comprising a plurality of electrically connected Josephson junctions; and a tuneable resonator.

[0030] Lastly, in accordance with a third general aspect of the present disclosure, the above object is achieved with an annealing apparatus for Josephson junctions. The annealing device comprises at least an optical beam source configured to apply an optical beam to at least one Josephson junction and means for applying a voltage across the Josephson junction.BRIEF DESCRIPTION OF THE DRAWING

[0031] The above-described embodiments of the method, the superconducting circuitry device and the annealing apparatus are described in more detail here below with reference to the appended drawing, in which:

[0032] FIG. 1 shows a circuit diagram of a superconducting circuitry device, in accordance with various embodiments;

[0033] FIG. 2 shows a top view of a superconducting circuitry device, in accordance with various embodiments;

[0034] FIG. 3 shows a cross section of a Josephson junction of a superconducting circuitry device undergoing an anneal, in accordance with various embodiments;

[0035] FIG. 4 depicts a flowchart illustrating operations of forming a superconducting circuitry device, in accordance with various embodiments;

[0036] FIG. 5 depicts a further flowchart illustrating operations of forming a superconducting circuitry device, in accordance with various preferred embodiments;

[0037] FIG. 6 shows a graph showing measurement results elucidating the advantages of the proposed method, in accordance with various embodiments; and

[0038] FIG. 7 shows an exemplary embodiment of an annealing apparatus.DETAILED DESCRIPTION

[0039] Here below various embodiments are described with reference to the appended drawing. It will be appreciated that these embodiments are merely of an exemplary nature and should not be construed to limit the sought-after protection as defined in the appended claims.

[0040] Reference is made not to FIG. 1, which depicts an exemplary circuit diagram of a superconducting circuitry device 100. The superconducting circuitry device 100 may be asuperconducting qubit 100 comprising one or more than one Josephson junction 101 connected in parallel to a shunt capacitor 102, thereby forming an anharmonic oscillator functioning as a two-level system capable of performing quantum computations. The Josephson junction 101 and the shunt capacitor 102 may be connected to an electrical ground via a ground capacitor 103.

[0041] The at least one Josephson junction 101, the shunt capacitor 102 and / or the ground capacitor 103 may be connected to one another, or be partially formed by, a circuit transmission line 104. The circuit transmission line 104 may comprise or more of a coplanar waveguide, a microstrip, a stripline, or any other type of suitable transmission line geometry. The circuit transmission line 104 may comprise a section that couples the superconducting qubit 100 to yet further components (not shown), including e.g. a readout resonator, an additional qubit, or a feedline.

[0042] In accordance with various embodiments, the shunt capacitor 102 and the ground capacitor 103 may each comprise a capacitance within the range of 0.01 femtofarad to 300 femtofarad. The one or more than one Josephson junction 100 may comprise a critical current of 1 to 500 nanoamperes.

[0043] In accordance with various embodiments, the superconducting qubit 100 may comprise one, two or more Josephson junctions 101. In these embodiments, a plurality of Josephson junctions connected in parallel or in series may substitute the Josephson junction 101 shown in FIG. 1. The superconducting qubit 100 may furthermore be e.g. a charge qubit of the transmon type or a superconducting qubit 100 of the fluxonium type. In accordance with various embodiments, the superconducting qubit may furthermore be susceptible to have its resonance frequency adjusted by means of an externally applied magnetic field.

[0044] FIG. 2 shows a top view of a superconducting circuitry device 200 corresponding to the circuit diagram of FIG. 1. The superconducting circuitry device 200 may comprise a substrate 210 having arranged thereon a Josephson junction 201 comprising a first superconducting electrode 211 and a second superconducting electrode 212. The superconducting electrodes 211, 212 overlap at an area of overlap 213. The first superconducting electrode 211 and the second superconducting electrode 212 may be connected, respectively, to a first electrical node 221 and a second electrical node 222. In accordance with various embodiments, the first electrode node 221 and the second electrical node 222 may be constituted by capacitive plates of, for example, a parallel plate capacitor applied to the substrate 210.

[0045] In accordance with various embodiments, the substrate 210 may comprise silicon, sapphire, or any other suitable substrate material

[0046] The first superconducting electrode 211 and the second superconducting electrode 222 may comprise any material that exhibits superconductivity at cryogenic temperatures, for example aluminium and / or niobium. In accordance with various embodiments, the first superconducting electrode 211 and the second superconducting electrode 222 may comprise a length of e.g. 2 to 20 microns.

[0047] The first superconducting electrode 211 and the second superconducting electrode 222 may be separated from one another by an insulating barrier of, for example, 1 to 3 nanometres thick. In certain embodiments, the insulating barrier layer may be an oxide layer that is obtained by oxidizing the material constituting the first superconducting electrode 211 and / or the second superconducting electrode 222.

[0048] In accordance with various embodiments, the Josephson junction 201 constituted by the first superconducting electrode 211 and the second superconducting electrode 212 may be manufactured using a combination of different manufacturing techniques. These techniques include electron beam lithography (e-beam lithography) and shadow evaporation, which are both part of the common Manhattan and Dolan-bridge fabrication processes.

[0049] As an illustrative example, the Josephson junction 201 may be formed by coating the substrate 210 with an electron-sensitive resist. Using e-beam lithography, a focused beam of electrons is scanned over the electron-sensitive resist. The electron beam modifies the resist's solubility, allowing selective removal of either the exposed or unexposed regions during a subsequent development process. Thereby, elongate recesses may be formed in the resist in which the underlying substrate is exposed, for forming the first superconducting electrode 211 and the second superconducting electrode 212.

[0050] Thereafter, the first and second superconducting electrodes 211, 212 may be formed in the elongate recesses by means of shadow evaporation. Using shadow evaporation, vaporous superconducting material may be deposited onto the substrate 210 and the electron-sensitive resist from two different deposition directions over two application iterations, thereby forming the multi-layered structure of the first superconducting electrode 211 and the second superconducting electrode 212. The insulating barrier layer may be formed by briefly introducing oxygen into an enclosure housing the superconducting circuitry device 200 and allowing an oxide layer to form on the first super conducting electrode 211. Thereafter, the second superconducting electrode 212 may be formed using a second iteration of the shadow evaporation fabrication technique from a different evaporation direction, resulting in the second superconducting electrode to be formed electrically isolated from the first superconducting electrode 211.

[0051] The transition frequency of the superconducting qubit 200 is highly sensitive to the exact parameters of the at least one Josephson junction 201. These parameters include the junction area (which is the area of overlap between the first electrode 211 and the second electrode 212), the thickness of the insulating barrier, and the uniformity of the materials used.

[0052] Notwithstanding the above, despite the advanced capabilities of e-beam lithography, precisely targeting the qubit frequencies remains a significant challenge. Even minute variations at the nanoscale can lead to substantial shifts in the transition frequency of the qubit 200. These discrepancies can arise from limitations in the e-beam lithography process itself, such as proximity effects where exposure of nearby areas affects the intended pattern, or from variations in electron beam focus and dose control.

[0053] Moreover, other factors during fabrication contribute to transition frequency targeting difficulties. Variations in (shadow evaporation) material deposition rates, inconsistencies in the oxidation process that forms the insulating barrier, and imperfections in the substrate can all introduce deviations from the intended design. These small but significant discrepancies can result in qubits that operate at frequencies different from those as intended, leading to challenges in qubit control and interaction. Therefore, it is often necessary to compensate for these discrepancies post fabrication of the Josephson junction 201, such that the transition frequency of the Josephson junction matches a predetermined intended target value.

[0054] The frequency of a superconducting qubit is intimately connected to the properties of its Josephson junctions, especially the critical current and the capacitance, which determine the qubit's energy levels and transition frequencies. The room temperature resistance of a Josephson junction can be determined immediately after fabrication and may serve as a predictive tool for the qubit's operational frequency at superconducting temperatures. This is possible because the room temperature resistance is inversely related to the critical current through the Ambegaokar-Baratoff relation, allowing for the estimation of the critical current from the room temperature resistance. With the critical current known, the Josephson energy can be calculated, and together with the charging energy derived from the capacitance, the qubit's transition frequency can be determined using quantum mechanical models specific to the qubit design.

[0055] By leveraging the relationship between room temperature resistance and qubit's transition frequency, frequencies can be predicted and adjusted, identifying deviations from desired specifications can be identified early in the fabrication process before cooling the system to cryogenic temperatures. As such, it may be determined whether the transition frequency matches the required specifications or that the transition frequency must be adjust post-fabrication.

[0056] FIG. 3 illustrates an example of a Josephson junction 301 undergoing an anneal in accordance with various embodiments. The annealing will be elucidated here below with reference to FIG. 4, which depicts a flowchart showing various steps S401 to S403 of annealing the Josephson junction 301, in accordance with various embodiments.

[0057] FIG. 3 shows a cross-section of a Josephson junction 301 comprising a first electrode 311 and a second electrode 312 that are separated from one another by an insulating barrier 314. The Josephson junction 301 may be provided S401 on a substrate using the exemplary manufacturing method described here above and the transition frequency may be determined using the scheme described here above.

[0058] To anneal the Josephson junction 301, an optical beam 340 may applied to at least a portion of the Josephson junction 301 that comprises the first electrode 311, the second electrode 312 and the insulating barrier 314. In accordance with embodiments such optical beam 340 may be applied locally, heating only one or more specific Josephson junctions while not heating additional Josephson junctions located elsewhere on the substrate. In some embodiments, the optical beam 340 may be applied directly to these specific Josephson junctions

[0059] In accordance with various embodiments, the optical beam may be applied S402 to the Josephson junction 301 continuously during the annealing process.

[0060] The optical beam 340 may be a monochromatic optical beam, e.g. may be a laser beam. The optical beam 340 may be applied directly to the Josephson junction 301. The optical beam 340 may comprise a Gaussian beam profile, which may have a wavelength e.g. within in the 100 nm to 3000 nanometers range. One or more properties of the optical beam 340, e.g. beam intensity, polarisation state, phase, beam profile, divergence, etc., may be configured before and / or during the step of applying S402 the optical beam (340) to the Josephson junction (301). The optical beam 340 may be configured to pass through a polarising beam splitter. After passing through the polarising beam splitter, optical beam 340 may reach the superconducting circuitry device, after which and / or at which it may be reflected and propagate via the polarising beam splitter toward an image capturing device. The image capturing device may be used to determine whether the optical beam 340 illuminates the superconducting circuitry device at an intended location, which typically is the location of a Josephson junction 301 or a location sufficiently close thereto.

[0061] The optical beam may have a radiant flux comprised between 0.05 watt (W) and 10 W, preferably comprised between 0.1 W and 8 W, more preferably comprised between 0.2 W and 6 W, even more preferably comprised between 0.4 W and 4 W, most preferably comprised between 0.8 and 2 W. The optical beam may have an intensity comprised between 107Watts per square meter (W / m2) and 3x l012W / m2, preferably comprised between 5x l07W / m2and 5x l0nW / m2, more preferably comprised between 108W / m2and 1011W / m2, even more preferably comprised between 5x l08W / m2and 5 x 1010W / m2, most preferably between 109W / m2and 1010W / m2.

[0062] The optical beam 340 may substantially have a frequency. The frequency of the optical beam 340 may be related to the energy per photon comprised by the optical beam 340. The frequency of the optical beam 340 may be configured to be below an excitation energy of the substrate, e.g. an excitation energy of electrons comprised by the substrate, and / or may be configured to substantially not excite electrons comprised by the substrate to a conduction energy band of the substrate. Exciting electrons, e.g. exciting to the conduction energy band, may allow the excited electrons to conduct an electrical current, so that applying S403 a voltage across the Josephson junction 301 when applying an optical beam 340 having a frequency above excitation energy of the substrate, may lead to an electrical current being conducted through at least a part of the substrate. Configuring the frequency of the optical beam 340 to be below the excitation energy of the substrate may serve to reduce, preferably prevent, an electrical current being induced by the step of applying S403 a voltage across the Josephson junction 301. Reducing, preferably preventing, an electrical current may serve to e.g. prevent confounding and / or interfering effects which may result from the electrical current, which may e.g. ensure that the step of annealing is better controlled and / or more predictable. The step of annealing being better controlled may refer to the degree to which the one or more properties of the Josephson junction 301 are altered by the step of annealing being better controlled.

[0063] In other embodiments, the frequency of the optical beam 340 may be configured to be above the excitation energy of the substrate, which may serve to induce an electrical current e.g. as a result of applying the current across the Josephson junction 301. Configuring the frequency of the optical beam 340 to be above the excitation energy of the substrate and / or inducing an electrical current may serve to e.g. increase the effect of annealing and / or increase the degree to which the one or more properties of the Josephson junction 301, e.g. the resistance, resonance frequency, and / or critical current, are altered by the step of annealing,

[0064] The step of applying the optical beam 340 to the Josephson junction 301 may be performed locally. The step of applying the optical beam 340 locally may be configured to ensure that no more than a fraction of the substrate that comprises the Josephson junction 301 may be heated, e.g. that at most 10%, at most 30%, at most 50% at most 70% or at most 90% of the substrate may be heated. The step of applying the optical beam 340 locally may be configured to ensure that the optical beam 340 impinges on no more than a fraction of the substrate that comprises the Josephson junction 301, e.g. that the optical beam 340 impinges on at most 10%, at most 30%, at most 50%, at most 70%, or at most 90% of the substrate. Heating only a fraction of the substrate and / or ensuring that the optical beam 340 impinges on no more than a fraction of the substrate may serve to ensure that applying the optical beam 340 substantially heats only the Josephson junction 301, e.g. heats only the Josephson junction 301 that is being annealed. Heating only a fraction of the substrate and / or ensuring that the optical beam 340 impinges on no more than a fraction of the substrate may be configured to heat only the Josephson junction 301 being annealed to a temperature at which the one or more properties, e.g. the resistance, resonance frequency, and / or critical current, of the Josephson junction 301 may be altered as part of the step of annealing the Josephson junction 301. Heating only a fraction of the substrate and / or ensuring that the optical beam 340 impinges on no more than a fraction of the substrate that comprises the Josephson junction 301 may serve to ensure that applying the optical beam 340 substantially does not heat other Josephson junctions 301 than the Josephson junction 301 being annealed to a temperature at which one or more properties, e.g. the resistance, resonance frequency, and / or critical current, of the other Josephson junctions may be altered as part of the step of annealing the Josephson junction 301.

[0065] Annealing the Josephson junction may furthermore comprise applying S403 a voltage across the Josephson junction 301 using a voltage source 330. The voltage may be applied simultaneously with the application of the optical beam 340, after the optical beam 340 has been allowed to increase the temperature of the Josephson junction 301 to a sufficient degree. In accordance with various embodiments, the optical beam may increase the temperature of the Josephson junction 301 within the order of magnitude of one several one hundred degrees Celsius.

[0066] The step of annealing the Josephson junction 301 may comprise applying S403 the voltage across the Josephson junction 401 and / or applying the optical beam 340 to the Josephson junction 301. One or more properties of the Josephson junction 301, e.g. a resistance, resonance frequency, and / or critical current of the Josephson junction 301, may be altered as a result of applying S403 the voltageand / or applying the optical beam 340. The altering of the one or more properties may be result from the step of annealing and / or the step of annealing may be configured to substantially alter the one or more properties of the Josephson junction 301. For example, applying S403 the voltage may be configured to alter one or more properties ofthe Josephson junction 301 and / or applying the optical beam 340 may be configured to alter one or more properties of the Josephson junction 301.

[0067] In accordance with various embodiments, the voltage may be applied S403 across the Joseph junction 301 while the optical beam 340 is applied S402 to the Josephson junction. The voltage may be applied S403 across the Josephson junction 301 after applying S402 the optical beam 340, e.g. when the Josephson junction 301 is still heated as a result of previously applying S402 the optical beam 340. Annealing the Josephson junction 301 may e.g. comprise repeated two or more alternating steps of applying S402 the optical beam 340 and applying S403 the voltage, wherein the repeated steps may alternate and / or at least partially overlap in time.

[0068] In accordance with various embodiments, the applied voltage is a DC voltage, more preferably an alternating DC voltage. The alternating DC voltage may comprise a series of voltage pulses having respective pulse widths of 1.0 milliseconds or more. In accordance with various embodiments, the voltage pulses may be applied in the form of a square wave form. Preferably, this square wave form is a smoothed square wave form, with no or only minimal voltage overshoot that may otherwise cause damage to the Josephson junction 301.

[0069] In accordance with various embodiments, a peak-to-peak voltage of the applied voltage comprises 0.88 volts or less, preferably no more than 0.84 volts, more preferably no more than 0.80 volts, and most preferably 0.76 volts or less.

[0070] In accordance with various embodiments, a peak-to-peak voltage of the applied voltage may comprise at least 0.1 volts, preferably at least 0.3 volts, more preferably at least 0.5 volts, most preferably at least 0.7 volts.

[0071] In accordance with various embodiments, a peak-to-peak voltage of the applied voltage may be comprised between 0.1 volts and 3 volts, preferably between 0.3 volts and 2 volts, more preferably between 0.5 volts and 1.5 volts, most preferably between 0.7 and 1 volts.

[0072] The proposed method is furthermore particularly well suited for qubit designs, which are susceptible to dielectric breakdown under higher voltage stresses, in accordance with various embodiments. Higher voltage stresses may also contribute to aging effects over time. Aging refers to the gradual degradation in qubit performance due to changes in the material properties of the Josephson junctions, often exacerbated by the stresses introduced during tuning processes. High voltages and prolonged electrical stressing can introduce defects and accelerate material degradation. By reducing the required voltage through simultaneous optical (laser) heating, the electrical and thermal stress imposed on the junctions during the annealing process is lessened, in accordance with various embodiments. The optical beam 340 may assist in achieving the desired adjustments efficiently, meaning the junctions are exposed to potentially damaging conditions for relatively short durations andat relatively low intensities. As a result, various embodiments may introduce significantly less aging over time, preserving the coherence times and operational fidelity of the qubits. It will be appreciated that in practical quantum computing applications, long-term qubit stability and reliability are essential.

[0073] In accordance with various embodiments, a relatively low voltage of 0.9 volts or less than 0.9 may be used during the annealing process, for example 0.85 volts. This is considered advantageous because a lower voltage reduces the risk of damage occurring to the Josephson junction during the annealing process in the form of a short circuit.

[0074] Hypothetically, the risk of a short circuit could alternatively be mitigated by employing excessively thick oxide layers to facilitate higher voltages. However, such qubit designs would introduce additional challenges. Firstly, such oxide layers increase the junction's stray capacitance, which can adversely affect the qubit's performance by introducing unwanted capacitive loading, shifting the qubit frequency, and reducing the qubit's anharmonicity. Increased stray capacitance can lead to mistargeting errors which in turn lead to slower gate operations and heightened susceptibility to noise.

[0075] Secondly, such oxide layers necessitate larger junction areas to achieve the desired critical current due to the inverse relationship between current density and junction area. However, increasing the junction size is limited by practical fabrication constraints and can lead to increased susceptibility to defects and inhomogeneities across the junction.

[0076] Moreover, larger junction areas exacerbate the problem of two-level systems (TLS) defects or impurities in the insulating barrier that can resonate with the qubit and cause decoherence. The number of TLS scales with the junction area, so larger junctions have a higher density of these detrimental states. TLS can absorb energy from the qubit, leading to reduced coherence times and lower fidelity of quantum operations. Therefore, using thick oxide junctions with low critical current densities can significantly impair qubit performance and limit the scalability of superconducting quantum processors.

[0077] FIG. 5 shows another example of a method 500 of forming a superconducting circuitry device in accordance with various embodiments.

[0078] The method may comprise providing S501 at least one Josephson junction formed on a substrate between a first electrical node and a second electrical node and defining a resonant frequency at cryogenic temperatures.

[0079] In step S502, a resistance of the Josephson junction may be determined or the transition frequency may be determined. In accordance with various embodiments, the resistance may be determined at room temperature, a temperature close to room temperature, or any other temperature. The determined resistance and / or transition frequency may be compared to a target value in accordance with a design of the superconducting circuitry device, to determine whether the determined value substantially matches said target value, and whether further adjustment is necessary. Determining the resistance and / or the transition frequency of the Josephson junction may involve placing probes on thesuperconducting circuitry device. With reference to FIG. 2, in certain embodiments this may involve placing probes in the first and / or second node 221, 222 of the superconducting circuitry device 200. In accordance with yet a further embodiment, the probes may be placed on the first superconducting electrode 211 and the second superconducting electrode 212.

[0080] The step S502 of determining a resistance and / or transition frequency of the Josephson junction 301 may comprise applying a further voltage across the Josephson junction 301. Applying the further voltage across the Josephson junction may be configured to determine the resistance and / or transition frequency of the Josephson junction 301, e.g. on the basis of an electrical current, e.g. on the basis of an amplitude and / or frequency of the electrical current, which may be induced by applying the further voltage across the Josephson junction. The further voltage may be at most 2x l0-1volts, preferably at most MO'2volts, more preferably at most MO'3volts, even more preferably at most 1 x 10'4volts, most preferably at most MO'5volts.

[0081] In step S503, an optical beam may be applied to the Josephson junction. The optical beam may be in accordance with anyone of the embodiments described here above with reference to the foregoing figures and is preferably a laser beam. The optical beam may furthermore comprise a Gaussian beam profile.

[0082] In step S504, a voltage is applied to the Josephson junction. The voltage may be applied in accordance with any one of the embodiments as described here above with reference to step S403, FIG. 4.

[0083] In step S505, at least one of the resistance and the transition frequency of the Josephson junction may be determined or may be determined again. In one embodiment, steps S505 and S504 may be performed simultaneously, i.e. the resistance or the transition frequency may be determined while voltage is applied to the Josephson junction.

[0084] In step S506, it is determined whether the determined resistance and / or the transition frequency substantially matches a predetermined target value, which is typically set in accordance with design of the superconducting circuitry device. If the determined resistance and / or the transition frequency substantially matches the predetermined target value, the method may end. In the alternative case in which the determined resistance and / or the transition does not match the predetermined target value, step S504 may be reiterated or continued, followed by a reiteration of steps S505 and S506, until the predetermined target value is achieved.

[0085] FIG. 6 shows a graph 600 illustrating the effect of an annealing operation according to embodiments performed over time, demonstrating a 40% changed in resistance determined at room temperature. In accordance with various embodiments, such a change in resistance may be achieved with voltages as low as 0.88 V or significantly lower. Because the resistance is inversely proportional to the transition frequency of a Josephson junction, a positive change in resistance may result in a corresponding negative resonance frequency shift of the annealed Josephson junction.

[0086] It will be appreciated that a relatively lowered voltage across the Josephson junction is associated with a correspondingly decreased risk of damage to the Josephson junction, which may result from the occurrence of a short circuit. FIG. 7 shows an exemplary embodiment of an apparatus 790 for Josephson junctions with which various embodiments of the herein disclosed invention may be performed.

[0087] The annealing device may comprise an optical beam source 741 configured to emit an optical beam 740 to one or more than one Josephson junction 701, 701' comprised by a superconducting circuitry device 700. In accordance with various embodiments, the optical beam source 741 may be a monochromatic beam source, such as a laser. In accordance with various embodiments, t he optical beam source 741 may be configured to emit the optical beam 740 having a Gaussian beam profile having a wavelength anywhere within in the 100 nm to 3000 nanometers range. The annealing apparatus 790 may furthermore comprise one or more optical devices 750. The optical devices 750 may comprise any one or more than one of lenses, beam splitters, polarisers, shutters, collimators, diffractors, and wavelength plates that are arranged anywhere within the optical path of the optical beam 740. The optical devices 750 may be configured to adjust the properties of the optical beam 740 - e.g. beam intensity, polarisation state, phase, beam profile, divergence, etc. - before it the superconducting circuitry device 700 having the reaches the Josephson junction(s) 701, 701' to be annealed.

[0088] In accordance with various embodiments, the annealing apparatus 790 moreover may comprise a polarising beam splitter 760 configured to pass the optical beam 740 such that it reaches the superconducting circuitry device 790, after which it is reflected and propagates via the polarising beam splitter 760 toward an image capturing device 770. The image capturing device 770 may be used to determine whether the optical beam 740 illuminates the superconducting circuitry device at an intended location, which typically is the location of a Josephson junction 701, 70 T or a location sufficiently close thereto.

[0089] In some embodiments, the superconducting circuitry device 700 may be positioned on a stage 780 comprised by the annealing device 790 during the annealing process. The stage 780 may be configured position the superconducting circuitry device relative to the optical beam 740, such that the optical beam illuminates the superconducting circuitry device at a desired location suitable for performing the anneal. In some embodiments, the stage 780 may be electrically controlled to make minute adjustments to the positioning of the superconducting circuitry device. In yet further embodiments, controlling of the stage may be performed in an automated manner based on signals obtained from the image acquisition device 770.

[0090] The annealing apparatus 730 may furthermore comprise means 730 for applying a voltage across one or more of the Josephson junctions 701, 701' comprised by the superconducting circuitry device 700. In accordance with various embodiments, the means 730 for applying a voltage may comprise a voltage source configured to generate a DC voltage or an alternating DC voltage. The voltage generated by the voltage source 730 may be than 0.9 V, preferably 0.64 V to 0.88 V, morepreferably 0.70 V to 0.82 V, and most preferably 0.74 V to 0.78 V. The voltage may be generated in the form of a, preferably smoothed, square wave form. In at least some embodiments, such a square wave form may comprise pulse widths of 1.0 milliseconds or more.

[0091] The voltage from the voltage source 730 may be applied across the Josephson junctions 701, 70 T by means of probe needles 731, 732. The voltage may be applied to first and second electrical nodes 721, 722 between which the Josephson junctions 701, 70 T are formed. In accordance with various embodiments, the first and second electrical nodes 721, 722 may be capacitive plates, probe pads, or electrodes of neighbouring Josephson junctions. In at least some embodiments, the probe needles 731, 732 may be controlled and positioned to where they may apply the voltage in an automated manner.

[0092] In accordance with various embodiments, a superconducting circuitry device that is annealed using the herein disclosed method and / or annealing apparatus may constitute any one of quantum processing unit (QPU) comprising at superconducting qubit, travelling wave parametric amplifier comprising a plurality of electrically connected Josephson junctions, and a tuneable resonator.

[0093] One or more properties of each of the Josephson junctions 701, 701’ e.g. a resistance, resonance frequency, and / or critical current of each of the Josephson junctions 701, 701’, may be altered as a result of applying a voltage from the voltage source 730 and / or applying the optical beam 740 emitted from the optical beam source 741. The altering of the one or more properties may be result from the step of annealing and / or the step of annealing may be configured to substantially alter the one or more properties of each of the Josephson junctions 701, 701’. For example, applying the voltage may be configured to alter one or more properties of each of the Josephson junctions 701, 701’ and / or applying the optical beam 340 may be configured to alter one or more properties of each of the Josephson junctions 701, 701’.

[0094] It will be appreciated that the scope of the sought after protection is not limited to any one of the above described embodiments. The skilled person will acknowledge that various components and features of the described embodiments can be combined with one another or otherwise modified. The scope of the sought after protection is therefore not limited to any one of the above listed practical applications or embodiments, but is defined solely by the features as described in the claims and, at least in certain jurisdictions, their equivalents.

[0095] Clauses:1. A method for forming a superconducting circuitry device, comprising: providing at least one Josephson junction formed on a substrate between a first electrical node and a second electrical node; and annealing the at least one Josephson junction by:- applying an optical beam to the at least one Josephson junction; and- applying a voltage across the at least one Josephson junction.2. The method of clause 1, wherein the voltage is applied across the Joseph junction while the optical beam is applied thereto.3. The method of clause 1 or 2, wherein the applied voltage is a DC voltage.4. The method of clause 3, wherein the applied voltage is an alternating DC voltage.5. The method of clause 4, wherein the alternating DC voltage comprises a series of voltage pulses, said pulses, each preferably having pulse widths of 1.0 millisecond or more.6. The method of clause 5 or 6, wherein the alternating DC voltage comprises a, preferably smoothed, square wave form.7. The method of any one of the foregoing clauses, wherein the applied voltage comprises 0.88 volts or less, preferably no more than 0.84 volts, more preferably no more than 0.80 volts, and most preferably 0.76 volts or less.8. The method of any one of the foregoing clauses, further comprising determining at least one of a resistance and the resonance frequency of the Josephson junction.9. The method of clause 8, wherein the step of applying a voltage across the Josephson junction is reiterated, based at least on the determined resistance and / or the resonance frequency, until a target value of the resistance and / or the resonance frequency is reached.10. The method of any one of the foregoing clauses, wherein the step of applying the optical beam to the Josephson junction is performed locally, wherein no more than a fraction of the substrate that comprises the Josephson junction is heated.11. The method of any one of the foregoing clauses, wherein the optical beam is a monochromatic optical beam, preferably a laser beam.12. The method of any one of the foregoing clauses, wherein the optical beam is applied directly to the Josephson junction.13. The method of any one of the foregoing clauses, wherein the optical beam comprises a Gaussian beam profile.14. The method of any one of the foregoing clauses, wherein the substrate comprises sapphire.15. The method of any one of the foregoing clauses 1 - 14, wherein the substrate comprises silicon.16. The method of any one of the foregoing clauses, wherein annealing the at least one Josephson junction causes a negative resonance frequency shift.17. A superconducting circuitry device comprising one or more than one Josephson junctions, wherein said Josephson junction has been annealed using the method according to any one of the foregoing clauses 1 - 16.18. The superconducting circuitry device of clause 17, wherein the superconducting circuitry device is one of a quantum processing unit, QPU, with at least one superconducting qubit having the Josephson junction; a travelling wave parametric amplifier comprising a plurality of electrically connected Josephson junctions; and a tuneable resonator.19. An annealing apparatus for Josephson junctions, the annealing device comprising: an optical beam source configured to apply an optical beam to at least one Josephson junction; and means for applying a voltage across the Josephson junction.

Claims

CLAIMS1. A method for forming a superconducting circuitry device (200), comprising: providing (S401) at least one Josephson junction (201) formed on a substrate (210) between a first electrical node (221) and a second electrical node (222); and annealing the at least one Josephson junction (201) by:- applying (S402) an optical beam (340) to the at least one Josephson junction (201); and- applying (S403) a voltage across the at least one Josephson junction (201).

2. The method of claim 1 , wherein the voltage is applied across the Joseph junction while the optical beam is applied thereto.

3. The method of claim 1 or 2, wherein the applied voltage is a DC voltage and / or wherein the applied voltage is an alternating DC voltage.

4. The method of claim 3, wherein the alternating DC voltage comprises a series of voltage pulses, said pulses, each preferably having pulse widths of 1.0 millisecond or more.

5. The method of claim 3 or 4, wherein the alternating DC voltage comprises a, preferably smoothed, square wave form.

6. The method of any one of the foregoing claims, wherein a peak-to-peak voltage of the applied voltage is comprised between 0.1 volts and 3 volts, preferably between 0.3 volts and 2 volts, more preferably between 0.5 volts and 1.5 volts, most preferably between 0.7 and 1 volts; and / or wherein the optical beam has an intensity comprised between 107Watts per square meter (W / m2) and 3* 1012W / m2, preferably comprised between 5* 107W / m2and 5x l0nW / m2, more preferably comprised between 108W / m2and 1011W / m2, even more preferably comprised between 5* 108W / m2and 5x 1010W / m2, most preferably between 109W / m2and 1010W / m2.

7. The method of any one of the foregoing claims, wherein the step of applying the optical beam to the at least one Josephson junction is configured to alter one or more properties of the Josephson junction, preferably configured to alter a resistance, resonance frequency, and / or critical current of the at least one Josephson junction; and / or wherein the step of applying the voltage across the at least one Josephson junction is configured to alter one or more properties of the Josephson junction, preferably configured to alter a resistance, resonance frequency, and / or critical current of the at least one Josephson junction.

8. The method of any one of the foregoing claims, further comprising determining at least one of a resistance and a resonance frequency of the Josephson junction.

9. The method of claim 8, wherein the step of applying a voltage across the Josephson junction is reiterated, based at least on the determined resistance and / or the resonance frequency, until a target value of the resistance and / or the resonance frequency is reached.

10. The method of any one of the foregoing claims, wherein the step of applying the optical beam to the Josephson junction is performed locally, wherein no more than a fraction of the substrate that comprises the Josephson junction is heated.

11. The method of any one of the foregoing claims, wherein the optical beam is a monochromatic optical beam, preferably a laser beam.

12. The method of any one of the foregoing claims, wherein the optical beam is applied directly to the Josephson junction.

13. The method of any one of the foregoing claims, wherein the optical beam comprises a Gaussian beam profile.

14. The method of any one of the foregoing claims, wherein the substrate comprises sapphire.

15. The method of any one of the foregoing claims 1 - 14, wherein the substrate comprises silicon.

16. The method of any one of the foregoing claims, wherein annealing the at least one Josephson junction causes a negative resonance frequency shift.

17. A superconducting circuitry device (200) comprising one or more than one Josephson junctions (201), wherein said Josephson junction (201) has been annealed using the method according to any one of the foregoing claims 1 - 16.

18. The superconducting circuitry device of claim 17, wherein the superconducting circuitry device is one of a quantum processing unit, QPU, with at least one superconducting qubit having the Josephson junction; a travelling wave parametric amplifier comprising a plurality of electrically connected Josephson junctions; and a tuneable resonator.-19-19. An annealing apparatus (790) for Josephson junctions (701, 701’), the annealing device (790) comprising: an optical beam source (741) configured to apply an optical beam (740) to at least one Josephson junction (701); and means for applying a voltage across the Josephson junction (701).

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