Qubit adjustment

Abstract

A method for tuning the frequency of a qubit, which includes a Josephson junction. The method includes the step of heating the Josephson junction by directing an electron beam. The method further includes the step of cooling the Josephson junction following the heating of the Josephson junction with the electron beam. The heating and cooling of the Josephson junction function to change the resistance of the Josephson junction, and the change in the resistance of the Josephson junction changes the frequency of the qubit.

Description

[Technical Field]

[0001] This disclosure relates to quantum computing. In particular, this disclosure relates to a method and apparatus for tuning the frequency of qubits, which can constitute part of a quantum computer. [Background technology]

[0002] Quantum computing is a device that processes quantum information by utilizing quantum mechanical effects. The basic unit of quantum information used in quantum computing is the qubit. A qubit has two ground states and is similar to a bit used in conventional computing. However, unlike a conventional bit, which can exist in only one of two states at any given time, a qubit can exist simultaneously in a superposition state of both states. The overall superposition of states in a quantum computer is 2, where n is the number of qubits in the superposition state. n It doubles. Quantum computers can use these superpositions of states, along with other quantum mechanical effects such as quantum entanglement, to solve a variety of computational problems. In particular, quantum computing has the potential to solve a wide range of computational problems that even the world's largest conventional supercomputers have not yet reached.

[0003] A practical quantum computer is configured to establish, maintain, and manipulate multiple physical qubits. Physical qubits can be realized by maintaining and manipulating a two-state quantum mechanical system. One form of realization of a physical qubit is the so-called superconducting qubit. A superconducting qubit comprises a superconducting electronic circuit that typically includes a Josephson junction. The Josephson junction is a nonlinear inductive element that actually functions to generate a clear difference between the energy levels of the superconducting qubit. This clear energy level difference allows the energy levels of the qubit to be manipulated (typically by microwave irradiation), enabling the superconducting qubit to be manipulated and transitions between energy levels to occur.

[0004] A superconducting qubit, including a Josephson junction, has an associated resonant frequency. The resonant frequency of a superconducting qubit determines the frequency at which the qubit is driven to achieve transitions between energy levels. In its simplest form, the resonant frequency of a superconducting qubit is fixed during the fabrication of the qubit and is a property of a variable such as the critical current of the Josephson junction or the capacitance of the qubit.

[0005] The fabrication of Josephson junctions can be subject to variation. For example, a Josephson junction can be fabricated using a predetermined set of target or design parameters. However, in practice, the parameters of the fabricated Josephson junction (e.g., physical dimensions, critical current, resistance, and / or qubit frequency) may deviate from the target values ​​for which the fabrication process was designed. For instance, if multiple superconducting qubits are fabricated using a nearly identical fabrication process (e.g., using the same target or design parameters), variations in the fabrication process can lead to dispersion in the qubit frequencies.

[0006] Superconducting qubits whose frequencies can be dynamically adjusted during operation have been proposed, typically with some form of control signal applied. However, such dynamically adjustable qubits require special components and electromagnetic signals to be input to the qubit, which can increase complexity and noise. Therefore, it is sometimes desirable to set the frequency of the qubit more precisely before operation to avoid the need for dynamic frequency adjustment during operation. As an addition or alternative, even when using frequency-adjustable qubits, there are still advantages associated with being able to more precisely control the resonant frequency of the superconducting qubit before operation (and before any frequency adjustments that may occur during operation).

[0007] Methods have been proposed to change the frequency of superconducting qubits after the fabrication of a Josephson junction. For example, a method of annealing the Josephson junction using a laser beam has been proposed. Furthermore, a method of annealing the Josephson junction through exposure to high-frequency radiation has also been proposed. [Overview of the project] [Problems that the invention aims to solve]

[0008] The subject matter included in this application was conceived in this context. [Means for solving the problem]

[0009] It was discovered that the resonant frequency of a qubit can be tuned before operation by directing an electron beam to heat the Josephson junction that forms part of the qubit. This heating of the Josephson junction using an electron beam proved to provide a highly controllable technique for changing the resistance of the Josephson junction, which enables the tuning of the resonant frequency of the qubit incorporating the Josephson junction. In particular, it was found that the electron beam can provide localized heating of the Josephson junction, enabling independently controllable tuning of individual qubits without significantly affecting the frequencies of adjacent qubits. Furthermore, it was found that, with appropriate control of the electron beam current and total charge used to heat the Josephson junction, the resistance of the Josephson junction can be selectively controlled to increase or decrease. Accordingly, the frequency of the qubit incorporating the Josephson junction can be selectively tuned to decrease or increase as needed.

[0010] A first aspect of this disclosure provides a method for tuning the frequency of a qubit, which includes a Josephson junction. This method includes the steps of directing an electron beam to heat the Josephson junction, and subsequently cooling the Josephson junction with the electron beam. Heating and cooling the Josephson junction changes the resistance of the Josephson junction. The change in the resistance of the Josephson junction changes the frequency of the qubit.

[0011] Heating and cooling a Josephson junction can function to anneal the junction and is sometimes referred to as electron beam annealing of a Josephson junction. Heating and cooling a Josephson junction can function to alter the material properties of at least one component of the Josephson junction.

[0012] The inventors have demonstrated that the frequency of qubits in a quantum information processor can be tuned using electron beam annealing of a Josephson junction, as described herein. In particular, the inventors have demonstrated that the frequency of qubits in a quantum information processor can be tuned using electron beam annealing, thereby reducing the frequency spread of the qubits. They have further demonstrated that the coherence time of the qubits is not adversely affected after applying electron beam annealing to the qubits (to tune their frequencies), and that the qubits remain high-coherence qubits (having relatively long coherence times) even after the application of electron beam annealing.

[0013] The cooling of the Josephson junction following heating may include enabling the Josephson junction to be cooled. For example, the Josephson junction can be cooled because the electron beam for heating the Josephson junction is not directed during the cooling period. Cooling of the Josephson junction does not necessarily include active cooling of the Josephson junction. However, in another example, active cooling may be applied to the Josephson junction to cool it.

[0014] A Josephson junction may include two superconductors separated by a barrier. The superconductors may include, for example, aluminum. The barrier may include a non-superconducting material and / or an electrical insulating material. The barrier may include aluminum oxide. The barrier may be thin enough to allow quantum tunneling between the two superconductors across the barrier.

[0015] In some examples, a qubit may contain a single Josephson junction. In other examples, a qubit may contain multiple Josephson junctions. In examples where a qubit contains multiple Josephson junctions, the method may include directing an electron beam to heat (and cool) one of the multiple Josephson junctions. Alternatively, the method may include directing an electron beam to heat one or more Josephson junctions (simultaneously or at different times) and then cooling one or more Josephson junctions. One or more Josephson junctions may include all of the multiple Josephson junctions contained in the qubit, or fewer than all of the multiple Josephson junctions contained in the qubit.

[0016] The step of directing the electron beam to heat the Josephson junction may include the step of directing the electron beam and directing it into the Josephson junction.

[0017] For example, the electron beam may be directed to directly inject at least a portion of the Josephson junction itself, thereby inducing direct heating of at least a portion of at least one component of the Josephson junction.

[0018] In some cases, the electron beam may be directed so that it does not directly enter the Josephson junction.

[0019] The step of directing an electron beam to heat a Josephson junction may include the step of directing an electron beam to impinge on a component thermally coupled to the Josephson junction, thereby causing heating of the component and heating of the Josephson junction via heat conduction from the heated component.

[0020] The step of directing an electron beam to impinge on a component thermally coupled to the Josephson junction causes indirect heating of the Josephson junction. That is, the component is directly heated by the electron beam and functions to indirectly heat the Josephson junction via heat conduction from the heated component. Indirect heating of the Josephson junction can reduce the risk of causing damage to the Josephson junction. The reason is that direct heating can cause damage to the Josephson junction under at least some conditions, which may have an adverse effect on its performance.

[0021] The component may be close to at least a part of the Josephson junction.

[0022] The component may include a part of a substrate that supports the Josephson junction. The Josephson junction may be supported on a substrate including, for example, silicon or sapphire. The component may include a part of the substrate close to the Josephson junction. That is, the electron beam may be directed to impinge on the substrate at a position close to the Josephson junction.

[0023] The Josephson junction may be connected between two superconducting electrodes.

[0024] The superconducting electrodes may be arranged coaxially with each other. The superconducting electrodes may be arranged on the same plane as each other. For example, the superconducting electrodes may be located on the same surface (e.g., the surface of a substrate).

[0025] The step of directing the electron beam to heat the Josephson junction may include the step of directing the electron beam with a first current below a threshold current to increase the resistance of the Josephson junction and decrease the frequency of the qubit.

[0026] The step of directing the electron beam to heat the Josephson junction may include the step of directing the electron beam with a first current greater than the threshold current to reduce the resistance of the Josephson junction and increase the frequency of the qubit.

[0027] The step of directing the electron beam to heat the Josephson junction may include the step of directing the electron beam to heat the Josephson junction over a single continuous exposure time.

[0028] The step of directing an electron beam to heat the Josephson junction may include the step of directing multiple pulses of the electron beam to heat the Josephson junction.

[0029] Multiple pulses of the electron beam may be directed to heat the Josephson junction over multiple consecutive exposure periods. These consecutive exposure periods may be separated by periods during which the electron beam is not directed to heat the Josephson junction. Alternatively, at least some of the multiple pulses of the electron beam may be directed to heat the Josephson junction simultaneously. For example, multiple electron sources may be used to direct multiple electron beams and heat the Josephson junction simultaneously.

[0030] At least some of the multiple pulses of the electron beam may be directed to incident at multiple different locations.

[0031] The step of directing an electron beam to heat the Josephson junction may include the step of directing an electron beam to incident on multiple different locations. For example, an electron beam may be directed to incident on multiple different parts of the Josephson junction and / or components thermally coupled to the Josephson junction (e.g., a substrate supporting the Josephson junction). An electron beam may be directed to incident on multiple different locations in a continuous time. For example, an electron beam may be directed to incident on a first location in a second time, and then on a second location in a second time. As an addition or alternative, an electron beam may be directed to incident on multiple different locations simultaneously. For example, multiple electron sources may be used to direct multiple electron beams to incident on multiple different locations simultaneously to heat the Josephson junction.

[0032] The heating of the Josephson junction may be controlled by controlling the direction and incidence of the electron beam. The electron beam typically has a beam diameter smaller than the dimensions of the Josephson junction (for example, the beam diameter may be several times the dimensions of the Josephson junction, and in some cases may be an order of magnitude larger or smaller). The relatively small beam diameter of the electron beam (compared to the Josephson junction) allows for precise control of the positioning of the electron beam relative to the Josephson junction, and thus allows for careful control of the heating of the Josephson junction.

[0033] Different locations from which the electron beam is directed and incident can be arranged to form an exposure pattern. The exposure pattern can be controlled to control the degree of heating of the Josephson junction (and the resistance change induced by the heating). The exposure pattern may include multiple different exposure spots from which the electron beam is directed and incident. Multiple different exposure spots may include at least some exposure spots on at least a portion of the Josephson junction. Additionally or alternatively, multiple different exposure spots may include at least some exposure spots that are not located on the Josephson junction. For example, at least some of the exposure spots may be located on a component thermally coupled to the Josephson junction (e.g., a support substrate).

[0034] In some examples, the exposure pattern may include multiple exposure spots arranged in a substantially uniform grid pattern. This grid pattern may, for example, be positioned approximately in the center of the Josephson junction.

[0035] Multiple different locations may be arranged to form an exposure pattern surrounding the Josephson junction.

[0036] The exposure pattern may include, for example, multiple exposure spots arranged to form one or more loops around the Josephson junction. The arrangement of exposure spots may include gaps between adjacent exposure spots, so that the exposure spots do not form a complete closed loop that completely surrounds the Josephson junction. However, even when gaps exist between adjacent exposure spots, such an arrangement forms a pattern that is arranged to generally surround the Josephson junction.

[0037] The step of directing an electron beam to heat the Josephson junction may include the step of directing an electron beam having a beam diameter of less than 200 nm to heat the Josephson junction.

[0038] The step of directing an electron beam to heat the Josephson junction may include the step of directing an electron beam having a beam diameter of less than 100 nm to heat the Josephson junction.

[0039] The step of directing an electron beam to heat the Josephson junction may include the step of directing an electron beam having a beam diameter of less than 50 nm to heat the Josephson junction.

[0040] The use of electron beams allows for the use of relatively small beam diameters, enabling highly localized and / or highly controllable heating of Josephson junctions. Localized heating of a Josephson junction allows for the independent and selective heating of a single Josephson junction without significantly heating neighboring junctions (and thus without altering their resistances and equivalent qubit frequencies). Generally, electron beams with smaller beam diameters than laser beams can be used. Therefore, electron beams can be advantageously used to provide more localized and / or controllable heating of Josephson junctions than laser beams.

[0041] The step of directing an electron beam to heat the Josephson junction may include the step of directing an electron beam having a current greater than 0.1 nA to heat the Josephson junction.

[0042] The step of directing the electron beam to heat the Josephson junction may include directing an electron beam having a current greater than 1 nA. The step of directing the electron beam to heat the Josephson junction may also include directing an electron beam having a current of less than 1000 nA. For example, the electron beam may have a current of less than about 500 nA, and may be generated using a current of less than about 200 nA.

[0043] The step of directing the electron beam and heating the Josephson junction may include the step of directing the electron beam and heating the Josephson junction using an electron beam lithography apparatus.

[0044] The electron beam lithography apparatus may include an electron source configured to generate an electron beam, direct the electron beam, and heat the Josephson junction. The electron beam lithography apparatus may also include a stage for supporting a substrate on which the Josephson junction is located and for aligning the Josephson junction with respect to the electron beam. The electron beam lithography apparatus may further be configured to direct the electron beam and generate vacuum pressure conditions for heating the Josephson junction.

[0045] In another example, a separate apparatus and / or electron source may be used to heat the Josephson junction. For example, a scanning electron microscope may be used to direct the electron beam and heat the Josephson junction.

[0046] A second aspect of this disclosure provides a method for tuning the qubit frequencies of a quantum information processor comprising a plurality of qubits, each qubit comprising a Josephson junction. The method includes the steps of: determining the frequency of each of the plurality of qubits; identifying at least one of the qubits for frequency tuning based on the determined frequencies of the plurality of qubits; and tuning the frequency of the at least one qubit identified for frequency tuning. The step of tuning the frequency of the at least one qubit identified for frequency tuning may include the steps of: directing an electron beam to heat a Josephson junction comprising the at least one qubit identified for frequency tuning; and, following the heating of the Josephson junction by the electron beam, cooling the Josephson junction. The heating and cooling of the Josephson junction function to change the resistance of the Josephson junction, and the change in the resistance of the Josephson junction changes the frequency of the at least one identified qubit.

[0047] The step of determining the frequency of each of the multiple qubits may include a step of directly determining the frequency itself. Alternatively, the step of determining the frequency of each of the multiple qubits may include a step of determining a frequency-indicating variable (e.g., the resistance of the Josephson junction).

[0048] The step of determining the frequency of each of the multiple qubits may include the step of measuring the resistance of the Josephson junction contained in each of the multiple qubits.

[0049] The step of identifying at least one of a plurality of qubits for frequency tuning may include the step of identifying at least one of a plurality of qubits having a tunable frequency in order to reduce the dispersion of the frequencies of the plurality of qubits.

[0050] For example, the step of identifying at least one of a group of qubits for frequency tuning may include the step of identifying at least one qubit having a frequency different from the average frequency of all the qubits. The step of identifying at least one of a group of qubits for frequency tuning may include the step of identifying at least one qubit having a frequency lower than the average frequency. The step of identifying at least one of a group of qubits for frequency tuning may include the step of identifying at least one qubit having a frequency higher than the average frequency.

[0051] The step of tuning the frequency of at least one identified qubit for frequency tuning may include the step of tuning the frequency of at least one identified qubit so as to reduce the dispersion of the frequencies of multiple qubits.

[0052] The dispersion of the frequencies of multiple qubits may include measures such as the variance and / or standard deviation of the frequencies of multiple qubits.

[0053] The step of tuning the frequency of at least one identified qubit for frequency tuning may include tuning the frequency of at least one identified qubit so that it is closer to the average frequency of all qubits. Such tuning can function to reduce the variance of the frequencies of multiple qubits.

[0054] The step of tuning the frequency of at least one qubit identified for frequency tuning may include increasing the resistance of the Josephson junction of at least one of the at least first qubits identified for frequency tuning to decrease the frequency of that at least first qubit identified for frequency tuning.

[0055] The step of increasing the resistance of the Josephson junction may include the step of heating the Josephson junction by directing an electron beam having a current below a threshold current.

[0056] The step of tuning the frequency of at least one qubit identified for frequency tuning may include the step of decreasing the resistance of at least a second of the at least one qubit identified for frequency tuning to increase the frequency of the at least second of the at least one qubit identified for frequency tuning.

[0057] The step of reducing the resistance of the Josephson junction may include the step of heating the Josephson junction by directing an electron beam having a current greater than the threshold current.

[0058] The step of tuning the frequency of at least one qubit identified for frequency tuning may further include the steps of determining the characteristics of an electron beam directed to heat a Josephson junction, depending on the determined frequency of the qubit containing the Josephson junction, and directing the electron beam to heat the Josephson junction using the determined characteristics of the electron beam.

[0059] The characteristics of the electron beam directed to heat the Josephson junction may include one or more of the following: electron beam current, amount of charge supplied by the electron beam, time spent directing the electron beam to heat the Josephson junction, number of positions where the electron beam is directed to heat the Josephson junction, and / or positions where the electron beam is directed to heat the Josephson junction (e.g., proximity of the electron beam to the Josephson junction).

[0060] A third aspect of this disclosure provides a quantum information processor comprising at least one qubit including a Josephson junction, wherein the frequency of the at least one qubit is tuned using the method of the first aspect.

[0061] A fourth aspect of this disclosure provides a quantum information processor comprising a plurality of qubits, each containing a Josephson junction, wherein the frequency of at least one of the plurality of qubits is tuned using the method according to the third aspect.

[0062] Within the scope of this application, it is expressly intended that the various aspects, embodiments, examples, and alternatives described in the preceding paragraphs, claims, and / or the following description and drawings, in particular the individual features thereof, may be adopted independently or in any combination. That is, all examples and / or features of any example may be combined in any way and / or combination, provided that such features do not conflict. The applicant reserves the right to modify the initially filed claims or to file new claims accordingly, including the right to amend the initially filed claims to depend on and / or incorporate features of any other claim, even if they were not originally claimed as such. [Brief explanation of the drawing]

[0063] One or more embodiments of the present invention are schematically shown in the accompanying drawings as examples. [Figure 1]This is a schematic diagram illustrating an example of how an electron beam is directed to heat a superconducting qubit. [Figure 2] This is a schematic diagram of a further example where an electron beam is directed and used to heat a superconducting qubit. [Figure 3] This is a schematic diagram illustrating an example of heating a Josephson junction, where an electron beam is directed to form part of a superconducting qubit. [Figure 4] This is a schematic diagram of a quantum information processor containing multiple superconducting qubits. [Figure 5] This is a flowchart illustrating an example method for adjusting the frequency of a qubit. [Figure 6] This is a schematic diagram of several different exposure patterns that a Josephson junction can undergo during electron beam annealing. [Figure 7] This is a schematic diagram showing exposure patterns at three different distances from the Josephson junction during electron beam annealing. [Figure 8A] This is a histogram showing the resistance values ​​of multiple Josephson junctions before and after undergoing the example electron beam annealing treatment. [Figure 8B] Figure 8A is a scatter plot showing the resistance values ​​of multiple Josephson junctions before and after undergoing the example electron beam annealing treatment. [Figure 9] This is a flowchart illustrating an example method for adjusting the qubit frequencies of a quantum information processor containing multiple qubits. [Figure 10A] This is a histogram showing the resistance values ​​of the first Josephson junction group contained in the qubit of the first quantum information processor. [Figure 10B] This is a histogram showing the resistance values ​​of the first Josephson junction group before and after further example electron beam annealing. [Figure 10C] This is a histogram showing the resistance values ​​of the first Josephson junction group before and after further example electron beam annealing. [Figure 10D] This is a scatter plot showing the resistance values ​​of the first Josephson junction group before and after further example electron beam annealing. [Figure 11A] This is a histogram showing the resistance values ​​of the second Josephson junction group contained in the qubit of the second quantum information processor. [Figure 11B] This is a histogram showing the resistance values ​​of the second Josephson junction group before and after electron beam annealing, as a further example. [Figure 11C] This is a histogram showing the resistance values ​​of the second Josephson junction group before and after electron beam annealing, as a further example. [Figure 11D] This is a scatter plot showing the resistance values ​​of the second Josephson junction group before and after further example electron beam annealing. [Figure 12A] This is a schematic diagram of exposure patterns placed at multiple different positions on a Josephson junction. [Figure 12B] This graph shows the change in resistance to the Josephson junction resulting from directing the exposure pattern and injecting light at different intervals from the Josephson junction. [Figure 13A] Figure 13B is a schematic diagram of the different exposure patterns used to produce the results shown. [Figure 13B] This graph shows the change in resistance of a Josephson junction resulting from applying different electron beam annealing treatments to the junction using different exposure patterns. [Figure 14] This is a schematic diagram of an electronic device that can be used to implement one or more method steps disclosed herein. [Modes for carrying out the invention]

[0064] Before describing specific embodiments of the present invention, it should be understood that this disclosure is not limited to the specific embodiments described herein. It should also be understood that the terms used herein are used solely to describe specific embodiments and are not intended to limit the scope of the claims.

[0065] In describing the apparatus and method of the present invention and in claiming rights, the following terms are used. That is, the singular forms "a," "an," and "the" include the plural form unless otherwise explicitly specified in the context. Thus, a reference to, for example, a "Josephson junction" or a "qubit" includes a reference to one or more of these elements.

[0066] Here, we refer to qubits and / or multiple qubits. Unless otherwise indicated, these references are intended to refer to physical qubits. That is, a reference to a qubit is intended to refer to a physical system that, when properly operated and controlled, yields a physical qubit. Such systems may only function as physical qubits under specific operating conditions. For example, a superconducting qubit only behaves like a qubit if its components are cooled to a temperature low enough to exhibit superconductivity. The references to qubits (or physical qubits) here are intended to encompass configurations of components that can function as qubits (e.g., when cooled to a sufficiently low temperature) even under conditions where they do not necessarily function as qubits. For example, a configuration of components that functions as a qubit when cooled to a sufficiently low temperature (e.g., a Josephson junction and a capacitor connected in parallel) may be referred to as a qubit even when not cooled to such a temperature (e.g., room temperature, or another temperature where it does not exhibit qubit behavior). Thus, the references to qubits here are intended to encompass configurations of components that can behave as qubits under appropriate operating conditions, even when they are not under these operating conditions.

[0067] Similarly, references here also refer to superconducting materials, superconducting components (e.g., electrodes), and / or superconducting qubits. It will be understood that these materials, components, and / or qubits behave as superconductors only when cooled to a suitable low temperature. However, the references here to superconducting materials, superconducting components (e.g., electrodes), and / or superconducting qubits are intended to include such materials, components, and / or qubits that can exhibit superconductivity even under conditions where they do not normally exhibit superconductivity. For example, a material, component, and / or qubit that behaves as a superconductor when cooled to a suitable low temperature may still be referred to as a superconducting material, component, and / or qubit even when not cooled to such a temperature (e.g., room temperature, or another temperature at which it does not behave as a superconductor). Thus, the references here to superconducting materials, components (e.g., electrodes), and / or qubits are intended to include materials, components, and / or qubits that can behave as a superconductor under suitable operating conditions, even when not under those operating conditions.

[0068] Figure 1 is a schematic diagram of an example of a superconducting qubit 102. The superconducting qubit 102 comprises a Josephson junction 104 connected in parallel with a capacitor 106. Such a configuration is sometimes called a charge qubit, or more specifically, a transmon qubit. The components and connections constituting the qubit 102 may be made of a superconducting material (e.g., aluminum) so as to exhibit superconducting properties under appropriate operating conditions (e.g., when cooled to an appropriate low temperature).

[0069] Figure 2 is a schematic diagram of an example arrangement of a superconducting qubit 202. The superconducting qubit 202 shown in Figure 2 comprises a Josephson junction 104 connected between a first superconducting electrode 204 and a second superconducting electrode 206. The first superconducting electrode 204 and the second superconducting electrode 206 are arranged coaxially with respect to each other. The first superconducting electrode 204 and the second superconducting electrode 206 may further be arranged to be coplanar with respect to each other. For example, the first superconducting electrode 204 and the second superconducting electrode 206 may be positioned on the same surface (e.g., the surface of a substrate). The components and connections constituting the qubit 202 may be made of a superconducting material (e.g., aluminum) so as to exhibit superconducting properties under appropriate operating conditions (e.g., when cooled to an appropriate low temperature).

[0070] A qubit 202 having the configuration shown in Figure 2 is considered to be in the form of a charge qubit and / or a transmon qubit, the capacitance of the transmon qubit provided by the capacitance between the first superconducting electrode 204 and the second superconducting electrode 206. The coaxial arrangement of electrodes 204,206 shown in Figure 2 has been shown to present numerous favorable effects for operation as a superconducting qubit. For example, the coaxial arrangement of electrodes 204,206 shown in Figure 2 provides improved isolation from the electromagnetic environment, thereby reducing crosstalk and improving coherence time. The type of qubit shown in Figure 2 is described in detail in International Publication No. 2017 / 021714, the contents of which are incorporated hereby by reference.

[0071] Although not shown in Figure 1 or Figure 2, if qubit 102,202 is implemented in a quantum computer, it may be connected to a control line and / or readout line. The control line may be connected to qubit 102,202 to control its state. For example, the control line can be used to expose qubit 102,202 to a suitable microwave radiation pulse, which can, for example, cause qubit 102,202 to transition between energy levels. The readout line may be connected to qubit 102,202 to measure its state. For example, a microwave signal can be applied to the readout line, and the amplitude and / or phase of the applied microwave signal can be measured to determine the resonant frequency of the readout line. The resonant frequency of the readout line may depend on the state of qubit 102,202 to which the readout line is connected, thereby enabling measurement of the state of qubit 102,202.

[0072] In a qubit 202 having the configuration shown in Figure 2, control lines and / or readout lines may be provided that are coaxial with the first superconducting electrode 204 and the second superconducting electrode 206. Furthermore, control lines and / or readout lines may be provided that are out-of-plan with respect to the first superconducting electrode 204 and the second superconducting electrode 206. Further details of the arrangement of control lines and / or readout lines that can be connected to a qubit 202 in the configuration shown in Figure 2 are provided in International Publication No. 2017 / 021714.

[0073] Figure 3 is a schematic diagram of an example of a Josephson junction 104 that can form part of any qubit described herein. For example, the type of Josephson junction 104 shown in Figure 3 may form a Josephson junction 104 included in the type of qubit 102 shown in Figure 1, and / or form a Josephson junction 104 included in the type of qubit 202 shown in Figure 2.

[0074] The Josephson junction 104 shown in Figure 3 comprises a first superconductor 304 and a second superconductor 306. The first superconductor 304 and the second superconductor 306 can be formed from suitable superconducting materials, such as aluminum. The first superconductor 304 and the second superconductor 306 are separated from each other by a barrier 308. The barrier 308 can be formed from an electrically insulating material or other non-superconducting material. In at least some examples, the barrier 308 is formed from aluminum oxide. The barrier 308 can be thin enough to provide a weak link between the first superconductor 304 and the second superconductor 306, enabling quantum tunneling between the first superconductor 304 and the second superconductor 306. In the example where the barrier 308 is formed from aluminum oxide, the barrier 308 can have a thickness in the range of about 0.1 to 10 nanometers (nm), which may be thin enough to enable quantum tunneling across the aluminum oxide barrier 308.

[0075] As shown in Figure 3, the Josephson junction 104 may be fabricated on or supported on the substrate 302. The substrate 302 may be formed of a low-loss dielectric material such as silicon or sapphire.

[0076] Although not shown in Figure 3, the first superconductor 304 and the second superconductor 306 may be electrically connected to other components of the qubits 102,202. For example, in the configuration of Figure 2, the first superconductor 304 and the second superconductor 306 may each be electrically connected to one of the first superconducting electrodes 204 and the second superconducting electrode 206. Similarly, in the configuration of Figure 1, the first superconductor 304 and the second superconductor 306 may each be electrically connected to different plates of the capacitor 106.

[0077] The Josephson junction 104 can be manufactured using any suitable manufacturing technique. For example, the Josephson junction 104 can be manufactured by forming a suitable pattern on a material provided on the substrate 302 using electron beam lithography.

[0078] As described above, the Josephson junction 104 is a nonlinear inductive element. When implemented in the superconducting qubits 102,202, the Josephson junction 104 can actually play a role in generating a clear difference between the energy levels of the superconducting qubits 102,202.

[0079] The properties of the Josephson junction 104 contained in the qubit 102,202 have a significant influence on the resonant frequency of the qubit 102,202. For example, the resonant frequency of the qubit 102,202 may depend, at least in part, on the resistance of the Josephson junction 104. Furthermore, as mentioned above, the manufacturing of the Josephson junction 104 can be subject to variation, so a given Josephson junction 104 may have properties that differ from the target or design parameters used during its manufacture. For example, the resistance of a manufactured Josephson junction 104 may vary. As a result, the resonant frequency of the manufactured qubit 102,202 containing the Josephson junction 104 may be affected by dispersion.

[0080] As an example, a quantum information processor can be formed by fabricating multiple qubits 102,202, each containing a Josephson junction 104, on a single substrate 302 or chip. Figure 4 is a schematic diagram of a quantum information processor 402 containing multiple qubits 202. In the example shown in Figure 4, the qubits 202 are in the same form as the qubits 202 described above with reference to Figure 2. That is, each qubit 202 contains a Josephson junction 104 connected between a first superconducting electrode 204 and a second superconducting electrode 206, which are arranged coaxially with each other (these components are not explicitly labeled in Figure 4). In the example in Figure 4, adjacent qubits 202 are connected to each other by a capacitor 404. In particular, the second superconducting electrodes 206 of adjacent qubits 202 (the outer electrodes of each qubit 202) are connected to each other by a capacitor 404. The connection of adjacent qubits 202 by the capacitor 106 enables interaction between the qubits 202, which can be used when performing quantum computations using the quantum information processor 402.

[0081] The configuration in Figure 4 is provided merely as an illustrative example, and it should be understood that other examples of quantum information processors may include a different number of qubits, a different arrangement of qubits, and / or a different type of qubit than that shown in Figure 4.

[0082] In some examples, a quantum information processor 402 containing multiple qubits 202 can be manufactured such that each qubit 202 and Josephson junction 104 is manufactured according to the same design parameters. For example, since the target or design parameters for each qubit 202 are the same, under a complete manufacturing process, each qubit 202 will have identical parameters (e.g., dimensions, resistance, and resonant frequency). In practice, variations in the manufacturing of the Josephson junction 104 can lead to variability in the properties (e.g., resonant frequency) of the qubits 202, even if each qubit 202 is manufactured according to the same design parameters. For example, in a typical manufacturing process, variations in the manufacturing of the Josephson junction 104 may result in the resistance values ​​of multiple manufactured Josephson junctions 104 (each manufactured according to the same design parameters) having a standard deviation of about 2-3% of the average resistance. This translates to a frequency spread of qubits 202 with a standard deviation of about 1-1.5%.

[0083] The frequency dispersion of qubit 202 can degrade the performance of a quantum information processor 402 incorporating qubit 202, including the Josephson junction 104. For example, the quantum information processor 402 can be designed so that each qubit 202 has the same resonant frequency. Such a design allows the state of qubit 202 to be controlled and transitions between the energy levels of qubit 202 to be driven using a single microwave radiation source with a frequency corresponding to the frequency of qubit 202. However, the frequency dispersion of qubit 202 introduced by manufacturing variations in the Josephson junction 104 included in qubit 202 can affect the efficiency of driving different qubit 202 using a single microwave radiation source. The frequency dispersion of qubit 202 may, as an addition or alternative, introduce one or more further undesirable effects, such as random crosstalk, frequency collisions, or slow entanglement gates.

[0084] While the above example describes a quantum information processor 402 designed to include qubits 202 with the same resonant frequency, in another example, the quantum information processor 402 can be designed so that different qubits 202 have different frequencies. For example, adjacent qubits 202 can be designed to have different frequencies to reduce crosstalk between them. In such an example, the variance of the frequencies of the fabricated qubits 202 from the design frequency may cause crosstalk between adjacent qubits 202.

[0085] In general, it is desirable to have more precise control over the frequencies of the fabricated qubits 102,202. For example, in an implementation where the quantum information processor 402 is designed to include qubits 202 having the same frequency, it may be desirable to tune the frequencies of at least some of the qubits 202 to reduce the frequency variance of the qubits 202. Additionally or alternatively, in an implementation where the quantum information processor 402 is designed to include qubits 202 having different frequencies, it may be desirable to tune the frequencies of at least some of the qubits 202 to reduce the difference between the frequency of the qubits 202 and their design frequency. In general, improved control over the frequencies of qubits 102,202 can reduce or mitigate the effects of, for example, crosstalk, frequency collisions, and slow entangled gates, thereby improving the overall fault tolerance of the quantum computer.

[0086] It was found that the resistance of the Josephson junction 104 can be adjusted by directing an electron beam to heat the Josephson junction 104. Figures 1, 2, and 3 schematically show examples of electron beams 110 that are directed to heat the Josephson junction 104. The electron beams 110 are generated by an electron source 108, such as an electron gun.

[0087] Figure 5 is a flowchart of method 500 for tuning the frequency of qubit 102,202 according to an example disclosed herein. Method 500 in Figure 5 can be performed as a post-manufacturing process. That is, method 500 in Figure 5 can be performed to tune the frequency of qubit 102,202 after it has been manufactured.

[0088] In step 502, the electron beam 110 is directed to heat the Josephson junction 104. The electron beam 110 is generated and directed by an electron source 108, such as an electron gun. The electron source 108 can use any suitable form of electron beam generation process, such as thermal ion emission or field electron emission. The electron source 108 may further be configured to focus and direct the electron beam 110 to heat the Josephson junction 104. For example, the electron source 108 may include one or more electrostatic or magnetic lenses positioned to focus and / or direct the electron beam 110 to heat the Josephson junction 104.

[0089] It will be understood that the Josephson junction 104 and the electron source 108 can be placed under vacuum pressure conditions in order to properly direct the electron beam 110 and heat the Josephson junction 104.

[0090] In at least some examples, an electron beam lithography apparatus can be used to generate and direct an electron beam 110 to heat a Josephson junction 104. Conveniently, the electron beam lithography apparatus may include equipment for aligning the generated electron beam 110 (in addition to the electron source 108) with respect to the Josephson junction 104 into which the electron beam 110 is incident. For example, the electron beam lithography apparatus may include a stage for supporting a substrate 302 on which the Josephson junction 104 is located and for aligning the substrate 302 with respect to the electron beam 110 so that the electron beam 110 is incident on the Josephson junction 104. The electron beam lithography apparatus may further include components for generating the vacuum pressure conditions in which the electron source 108 and the Josephson junction 104 are located.

[0091] In another example, other forms of equipment can be used to direct the electron beam 110 and heat the Josephson junction 104. For example, a scanning electron microscope can be used to direct the electron beam and heat the Josephson junction 104.

[0092] The electron beam 110 is configured to heat the Josephson junction 104. For example, the electron beam 110 is generated with an appropriate current so that electrons heat the Josephson junction. In particular, the electron beam 110 can be configured to heat the Josephson junction 104 to induce a material change in at least one of the components of the Josephson junction 104. In at least some examples, the electron beam 110 can induce a temperature change on the order of about 50°C to about 1000°C or more.

[0093] In at least some examples, the electron beam 110 can be generated using a current greater than 0.1 nanoamperes (nA). For example, the electron beam 110 can be generated using a current greater than approximately 1 nA. In at least some examples, the electron beam 110 can be generated using a current less than approximately 1000 nA. For example, the electron beam 110 can be generated using a current less than approximately 500 nA, and can be generated using a current less than approximately 200 nA.

[0094] In some examples, the electron beam 110 can be directed to directly incident on at least one component of the Josephson junction 104. In such examples, because the electron beam 110 directly incidents on the Josephson junction 104, direct heating of at least a portion of the Josephson junction 104 can be caused.

[0095] In some examples, the electron beam 110 may be directed so as not to directly incident on the Josephson junction 104. In such examples, the electron beam 110 can cause indirect heating of the Josephson junction 104 by heating other components or materials, from which heat can be conducted to heat the Josephson junction 104. For example, the electron beam 110 may be directed so as to incident on a portion of the substrate 302 that is sufficiently close to the Josephson junction 104 and is thermally coupled to it. Heating of the portion of the substrate 302 by the electron beam 108 causes heating of the Josephson junction 104 by heat conduction from the heated portion of the substrate 302.

[0096] Indirect heating of the Josephson junction 104 (for example, by directing the electron beam 110 to incident on a portion of the substrate 302 adjacent to the Josephson junction 104) can reduce the risk of damage. This is because, under at least some conditions, direct heating can damage the Josephson junction and adversely affect its performance.

[0097] The electron beam 110 is directed to heat the Josephson junction 104 for an exposure time that supplies an amount of charge to the component into which the electron beam 110 is incident (e.g., the Josephson junction 104 itself, or a component thermally coupled to the Josephson junction 104). The amount of charge supplied is sufficient to heat the Josephson junction 104. For example, the amount of charge supplied may be sufficient to heat the Josephson junction 104 and induce a material change in at least one of the components of the Josephson junction 104. In some examples, the electron beam 110 may be directed to heat the Josephson junction 104 during a single continuous exposure time. Such techniques for directing the electron beam 110 to heat the Josephson junction 104 during a single continuous exposure time are sometimes referred to here as supplying a single shot of charge to the Josephson junction 104.

[0098] In some examples, multiple pulses of the electron beam 110 may be directed to heat the Josephson junction 104 during multiple consecutive exposure periods. These multiple consecutive exposure periods may be separated by periods in which there is no electron beam 110 directed to heat the Josephson junction 104. This technique of directing pulses of the electron beam 110 to heat the Josephson junction 104 during multiple consecutive exposure periods (separated by periods in which there is no electron beam 110 directed to heat the Josephson junction 104) may be referred here to supplying multiple shots of charge to the Josephson junction 104.

[0099] In some examples, the electron beam 110 of multiple pulses may be directed to incident on multiple different locations. For example, the electron beam 110 of multiple pulses may be directed to incident on the Josephson junction 104 itself and / or on multiple different locations on the substrate 302 adjacent to the Josephson junction 104.

[0100] In some examples, the exposure pattern may be defined by directing multiple pulses of the electron beam 110 to incident at multiple different locations. The exposure pattern may include, for example, grid positions to which the electron beam 110 is incident. The positions to which the electron beam 110 is incident can be controlled to control the heating supplied to the Josephson junction 104.

[0101] In some examples, the electron beam 110 is approximately 10 microcoulombs / square centimeter (μC / cm²). 2 The Josephson junction 104 may be directed (during one or more exposure times) to heat in order to distribute a larger amount of charge. For example, approximately 50 μC / cm² may be applied to the Josephson junction 104 and / or components thermally bonded to the Josephson junction 104 (e.g., substrate 302). 2 A larger charge may be supplied. In some examples, the electron beam 110 is approximately 5000 μC / cm². 2 The Josephson junction 104 may be directed (during one or more exposure times) to heat in order to distribute a smaller amount of charge. For example, approximately 2000 μC / cm² may be applied to the Josephson junction 104 and / or components thermally bonded to the Josephson junction 104 (e.g., substrate 302). 2 A smaller amount of charge may be distributed.

[0102] Figure 6 is a schematic diagram of several different exposure patterns 602a, 602b, and 602c that the Josephson junction 104 receives. Each of the exposure patterns 602a, 602b, and 602c shown in Figure 6 contains multiple exposure spots 604. In Figure 6, each exposure spot 604 is represented by a gray circle. For ease of illustration, only a portion of the exposure spots 604 are explicitly labeled in Figure 6. Each exposure spot 604 represents a position to which the electron beam 110 is directed (for example, by an electron source 108). The electron beam 110 may be directed to each exposure spot 604 forming the exposure patterns 602a, 602b, and 602c at the same or different times. For example, the exposure patterns 602a, 602b, and 602c can be formed by directing the electron beam 110 to each exposure spot 604 continuously and at different times using a single electron source 108. Alternatively, multiple electron sources 108 may be used to direct multiple electron beams 110 to simultaneously incident on different exposure spots 604 within exposure patterns 602a, 602b, and 602c.

[0103] In the example shown in Figure 6, each exposure pattern 602a, 602b, and 602c is positioned at the center of the Josephson junction 104. However, as will be described later, the exposure patterns 602a, 602b, and 602c may be directed to incident at locations that are not necessarily at the center of the Josephson junction 104. For example, the exposure patterns 602a, 602b, and 602c may be directed to locations that are separated from the Josephson junction 104 but are thermally bonded to it.

[0104] A first example of exposure pattern 602a is shown in the leftmost region of Figure 6. The first example of exposure pattern 602a includes a substantially uniform grid of exposure spots 604. The first example of exposure pattern 602a includes at least some exposure spots 604 positioned on a portion of the Josephson junction 104, thereby directing the electron beam 110 to incident on at least some exposure spots 604, which leads to direct heating of at least a portion of the Josephson junction 104. The first example of exposure pattern 602a further includes at least some exposure spots 604 that are not directly positioned on the Josephson junction 104 but are in close proximity to it. Directing the electron beam 110 to incident on such exposure spots 604 may also include directing the electron beam 110 to incident on a component thermally coupled to the Josephson junction 104 (e.g., a portion of the substrate 302), thereby causing indirect heating of the Josephson junction 104. An exposure pattern 602a having the general form of the first example of exposure pattern 602a may here be referred to as a completely closed exposure pattern.

[0105] A second example of exposure pattern 602a is shown in the central region of Figure 6. A second example of exposure pattern 602b is formed by exposure spots 604 surrounding the Josephson junction 104. The second example of exposure pattern 602b includes exposure spots 604 that are not directly positioned on the Josephson junction 104, and does not include exposure spots 604 positioned on the Josephson junction 104 itself. Thus, the second example of exposure pattern 602b leads to indirect heating of the Josephson junction 104. As can be seen from Figure 6, the second example of exposure pattern 602b is of different sizes and both are formed by exposure spots 604 that depict two loops (in the illustrated example, in the form of a square) surrounding the Josephson junction 104. An exposure pattern 602b having the general shape of the second example of exposure pattern 602b may here be referred to as the thick-loop exposure pattern 602b.

[0106] A third example of exposure pattern 602c is shown in the rightmost region of Figure 6. Similar to the second example of exposure pattern 602b, the third example of exposure pattern 602c is formed by exposure spots 604 surrounding the Josephson junction 104. Similarly, the third example of exposure pattern 602c includes exposure spots 604 that are not directly positioned on the Josephson junction 104, and does not include exposure spots 604 that are positioned on the Josephson junction 104. Thus, the third example of exposure pattern 602 leads to indirect heating of the Josephson junction 104. The third example of exposure pattern 602c differs from the second example of exposure pattern 602b in that it includes exposure spots 604 that depict a single loop (in the illustrated example, in the form of a square) surrounding the Josephson junction 104 (in contrast to the two loops in the second example of exposure pattern 602b). Thus, the third example of exposure pattern 602b contains fewer exposure spots 604 than the second example of exposure pattern 602b. The exposure pattern 602c having the general shape of the third example of exposure pattern 602c may here be referred to as a thin loop exposure pattern.

[0107] The exposure patterns in the second example of exposure pattern 602b and the third example of exposure pattern 602c are described here as being arranged to surround the Josephson junction 104 and to form a loop of exposure spots 604. It will be understood that there are gaps between adjacent exposure spots 604, and therefore the exposure spots 604 do not form a completely closed loop (as can be seen in Figure 6). Nevertheless, even in these exposure patterns, they are considered to be arranged in a loop and to roughly surround the Josephson junction 104.

[0108] Referring to Figure 6, three different examples of exposure patterns 602a, 602b, and 602c are described. The second example 602b and the third example 602c are arranged to produce only indirect heating of the Josephson junction 104, while the first example 602a is arranged to produce both direct and indirect heating of the Josephson junction 104. As previously mentioned, indirect heating of the Josephson junction 104 (compared to direct heating) can reduce the risk of damaging the Josephson junction 104. This is because, under at least some conditions, direct heating can damage the Josephson junction and adversely affect its performance. Therefore, exposure patterns in the form of the second exposure pattern 602b and the third exposure pattern 602c can be advantageously used to produce heating of the Josephson junction 104 without directing the electron beam 110 to the Josephson junction 104 (which in some examples carries the risk of damaging the Josephson junction 104). The exposure patterns 602b and 602c that form a loop surrounding the Josephson junction 104 (as in the second example 602b and the third example) can cause relatively uniform heating of the Josephson junction 104 because indirect heating is distributed to all sides of the Josephson junction 104.

[0109] As demonstrated in the results shown below with reference to Figures 13A and 13B, the use of exposure patterns 602a, 602b, and 602c, which include multiple exposure spots 604, can provide a greater degree of control over the amount the Josephson junction 104 is heated and how much its resistance is adjusted. In at least some examples, different forms of exposure patterns can be used to produce different changes in the resistance of the Josephson junction 104.

[0110] The example exposure pattern shown in Figure 6 is presented for illustrative purposes only. In another example, one or more electron beams 110 can be directed to form an exposure pattern that includes multiple exposure spots 604 in a different arrangement than that shown in Figure 6.

[0111] As described above, in at least some examples, the Josephson junction 104 can be heated by directing multiple pulses of the electron beam 110 to incident on multiple different locations (exposure spots 604). The multiple different locations define and control the exposure pattern, thereby controlling the heating supplied to the Josephson junction 104. In some examples, the heating supplied to the Josephson junction 104 can be controlled by controlling the distance between the locations to which the electron beam 110 is directed (e.g., exposure spots 604) and the Josephson junction 104.

[0112] Figure 7 is a schematic diagram of exposure patterns 702 at three different distances from the Josephson junction 104 to be heated. In the example shown in Figure 7, a completely closed exposure pattern including a grid of exposure spots (similar to the exposure pattern 602a of the first example described above, with reference to Figure 6) is used. In the first exposure example 704a, shown in the panel labeled 704a in Figure 7, the exposure pattern 702 is separated from the Josephson junction 104 by a first distance. The first distance can be such that directing one or more electron beams 110 to form the exposure pattern 702 provides indirect heating to the Josephson junction 104 through heat conduction from the electron beam incidence point (exposure spot). In some examples, the first distance may be less than about 100 micrometers (μm). For example, the first distance may be less than about 50 μm, or about 30 μm.

[0113] In the second exposure example 704b, shown in the panel labeled 704b in Figure 7, the exposure pattern 702 is separated from the Josephson junction 104 by a second distance, which is smaller than the first distance used in the first exposure example 704a. It will be understood that the smaller separation distance between the exposure pattern 702 and the Josephson junction 104 allows the Josephson junction 104 to be heated to a greater extent using the second exposure example 704b than using the first exposure example 704a (assuming all other characteristics such as electron beam current, charge amount, and exposure time are the same).

[0114] In the third exposure example 704c, shown in the panel labeled 704b in Figure 7, the exposure pattern 702 is positioned at the center of the Josephson junction 104, so that at least a portion of the exposure spots forming the exposure pattern corresponds to an electron beam 110 directly incident on the Josephson junction 104. Thus, the third exposure example 704c may involve direct heating of at least a portion of the Josephson junction 104. It will be understood that the third exposure example 704c can heat the Josephson junction 104 to a greater extent than the first exposure example 704a or the second exposure example 704b (assuming, for example, that all other characteristics such as electron beam current, charge amount, exposure time, etc., are the same).

[0115] As described above, the amount of heat supplied to the Josephson junction 104 may depend, at least in part, on the distance between the Josephson junction 104 and the position to which the electron beam 110 is directed (for example, which may include a plurality of exposure spots 604 that form the exposure pattern 702). Therefore, the amount of heat supplied to the Josephson junction 104 can be controlled by controlling the distance between one or more positions (exposure spots 604) to which the electron beam 110 is directed and the Josephson junction 104. Using such control, the change in the resistance value of the Josephson junction 104 caused by heating can be controlled.

[0116] Returning to method 500 in Figure 5, step 504 involves heating the Josephson junction 104 with the electron beam 110 followed by cooling the Josephson junction 104. Cooling the Josephson junction 104 following heating the Josephson junction 104 with the electron beam 110 may include not directing the electron beam 110 to heat the Josephson junction 104 (e.g., turning off the electron beam 110, moving the electron beam 110 far away from the Josephson junction 104, and / or moving the Josephson junction 104 far away from the path of the electron beam 110) and cooling the Josephson junction 104 under ambient temperature conditions in which the Josephson junction 104 is located. That is, cooling the Josephson junction 104 does not necessarily involve providing active cooling of the Josephson junction 104, and may simply involve cooling the Josephson junction 104 following heating the Josephson junction 104 with the electron beam 110. However, in some examples, cooling the Josephson junction 104 may include applying active cooling to the Josephson junction 104.

[0117] It was found that heating the Josephson junction 104 by directing an electron beam 110 and then cooling the Josephson junction 104 (as described above with reference to steps 502 and 504 of method 500 in Figure 5) can be used to change the resistance of the Josephson junction 104. As a result, the frequencies of the qubits 102,202 incorporating the Josephson junction 104 can be tuned by heating the Josephson junction 104 with an electron beam 110. Without being bound by any particular theory, it is thought that heating the Josephson junction 104 with an electron beam 110 functions to anneal at least one of the components of the Josephson junction 104 and change the material properties of at least one component. This change in the material properties of at least one component of the Josephson junction 104 is thought to result in a change in the resistance of the Josephson junction 104. The process of heating the Josephson junction 104 by directing an electron beam 110 to heat the Josephson junction 104 and then cooling the Josephson junction 104 (as described above with reference to steps 502 and 504 of method 500 in Figure 5) may here be referred to as electron beam annealing of the Josephson junction 104.

[0118] It was found that the electron beam 110 provides a highly controllable and localized method for heating the Josephson junction 104 to tune the frequency of the qubits 102,202, in which the Josephson junction 104 is incorporated. The electron beam 110, directed to heat the Josephson junction 104 by a suitable electron source 108, may have a beam diameter smaller than about 200 nm, and even smaller than about 100 nm. In at least some examples, the electron beam 110 may have a beam diameter smaller than about 50 nm. For example, the electron beam 110 may have a beam diameter on the order of about 10 to 50 nanometers (nm). For comparison, the Josephson junction 104 may have approximate dimensions on the order of about 50 nm to 500 nm.

[0119] Generally, the beam diameter of the electron beam 110 may be smaller than the diameter of the laser beam that can be used for thermal annealing. For example, a typical laser beam with a wavelength of about 500 nm may be focused to have a spot size on the order of 10 micrometers (μm). Therefore, the beam diameter of the laser beam may be several orders of magnitude larger than the beam diameter of the electron beam 110.

[0120] Sub-beams 110 having small beam diameters (e.g., less than approximately 200 nm, less than approximately 100 nm, or less than approximately 50 nm) may be particularly advantageous for providing highly localized and / or highly controllable heating to a Josephson junction 104. For example, in a typical quantum information processor 402, adjacent qubits 202 (and adjacent Josephson junctions 104) may be spaced on the order of several hundred micrometers, or about 1 millimeter (mm), apart. To provide precisely controllable tuning of qubit frequencies, it may be desirable to heat a Josephson junction contained in one qubit independently of another Josephson junction 104 contained in another qubit. For example, it may be desirable to heat a Josephson junction 104 contained in a first qubit independently, without causing significant heating to another neighboring Josephson junction (i.e., without significantly affecting the resistance of another neighboring Josephson junction). The relatively small beam diameter of the electron beam 110 (compared to, for example, the beam diameter of a laser beam) can favorably provide highly localized heating to the Josephson junction 104, and enable independent control of the resistance of the Josephson junction (and independent control of the qubit frequency) without significantly changing the resistance of other neighboring Josephson junctions 104 (and without significantly changing the frequency of other neighboring qubits).

[0121] In some implementations, a qubit may contain multiple Josephson junctions 104. For example, a qubit may contain two Josephson junctions 104. In some examples, a qubit may contain a coaxially arranged first superconducting electrode 204 and a second superconducting electrode 206, as shown in Figure 2. The qubit may further contain multiple Josephson junctions 104 connected between the first superconducting electrode 204 and the second superconducting electrode 206, respectively. In examples where a qubit contains multiple Josephson junctions 104, it will be understood that the spacing between adjacent Josephson junctions 104 may be smaller than in examples where a qubit contains a single Josephson junction 104. For example, the spacing between Josephson junctions 104 that form part of the same qubit may be smaller than the spacing between Josephson junctions 104 that form part of adjacent qubits. As an addition or alternative, the inclusion of multiple Josephson junctions 104 per qubit can reduce the spacing between Josephson junctions 104 that form part of adjacent qubits.

[0122] In examples where the qubit includes multiple Josephson junctions 104, providing highly localized heating to the Josephson junctions 104 (by directing the electron beam 110 to heat the Josephson junctions 104) can be particularly advantageous in that it allows for independent heating of the Josephson junctions 104 without causing significant heating to neighboring Josephson junctions 104.

[0123] The relatively small beam diameter of the electron beam 10 (for example, compared to the diameter of a laser beam) makes it possible to precisely control the exposure pattern (for example, including multiple different positions to which the electron beam 110 is directed) in order to control the heating provided to the Josephson junction 104.

[0124] As described above with reference to Figures 6 and 7, the heating of the Josephson junction and the resistance change induced by heating may be controlled by controlling additional factors, such as the exposure pattern and / or the distance between the position of the electron beam 110 and the Josephson junction 104. The relatively small beam diameter of the electron beam 110 allows for precise and accurate control of these additional factors in a manner that would be impossible by other means. For example, as described above with reference to Figure 6, different exposure patterns can be used to control the heating of the Josephson junction 104. In some examples, a loop-shaped exposure pattern surrounding the Josephson junction 104 can be used, which allows for localized and controllable indirect heating of the Josephson junction 104. It will be understood that such control and heating may be impossible when heating the Josephson junction by other means (e.g., using a laser beam).

[0125] As described in detail above, the electron beam 110 can be used to provide local heating to the Josephson junction 104, thereby changing the resistance of the Josephson junction 104 and adjusting the frequencies of the qubits 102,202 that incorporate the Josephson junction 104 accordingly (this is sometimes called electron beam annealing). The frequencies of the qubits 102,202 that incorporate the Josephson junction 104 may be inversely proportional to the resistance of the Josephson junction 104. That is, an increase in the resistance of the Josephson junction 104 may result in a decrease in the frequency of the qubits 102,202, which is proportional to the increase in resistance. A decrease in the resistance of the Josephson junction 104 may result in an increase in the frequency of the qubits 102,202, which is proportional to the decrease in resistance.

[0126] The inventors have successfully demonstrated that applying local heating to a Josephson junction 104 using an electron beam 110, thereby changing the resistance of the Josephson junction 104 and adjusting the frequencies of qubits 102,202 accordingly, does not adversely affect the coherence time of the qubits. The coherence time of a qubit is a measure of the length of time that a qubit can retain its information and be manipulated to perform quantum computations. The inventors have demonstrated that after applying the electron beam annealing process described herein to a qubit, the coherence time of the qubit is not adversely affected, and the qubit remains a high-coherence qubit (having a relatively long coherence time).

[0127] As described above (see, for example, the method in Figure 5), directing the electron beam 110 to heat the Josephson junction 104 has been found to be usable to selectively increase or decrease the resistance of the Josephson junction 104. Accordingly, the frequencies of the qubits 102,202, including the Josephson junction 104, can be selectively decreased or increased. In particular, it has been found that electron beam 110 currents greater than the threshold current, and / or charge amounts greater than the threshold amount, act to decrease the resistance of the Josephson junction 104 (and consequently increase the qubit frequency). Conversely, electron beam 110 currents less than the threshold current, and / or charge amounts less than the threshold amount, act to increase the resistance of the Josephson junction 104 (and consequently decrease the qubit frequency).

[0128] The thresholds for current and / or charge (below which resistance increases, and above which resistance decreases) depend on the characteristics of a given Josephson junction 104 and are not fixed for all Josephson junctions 104. As an example for illustrative purposes only, the results are presented in Figures 8A and 8B, showing that electron beam annealing can be used to reduce the resistance of a Josephson junction 104.

[0129] Figure 8A is a histogram of the resistance (in ohms) of a group of 192 Josephson junctions. The group of 192 Josephson junctions was manufactured using the same design parameters and has the same dimensions. Under a perfect manufacturing process, each of the 192 Josephson junctions would have the same resistance value. However, as can be seen from Figure 8A, variations in the manufacturing of the Josephson junctions result in a dispersion of their resistance values. In particular, the resistance values ​​of the 192 Josephson junctions after manufacturing have a standard deviation of approximately 1.85% of the average resistance value.

[0130] To demonstrate that the resistance of Josephson junctions can be reduced using electron beam 110, each of the 192 Josephson junctions was exposed to electron beam 110 at 100 nA, with a temperature of 300–1300 μC / cm². 2 The following charge was supplied. After performing electron beam annealing using a 100 nA electron beam, the corresponding histograms of the resistance values ​​of 192 Josephson junctions in the same group are also shown in Figure 8A. As can be clearly seen from Figure 8A, the 100 nA electron beam annealing reduces the average resistance of the Josephson junction by approximately 411 ohms. Furthermore, from Figure 8B, it can be seen that the variance of the resistance values ​​has not changed significantly.

[0131] Figure 8B is a scatter plot of the resistance values ​​of the same 192 Josephson junctions shown in Figure 8A. In Figure 8B, the horizontal axis represents the resistance value of the Josephson junctions after manufacturing and before the electron beam annealing process described above with reference to Figure 8A. The vertical axis of Figure 8B represents the resistance value of the Josephson junctions after the electron beam annealing process described above with reference to Figure 8A. Figure 8B provides a further explanation of the increase in the resistance value of the Josephson junctions caused by the electron beam annealing process.

[0132] Electron beam annealing is described above, for example, with reference to Figures 8A and 8B, where the same electron beam annealing is applied to each group of Josephson junctions. It is shown that this process increases or decreases the average resistance of the Josephson junctions and has little effect on the frequency dispersion of the Josephson junctions.

[0133] In some cases, electron beam annealing may be selectively applied to groups of Josephson junctions. For example, electron beam annealing may be performed only on a subset of groups of Josephson junctions. This method can be applied, for example, to reduce the resistance dispersion of groups of Josephson junctions. Accordingly, the frequency dispersion of qubits incorporating Josephson junctions can be reduced.

[0134] Figure 9 is a flowchart of an example of a method 900 for tuning the qubit frequencies of a quantum information processor containing multiple qubits. Each qubit of the quantum information processor contains at least one Josephson junction. The quantum information processor 402 may have any of the features described above with respect to the quantum information processor 402 shown in Figure 4, for example.

[0135] In step 902 of method 900 in Figure 9, the frequency of each of the multiple qubits is determined. The frequency of each of the multiple qubits can be measured directly while the qubit is operating. Alternatively, one or more properties of the qubit can be measured to determine a value that indicates the frequency of the qubit. For example, the resistance of the Josephson junction contained in each qubit may be measured. Such resistance measurements can be easily performed without cooling the qubit to a sufficiently low temperature to exhibit superconductivity. The frequency of the qubit can be determined using the measured resistance of the Josephson junction. Alternatively, the measured resistance value itself can function as a determinant of the frequency of the qubit. That is, the resistance value can be used as a substitute for the frequency value, assuming a well-understood inverse relationship between these variables.

[0136] In step 904 of method 900 in Figure 9, at least one of the qubits of the quantum information processor is identified for frequency tuning. The at least one qubit for frequency tuning is identified based on the determined frequencies of a plurality of qubits. In at least some examples, identifying at least one of a plurality of qubits for frequency tuning includes identifying at least one of a plurality of qubits that has a frequency that can be tuned to reduce the dispersion of the frequencies associated with each of the plurality of qubits. In some examples, identifying at least one of a plurality of qubits for frequency tuning includes identifying at least one of a plurality of qubits that has a frequency different from the target frequency or design frequency of that qubit.

[0137] As an example, Figure 10A shows a histogram of the resistance values ​​(in ohms) of the first Josephson junction group 104. Each of the first Josephson junction groups is incorporated into a qubit of the first quantum information processor, and the frequency of the qubit is inversely proportional to the resistance value of the Josephson junction. Figure 11A shows a further example, displaying a further histogram of the resistance values ​​(in ohms) of the second Josephson junction groups. Similar to the first Josephson junction groups, each of the second Josephson junction groups is incorporated into a qubit of the second quantum information processor (the frequency of the qubit is inversely proportional to the resistance value of the qubit).

[0138] In the exemplary implementation of step 904 of the method in Figure 9, a subset of qubits having frequencies higher or lower than the average frequency of all qubits can be identified. For example, referring to Figures 10A and 11A, all Josephson junctions having resistances lower than the average resistance (all Josephson junctions enclosed in dotted boxes in Figures 10A and 11A) are identified as Josephson junctions for resistance tuning. This identification of Josephson junctions corresponds to identifying qubits for frequency tuning, each identified qubit having a frequency higher than the average frequency.

[0139] In step 906 of the method in Figure 9, the frequency of at least one qubit identified for frequency tuning is tuned. For example, the frequency of a qubit can be tuned by applying an electron beam annealing process, such as the one described here (for example, according to the method described above with reference to Figure 5), to the Josephson junction contained within the identified qubit. In at least some examples, the electron beam annealing process applied to the identified qubit may depend on the frequency of the qubit. For example, different electron beam currents, different charge amounts, different exposure patterns, and / or different spacings between the electron beam and the Josephson junction can be used to anneal different qubits of the identified qubit and achieve different frequency tunings. However, in another example, the same electron beam annealing process may be applied to each of the identified qubits.

[0140] Illustrative examples of results obtained by applying frequency tuning according to the example of step 906 of the method in Figure 9 are shown in Figures 10B, 10C, 10D, 11B, 11C, and 11D. To obtain the results shown in Figures 10B, 10C, 10D, 11B, 11C, and 11D, each of the first and second Josephson junction groups identified for resistance tuning (their resistance values ​​are shown in Figures 10A and 11A) was subjected to substantially the same electron beam annealing treatment. That is, each Josephson junction having a resistance lower than the average resistance of the individual Josephson junction groups (located within the dotted boxes shown in Figures 10A and 11A) was subjected to substantially the same electron beam annealing treatment. In particular, each of the identified Josephson junctions was subjected to a 2nA electron beam for multiple shot exposures to a total charge of 500 μC / cm². 2 They supplied it.

[0141] Figures 10B and 11B show two histograms of the resistance values ​​of the first and second Josephson junction groups, respectively, before and after the electron beam annealing treatment described above. The results obtained using the first Josephson junction group are shown in Figure 10B. The results obtained using the second Josephson junction group are shown in Figure 11B. In each of Figures 10B and 11B, the histogram on the left represents the resistance value of each Josephson junction group before electron beam annealing. In each of Figures 10B and 11B, the histogram on the right represents the resistance value of each Josephson junction group after electron beam annealing. In the histograms shown in Figures 10B and 11B, the resistance values ​​are plotted as normalized resistance (ratio of each resistance value to the average resistance value).

[0142] Figures 10C and 11C show histograms of the resistance values ​​of the first and second Josephson junction groups before and after electron beam annealing, respectively. The histograms before and after annealing are plotted on the same axis, and the resistance values ​​are plotted in units of ohms. The results obtained using the first Josephson junction group are shown in Figure 10C. The results obtained using the second Josephson junction group are shown in Figure 11C.

[0143] Figures 10D and 11D show scatter plots of the resistance values ​​of the first and second Josephson junction groups before and after electron beam annealing, respectively. The horizontal axis in Figures 10D and 11D represents the resistance value (in ohms) of the Josephson junction before electron beam annealing. The vertical axis in Figures 10D and 11D represents the resistance value (in ohms) of the Josephson junction after electron beam annealing. The results obtained for the first Josephson junction group are shown in Figure 10D. The results obtained for the second Josephson junction group are shown in Figure 11D.

[0144] For the first Josephson junction group (the results are shown in Figures 10B, 10C, and 10D), the standard deviation of the Josephson junction resistance was 2.57% of the average resistance before electron beam annealing (shown in the histogram on the left in Figure 10B). After applying electron beam annealing to the Josephson junctions identified for resistance adjustment, the standard deviation of the Josephson junction resistance decreased to 1.57%.

[0145] For the second Josephson junction group (the results are shown in Figures 11B, 11C, and 11D), the standard deviation of the Josephson junction resistance was 1.85% of the average resistance before applying electron beam annealing (shown in the histogram on the left in Figure 11B). After applying electron beam annealing to the Josephson junctions identified for resistance adjustment, the standard deviation of the Josephson junction resistance decreased to 1.07%.

[0146] As shown in Figures 10D and 11D respectively, the electron beam annealing process produced an increase of approximately 100 ohms in the resistance of the Josephson junctions to which it was applied and identified (for both the first and second Josephson junction groups).

[0147] The results shown in Figures 10A, 10B, 10C, 10D, 11A, 11B, 11C, and 11D demonstrate that the dispersion of the resistance values ​​of Josephson junctions can be reduced by using an electron beam annealing process applied to an identified subset of Josephson junctions. Similarly, the dispersion of the frequency of qubits incorporating Josephson junctions can also be reduced. Although not shown in the figures, similar results were obtained by performing electron beam annealing on Josephson junctions incorporated into qubits in a quantum information processor containing multiple superconducting qubits. These results demonstrate the effective use of electron beam annealing to adjust the resistance values ​​of Josephson junctions incorporated into superconducting qubits and thereby adjust the frequency of the qubits. In particular, the electron beam annealing process was used to reduce the frequency spread of qubits incorporated into a single quantum information processor.

[0148] In the example of electron beam annealing described with reference to Figures 10A, 10B, 10C, 10D, 11A, 11B, 11C, and 11D, electron beam annealing was applied to each of the Josephson junctions identified for resistance adjustment to increase their resistance. However, equivalent results could also be achieved by applying electron beam annealing to an identified subset of Josephson junctions to decrease their resistance. For example, Josephson junctions with resistances exceeding the average resistance can be identified for resistance adjustment. Then, electron beam annealing can be applied to the identified Josephson junctions (those with resistances exceeding the average resistance) to reduce their resistance.

[0149] In the examples of electron beam annealing described with reference to Figures 10A, 10B, 10C, 10D, 11A, 11B, 11C, and 11D, substantially identical electron beam annealing was applied to each of the Josephson junctions identified for resistance adjustment. However, in other examples, different electron beam annealing may be applied to different Josephson junctions. That is, electron beam annealing having one or more different parameters (e.g., different electron beam currents, different charge amounts, different times for directing the electron beam to heat the Josephson junction, the number of positions for directing the electron beam to heat the Josephson junction, and / or positions for directing the electron beam to heat the Josephson junction (e.g., proximity of the electron beam to the Josephson junction)) may be applied to different Josephson junctions. In at least some examples, the parameters of the electron beam annealing applied to the Josephson junction may be determined depending on the resistance value of the Josephson junction (or the frequency of the qubits into which the Josephson junction is incorporated). For example, a Josephson junction whose resistance is far from the average resistance may be subjected to an electron beam annealing treatment that results in a larger change in resistance than the electron beam annealing treatment applied to a Josephson junction whose resistance is closer to the average resistance. Referring to Figures 10A, 10B, 10C, 10D, 11A, 11B, 11C, and 11D, it will be understood that such a treatment results in a greater reduction in resistance and frequency dispersion than the treatment described above.

[0150] The parameters for electron beam annealing applied to a given Josephson junction can be determined by understanding the relationship between the electron beam annealing parameters and the resistance change caused by the electron beam annealing process. This relationship can be stored, for example, in a calibration curve or lookup table representing the relationship between the electron beam annealing parameters and the resistance change caused by the process.

[0151] In the example of electron beam annealing described with reference to Figures 10A, 10B, 10C, 10D, 11A, 11B, 11C, and 11D, all Josephson junctions identified for resistance adjustment were subjected to electron beam annealing to increase the resistance of the identified Josephson junctions. In another example, all Josephson junctions identified for resistance adjustment may be subjected to electron beam annealing to decrease the resistance of the identified Josephson junctions.

[0152] In further examples, an electron beam annealing treatment may be applied to a first subset of identified Josephson junctions to reduce their resistance. An electron beam annealing treatment may be applied to a second subset of identified Josephson junctions to reduce their resistance. That is, the resistance of at least one identified Josephson junction may be increased, and the resistance of at least one identified Josephson junction may be decreased.

[0153] In at least some examples, Josephson junctions with resistance values ​​lower than the average resistance can be subjected to electron beam annealing to increase their resistance. Josephson junctions with resistance values ​​higher than the average resistance can be subjected to electron beam annealing to decrease their resistance. Using these treatments, at least a portion of the resistance of a Josephson junction can be brought closer to the average resistance, resulting in further reductions in resistance and frequency dispersion than the treatments described above with reference to Figures 10A, 10B, 10C, 10D, 11A, 11B, 11C, and 11D.

[0154] As described above with reference to Figures 6 and 7, the adjustment of the resistance of the Josephson junction 104 (and consequently the frequency change of the qubit into which the Josephson junction 104 is incorporated) can be controlled by controlling the incident position of the electron beam on the Josephson junction. The results are shown in Figures 12A, 12B, 13A, and 13B, which demonstrate that different positions of the electron beam 110 can be used to bring about different changes in the resistance of the Josephson junction 104.

[0155] Figure 12A is a schematic diagram of exposure patterns 702 positioned at multiple different locations on the Josephson junction 104. The exposure patterns 702 used in the example in Figure 12A are similar to the exposure patterns 702 described above with reference to Figure 7. In particular, the exposure patterns 702 include multiple exposure spots (arranged in a grid) that are directed to receive the electron beam.

[0156] In the exposure example indicated by reference numeral 1202a in Figure 12A, the exposure pattern 702 is oriented so as to be approximately 30 μm away from the Josephson junction 104 in the positive y direction. In the exposure example indicated by reference numeral 1202b in Figure 12A, the exposure pattern 702 is oriented so as to be approximately 10 μm away from the Josephson junction 104 in the positive y direction. In the exposure example indicated by reference numeral 1202c in Figure 12A, the exposure pattern 702 is oriented so as to be located at the center of the Josephson junction 104. In the exposure example indicated by reference numeral 1202d in Figure 12A, the exposure pattern is oriented so as to be approximately 10 μm away from the Josephson junction 104 in the negative y direction. In the exposure example indicated by reference numeral 1202e in Figure 12A, the exposure pattern 702 is oriented so as to be approximately 30 μm away from the Josephson junction 104 in the negative y direction.

[0157] FIG. 12B is a graph of the change in the resistance value of the Josephson junction 104, which results from the orientation such that the exposure pattern 702 is incident on the Josephson junction 104 at different intervals, as described above with reference to FIG. 12A. The results plotted in the graph of FIG. 12B were obtained by an experiment using an electron beam having a current of 100 nA. The change in the resistance value (unit: ohm Ω) resulting from each electron beam annealing process was plotted on the y-axis. The interval between the exposure pattern 702 used in each electron beam annealing process and the Josephson junction 104 was plotted on the x-axis. The results for intervals of 30 μm (corresponding to exposure example 1202a), 20 μm, 10 μm (corresponding to exposure example 1202b), 3 μm, 0 μm (corresponding to exposure example 1202c), -3 μm, -10 μm (corresponding to exposure example 1202d), -20 μm, -30 μm (corresponding to exposure example 1202e) are shown. For each interval, results using different amounts of charge supplied to each exposure spot within the individual exposure pattern 702 were obtained. In particular, 500 μC / cm 2 (shown by the line 1208 in FIG. 12B), 800 μC / cm 2 (shown by the line 1206 in FIG. 12B), 1100 μC / cm 2 (shown by the line 1204 in FIG. 12B) of the amount of charge were obtained.

[0158] As can be seen from the results shown in FIG. 12B, the change in the resistance value induced by the electron beam annealing process depends at least partially on the distance between the exposure pattern 702 and the Josephson junction 104. For the current and the amount of charge used to generate the results shown in FIG. 12B, the smaller the distance between the Josephson junction 104 and the exposure pattern 702, the generally greater the change in the resistance value. For all of the electron beam annealing processes for the current and the amount of charge used to generate the results shown in FIG. 12B, an increase in the resistance value of the Josephson junction 104 was brought about. However, as described above, it has been found that by changing the parameters (for example, current, amount of charge, etc.) used in the electron beam annealing process, a decrease in the resistance value of the Josephson junction 104 can be induced for at least some parameter values.

[0159] The results shown in Figure 12B further demonstrate that the resistance change induced in the Josephson junction 104 is even more dependent on the amount of charge supplied during the electron beam annealing process.

[0160] As shown by the results in Figure 12B, the resistance change induced in the Josephson junction 104 was found to depend on both the distance between the exposure pattern 702 and the Josephson junction 104, and the amount of charge supplied during the electron beam annealing process. In at least some examples, the resistance change induced in the Josephson junction 104 can be controlled by controlling one or more of the distance between the exposure pattern 702 (which may include a single exposure spot 604 or multiple exposure spots 604) and the Josephson junction 104, and the amount of charge. As described above, by controlling the resistance change of the Josephson junction 104, the frequency change of the qubit into which the Josephson junction 104 is incorporated can be controlled.

[0161] Figure 13A is a schematic diagram of the different exposure patterns 1302, 1304, and 1306 used to produce the results shown in Figure 13B. As shown in Figure 13A, electron beam annealing was applied to the Josephson junction 104 using several different exposure patterns 1302, 1304, and 1306, each containing multiple exposure spots 604 directed to the incidence of the electron beam. The exposure patterns include a fully closed exposure pattern 1302 (corresponding to exposure pattern 602a described above with reference to Figure 6), a wide-loop exposure pattern 1304 (corresponding to exposure pattern 602b described above with reference to Figure 6), and a narrow-loop exposure pattern 1306 (corresponding to exposure pattern 602c described above with reference to Figure 6). Finally, for comparison, results were obtained for a control 1308 that did not use the electron beam annealing process.

[0162] Figure 13B is a graph showing the change in resistance of the Josephson junction 104 obtained by subjecting the Josephson junction 104 to different electron beam annealing treatments using different exposure patterns, as described above with reference to Figure 13A. The results plotted in the graph of Figure 13B were obtained by experiments using an electron beam with a current of 100 nA. The change in resistance obtained from each electron beam annealing treatment (unit: ohms Ω) is plotted on the y axis. The amount of charge used in each electron beam annealing treatment (unit: μC / cm²) 2 The values ​​were plotted on the x-axis. Results are shown for exposure pattern 1304 with a thick loop, exposure pattern 1306 with a thin loop, and control 1308. For each exposure pattern, results were obtained using different amounts of charge supplied to each exposure spot in the individual exposure pattern. In particular, 500 μC / cm 2 , 800 μC / cm 2 and 1100 μC / cm 2 The results obtained were obtained using the amount of charge.

[0163] As can be seen from the results shown in Figure 13B, the change in resistance induced in the Josephson junction 104 depends on both the amount of charge used and the exposure pattern used. With the parameter values ​​used to produce the results shown in Figure 13B, increasing the amount of charge generally increased the induced change in resistance. The largest change in resistance was obtained using the fully closed exposure pattern 1302, followed by the wide-loop exposure pattern 1304, and it was further found that the narrow-loop exposure pattern 1306 induced the smallest change in resistance.

[0164] All the results shown in Figure 13B indicate an increase in the resistance of the Josephson junction 104. However, as described above, it was found that other parameter values ​​used in the electron beam annealing process (e.g., current, charge amount, etc.) may induce a decrease in the resistance of the Josephson junction 104.

[0165] As shown in the results in Figure 13B, the resistance change induced in the Josephson junction 104 was found to depend on both the exposure pattern used and the amount of charge supplied during the electron beam annealing process. In at least some examples, the resistance change induced in the Josephson junction 104 can be controlled by controlling one or more of the exposure pattern and the amount of charge. As described above, by controlling the resistance change of the Josephson junction 104, the frequency change of the qubit into which the Josephson junction 104 is incorporated can be controlled.

[0166] Several embodiments have been described above in the context of tuning the resistance of a Josephson junction and, equivalently, the qubit frequencies to reduce the dispersion of qubit frequencies in a quantum information processor. However, the methods described herein can be used to perform any form of tuning to qubit frequencies. For example, for a given quantum information processor having multiple qubits, there may be a predetermined target or design set of qubit frequencies that are desirable to achieve. The target set of frequencies may include each of multiple qubits having substantially the same frequency. Alternatively, the target set of frequencies may include at least some of multiple qubits having different frequencies. For example, to reduce unwanted crosstalk between different qubits, qubit frequencies may be designed so that different qubits have different frequencies. Regardless of the target frequency of a given quantum information processor, variations in the fabrication of the Josephson junction may result in a difference between the qubit frequencies in the quantum information processor and the target frequency. The methods described herein can be used to tune the frequency of at least one qubit to reduce the difference between the qubit frequencies and the target frequency.

[0167] Examples of qubits in which each qubit contains a Josephson junction are described and illustrated here. In some examples, one or more qubits may contain multiple Josephson junctions. For example, one qubit may contain two Josephson junctions. Any of the methods for tuning the frequency of qubits described here can be applied to qubits containing multiple Josephson junctions. Such methods can be applied, for example, by applying electron beam annealing to one of the multiple Josephson junctions. In some examples, electron beam annealing may be applied to multiple Josephson junctions contained within a single qubit. For example, the frequency of a qubit containing multiple Josephson junctions can be tuned by applying electron beam annealing to two or more of the multiple Josephson junctions. Two or more of the multiple Josephson junctions may contain a subset of the multiple Josephson junctions (e.g., fewer than all of the multiple Josephson junctions) or may contain all of the multiple Josephson junctions.

[0168] Here, various methods are described, and some of the method steps can be implemented on any suitable electronic device (e.g., a computing device) and / or a combination of electronic devices (e.g., multiple computing devices). For example, a method step like step 904 of the method in Figure 9 can be performed by an electronic device such as a computing device. Figure 14 is a schematic diagram of an exemplary electronic device 1402 that can be used to implement all or part of the methods described herein.

[0169] The electronic device 1402 may include at least one processing unit 1404, memory 1408, and an input / output interface 1406. The processing unit 1404 may include any suitable processor and / or combination of processors. For example, the processing unit 1404 may include one or more central processing units (CPUs) and graphical processing units (GPUs). The memory 1408 may include volatile memory and / or non-volatile / persistent memory. The memory 1408 can be used to store data such as, for example, an operating system, instructions executed by the processing unit (e.g., in the form of software executed by the processing unit), configuration information related to the electronic device 1402, session information associated with another device, node, or module in the network, and / or configuration or registration information. In some examples, the memory 1408 can be used to store instructions for executing any of the methods disclosed herein.

[0170] At least the processing unit 1404 is connected to the input / output interface 1406. The input / output interface 1406 facilitates communication with one or more other devices. For example, the input / output interface 1406 can be operated to send and / or receive communications with other devices in the network.

[0171] If necessary, the electronic device 1402 may further include a display (not shown). The display may include any suitable electronic display, such as a touch-sensitive display. The display may be connected to at least the processing unit 1404. The processing unit 1404 can generate display signals to be sent to the display in order to produce display information.

[0172] For the sake of brevity, all possible alternatives that fall within the scope of this disclosure are not explicitly discussed here. As those skilled in the art will understand, any aspect discussed in this disclosure in terms of an element capable of performing a certain operation also discloses the same characteristics in terms of a method including a method step corresponding to that operation. Similarly, any discussion presented in terms of a method step also discloses the same characteristics in terms of any one or more suitable elements that are capable of or configured to perform some or all of that method step. Furthermore, this disclosure assumes that for any method step, there may be a computer program configured to perform that method step at runtime.

[0173] Examples of the present disclosure can be implemented in the form of hardware, software, or a combination of hardware and software. Such software can be stored in the form of volatile or non-volatile storage devices, such as storage devices (whether erasable or rewritable), such as ROM; in the form of memory, such as RAM, memory chips, devices, or integrated circuits; or in the form of optically or magnetically readable media, such as CDs, DVDs, magnetic disks, or magnetic tapes. It will be understood that the storage devices and storage media are embodiments of machine-readable storage devices suitable for storing a program or a set of programs that implement embodiments of the present disclosure at runtime. Accordingly, embodiments provide programs containing code for implementing a system or method described in any of the prior claims, and machine-readable storage for storing such programs. Furthermore, examples of the present disclosure can be transmitted electronically over any medium, such as communication signals carried over wired or wireless connections, and embodiments appropriately encompass this.

[0174] Features, integers, characteristics, or groups described in connection with the present invention or specific aspects, embodiments, or examples of this disclosure should be understood to be applicable to other aspects, embodiments, or examples described herein, insofar as they do not conflict with this understanding. All features disclosed herein (including the appended claims, abstract, and drawings) and / or all steps of the methods or processes so so disclosed can be combined in any combination, except for combinations in which at least some of the features and / or steps are mutually exclusive. The present invention is not limited to the details of the examples described above.

Claims

1. A method for tuning the frequency of a qubit, including a Josephson junction, The steps include directing the electron beam to heat the Josephson junction, The steps include heating the Josephson junction with an electron beam, followed by cooling the Josephson junction, Heating and cooling a Josephson junction works to change the resistance of the Josephson junction, and this change in resistance changes the frequency of the qubit.

2. The method according to claim 1, wherein the step of directing an electron beam to heat a Josephson junction includes the step of directing an electron beam and injecting it into the Josephson junction.

3. The method according to claim 1, wherein the step of directing an electron beam to heat a Josephson junction includes directing an electron beam to irradiate a component thermally coupled to the Josephson junction, thereby causing heating of the component and heating of the Josephson junction through heat conduction from the heated component.

4. The method according to claim 3, wherein the component includes a portion of a substrate supporting a Josephson junction.

5. The method according to any one of claims 1 to 4, wherein the qubit includes a Josephson junction connected between two superconducting electrodes.

6. The method according to claim 5, wherein the superconducting electrodes are arranged coaxially with respect to each other.

7. The method according to any one of claims 1 to 6, wherein the step of directing an electron beam to heat a Josephson junction includes the step of directing the electron beam with a first current less than a threshold current to increase the resistance of the Josephson junction and decrease the frequency of the qubit.

8. The method according to any one of claims 1 to 6, wherein the step of directing an electron beam to heat a Josephson junction includes the step of directing the electron beam with a first current greater than a threshold current to reduce the resistance of the Josephson junction and increase the frequency of the qubit.

9. The method according to any one of claims 1 to 8, wherein the step of directing an electron beam to heat the Josephson junction includes the step of directing an electron beam to heat the Josephson junction over a single continuous exposure time.

10. The method according to any one of claims 1 to 8, wherein the step of directing an electron beam to heat the Josephson junction includes the step of directing a plurality of pulses of an electron beam to heat the Josephson junction.

11. The method according to claim 10, wherein at least a portion of the multiple pulses of the electron beam are directed to be incident at multiple different locations.

12. The method according to claim 11, wherein multiple different positions are arranged to form an exposure pattern surrounding the Josephson junction.

13. The method according to any one of claims 1 to 12, wherein the step of directing an electron beam to heat a Josephson junction includes the step of directing an electron beam having a beam diameter of less than 200 nm to heat a Josephson junction.

14. The method according to any one of claims 1 to 13, wherein the step of directing an electron beam to heat the Josephson junction includes the step of directing an electron beam having a current greater than 0.1 nA to heat the Josephson junction.

15. The method according to any one of claims 1 to 14, wherein the step of directing an electron beam to heat the Josephson junction includes the step of directing an electron beam using an electron beam lithography apparatus to heat the Josephson junction.

16. A method for tuning the qubit frequencies of a quantum information processor containing multiple qubits, wherein each qubit contains a Josephson junction, The steps include determining the frequency of each of the multiple qubits, A step of identifying at least one qubit for frequency tuning based on the determined frequencies of multiple qubits, A method comprising the step of adjusting the frequency of at least one qubit identified for frequency tuning, according to the method of any one of claims 1 to 15.

17. The method according to claim 16, wherein the step of determining the frequency of each of the plurality of qubits includes the step of measuring the resistance of a Josephson junction contained in each of the plurality of qubits.

18. The method according to claim 16 or 17, wherein the step of identifying at least one of a plurality of qubits for frequency tuning includes the step of identifying at least one of a plurality of qubits having a frequency that can be tuned to reduce the frequency dispersion of the plurality of qubits.

19. The method according to any one of claims 16 to 18, wherein the step of tuning the frequency of at least one qubit identified for frequency tuning includes tuning the frequency of at least one identified qubit to reduce the dispersion of the frequencies of multiple qubits.

20. The method according to any one of claims 16 to 19, wherein the step of tuning the frequency of at least one qubit identified for frequency tuning includes increasing the resistance of the Josephson junction of at least one of the at least first qubits identified for frequency tuning to decrease the frequency of the at least first qubit identified for frequency tuning.

21. The method according to any one of claims 16 to 20, wherein the step of tuning the frequency of at least one qubit identified for frequency tuning includes the step of decreasing the resistance of at least a second of the at least one qubit identified for frequency tuning to increase the frequency of the at least second of the at least one qubit identified for frequency tuning.

22. The step of adjusting the frequency of at least one qubit identified for frequency tuning, according to any one of claims 1 to 13, further includes: The steps include determining the characteristics of the electron beam directed to heat the Josephson junction, depending on the determined frequency of the qubit containing the Josephson junction, The method according to any one of claims 16 to 21, comprising the step of directing an electron beam and heating a Josephson junction using the determined properties of the electron beam.

23. A quantum information processor comprising at least one qubit including a Josephson junction, A quantum information processor in which the frequency of at least one qubit is tuned according to the method described in any one of claims 1 to 15.

24. A quantum information processor comprising a plurality of qubits, each containing a Josephson junction, A quantum information processor in which the frequency of at least one of a plurality of qubits is tuned using the method according to any one of claims 16 to 22.

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