Tunable qubit coupler

Abstract

Methods, systems, and apparatus for implementing tunable qubit couplers. In one aspect, a device includes a first data qubit, a second data qubit, and a third qubit, the third qubit being a tunable qubit coupler arranged to be coupled to the first data qubit and to the second data qubit such that during operation of the device, the first data qubit is coupled to the first data qubit, and the second data qubit is coupled to the second data qubit. The tunable qubit coupler allows tunable coupling between the first data qubit and the second data qubit.

Description

[0001] This application is a divisional application of the invention patent application with application date of June 28, 2019, application number 201980010469.4, and invention name “tunable quantum bit coupler”. Technical Field

[0002] The present disclosure relates to tunable qubit couplers. Background Art

[0003] Large-scale quantum computers have the potential to provide rapid solutions to certain classes of different difficult problems. The design and implementation of quantum architectures and the multiple challenges of controlling, programming, and maintaining quantum hardware have hindered the realization of large-scale quantum computing. Summary of the invention

[0004] This disclosure describes techniques for implementing tunable qubit couplers.

[0005] In general, innovative aspects of the presently disclosed subject matter may be embodied in a device comprising: a first data qubit; a second data qubit; and a third qubit, wherein the third qubit is a tunable qubit coupler arranged to be coupled to the first data qubit and to the second data qubit such that during operation of the device, the tunable qubit coupler allows for tunable coupling between the first data qubit and the second data qubit.

[0006] Embodiments may include any, all, or none of the following features. For example, in some embodiments, the device of claim 1 includes a first substrate, wherein the first data qubit and the second data qubit are on a major surface of the first substrate; and a second substrate separated from and coupled to the first substrate, wherein the tunable qubit coupler is on the major surface of the second substrate and is arranged to overlap with a portion of the first data qubit and a portion of the second data qubit. The tunable qubit coupler can be arranged on a first axis, wherein the first axis: is orthogonal to a second axis connecting the first data qubit and the second data qubit; and intersects with a second axis between the first data qubit and the second data qubit. The space between the first substrate and the second substrate is less than at most 10 -5 The first data qubit and the second data qubit may each include a corresponding elongate arm, and the elongate arm of the first data qubit and the elongate arm of the second data qubit may be separated by a gap. The tunable qubit coupler may include an elongate wire, wherein the elongate wire overlaps the elongate arm of the first data qubit, the elongate arm of the second data qubit, and the gap.

[0007] In some embodiments, the tunable qubit coupler includes a superconducting quantum interference device (SQUID) directly connected to the elongated lead. Each of the first data qubit and the second data qubit may include a corresponding differential qubit. The tunable qubit coupler may include a transmon qubit. A major surface of the first substrate may face a major surface of the second substrate. The first data qubit and the second data qubit may be arranged on the major surface of the first substrate such that during operation of the device, the first data qubit and the second data qubit are directly coupled.

[0008] In some innovative aspects, a method of controlling coupling between a first data qubit and a second data qubit using a third qubit as a tunable qubit coupler, wherein the tunable qubit is arranged to couple to the first data qubit and to the second data qubit, includes: controlling the coupling between the first data qubit and the second data qubit by changing an operating frequency of the tunable qubit coupler.

[0009] Implementations of the method may include one or more of the following features, or none of the following features. For example, in some implementations, the tunable qubit coupler includes a superconducting quantum interference device (SQUID), and changing the operating frequency of the tunable qubit coupler includes changing the magnetic flux of the SQUID of the tunable qubit coupler. Changing the operating frequency of the tunable qubit coupler may include changing the operating frequency within a range of not less than about 4 GHz and not more than about 6 GHz.

[0010] The method may include tuning each of the first data qubit and the second data qubit to a same resonance frequency; and subsequently changing an operating frequency of a tunable qubit coupler to turn on coupling between the first data qubit and the second data qubit.

[0011] The resonant frequency of the first data qubit and the second data qubit may be in a range of about 4 GHz to about 8 GHz. The resonant frequency of the first data qubit and the second data qubit may differ from an operating frequency of the tunable qubit coupler by about 0.5 GHz to 7 GHz.

[0012] In some embodiments, the method may include, prior to tuning each of the first data qubit and the second data qubit to the same resonant frequency, changing an operating frequency of the tunable qubit coupler to a first frequency to turn off coupling between the first data qubit and the second data qubit. Changing the operating frequency of the tunable qubit coupler to turn off coupling may include changing the operating frequency such that direct coupling between the first data qubit and the second data qubit is offset by indirect coupling between the first data qubit and the second data qubit through the tunable qubit coupler. The coupling between the first data qubit and the second data qubit as a combination of direct coupling and indirect coupling may operate over a frequency range of approximately 45 MHz. The indirect coupling between the first data qubit and the second data qubit through the tunable qubit coupler may be less than at least 10 -5 It occurs across the vacuum space under a vacuum pressure of Torr.

[0013] The first data qubit and the second data qubit may be disposed on a first substrate, and the tunable qubit coupler is disposed on a second substrate spaced apart from the first substrate.

[0014] According to an embodiment of the present disclosure, there is provided a device, comprising: a first data qubit; a second data qubit, wherein a first portion of the first data qubit is separated from a first portion of the second data qubit by a gap; a tunable qubit coupler arranged to couple to the first data qubit and to the second data qubit such that during operation of the device, the tunable qubit coupler allows tunable coupling between the first data qubit and the second data qubit, wherein the tunable qubit coupler comprises a single-ended transmon qubit; a first substrate, wherein the first data qubit and the second data qubit are on a major surface of the first substrate; and a second substrate, the second substrate being separated from and coupled to the first substrate, wherein the tunable qubit coupler is on a major surface of the second substrate and is arranged to overlap with the first portion of the first data qubit, the first portion of the second data qubit, and the gap.

[0015] The subject matter described in this specification can be implemented in a specific way to realize one or more of the following advantages.

[0016] For example, in some embodiments, the tunable qubit couplers described in this specification allow for fast tunable coupling of qubits. In some embodiments, coupling can be achieved without significantly reducing the quality or performance of the qubits. In some embodiments, the coupling provides a dynamic control range for a two-qubit gate applied to the coupled qubits and zero coupling of the qubits during the OFF state. Therefore, in certain embodiments, quantum computing hardware implementing the tunable couplers described in this specification can achieve improved performance levels, such as improved algorithm execution speed and reduced losses, and perform quantum computations with increased accuracy and reliability. In addition, in some embodiments, the ability to turn off interactions between qubits also provides reduced frequency crowding, because qubits can be configured to operate at the same frequency, even sweeping past each other without interaction. In addition, in some embodiments, multi-qubit state transitions can be suppressed by turning off coupling during readout.

[0017] The details of one or more implementations of the subject matter of this specification are set forth in the accompanying drawings and the description below. Other features, aspects, and advantages of the subject matter will become apparent from the description, drawings, and claims. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 An exemplary system is depicted that serves as an operating environment for two data qubits coupled by a tunable qubit coupler.

[0019] Figure 2A is a schematic diagram of an example design of a first data qubit and a second data qubit coupled by a tunable qubit coupler.

[0020] Figure 2B is a schematic diagram of an example design of a first data qubit and a second data qubit coupled by a tunable qubit coupler.

[0021] Figure 3 Simulation results showing the design principles of a tunable qubit coupler.

[0022] Figure 4A and Figure 4B is a schematic diagram showing an example of a quantum computing chip design including four data qubits and three tunable qubit couplers.

[0023] Figure 5 Shows Figure 4A-4B Simulation results of the relaxation time T1 of four qubits of an example quantum computing chip design.

[0024] Figure 6is a flow chart of an example process for controlling coupling between a first data qubit and a second data qubit using a tunable qubit coupler arranged to couple to the first data qubit and to the second data qubit. DETAILED DESCRIPTION

[0025] Overview

[0026] Controlling the interactions between qubits is important for enabling quantum simulation and universal quantum computing. For example, in order to execute an algorithm on a quantum computer, one or more two-qubit gates may need to be applied. A two-qubit gate can be implemented by having two qubits interact with each other. In some embodiments, a tunable qubit coupler can be used to dynamically control the interactions between qubits.

[0027] When using superconducting qubits (e.g., transmon qubits), coupling between the first and second qubits can be achieved by placing the edge of the first qubit close to the edge of the second qubit. However, this design only allows dynamic control of the coupling between the qubits by detuning the resonant frequency of at least one of the two qubits. This requires a high degree of control because detuning often causes the qubit to be excited to a state outside the computational subspace. In addition, because sufficiently large detuning is not feasible, the OFF state in this design may not correspond to zero coupling and therefore have a constant loss associated with it. In order to provide tunable coupling between qubits without the above problems, components that allow the coupling strength between the qubits to be modulated can be introduced between the qubits. The introduction of additional components to achieve tunable qubit coupling and an OFF state with zero coupling creates various technical problems that must be solved. For example, the additional tunable qubit coupler element should not reduce the quality (factor) or performance of the qubit below some acceptable predetermined threshold, for example, the relaxation or coherence time should not be significantly reduced. . One source of reduced quality or increased losses may be, for example, the interaction of the tunable qubit coupler with the qubit, since the coupler also has a finite quality factor and relaxation or coherence time. Another source of losses may be the introduction of new materials in the hardware near the qubit itself. Implementing a tunable qubit coupler while maintaining a given quality of the qubit presents various design challenges both at the conceptual level and at the level of actual physical implementation. The present disclosure overcomes those technical challenges.

[0028] The device included in the present disclosure includes three elements, two qubits referred to as data qubits, and a tunable qubit coupler including a tunable nonlinear oscillator. The tunable nonlinear oscillator can be implemented by adding a large capacitor to the DC-SQUID and achieving a specific ratio of junction critical current and capacitance. The tunable qubit coupler implemented in this way is similar to a transmon qubit, where a specific ratio of junction critical current and capacitance is in the transmon state. The tunable qubit coupler is not used as a carrier of quantum information and is therefore technically not a transmon qubit, but for convenience it may still be referred to here as a (single-ended) transmon qubit. The two data qubits may be transmon qubits, but other qubits may also be used. Adding a large shunt capacitor to implement the tunable qubit coupler can mitigate charge noise and allow the two data qubits to be capacitively coupled.

[0029] The data qubits and couplers are configured and arranged such that, during operation of the data qubits, the couplers allow for fast tunable coupling of the data qubits without significantly degrading the quality or performance of the data qubits, while providing a dynamic control range for a two-qubit gate implemented by the interacting data qubits and zero coupling of the digital qubit during an OFF state.

[0030] This is achieved by satisfying one or more design principles, namely, the probability of large detuning between the data qubits and the couplers, arranging the couplers in a parallel plate geometry relative to the data qubits to achieve strong coupling, providing a vacuum gap between the plates to ensure low losses, and providing direct coupling between the data qubits in addition to the indirect coupling between the data qubits via the couplers to achieve zero-sum coupling between the data qubits in the OFF state.

[0031] The example implementations of the present disclosure are used to meet those design principles. Two data qubits can be implemented by two transmon qubits arranged on some suitable substrates, where the transmon qubits can be single-ended or can have a differential design. Direct coupling between data qubits can be achieved by positioning the transmon qubits so that the edges of the individual qubits (e.g., individual superconductor arms) facing each other are parallel to each other and separated by a gap. Here, each superconductor arm is also referred to as an elongated arm or a coupling arm. An additional transmon qubit (e.g., a single-ended transmon qubit) implementing a coupler is located on a second substrate. The two substrates are arranged so that the side of the substrate on which the data qubit is located faces the side of the substrate on which the coupler is located. The coupler is placed so that its area covers the coupled arms of the data qubit and the gap between these arms, as well as the gap (e.g., a vacuum gap) established between the data qubit and the coupler. The two substrates can be aligned using a bump joint. The coupler is coupled to the two data qubits. By changing the frequency of the coupler, the coupling between the data qubits can be tuned.

[0032] This design satisfies the design principles mentioned above, i.e., the design allows for fast tunable coupling of data qubits using tunable couplers while maintaining the performance of the data qubits and providing a dynamic control range for a two-qubit gate implemented by the interacting data qubits as well as an OFF state with zero coupling.

[0033] Example operating environment

[0034] Figure 1 Depicted for reference Figure 2A , Figure 2B 4 and an exemplary system of an operating environment for the device described in FIG.

[0035] System 100 includes quantum hardware 102, which includes at least a first data qubit 104, a second data qubit 106, and a tunable qubit coupler 108 between the first data qubit and the second data qubit. First data qubit 104, second data qubit 106, and tunable qubit coupler 108 may be subcomponents of quantum hardware 102. For example, quantum hardware 102 may include additional data qubits and additional tunable qubit couplers. Each of first data qubit 104, second data qubit 106, and tunable qubit coupler 108 may be frequency tunable.

[0036] First data qubit 104 and second data qubit 106 may be superconducting qubits. For example, first data qubit 104 and second data qubit 106 may be transmon qubits. Furthermore, the transmon qubit may have a differential design or may be single ended. As an example, for a transmon qubit formed by a DC SQUID having two sides, each side being defined by a Josephson junction, both sides may be left electrically open, which may be referred to as a differential design, or one side may be shunted to a ground plane, which may be referred to as a single ended design. Other qubit architectures may also be used. Reference will be made below to Figure 2A and Figure 2B-Figure 3 The tunable qubit coupler 108 is explained in more detail.

[0037] The system 100 includes control electronics 110. The control electronics 110 may include arbitrary waveform generators, filters, attenuators and mixers, among other circuit elements. For readout, the control electronics 110 may also include amplifiers and analog-to-digital converters, among other circuit elements.

[0038] System 100 includes control lines 112 from control electronics 110 to quantum hardware 102. Control lines 112 can directly or indirectly control first data qubit 104, second data qubit 106, and tunable coupler 108. In some cases, control lines 112 can include qubit control lines that allow for direct control of first data qubit 104 and second data qubit 106. The frequencies of first data qubit 104 and second data qubit 106 can be tuned using signals provided on control lines 112. The frequencies of first data qubit 104 and second data qubit 106 can be tuned by applying control signals to control lines 112 via control electronics 110. In addition, control electronics 110 can perform measurements of first data qubit 104 and second data qubit 106 via control lines 112. The measurements of first data qubit 104 and the measurements of second data qubit 106 determine the states of first data qubit 104 and second data qubit 106, respectively. Control electronics 110 may store, display, and / or further process the results of each of the measurements of first data qubit 104 and second data qubit 106 .

[0039] System 100 includes tunable qubit coupler control line 114. Control electronics 110 can dynamically tune the coupling or interaction between first data qubit 104 and second data qubit 106 by applying a control signal on tunable qubit coupler control line 114 to tune the frequency of tunable qubit coupler 108. For example, control electronics 110 can apply a voltage pulse to tunable qubit coupler control line 114 to tune the frequency of tunable qubit coupler 108. Referring to FIG. Figure 6 Explain in more detail by using Figure 2A and Figure 2B-Figure 3 The example apparatus shown applies a control signal to tunable qubit coupler control line 114 to tune the frequency of tunable qubit coupler 108 to tune the coupling or interaction between first data qubit 104 and second data qubit 106 .

[0040] In some embodiments, control electronics 110 may include a data processing device and associated memory. The memory may include a computer program having instructions that, when executed by the data processing device, cause the data processing device to perform one or more functions described herein, such as applying control signals to qubits and / or tunable qubit couplers.

[0041] Example tunable qubit coupler

[0042] Figure 2A Schematic diagram 200 of an example design of first data qubit 204 and second data qubit 206 coupled by tunable qubit coupler 208 .

[0043] In this example design, first data qubit 204 and second data qubit 206 are transmon qubits with a differential design. Each qubit 204, 206 includes four elongated arms 220 of superconducting material and two diagonal strips 222 of superconducting material arranged parallel to each other and separated by a gap. Other qubit architectures and designs are also possible. In particular, in some embodiments, one or both of first data qubit 204 and second data qubit 206 can be a single-ended transmon qubit. However, in either case, the tunable qubit coupler is single-ended to provide indirect coupling, which allows the direct and indirect coupling to be canceled and the overall coupling between the data qubits to be turned off.

[0044] First data qubit 204 and second data qubit 206 are arranged so that one of the elongated arms of each qubit extends toward each other. Figure 2A206. As shown, elongated arm 214 of first data qubit 204 extends toward elongated arm 216 of second data qubit 206. The elongated arms extending toward each other are separated by a gap. For example, elongated arm 214 of first data qubit 204 and elongated arm 216 of second data qubit 206 are separated by a distance 218. This arrangement provides direct coupling between first data qubit 204 and second data qubit 206 through capacitive coupling. First data qubit 204 and second data qubit 206 may be on a surface of a first substrate. For example, first data qubit 204 and second data qubit 206 may be arranged on a major surface of the first substrate such that during operation, the qubits may be coupled directly and indirectly via tunable qubit coupler 208.

[0045] Tunable qubit coupler 208 is disposed on a second substrate located above the first substrate on which data qubits 204, 206 are located. The second substrate is separated from the first substrate by a gap, but may also be coupled to the first substrate by, for example, a bump bond. A first axis (e.g., axis A) is orthogonal to a second axis (e.g., axis B). Second axis B extends through first data qubit 204 and second data qubit 206, i.e., first data qubits 204 and 206 are both located on the second axis. First axis A intersects second axis B between first data qubit 204 and second data qubit 206. Tunable coupler 208 may be on a surface of the second substrate that faces a surface on which first data qubit 204 and second data qubit 206 are disposed.

[0046] Tunable qubit coupler 208 includes a superconductor island 210, for example, a single superconductor island, such as an elongated lead, which faces first data qubit 204 and second data qubit 206 and overlaps elongated arm 214 of first data qubit 204, elongated arm 216 of second data qubit 206, and separation distance 218. Superconductor island 210 can be at least partially surrounded by ground plane 212 on the second substrate. In some cases, superconductor island 210 and ground plane 212 can be made of different materials. In other cases, superconductor island 210 and ground plane 212 can be made of the same material. For example, superconductor island 210 can be a superconducting metal, such as aluminum. Ground plane 212 can also be made of aluminum or a different superconductor material. In addition, superconductor island 210 can be made of a superconducting metal ... In addition, superconductor island Figure 2A 2) is coupled to the ground plane 212, wherein the SQUID may be located between the island 210 and the control line (not shown). Figure 4A-4B More details are described in more detail on how first data qubit 204, second data qubit 206, and tunable qubit coupler 208 are located on first and second substrates, respectively, and connected to control lines.

[0047] The amount of overlap of island 210 with elongated arms 214, 216 is related to the coupling strength of the indirect coupling between the first data qubit and the second data qubit through tunable qubit coupler 208, where increasing overlap increases the coupling. Stronger coupling allows for greater detuning of tunable qubit coupler 208 from first data qubit 204 and second data qubit 206, which in turn reduces the additional losses due to the presence of tunable qubit coupler 208. As described in reference Figure 3 As mentioned, the overlap can be designed to achieve certain design parameters.

[0048] Figure 2B It is shown by Figure 2A Schematic diagram of a cross-sectional view of line B. The first data qubit 204 and the second data qubit 206 are both located on the main surface 242 of the first substrate 240. For ease of observation, Figure 2B Only elongated arm 214 of first data qubit 204 and elongated arm 216 of second data qubit 206 are shown. Elongated arm 214 is separated from elongated arm 216 by a distance 218. During operation of the qubit system, direct coupling between first data qubit 204 and second data qubit 206 may occur through elongated arms 214, 216. For alternative qubit designs, direct coupling between qubits may occur through other edges or surfaces of the qubits.

[0049] Tunable qubit coupler 208 is formed on major surface 252 of second substrate 250. Second substrate 250 may be located on first substrate 240 such that major surface 252 faces major surface 242. Figure 2B As shown, tunable qubit coupler 208 overlaps elongated arm 214 and elongated arm 216. Second substrate 250 can be bonded (e.g., bump bonded) to first substrate 240 using bond 260 (e.g., bump bond). Gap 270 separates first substrate 240 from second substrate 250. The space within gap 270 can be a low pressure environment, such as a vacuum. Each of first substrate 240 and second substrate 250 can be formed of a dielectric, such as silicon or sapphire.

[0050] exist Figure 2A and Figure 2BIn the example of , the tunable qubit coupler 208 is designed as a tunable nonlinear oscillator having a large capacitor added to a DC-SQUID and a specific ratio of the junction critical current and capacitance of the SQUID in the transmon state. The addition of a large shunt capacitor mitigates the charge noise of the tunable qubit coupler 208 and allows capacitive coupling to the first data qubit 204 and the second data qubit 206. This design of the tunable qubit coupler 208 is equivalent to the design of a single-ended transmon qubit. Therefore, the tunable qubit coupler 208 can also be referred to as a qubit, such as a transmon qubit, although it is not used to carry or encode quantum information. Other designs are also possible. For example, the ratio of the junction critical current and capacitance of the SQUID that is not in the transmon state can be selected. In particular, when a design other than a differential design is selected for the first data qubit 204 and the second data qubit 206, a different ratio can be selected.

[0051] Example Design Parameters and Corresponding Results

[0052] Figure 3 The simulation results 300, 320 and 340 of the design principle of the tunable qubit coupler are shown. The simulation results 300, 320 and 340 may correspond to the reference Figure 2A First data qubit 204, second data qubit 206, and tunable qubit coupler 208 are depicted.

[0053] Tunable qubit couplers (e.g. Figure 2A An example design principle of the tunable qubit coupler 208 is that the tunable qubit coupler should not significantly affect the coherence or relaxation time of the first data qubit and the second data qubit coupled by the tunable qubit coupler. To avoid these adverse effects, the tunable qubit coupler can be detuned from the first data qubit and the second data qubit, that is, the tunable qubit coupler is operated very far away in frequency from the first data qubit and the second data qubit. In some embodiments, given that the coupling of the first data qubit and the second data qubit through the tunable qubit coupler is an indirect coupling, it is preferred to provide a relatively strong coupling from the tunable qubit coupler to the first and second data qubits, which is a second order process. Adding a tunable qubit coupler may introduce losses in various ways and reduce the quality (factor) of the qubit. Figure 3 The simulation results show that the implementation of the currently described tunable qubit coupler (such as Figure 2AThe coupler 208) enables dynamic control of the coupling between the qubits with large detuning of the coupler and the qubits, strong coupling of the qubits through the coupler, and no significant degradation of the quality of the qubits. In addition, when the first data qubit and the second data qubit are arranged to also allow direct coupling between them, such as, for example, in Figure 2A In , the direct coupling strength can be chosen such that it is offset by a certain value of the indirect coupling and an overall coupling with zero coupling strength is achieved, which can be used as an OFF state.

[0054] The physical implementation of tunable qubit couplers as part of quantum hardware may result in loss or degradation of the quality of qubits not included in the consideration, for example, the introduction of additional materials in the vicinity of the qubits may significantly affect them. Figure 5 A tunable qubit coupler (e.g., Figure 2A An example design of a quantum computing chip that can be used to provide a tunable qubit coupler 208) without significantly degrading the quality of the qubits. Specifically, in the aforementioned design, the qubits are located on a first substrate, and the tunable qubit coupler is located on a second substrate along with other control elements, using a parallel plate geometry, and the qubits and coupler are separated by a vacuum gap.

[0055] Figure 3 The three graphs 300, 320 and 340 of FIG. 3 include horizontal axes 304, 324 and 344, respectively. Each horizontal axis 304, 324 and 344 represents the coupler flux applied to the tunable qubit coupler. , and have the same scale.

[0056] Graph 300 includes a vertical axis 302 of a frequency spectrum in GHz. Solid straight line 318 represents the frequency of the first data qubit and the second data qubit. In this example, the frequency of the first data qubit and the second data qubit is approximately 6 GHz. Solid line 316 represents the coupler frequency. For zero coupler flux, the coupler is at a frequency of approximately 13 GHz and is detuned from the first data qubit and the second data qubit by approximately 7 GHz. Increasing the coupler flux decreases the coupler frequency. Dashed line 308 represents a lower limit of the coupler frequency of approximately 9 GHz, i.e., approximately 3 GHz detuned from the first data qubit and the second data qubit as indicated by arrow 312. As indicated by arrow 310, the coupler frequency is dynamically tuned by the coupler flux over a range of 4 GHz. The coupling efficiency is approximately 15%.

[0057] Graph 320 includes a vertical axis 322 of coupling between a first data qubit and a second data qubit through a coupler, expressed in MHz. Line 326 represents coupling based on an approximation of a physical system including a tunable qubit coupler and the first and second data qubits, where the approximation has a value that can be expressed as , where g represents the coupling between the tunable qubit coupler and the data qubit, also understood as the interaction strength in the corresponding Jaynes Cummings Hamiltonian, and is the frequency difference between the tunable qubit coupler and the data qubit, also understood as the detuning between the tunable qubit coupler and the first data qubit and the second data qubit. is the frequency of the data qubit The lowest order correction.

[0058] Line 328 represents indirect coupling based on an exact linear model of a physical system including a tunable qubit coupler and a first data qubit and a second data qubit. Lines 326 and 328 substantially coincide within the coupling range. Dashed straight line 330 represents an offset value of the indirect coupling through the tunable qubit coupler, which contributes to the second-order interaction between the first data qubit and the second data qubit. By designing the direct coupling between the first data qubit and the second data qubit to have the same value as the offset value, the total coupling, which is a combination of the direct coupling between the first data qubit and the second data qubit and the indirect coupling between the first data qubit and the second data qubit through the tunable qubit coupler, can be zero for a particular coupler flux value (e.g., where line 330 crosses the indirect coupling frequency). The total coupling of zero provides an OFF state where there is no coupling between the first data qubit and the second data qubit. In addition, graph 320 shows a small coupling when the coupler is detuned at the farthest distance from the first data qubit and the second data qubit and monotonically increases the coupling to reduce the detuning. The coupler frequency is approximately related to the coupling strength, so that the time required to perform a two-qubit operation or two-qubit gate (e.g., entangle two qubits) is inversely proportional to the coupling strength. For example, for 20 MHz coupling, it takes on the order of 50 nanoseconds to entangle two qubits. Increasing the coupling strength reduces the time to perform a two-qubit gate, i.e., increased coupling strength provides a faster two-qubit gate, which in turn also reduces the two-qubit gate error.

[0059] Graph 340 includes a vertical axis 342 representing the quality factor of a qubit (e.g., a first data qubit or a second data qubit) modified by the quality factor of the tunable qubit coupler divided by the tunable qubit coupler. The data presented in graph 340 relates to the losses induced by the qubit from the tunable qubit coupler, and the ratio represented by vertical axis 342 can be understood as the degree to which the qubit is protected from the losses that may be induced by the tunable qubit coupler. Line 346 represents the qubit losses induced by the coupler based on an approximation of a physical system including the tunable qubit coupler and the first data qubit and the second data qubit, where the approximation has a value that can be expressed as , where g represents the interaction strength in the corresponding Jaynes Cummings Hamiltonian, and represents the amount of detuning between the tunable qubit coupler and the first and second data qubits. Line 348 represents coupling based on an accurate linear model of a physical system including the tunable qubit coupler and the first and second data qubits. Lines 346 and 348 substantially coincide over the coupling range. When the qubit and the tunable qubit coupler are most detuned from each other, i.e., at about 7 GHz, the loss imposed on the qubit by the coupler is about 140 times less than the intrinsic loss of the coupler. When the distance in frequency between the qubit and the coupler is reduced (and the coupling between the qubit and the coupler is increased), the loss imposed on the qubit by the coupler is at least about 20 times less than the intrinsic loss of the coupler.

[0060] As described in this disclosure, implementing a tunable qubit coupler for a first data qubit and a second data qubit provides a controllable dynamic range of coupling (including strong coupling) between the first data qubit and the second data qubit, a fast two-qubit gate time, zero total coupling for a particular indirect coupling strength through the coupler, and appropriate selection of direct coupling between the first data qubit and the second data qubit without significantly degrading the quality factors of the first data qubit and the second data qubit.

[0061] Example quantum computing chip design

[0062] Figure 4A and Figure 4B 4 is a schematic diagram showing an example of a quantum computing chip design 400 including four data qubits and three tunable qubit couplers. The quantum computing chip design 400 implements the reference Figure 3The design principle is explained in more detail. The quantum computing chip design achieves tunable coupling of adjacent pairs of four qubits through three tunable qubit couplers, and provides a dynamic and controllable range of coupling strength between adjacent qubits, fast two-qubit gate execution, and an OFF state with zero coupling between adjacent qubits without degrading the intrinsic performance of the qubits and couplers.

[0063] The quantum computing chip 400 includes a first substrate 402 and a second substrate 422 . Figure 4A is a schematic diagram showing an example of a first substrate including data qubits, and Figure 4B 4 is a schematic diagram showing an example of a second substrate including a tunable qubit coupler and bonded to a first substrate. For convenience, the two substrates 402, 422 are shown separated. The first substrate 402 includes a major surface. The elements described with reference to the first substrate 402 (e.g., qubits 404a-d) are located on the major surface of the first substrate 402. Figure 4A In the embodiment, the major surface of the first substrate 402 supports the elements 404-412. The second substrate 422 includes a major surface. The elements described with reference to the second substrate 422 (e.g., couplers 424a-c) are located on the major surface of the second substrate 422, such as Figure 4B shown.

[0064] In the assembled state, the second substrate 422 is stacked on top of the first substrate 402, with the major surfaces facing each other. The second substrate 422 is located on top of the first substrate 402 so that the corresponding tunable couplers 424a-c overlap portions of the two qubits they couple. The two substrates are joined together by bonding elements 406 and 426, respectively. For example, the bonding elements 406 and 426 can be bump bonds. The bonding elements 406 and 426 can be made of indium. When the two substrates are joined together, the first substrate and the second substrate are separated by a gap, and in addition, the elements described with reference to the first substrate 402 (e.g., the qubits 404a-d except the bonding element 406) are separated from the elements described with reference to the second substrate 422 (e.g., the couplers 424a-c except the bonding element 426) by the gap. The space between the first substrate and the second substrate can be less than at most Torr vacuum pressure.

[0065] The first substrate 402 includes four qubits 404a-d. Qubits 404a-d may correspond to reference Figure 2A1 and 2. For example, qubits 404a and 404b may correspond to one instance of qubits 204 and 206, respectively. Qubits 404b and 404c may correspond to a second instance of qubits 204 and 206, respectively. Qubits 404c and 404d may correspond to a third instance of qubits 204 and 206, respectively. Figure 2A In the example of the example quantum computing chip design 400, the qubits 404a-d are transmon qubits with a differential design. However, other qubit structures and designs may also be used. In particular, a single-ended transmon qubit may be used instead.

[0066] The first substrate 402 also includes an electrical test structure 408 for measuring the room temperature resistance of the DC SQUIDS.

[0067] The second substrate 422 includes three tunable qubit couplers 424a-c. The tunable qubit couplers 424a-c can be reference Figure 2A When assembled, the first substrate 402 and the second substrate 422 are positioned so that the qubits 404a-d and the tunable couplers 424a-c are tunable according to Figure 2A The arrangement of first data qubit 204, second data qubit 206, and tunable qubit coupler 208 is arranged. That is, according to the reference Figure 2A 1. In the depicted arrangement, tunable qubit coupler 424a couples qubits 404a and 404b, tunable qubit coupler 424b couples qubits 404b and 404c, and tunable qubit coupler 424c couples qubits 404c and 404d.

[0068] Each of tunable qubit couplers 424a-c includes a SQUID (e.g., SQUID 454) electrically connected directly to a superconductor island, where the island may be an elongated lead. Each of the SQUIDs (e.g., SQUID 454) is located between a corresponding superconductor island of each of tunable qubit couplers 424a-c and a tunable qubit coupler control line 432.

[0069] The second substrate 422 includes qubit control lines 456, 458, each having an electrically open or floating end 450, 452, respectively, for coupling to a qubit. When the two substrates are bonded together, the qubit control lines can allow frequency control of the corresponding qubit on the first substrate.

[0070] The second substrate 422 includes measurement lines 460, each of which is electrically coupled to a half-wave resonant filter 446 having an open boundary. The half-wave resonant filter 446 is capacitively coupled at end 448 to a qubit.

[0071] The second substrate 422 also includes bonding pads 430 for connecting the on-chip leads to external control lines using wire bonding, a test structure 438 for measuring the room temperature resistance of DC SQUIDS, a test structure 440 for measuring the contact resistance of the electrical cross-over, a capacitive coupling element 448 between the readout resonator and the qubit, and a measurement input / output line 460.

[0072] The design of the quantum computing chip 400 in an assembled state may be referred to herein as having a parallel plate geometry. Figure 2A and Figure 2B The described tunable qubit coupler and the design of coupling qubits through the coupler meet the design principles of providing strong coupling, dynamic and controllable coupling range, large detuning with the qubit, an OFF state with zero coupling at a conceptual level, and maintenance of the quality and performance of the qubit. The parallel plate geometry of the tunable qubit coupler, where the two substrates are located on a different substrate than the qubits and separated by a vacuum gap, solves the problem of physical implementation of the tunable qubit coupler and meets the key design principles, in particular strong (capacitive) coupling, without introducing significant additional qubit errors or losses.

[0073] Example quantum computing chip results

[0074] Figure 5 Shows Figure 4A-4B 500 is a simulation result of the relaxation time T1 of four qubits of an example quantum computing chip design.

[0075] The graph includes a horizontal axis 504 representing the qubit frequency in GHz and a vertical axis 502 representing the relaxation time T1 in microseconds. Figure 4A-4BThe quantum computing chip shown is cooled to operating temperature (e.g., a temperature significantly below 1K), and each of the relaxation times of the four qubits 506, 508, 510, and 512 is repeatedly measured for different qubit frequencies to obtain the results. For qubit frequencies above about 5.1 GHz, in most cases, each of the four qubits has a relaxation time of 20 microseconds or longer. In particular, the relaxation time T1 of the four qubits is not significantly different from the relaxation time of a standard transmon qubit without a tunable qubit coupler (not shown). The results show that, as described in the present invention, adding a tunable qubit coupler does not significantly degrade the performance of the qubit, that is, adding such a tunable qubit coupler provides a dynamic and controllable range of qubit coupling, fast two-qubit gate execution, and an OFF state with zero coupling between qubits without significantly degrading the quality factor of the qubit.

[0076] Example Methods for Implementing Tunable Qubit Couplers

[0077] Figure 6 is a flow chart of an example process 600 for controlling coupling between a first data qubit and a second data qubit using a tunable qubit coupler arranged to couple to the first data qubit and to the second data qubit. For example, process 600 may be performed to use Figure 2A , Figure 2B 4, controlling the coupling between the first data qubit and the second data qubit by a tunable qubit coupler. For convenience, process 600 will be described as being performed by quantum hardware communicating with control electronics located at one or more locations. For example, quantum computing chip 400 of FIG. 4 appropriately programmed according to the present specification can perform process 600.

[0078] A first data qubit and a second data qubit are tuned to the same resonant frequency (step 602). The resonant frequency of the first data qubit and the second data qubit may be in a range of about 4 GHz to about 8 GHz. Furthermore, the resonant frequency of the first data qubit and the second data qubit may differ from an operating frequency of the tunable qubit coupler by about 0.5 GHz to 7 GHz.

[0079] The coupling between the first data qubit and the second data qubit is controlled by changing an operating frequency of a tunable qubit coupler (step 604). The tunable qubit coupler may include a superconducting quantum interference device (SQUID), and changing the operating frequency of the tunable qubit coupler may include changing a magnetic flux of the SQUID of the tunable qubit coupler. Changing the operating frequency of the tunable qubit coupler may include changing the operating frequency within a range of not less than about 4 GHz and not greater than about 6 GHz.

[0080] After tuning each of the first data qubit and the second data qubit to the same resonant frequency at step 602, the operating frequency of the tunable qubit coupler may be changed to the first frequency to turn off coupling between the first data qubit and the second data qubit having the same resonant frequency. Changing the operating frequency of the tunable qubit coupler to turn off coupling may include changing the operating frequency so that direct coupling between the first data qubit and the second data qubit is offset by indirect coupling between the first data qubit and the second data qubit through the tunable qubit. The coupling between the first data qubit and the second data qubit as a combination of direct coupling, which is the coupling between the first data qubit and the second data qubit, and indirect coupling, which is the coupling between the first data qubit and the second data qubit through the tunable qubit coupler, may operate over a frequency range of about 45 MHz. Furthermore, the indirect coupling between the first data qubit and the second data qubit through the tunable qubit coupler may be operated at a frequency range of less than at least It occurs across the vacuum space under a vacuum pressure of Torr.

[0081] The digital and / or quantum subject matter and implementations of digital functional operations and quantum operations described in this specification may be implemented in digital electronic circuits, suitable quantum circuits, or more generally, in quantum computing systems, in tangibly embodied digital and / or quantum computer software or firmware, in digital and / or quantum computer hardware, including the structures disclosed in this specification and their structural equivalents, or in a combination of one or more of them. The term "quantum computing system" may include, but is not limited to, a quantum computer, a quantum information processing system, a quantum cryptographic system, or a quantum simulator.

[0082] The embodiments of the digital and / or quantum subject matter described in this specification may be implemented as one or more digital and / or quantum computer programs, i.e., one or more modules of digital and / or quantum computer program instructions encoded on a tangible non-transitory storage medium, for execution by a data processing device or for controlling the operation of a data processing device. The digital and / or quantum computer storage medium may be a machine-readable storage device, a machine-readable storage substrate, a random or serial access memory device, one or more qubits, or a combination of one or more of them. Alternatively or additionally, the program instructions may be encoded on an artificially generated propagation signal capable of encoding digital and / or quantum information, e.g., a machine-generated electrical, optical, or electromagnetic signal, which is generated to encode digital and / or quantum information for transmission to a suitable receiver device for execution by a data processing device.

[0083] The terms quantum information and quantum data refer to information or data carried, stored or stored by a quantum system, wherein the smallest non-trivial system is a qubit, i.e., a system that defines a unit of quantum information. It should be understood that the term "qubit" encompasses all quantum systems that can be appropriately approximated as a two-level system in the corresponding context. Such quantum systems may include multi-level systems, such as systems with two or more levels. For example, such systems may include atoms, electrons, photons, ions, or superconducting qubits. In various embodiments, the computational basis state is identified by the ground state and the first excited state, however, it should be understood that other arrangements in which the computational state is identified by a higher level excited state are also possible.

[0084] The term "data processing device" refers to digital and / or quantum data processing hardware, and includes all kinds of devices, equipment and machines for processing digital and / or quantum data, including, for example, programmable digital processors, programmable quantum processors, digital computers, quantum computers, multiple digital and quantum processors or computers and combinations thereof. The device may also be or further include a dedicated logic circuit, such as a field programmable gate array (FPGA), an application-specific integrated circuit (ASIC), or a quantum simulator, i.e., a quantum data processing device designed to simulate or generate information about a specific quantum system. In particular, a quantum simulator is a special-purpose quantum computer that does not have the ability to perform general-purpose quantum computations. In addition to the hardware, the device may optionally include code that creates an execution environment for a digital and / or quantum computer program, such as code that constitutes a processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of them.

[0085] A digital computer program may also be referred to or described as a program, software, software application, module, software module, script or code, which may be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and which may be deployed in any form, including as a stand-alone program or as a module, component, subroutine or other unit suitable for use in a digital computing environment. A quantum computer program, which may also be referred to or described as a program, software, software application, module, software module, script or code, may be written in any form of programming language, including compiled or interpreted languages, or declarative or procedural languages, and translated into a suitable quantum programming language, or may be written in a quantum programming language, such as QCL or Quipper.

[0086] A digital and / or quantum computer program may, but need not, correspond to a file in a file system. The program may be stored in a portion of a file that holds other programs or data, such as one or more scripts stored in a markup language document, in a single file dedicated to the program in question, or in multiple coordinated files, such as files storing one or more modules, subroutines, or portions of code. A digital and / or quantum computer program may be deployed to be executed on a digital or quantum computer or on multiple digital and / or quantum computers located at one location or distributed at multiple locations and interconnected by a digital and / or quantum data communication network. A quantum data communication network is understood to be a network that can transmit quantum data using quantum systems (e.g., qubits). Generally, a digital data communication network cannot transmit quantum data, but a quantum data communication network can transmit quantum data and digital data.

[0087] The processes and logic flows described in this specification may be performed by one or more programmable digital and / or quantum computers, operating in conjunction with one or more digital and / or quantum processors where appropriate, executing one or more digital and / or quantum computer programs to perform functions by operating on input digital and quantum data and generating output. The processes and logic flows may also be performed by dedicated logic circuits, and the apparatus may also be implemented as dedicated logic circuits, such as FPGAs or ASICs, or quantum simulators, or by a combination of dedicated logic circuits or quantum simulators and one or more programmed digital and / or quantum computers.

[0088] For a system of one or more digital and / or quantum computers, "configured to" perform a particular operation or action means that the system has installed thereon software, firmware, hardware, or a combination thereof that, in operation, causes the system to perform those operations or actions. For one or more digital and / or quantum computer programs configured to perform a particular operation or action, it means that the one or more programs include instructions that, when executed by a digital and / or quantum data processing device, cause the device to perform the operation or action. A quantum computer can receive instructions from a digital computer that, when executed by the quantum computing device, cause the device to perform the operation or action.

[0089] A digital and / or quantum computer suitable for executing a digital and / or quantum computer program may be based on a general or special purpose digital and / or quantum processor or both, or any other type of central digital and / or quantum processing unit. In general, the central digital and / or quantum processing unit will receive instructions and digital and / or quantum data from a read-only memory, a random access memory or a quantum system suitable for transmitting quantum data (e.g., photons or a combination thereof).

[0090] The elements of a digital and / or quantum computer include a central processing unit for performing or running instructions and one or more memory devices for storing instructions and digital and / or quantum data. The central processing unit and the memory can be supplemented or incorporated into a dedicated logic circuit or a quantum simulator. Generally, a digital and / or quantum computer will also include or be operably coupled to receive digital and / or quantum data from one or more large-capacity storage devices for storing digital and / or quantum data, or transmit digital and / or quantum data to one or more large-capacity storage devices, such as magnetic, magneto-optical disks, optical disks, or quantum systems suitable for storing quantum information. However, a digital and / or quantum computer does not require such a device.

[0091] Quantum circuit elements (also called quantum computing circuit elements) include circuit elements for performing quantum processing operations. That is, quantum circuit elements are configured to exploit quantum mechanical phenomena, such as superposition and entanglement, to perform operations on data in a non-deterministic manner. Certain quantum circuit elements, such as qubits, can be configured to represent and manipulate information in multiple states simultaneously. Examples of superconducting quantum circuit elements include circuit elements such as quantum LC oscillators, qubits (e.g., flux qubits, phase qubits, or charge qubits), and superconducting quantum interference devices (SQUIDs) (e.g., RF-SQUIDs or DC-SQUIDs).

[0092] In contrast, classical circuit elements generally process data in a deterministic manner. Classical circuit elements can be configured to collectively execute the instructions of a computer program by performing basic arithmetic, logic, and / or input / output operations on data, where the data is represented in analog or digital form. In some embodiments, classical circuit elements can be used to transmit data to and / or receive data from quantum circuit elements via electrical or electromagnetic connections. Examples of classical circuit elements include CMOS-based circuit elements, rapid single flux quantum (RSFQ) devices, reciprocal quantum logic (RQL) devices, and ERSFQ devices, which are energy-efficient versions of RSFQ that do not use bias resistors.

[0093] In some cases, some or all of the quantum and / or classical circuit elements may be implemented using, for example, superconducting quantum and / or classical circuit elements. The manufacture of superconducting circuit elements may require the deposition of one or more materials (such as superconductors, dielectrics and / or metals). Depending on the selected material, these materials can be deposited using deposition processes (such as chemical vapor deposition, physical vapor deposition (e.g., evaporation or sputtering) or epitaxial techniques and other deposition processes). The process described herein for manufacturing circuit elements may require one or more materials to be removed from the device during manufacture. Depending on the material to be removed, the removal process may include, for example, wet etching techniques, dry etching techniques or stripping processes. The material of the circuit elements described herein may be patterned using known lithographic techniques (e.g., photolithography or electron beam lithography).

[0094] During operation of a quantum computing system using superconducting quantum circuit elements and / or superconducting classical circuit elements (such as the circuit elements described herein), the superconducting circuit elements are cooled in a cryostat to a temperature that allows the superconductor material to exhibit superconducting properties. Superconductor (alternatively, superconducting) materials can be understood as materials that exhibit superconducting properties at or below the superconducting critical temperature. Examples of superconducting materials include aluminum (superconducting critical temperature of 1.2 Kelvin) and niobium (superconducting critical temperature of 9.3 Kelvin). Therefore, superconducting structures (such as superconducting traces and superconducting ground planes) are formed of materials that exhibit superconducting properties at or below the superconducting critical temperature.

[0095] In certain embodiments, control signals for quantum circuit elements (e.g., qubits and qubit couplers) may be provided using classical circuit elements that are electrically and / or electromagnetically coupled to the quantum circuit elements. The control signals may be provided in digital and / or analog form.

[0096] Digital and / or quantum computer readable media suitable for storing digital and / or quantum computer program instructions and digital and / or quantum data include all forms of non-volatile digital and / or quantum memory, media and memory devices, including, for example, semiconductor memory devices, such as EPROM, EEPROM and flash memory devices; magnetic disks, such as internal hard disks or removable disks; magneto-optical disks; CD-ROM and DVD-ROM disks; and quantum systems, such as trapped atoms or electrons. It should be understood that quantum memory is a device capable of storing quantum data for a long time with high fidelity and efficiency, such as a light-matter interface, where light is used for transmission and matter is used to store and preserve quantum characteristics of quantum data, such as superposition or quantum coherence.

[0097] The control of the various systems or portions thereof described in this specification may be implemented in a digital and / or quantum computer program product that includes instructions stored on one or more non-transitory machine-readable storage media and that may be executed on one or more digital and / or quantum processing devices. The systems or portions thereof described in this specification may each be implemented as an apparatus, method, or system that may include one or more digital and / or quantum processing devices and memory to store executable instructions to perform the operations described in this specification.

[0098] Although this specification contains a number of specific implementation details, these details should not be interpreted as limitations on the scope of the claimed protection, but rather as descriptions of the features of a particular implementation. Certain features described in this specification in the context of separate embodiments may also be implemented in combination in a single embodiment. Conversely, the various features described in the context of a single embodiment may also be implemented in multiple embodiments individually or in any suitable sub-combination. In addition, although features may be described above as working in certain combinations, and even initially claimed as such, in some cases, one or more features from the claimed combination may be deleted from the combination, and the claimed combination may be directed to a sub-combination or a variant of a sub-combination.

[0099] Similarly, although operations are described in a particular order in the accompanying drawings, this should not be understood as requiring that the operations be performed in the particular order shown or sequentially, or that all of the operations shown be performed, to achieve the desired results. In some cases, multitasking and parallel processing may be advantageous. In addition, the separation of various system modules and components in the above implementations should not be understood as requiring such separation in all embodiments, and it should be understood that the described program components and systems can generally be integrated together in a single software product or packaged into multiple software products.

[0100] Particular implementations of the subject matter have been described. Other implementations are within the scope of the following claims. For example, the actions recited in the claims can be performed in a different order and still achieve the desired results. As an example, the processes described in the accompanying drawings do not necessarily require the particular order or sequence shown to achieve the desired results. In some cases, multitasking and parallel processing may be advantageous.

Claims

1. A device comprising: a first data qubit; a second data qubit, wherein a first portion of the first data qubit is separated from a first portion of the second data qubit by a gap; a tunable qubit coupler arranged to couple to the first data qubit and to the second data qubit such that during operation of the device the tunable qubit coupler allows tunable coupling between the first data qubit and the second data qubit, wherein the tunable qubit coupler comprises a single-ended transmon qubit; a first substrate, wherein the first data qubit and the second data qubit are on a major surface of the first substrate; and and a second substrate spaced apart from and coupled to the first substrate, wherein the tunable qubit coupler is on a major surface of the second substrate and is arranged to overlap the first portion of the first data qubit, the first portion of the second data qubit, and the gap.

2. The apparatus of claim 1, wherein the tunable qubit coupler is arranged on a first axis, wherein the first axis: orthogonal to a second axis connecting the first data qubit and the second data qubit; and Intersecting the second axis between the first data qubit and the second data qubit.

3. The apparatus according to claim 1, wherein the pressure in the space between the first substrate and the second substrate is less than 10 -5 Entrust.

4. The apparatus of claim 1 , wherein the tunable qubit coupler comprises a superconducting quantum interference device (SQUID).

5. The apparatus of claim 1, wherein the first data qubit and the second data qubit comprise a first differential qubit and a second differential qubit, respectively. 6 . The apparatus of claim 1 , wherein the major surface of the first substrate faces the major surface of the second substrate.

7. The device of claim 1 , wherein the first data qubit and the second data qubit are arranged on the major surface of the first substrate such that during operation of the device, the first data qubit and the second data qubit are directly coupled.

8. The apparatus of claim 1, wherein the first data qubit is a single-ended transmon qubit.

9. The apparatus of claim 8, wherein the second data qubit is a single-ended transmon qubit.

10. The apparatus of claim 1, wherein the tunable qubit coupler comprises a superconductor island at least partially surrounded by a ground plane.

11. The apparatus of claim 1 , wherein the tunable qubit coupler comprises: Tunable nonlinear oscillator; Capacitors; and Superconducting quantum interference device SQUID.

12. The apparatus of claim 1, wherein the tunable qubit coupler comprises a shunt capacitor.

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