Coplanar Waveguide Flux Qubits

Abstract

The present invention provides a coplanar waveguide flux qubit. [Solution] The quantum bit device includes an elongated thin film uninterrupted by a Josephson junction, a quantum device in electrical contact with the proximal end of the elongated thin film, and a ground plane coplanar with the elongated thin film and in electrical contact with the distal end of the elongated thin film, wherein the thin film, the quantum device, and the ground plane include materials that become superconducting at a designed operating temperature.

Description

[Technical field]

[0001] The present invention relates to coplanar waveguide flux qubits. [Background technology]

[0002] Quantum computing is a relatively new method of computing that exploits quantum effects such as superposition of fundamental states with entanglement to perform certain calculations more efficiently than classical digital computers. In contrast to digital computers, which store and manipulate information in the form of bits (e.g., "1" or "0"), quantum computing systems can manipulate information using quantum bits. A quantum bit can refer to a quantum device that allows for the superposition of multiple states (e.g., data in both "0" and "1" states) and / or the superposition of multiple states of data itself. According to conventional terminology, the superposition of "0" and "1" states in a quantum system can be represented, for example, as α│0>+β│0>. The "0" and "1" states of a digital computer are analogous to the fundamental states │0> and │1> of a quantum bit, respectively. The value │α│ 2 represents the probability that the qubit is in the │0〉 state, whereas the value │β│ 2 represents the probability that the qubit is in the │1> fundamental state. Summary of the Invention [Means for solving the problem]

[0003] The present disclosure relates to coplanar waveguide flux qubits. In general, in a first aspect, the subject matter of the present disclosure may be embodied in a qubit device that includes an elongated thin film uninterrupted by Josephson junctions, a quantum device (e.g., a superconducting quantum interference device (SQUID)) in electrical contact with a proximal end of the elongated thin film, and a ground plane that is coplanar with the elongated thin film and in electrical contact with a distal end of the elongated thin film, where the thin film, the quantum device, and the ground plane include materials that are superconducting at a designed operating temperature.

[0004] Implementations of qubit devices may optionally include one or more of the following features, alone or in combination. For example, in some implementations, the elongated thin film includes a first side and an opposing second side, each of the first side and the second side being separated from the superconducting ground plane by a respective gap. The width of each gap may be constant along the length of the elongated thin film.

[0005] In some implementations, the elongated thin film, the superconducting loop, and the ground plane each comprise aluminum or niobium.

[0006] In some implementations, the quantum device includes a superconducting loop interrupted by at least one Josephson junction. The quantum device may include only two Josephson junctions interrupting the superconducting loop.

[0007] In some implementations, the qubit further includes a substrate, and the elongated thin film, the ground plane, and the quantum device are on a surface of the substrate. The substrate may include sapphire.

[0008] In some implementations, the elongated thin film includes a first portion that extends along a first direction and a second portion that extends along a second, distinct direction.

[0009] In general, in another aspect, the subject matter of the present application may be embodied in a quantum bit device comprising an elongated thin film including a first portion extending along a first direction and a second portion extending along a second direction, the quantum bit device comprising an uninterrupted elongated thin film with a Josephson junction, a quantum device (e.g., a SQUID) in electrical contact with the elongated thin film at a location between the first portion and the second portion, and a ground plane coplanar with and in electrical contact with the elongated thin film, the thin film, the quantum device, and the ground plane comprising materials that are superconducting at a designed operating temperature.

[0010] In general, in another aspect, the subject matter of the present application may be embodied in a qubit control system including a qubit device having (a) an elongated thin film uninterrupted by Josephson junctions, (b) a quantum device (e.g., a SQUID) in electrical contact with a proximal end of the elongated thin film, and (c) a ground plane coplanar with the elongated thin film and in electrical contact with a distal end of the elongated thin film, the thin film, the quantum device, and the ground plane including materials that are superconducting at a designed operating temperature. The qubit control system further includes a qubit bias control device adjacent to the elongated thin film such that it is inductively coupled to the elongated thin film during operation, and a quantum device bias control device adjacent to the quantum device of the qubit device such that it is inductively coupled to the quantum device during operation.

[0011] Implementations of the qubit device may optionally include one or more of the following features, alone or in combination: For example, in some implementations, the qubit bias control device is in electrical contact with the elongated superconducting thin film.

[0012] In some implementations, the qubit bias control device includes a shunt, which may include a plurality of inductors, and may include a central thin film trace and outer thin film traces that form an open loop surrounding the central thin film trace and are in electrical contact with the elongated thin film, with ends of the central thin film trace in electrical contact with the outer thin film trace at multiple different locations along the open loop.

[0013] In some implementations, the quantum device bias control device can include an inner thin film loop and an outer thin film loop at least partially surrounding the inner thin film loop and in electrical contact with the quantum device.

[0014] In some implementations, the qubit bias control device has a mutual inductance with respect to the elongated thin film of between about 0.1 pH and 0.2 pH.

[0015] In some implementations, the quantum device bias control device has a mutual inductance of about 0 pH with respect to the quantum device.

[0016] In general, in another aspect, the subject matter of this disclosure relates to a quantum processor including a plurality of coplanar waveguide flux qubit devices, each coplanar waveguide flux qubit device having (a) an elongated thin film waveguide uninterrupted by a Josephson junction, (b) a quantum device (e.g., a SQUID) in electrical contact with a first end of the elongated thin film waveguide, and (c) a ground plane coplanar with and in electrical contact with the elongated thin film waveguide, wherein each coplanar waveguide flux qubit device in the quantum processor is operatively coupled to each other.

[0017] Implementations of the qubit device may optionally include one or more of the following features, alone or in combination. For example, in some implementations, in the processor, the elongated thin film waveguide of each coplanar waveguide flux qubit intersects with multiple elongated thin film waveguides associated with other coplanar waveguide flux qubits. The quantum processor may further include multiple inductive couplers, each inductive coupler disposed adjacent an intersection between two elongated thin film waveguides associated with different coplanar waveguide flux qubits.

[0018] The subject matter of the present disclosure may have various advantages. For example, in some implementations, a coplanar waveguide flux qubit may exhibit a relatively long decoherence time. Without wishing to be bound by theory, it is believed that the improvement in decoherence time is due in part to the coplanar waveguide flux qubit utilizing primarily a single layer of superconducting material to form the flux qubit. The use of a single layer of superconducting material on a substrate eliminates a source of decoherence that would otherwise be present due to an additional layer of material. Similarly, the dielectric material typically used to form Josephson junctions is also believed to be a significant source of decoherence in flux qubits. Thus, by replacing the third Josephson junction of a persistent current flux qubit with a coplanar waveguide, an additional source of decoherence is eliminated and the decoherence time associated with the qubit may be significantly increased.

[0019] In addition, in some implementations, the coplanar waveguide flux qubit allows coupling to many more qubits. In particular, the coupling to the coplanar waveguide flux qubit is achieved by inductive coupling to the waveguide portion of the qubit. Because the inductance and capacitance of the waveguide are distributed over a macroscopic length (several mm), the number of qubits that can be coupled can be increased significantly.

[0020] The use of two or more coplanar waveguides with a flux qubit may also provide various advantages. For example, in certain implementations, the use of two or more symmetric coplanar waveguides within a flux qubit may provide a stronger σ x σ x Moreover, by separating the measurement and bias connections, the amount of crosstalk can be reduced. In addition, the use of more than one coplanar waveguide per qubit can increase the number of qubits coupled in a complete connectivity graph, potentially by at least a factor of two.

[0021] Furthermore, in some implementations, by adjusting certain geometric aspects of the control device, it is possible to improve the coupling of the control device to the flux qubit or quantum device, reduce crosstalk / coupling with other qubits in the qubit bias control device and connection network, and reduce sources of decoherence.

[0022] The details of one or more embodiments are set forth in the accompanying drawings and the description below. Other features and advantages will become apparent from the description, drawings, and claims. [Brief description of the drawings]

[0023] [Figure 1A] FIG. 1 is a schematic diagram illustrating an example of a superconducting phase qubit. [Figure 1B] 1B is a graph illustrating a double-well potential for the superconducting phase qubit of FIG. 1A. [Figure 2A] FIG. 1 is a schematic diagram illustrating a top view of an example coplanar waveguide flux qubit. [Figure 2B] FIG. 2B is a close-up view of a superconducting quantum interference device (SQUID) used in the coplanar waveguide flux qubit of FIG. 2A. [Figure 2C] FIG. 2B is a schematic diagram showing a circuit diagram representing the coplanar waveguide flux qubit of FIG. 2A. [Diagram 3] FIG. 1 is a schematic diagram showing a circuit diagram of a control system for a coplanar waveguide flux qubit device. [Figure 4] FIG. 1 is a schematic diagram illustrating a top view of an exemplary qubit bias control device coupled to the end of a coplanar waveguide. [Diagram 5] FIG. 5 is a schematic diagram showing an equivalent circuit diagram of the quantum bit drive control device and the waveguide shown in FIG. [Figure 6] FIG. 1 is a schematic diagram illustrating a top view of an exemplary qubit bias control device coupled to the end of a coplanar waveguide. [Figure 7A]7 is a graph illustrating the calculated mutual inductance M for a qubit bias control device having the design shown in FIG. [Figure 7B] 7 is a graph illustrating the calculated mutual inductance M for a qubit bias control device having the design shown in FIG. [Figure 8] FIG. 1 is a schematic diagram illustrating a top view of an exemplary SQUID bias control device coupled to a DC-SQUID of a coplanar waveguide flux qubit. [Figure 9A] 9 is a graph showing the mutual inductance for a CPW mode of a coplanar waveguide calculated for a control device of a SQUID having the design shown in FIG. 8 . [Figure 9B] 9 is a graph showing the mutual inductance for a DC-SQUID calculated for a control device of a SQUID having the design shown in FIG. 8 . [Figure 10A] FIG. 1 is a schematic diagram illustrating an example of a multi-co-planar waveguide flux qubit that includes a DC-SQUID in electrical contact with / coupled to two grounded co-planar waveguides. [Figure 10B] FIG. 10B is a circuit diagram representing the coplanar waveguide flux qubit of FIG. 10A. [Figure 11] FIG. 1 is a schematic diagram illustrating a top view of an exemplary multi-branch flux qubit. [Figure 12] FIG. 1 is a schematic diagram showing a network diagram of an exemplary network of interconnected single-branch coplanar waveguide flux qubits. [Figure 13] FIG. 1 is a schematic diagram illustrating a network diagram of an exemplary network of interconnected multi-branch coplanar waveguide flux qubits. [Figure 14] FIG. 1 is a schematic diagram showing a network diagram of an exemplary fully-connected quantum network of self-connected multi-branch coplanar waveguide flux qubits. [Figure 15A] FIG. 15 is a computer-aided design schematic illustrating a top view of an exemplary quantum processor layout 1500 that relies on an interconnected network of coplanar waveguide flux qubits. [Figure 15B] FIG. 15B is a schematic diagram showing a close-up view of a single coplanar waveguide coupled to the qubit bias control device of FIG. 15A and the bias control device of the SQUID. [Figure 15C] FIG. 15B is a schematic diagram showing an enlarged view of a portion of the readout device area of ​​FIG. 15A. [Figure 15D] FIG. 15B is a schematic diagram showing an expanded view of a portion of the coupling region of the quantum processor of FIG. 15A. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0024] A flux qubit is an example of a qubit that can be realized using superconducting materials in a physical system. Flux qubits store information in the phase state or flux state of the device. One example of a flux qubit is a persistent current qubit, which includes a loop of superconducting material interrupted by three Josephson junctions. FIG. 1A is a schematic diagram of an example of a persistent current flux qubit 100. The persistent current flux qubit 100 includes a loop 102 of superconducting material interrupted by multiple Josephson junctions 104, 106, and 108. Each Josephson junction has a particular critical current.

[0025] During operation of qubit 100, a magnetic flux Φ x A source 110 can be used to introduce the magnetic flux BΦ 0 Φ 0 is the magnetic flux quantum and B is a dimensionless number. Magnetic flux Φ xWhen applying a potential V , qubit 100 exhibits a two-dimensional potential with respect to the phase across the Josephson junction. Regions of local energy minima that may be included in the two-dimensional potential are separated from each other by relatively small energy barriers and from other regions by relatively large energy barriers. An example of such a double-well potential is shown in FIG. 1B. Well 112 on the left represents a current circulating in one direction (e.g., clockwise) through the loop of qubit 100, and well 114 on the right represents a current traveling in the opposite direction (e.g., counterclockwise) through the loop. When wells 112 and 114 exhibit the same or nearly the same potential energy as shown in FIG. 1B, the two different states of qubit 100 (persistent clockwise and counterclockwise currents through the superconducting loop) may be referred to as being in superposition.

[0026] Quantum computing requires coherent processing of quantum information stored in qubits of a quantum computer. In particular, the qubits of a quantum computer are coupled to each other in a controllable manner such that the quantum state of each qubit affects the corresponding quantum state of the coupled qubit. The computational power of a quantum computer can be improved considerably when the number of other qubits that can be coupled to one qubit is increased. For certain designs, such as persistent current flux qubits, the number of qubits available for coupling is limited to the qubit's nearest neighbors. Moreover, interactions with other qubits provide a potentially strong source of decoherence, leading to shorter decoherence times for qubits. The decoherence time corresponds to the period of time it takes for a qubit to lose some of its quantum mechanical properties, e.g., to no longer be characterized by a superposition of fundamental states and to be unable to be used for quantum computing. Another source of decoherence includes noise arising from the materials used to construct the qubits, such as the dielectrics that form the Josephson junctions. These effects can lead to short decoherence times for flux qubits (e.g., on the order of 10 nanoseconds).

[0027] overview In general, in some embodiments, a flux qubit encompassed by the subject matter of the present disclosure includes at least one elongated coplanar waveguide resonator coupled to a superconducting quantum interference device. The elongated coplanar waveguide serves as a parallel LC resonant circuit that determines the energy level of the qubit. Coplanar waveguide flux qubits can exhibit substantial improvements in decoherence times due to their relatively simple structure and elimination of materials that act as sources of decoherence. Moreover, because the waveguide can be fabricated to have a relatively long overall length while retaining the ability to strongly couple to other qubits, coplanar waveguide flux qubits can be used to couple to many other qubits in a connected quantum network.

[0028] In some aspects, the subject matter of this disclosure also encompasses a control system for a coplanar waveguide flux qubit, the control system including a qubit bias control device and a quantum device bias control device (e.g., a SQUID bias control device). The qubit bias control device may include a shunt that is tuned to optimize its mutual inductance of the flux qubit to the coplanar waveguide, resulting in a substantially longer decoherence time. The quantum device bias control device may include a relatively concentric loop of a superconducting thin film disposed adjacent to the flux qubit. Varying various geometric aspects of the control device may improve coupling of the control device to the flux qubit or quantum device (e.g., a SQUID), reduce crosstalk / coupling to the qubit bias control device and other qubits in the connection network, and reduce sources of decoherence.

[0029] In some aspects, the subject matter of the present disclosure encompasses connected quantum networks of coplanar waveguide flux qubit devices. The modular design that the network may have allows for each qubit to add or remove the number of other qubits available for coupling along the length of the coplanar waveguide. Moreover, in some implementations, the connected quantum network may employ a flux qubit design with multiple coplanar waveguides, each of which may be used to couple to other qubits in the network. Thus, additional waveguides may provide the option to increase the number of qubits that can be coupled together, providing greater flexibility in the design of the connected quantum network.

[0030] Coplanar Waveguide Flux Qubits 2A is a schematic diagram showing a top view of an example of a coplanar waveguide flux qubit 200. Qubit 200 includes a coplanar waveguide 202 coupled to a quantum device 204. Quantum device 204 may include, but is not limited to, a superconducting quantum interference device (SQUID). In this example, quantum device 204 is a DC superconducting quantum interference device (DC-SQUID), although other SQUID devices may be used. Coplanar waveguide 202 and DC-SQUID 204 are in electrical contact with a surrounding ground plane 206. Each of waveguide 202, DC-SQUID 204, and ground plane 206 are formed from superconducting thin-film material using standard thin-film fabrication processes on a dielectric substrate. The waveguide 202 is configured as an elongated thin film on a substrate, with one end 208 of the film in electrical contact with a ground plane 206 and another opposite end 210 of the film in electrical contact with a DC-SQUID 204. The elongated faces of the waveguide 202 are separated from the ground plane 206 by corresponding gaps 205. In this example, the width of each gap 205 is constant along the length of the elongated waveguide, e.g., to prevent unwanted reflections of electromagnetic waves. The desired mode profile of the waveguide is a symmetric coplanar waveguide (CPW) mode, with the two ground planes on either side of the central trace held at the same voltage. In some implementations, the waveguide 202 can have a length (measured along the elongated faces) up to about several thousand micrometers and a width (measured transversely to the length) up to about tens of micrometers. The thickness of the deposited film forming the waveguide 202 (as well as the ground plane 206 and portions of the DC-SQUID) may be, for example, about 100-200 nm.

[0031] In some implementations, the end of the waveguide 202 furthest from the DC-SQUID has a hook shape to provide a region for inductively coupling the qubit to a readout device (not shown). Figure 2B is a close-up view of a DC-SQUID 204 coupled to the waveguide 202. The DC-SQUID 204 includes a loop 212 of superconducting material interrupted by two Josephson junctions 214, each of which may be formed from a thin film of a non-superconducting / insulating material. For example, the Josephson junctions 214 may be Al / Al2 O 3 The Josephson junctions 214 may be formed from three layers of thin films of ZnO / Al. Thus, the Josephson junctions 214 are coupled in parallel with each other, with a first common node in electrical contact with the waveguide 202 and a second common node in electrical contact with the ground plane 206. The Josephson junctions 214 are electrically connected to the loop 212 through contact pads 215, which may be formed from the same superconducting material as the loop 212 or a different superconducting material. In some implementations, there is no contact pad 215 and the Josephson junctions 214 are in direct physical and electrical contact with the loop 212. Each of the waveguide 202, the DC-SQUID 204, and the ground plane 206 may be formed from a material that exhibits superconducting properties below a superconducting critical temperature, such as aluminum (superconducting critical temperature of 1.2 Kelvin) or niobium (superconducting critical temperature of 9.3 Kelvin). The substrate on which the waveguide 202, the DC-SQUID 204, and the ground plane 206 are formed may be, for example, sapphire, SiO 2 , or a dielectric material such as Si. In some implementations, sapphire has the advantage of having lower dielectric losses and therefore longer decoherence times.

[0032] In some implementations, the coplanar waveguide flux qubit 200 may operate in a manner similar to a persistent current flux qubit. That is, when a magnetic flux is introduced into the coplanar waveguide (by the control device shown in FIG. 4), two persistent current states may be generated that circulate in opposite directions in the coplanar waveguide loop. The waveguide 202 also acts as a resonator, whereby strong and remote coupling to other qubits may be achieved. FIG. 2C is a schematic diagram showing a circuit diagram 216 representing the qubit 200. As shown in the circuit diagram 216, the qubit 200 is associated with both a capacitance 218 and an inductance 220 that are coupled in parallel to two Josephson junctions 214 provided by the DC-SQUID 204. The ground 222 in the circuit diagram 216 is provided by the ground plane 206. In comparison, a persistent current flux qubit incorporating three Josephson junctions that interrupt the superconducting loop is the same circuit diagram as shown in FIG. 2C. In a persistent current flux qubit, two of the Josephson junctions are equivalent to Josephson junctions 214, and the third Josephson junction and the superconducting loop provide both capacitance 218 and inductance 220. In contrast, for a coplanar waveguide flux qubit, such as qubit 200, capacitance 218 and inductance 220 are provided instead by waveguide 202.

[0033] The coplanar waveguide flux qubit design may have several advantages over persistent current flux qubits. For example, coplanar waveguide flux qubits may exhibit relatively long decoherence times. Without being bound by theory, it is believed that the improvement in decoherence times is due in part to the coplanar waveguide flux qubit utilizing primarily a single layer of superconducting material to form the flux qubit. The use of a single layer of superconducting material on a substrate eliminates a source of decoherence that would otherwise be present due to the additional layer of material. Similarly, the dielectric material typically used to form Josephson junctions is also believed to be a significant source of decoherence in flux qubits. Thus, by replacing the third Josephson junction of a persistent current flux qubit with a coplanar waveguide, an additional source of decoherence is eliminated and the decoherence time associated with the qubit may be significantly increased.

[0034] In addition, coplanar waveguide flux qubits allow coupling to many more qubits. In typical persistent current flux qubits, coupling inside a quantum computer is achieved using nearest neighbor devices, effectively limiting the number of qubits available for coupling with qubits that can fit within the area around a single qubit. Due to the limited connections to other qubits, quantum processors based on such qubit designs suffer from the so-called embedding problem. This means that computational problems need to be programmed on the machine subject to the constraints of the Chimera graph. Solving the embedding problem can be a computationally challenging task in itself, further limiting the power of quantum annealers.

[0035] In contrast, coupling with a coplanar waveguide flux qubit is achieved by inductive coupling to the waveguide portion of the qubit. Because the inductance and capacitance of the waveguide are distributed over a macroscopic length (several mm), the number of qubits that can be coupled can be significantly increased, thus potentially avoiding embedding problems. Moreover, persistent current flux qubits are typically very small, related to mesoscopic scale sizes (e.g., with critical dimensions on the order of a few microns or less). However, coplanar waveguide flux qubit structures can be made much larger (e.g., on the order of a few millimeters), resulting in higher manufacturing reliability.

[0036] Quantum Bit Control System During operation of the coplanar waveguide flux qubit, the qubit may be exposed to different flux biases for the purposes of initializing the potential of the qubit's double well, establishing a superposition of fundamental states, and varying the barrier between the potential wells to vary the probability of tunneling between the states, among other actions. Such flux biases may be generated using a flux bias drive device located adjacent to the qubit device. FIG. 3 is a schematic diagram showing a circuit diagram of a control system 300 for a flux qubit device. The control system 300 includes a qubit bias control device 302 that is inductively coupled to the coplanar waveguide of the qubit 304 during operation of the qubit 304. The qubit bias control device 302 serves to tilt / perturb the qubit's double well potential during operation. The control system 300 also includes a SQUID bias control device 306 that is inductively coupled to the DC-SQUID during operation of the qubit 304. The SQUID bias control device 306 serves to adjust the critical current of the DC-SQUID, and consequently the magnitude of the barrier potential between the qubit wells during operation. Because both the qubit bias control device 302 and the SQUID bias control device 306 are used during operation of the qubit 304, in some implementations it is desirable to reduce crosstalk between these control devices and between other qubits in the quantum processor to prevent unintended introduction of magnetic flux and to reduce decoherence.

[0037] FIG. 4 is a schematic diagram illustrating a top view of an exemplary qubit bias control device 400 coupled to an end of a coplanar waveguide 402 of a flux qubit according to the present disclosure. For ease of representation, only a portion of the waveguide is shown. The other end of the waveguide 402 is coupled to the DC-SQUID (not shown) of the flux qubit. The qubit bias control device 400 includes a current drive line 404 that branches symmetrically along three different paths to a shunt 406. Both the current drive line 404 and the shunt 406 are formed from a superconducting thin film on a substrate surface. For example, the current drive line 404 and the shunt 406 may be formed from the same superconducting material as the waveguide and the DC-SQUID. Current is provided to the qubit bias control device 400 from a current source 405 that is coupled to the current drive line 404. The current source 405 may be fabricated on the same chip / substrate as the flux qubit or may be an external source electrically coupled to the chip. The drive line 404 forms the central / inner trace of the shunt 406 and branches off along three different directions 407 to the outer thin film trace 408. The outer thin film trace 408 forms an open loop surrounding the central thin film trace 404. The outer thin film trace 408 is in electrical contact with the waveguide 402 at 403. The outer ends of the thin film traces 408 are also in electrical contact with a ground plane film 410. Before the drive line 404 reaches the first branch of the shunt 406, it is separated from the outer trace 408 by non-conductive gaps 412 on either side, and thus from the ground plane 410.

[0038] 4, the thin film branch 407 and outer trace 408 of the shunt 406 are symmetrically positioned about the center of the drive line 404. The symmetric structure of the shunt 406 helps the qubit bias control device 400 to couple to the CPW modes of the waveguide 402 and to prevent undesired excitation of slotline modes. In general, excitation of slotline modes can have parasitic effects that couple undesired modes to the qubits and other elements of the quantum processor, thus representing a source of radiation loss, decoherence and crosstalk.

[0039] In some implementations, a crossover air bridge 414 may be fabricated on the device to help suppress undesired slotline modes from the waveguide 402 by keeping the ground planes at the same voltage. The air bridge 414 may be fabricated using conventional semiconductor and lithographic processing techniques. For example, this process may generally involve forming and patterning a removable resist film over the gap in the ground planes (to set the height and placement of the air bridge), depositing a superconducting material (e.g., aluminum) over the resist, patterning the deposited superconductor to form a bridge, and then removing any residual resist. Although referred to as an "air bridge," the space between the bridge and the substrate corresponds to a vacuum rather than air, since the device operates at temperatures associated with the superconducting material. Additionally, although only two air bridges 414 are shown in FIG. 4, additional air bridges may be fabricated to cross over the coplanar waveguide 402 and the drive line 404 to keep a constant voltage across the ground plane 410.

[0040] In addition, the qubit bias control device 400 is also designed to reduce crosstalk, i.e., to allow independent flux biasing of each qubit, to prevent cross-coupling of magnetic fields to adjacent qubits and with the bias control device of the SQUID. Accurate and stable flux biasing is necessary because even small deviations in the applied magnetic flux can result in substantial asymmetries in the double-well potential that prevent the corrective operation of the qubits. To reduce coupling and decoherence, the qubit bias control device 400 is designed to ensure a relatively large real impedance and a relatively small mutual inductance. For example, the qubit bias control device 400 may be designed to provide a mutual inductance M between about 0.1 pH and 0.2 pH. In some implementations, the qubit bias control device may be designed to provide a mutual inductance of about 1 pH or less (e.g., about 0.9 pH or less, about 0.8 pH or less, about 0.7 pH or less, about 0.6 pH or less, about 0.5 pH or less, about 0.4 pH or less, about 0.3 pH or less, about 0.2 pH or less, or about 0.1 pH or less). The qubit bias control device 400 may be designed to provide an effective real impedance of about 10 MΩ or more through impedance transformation. Other ranges may also be used, depending on design criteria.

[0041] During operation of the flux qubit and qubit bias control device 400, a current is provided to the drive line 404 from a current source 405. When the current reaches the shunt 406 from the drive line 404, it is split along different branches 407. By splitting the current along different branches and returning through the outer thin film trace 408, a magnetic field is generated within the open area defined by the trace 408 and the drive line 404. The magnetic flux generated from the magnetic field is then coupled into the waveguide 402. Thus, changing the current within the drive line 404 will change the magnetic flux launched into the CPW mode of the waveguide 402.

[0042] 5 is a schematic diagram showing an equivalent circuit diagram of the quantum bit driving and control device 400 and the waveguide 402 shown in FIG. n where n=1...8. The inductor L 1 corresponds to the inductance due to the central trace / drive line 404, and the inductor L 4 corresponds to the inductance due to the coplanar waveguide 402, and the inductor L 3 corresponds to the inductance of the shared trace between the driver and the shunt, and the inductor L 7 corresponds to the inductance due to the center trace of the bias shunt 407, and L 2 / L 8 / L 5 corresponds to the inductance contributed by the ground plane, and the inductor L 6 corresponds to the inductance of the qubit driving and control device 400 at the point where the magnetic flux couples to the waveguide 402. As shown in the schematic diagram of FIG. 5, the current supplied by the central trace (represented by current source 401) is distributed by shunts to the different inductive elements, resulting in a loop current I 1 , I 2 , and I 3 Therefore, the mutual inductance of the qubit driving control device 400 can be expressed as:

[0043]

number

[0044] In general, if the waveguide 402 is relatively long and capable of coupling to many other qubits, then the inductance L 4 is large because the coplanar waveguide is much longer than the qubit control device, so 2L 4 +L 5 >>L 6 It is reasonable to assume that, so equation (1) can be reduced to

[0045]

number

[0046] Thus, the mutual inductance M can be finely tuned by varying the inductance of the shunt 406. One possible way to vary the inductance is to vary the area of ​​the qubit bias control device 400, for example by varying the height 600 and / or width 602 of the qubit bias control device as shown in FIG.

[0047] FIG 7A is a graph showing the calculated mutual inductance M for a qubit bias control device having a constant width 602 of 20 microns with the design shown in FIG 6. As shown in the graph, increasing the divider height from about 5 μm to about 30 μm reduces the mutual inductance from about 0.6 pH to about 0.1 pH or so. FIG 7B is a graph showing the calculated mutual inductance M for a qubit bias control device having a constant height 600 of 10 microns with the design shown in FIG 6. As shown in the graph, increasing the divider width from about 2 μm to about 8 μm increases the mutual inductance from about 0.1 pH to about 0.3 pH.

[0048] The following Table 1 includes calculated mutual coupling values ​​and qubit decoherence lifetimes for a coplanar waveguide flux qubit having the design shown in Figure 6. As shown in the table, for mutual coupling values ​​as low as 0.1 pH, the qubit decoherence lifetime can increase, for example, to 100 μs.

[0049] [Table 1]

[0050] 8 is a schematic diagram illustrating a top view of an exemplary SQUID bias control device 800 coupled to a DC-SQUID 802 of a coplanar waveguide flux qubit according to the present disclosure. For ease of representation, only a portion of the coplanar waveguide 803 is shown. The other end of the waveguide 803 may be coupled to the qubit bias control device. The SQUID bias control device 800 includes an inner thin film loop 804 and an outer thin film loop 806 that at least partially surrounds the inner thin film loop 804 and is in electrical contact with the DC-SQUID 802. Both the inner thin film loop 804 and the outer thin film loop 806 are formed from a superconducting thin film on a substrate surface. For example, the inner thin film loop 804 and the outer thin film loop 806 may be formed from the same superconducting material as the waveguide and the DC-SQUID. The area between the inner and outer thin film loops corresponds to outer gap region 808, and the area inside the inner thin film loop corresponds to inner gap region 810. Both inner gap region 810 and outer gap region 808 correspond to vacuum. One end of inner thin film loop 804 is in electrical contact with drive line 812. Drive line 812 is coupled to current source 814. Current source 814 may be fabricated on the same chip / substrate as the flux qubits or may be an external source electrically coupled to the chip. The other opposite end of inner thin film loop 804 is in electrical contact with outer thin film loop 806. Outer thin film loop 806 is in electrical contact with the loop of DC-SQUID 802 and is in electrical contact with ground plane 805.

[0051] In some implementations, the SQUID bias control device 800 allows for sufficiently strong coupling to the DC-SQUID loop (e.g., about 1-2 pH) while weakly coupling to the CPW modes of the coplanar waveguide that may otherwise be a source of crosstalk and decoherence. Some aspects of the SQUID bias control device 800 can be varied to achieve sufficient coupling to the DC-SQUID while reducing coupling to the CPW modes of the coplanar waveguide. For example, a first variable aspect is the distance of the outer gap region 808 between the outer thin film loop 804 and the inner thin film loop 802. For a SQUID bias control device formed from rectilinear inner and outer loops such as that shown in FIG. 8, the size of the outer gap region 808 can be adjusted by varying the distance 816 between the inner and outer thin film loops. By varying the distance 816, the coupling strength can be varied. As the distance increases, the coupling strength increases and eventually saturates at a value that depends on the particular device design.

[0052] The second variable aspect is the size of the inner gap region 810. Varying the inner gap region 810 can actually change two different characteristics of the SQUID bias control device 800. For example, by varying the distance 818 that the inner thin film loop 804 extends horizontally from the drive line 812, the coupling strength of the SQUID bias control device to the CPW mode of the coplanar waveguide 802 can be changed. In fact, for a particular distance 818, the coupling to the CPW mode can be reduced to zero. In addition, it is possible to change the sensitivity of the SQUID bias control device 800 to imperfections in device fabrication. In particular, by adjusting the distance 820 between the top and bottom of the inner thin film loop 804, the coupling strength to the CPW mode can be changed, and the coupling to the DC-SQUID changes with the change in the distances 816, 818. In other words, even if there are relatively significant changes in the structure of the fabricated device from the intended device design, the SQUID bias control device 800 can be designed such that the desired coupling to the DC-SQUID and CPW modes does not change significantly.

[0053] FIG. 9A is a graph showing mutual inductance versus length 818 for a CPW mode of a coplanar waveguide, calculated for a control device of a SQUID having the design shown in FIG. 8. As shown in the graph, when the distance 816 (graph G) and the distance 820 (graph H) are both 10 μm, the mutual inductance can be reduced to zero when the length 818 is around 8 μm. FIG. 9B is a graph showing mutual inductance versus length 818 for a DC-SQUID, calculated for a control device of a SQUID having the design shown in FIG. 8. As shown in the graph, when the distance 816 (graph G) and the distance 820 (graph H) are both 10 μm, the mutual inductance is almost constant even when the length 818 changes by an order of magnitude.

[0054] Multibranch coplanar waveguide flux qubits As described above with reference to FIG. 2, a coplanar waveguide flux qubit includes a single elongated waveguide for coupling to other qubits internal to a quantum processor. However, the flux qubit design is not limited to a single waveguide. Instead, the flux qubit may include multiple coplanar waveguides coupled to a DC-SQUID. The multi-waveguide flux qubit design has several advantages over the single-waveguide design, including, for example, (1) the ability to couple to a larger number of qubits in a fully connected setup (e.g., using two waveguides instead of one can double the number of qubits that can be coupled in a fully connected quantum processor), (2) readout / measurement lines and bias lines can be coupled to different coplanar waveguides for each qubit, thus reducing crosstalk, and (3) the ability to compensate for asymmetries in the mutual inductance coupling between qubits, allowing for the mutual coupling of more qubits. Indeed, for coplanar waveguide flux qubits with symmetric features of the waveguide resonators, the mutual coupling between the coplanar waveguides can lead to even stronger σ x σ x This may result in bonding.

[0055] 10A is a schematic diagram showing a top view of an exemplary multiple coplanar waveguide flux qubit 1000 including a DC-SQUID 1004 in electrical contact with two coplanar waveguides 1002a and 1002b. The multiple waveguide flux qubit 1000 may be fabricated on a dielectric substrate (e.g., sapphire) using the same or similar materials and in substantially the same manner as the flux qubit disclosed herein with respect to FIG. 2, using thin film processing. Each waveguide 1002a, 1002b is coupled to the DC-SQUID 1004 at a common point 1006, and the opposite end of each waveguide 1002a, 1002b is grounded to a ground plane 1008. Except for the electrical connections to the ground plane 1008 and the DC-SQUID 1004, the waveguides 1002a, 1002b are separated on either side from the thin film ground plane 1008 by a gap having a constant width. Each waveguide 1002a, 1002b also includes a hook-shaped or curved region 1010 near its connection to the ground plane 1008 that can be used, for example, for coupling to a readout device.

[0056] Figure 10B is a circuit diagram representing the coplanar waveguide flux qubit of Figure 10A. Compared to Figure 2C, which is a schematic of a single-waveguide flux qubit, the circuit shown in Figure 10B adds an additional parallel capacitance C due to an additional coplanar waveguide coupled to the DC-SQUID. 2 and inductance L 1 An example of a Hamiltonian describing the flux qubit depicted in FIG. 10B can be derived as follows. First, the exemplary circuit equations for the circuit schematic shown in FIG. 10B are specified as follows:

[0057]

number

[0058] In this formula, I 0 is the critical current of the Josephson junction, Φ is the magnetic flux difference across the junction, and Φ 0 is the magnetic flux quantum, which leads to the Hamiltonian

[0059]

number

[0060] In this formula, L=L 1 L 2 / (L 1 +L 2 ), C=C 1 +C 2 where Q is the charge,

[0061]

number

[0062] The magnetic flux passing through the multi-waveguide flux qubit is the external magnetic flux Φ x =Φ 0 is redefined by biasing the above circuit by / 2.

[0063]

number

[0064] Introducing

[0065]

number

[0066] Where:

[0067]

number

[0068] where e is the charge of the electron. The double-well potential for the flux qubit emerges for β>1. Although the flux qubit 1000 is shown with only two coplanar waveguides, this design can be easily extended to include additional coplanar waveguides, thus allowing for more complex architectures.

[0069] As explained above, a possible advantage of a multi-waveguide flux qubit is that readout / measurement and biasing for individual qubits can be performed using different coplanar waveguides, thus reducing crosstalk. An example multi-branch flux qubit 1100, shown in a schematic top view in FIG. 11, separates readout and biasing operations along different waveguides of the qubit. Flux qubit 1100 may be fabricated on a dielectric substrate (e.g., sapphire) using the same or similar materials, in substantially the same manner, and using thin film processing, as the flux qubits disclosed herein with respect to FIGS. 2 and 10A. Flux qubit 1100 has an identical configuration to flux qubit 1000 shown in FIG. 10A. Flux qubit 1100 also includes a qubit bias control device 1110 in electrical contact with an end of the first coplanar waveguide 1102 a , and a SQUID bias control device 1112 in electrical contact with the DC-SQUID 1104 .

[0070] A second coplanar waveguide 1102b of the flux qubit 1100 is disposed within a coupling distance of a readout device 1114. The readout device 1114 reads the state of the qubit 1100 during a readout operation. In the context of a quantum processor, a readout device such as device 1114 is used to read out the final state of the qubit, for example to yield a bit string. In the implementation shown in FIG. 11, the readout device 1114 includes an elongated thin-film superconductor (e.g., aluminum or niobium) arranged in a serpentine pattern on a dielectric substrate and configured to inductively couple from a first end of the flux qubit 1100 to the second waveguide 1102b. That is, the readout device 1114 may be inductively coupled to the qubit 1100 by the waveguide 1102b during use, rather than being electrically connected directly to the waveguide 1102b (rather than by the relatively weak electrical connection of the ground plane 1106). The separation between the coplanar waveguide and the readout device may be, for example, about 2 microns. At a second, opposite end of the readout device 1114, the readout device may be further coupled to other elements formed on the substrate / chip or external to the substrate / chip, such as routing circuitry (e.g., latch elements, shift registers, or multiplexer circuits).

[0071] Quantum networks connected using flux qubits in coplanar waveguides In some implementations, multiple coplanar waveguide flux qubits are arranged on a substrate surface to form an interconnected quantum processor network. Such a quantum processor network may be used in quantum computing applications, including, for example, quantum annealing and / or adiabatic quantum computing. For example, in some implementations, the quantum processor network may be initialized with a problem's Hamiltonian and adiabatically evolved to a desired Hamiltonian whose ground states describe a solution to the problem of interest.

[0072] A variety of different network configurations are possible employing flux qubit designs according to the present disclosure. For example, FIG. 12 is a schematic diagram showing a network diagram of an exemplary network 1200 of fully interconnected single-branch coplanar waveguide flux qubits 1202. Each flux qubit 1202 includes a single corresponding coplanar waveguide 1204 that allows the qubit to be inductively coupled to all other qubits in the network 1200 at points 1206 where the waveguides cross in the schematic diagram. The coplanar waveguides do not physically contact each other at points 1206. Rather, separate superconducting thin film couplers are fabricated adjacent to each waveguide to enable inductive coupling between the waveguides. Although not shown in FIG. 12, each flux qubit may also include a corresponding qubit bias control device and a SQUID bias control device, such as those described herein. Each flux qubit may also include a qubit readout device inductively coupled to the end of the flux qubit waveguide. The relatively straight forward arrangement of coplanar waveguide flux qubits shown in Figure 14 can be used to significantly increase the number of fully coupled qubits within a quantum processor. For example, a quantum processor incorporating 32 fully coupled coplanar waveguide flux qubits arranged in the configuration shown in Figure 14 will, in certain implementations, have the same quantum processing power as a quantum processor relying on 1000 persistent current flux qubits using a nearest neighbor coupling arrangement.

[0073] In some implementations, multi-branched flux qubits may be used in quantum processors. FIG. 13 is a schematic diagram showing a network diagram of an exemplary network 1300 of interconnected multi-branch coplanar waveguide flux qubits. The sign of the mutual inductance (top and bottom branches) can be positive or negative, the sum of which determines the sign of the overall qubit-qubit coupling. Thus, as shown in FIG. 13, in each flux qubit 1302 contains a corresponding double-branched coplanar waveguide 1304, the first branch of the waveguide couples positively to the first branch of each of the other qubits 1302 of the network 1300 at point 1306. The second branch of each waveguide couples negatively to the second branch of each of the other qubits 1302 of the network 1300 at point 1308. Again, separate superconducting thin-film couplers are fabricated adjacent to each waveguide to enable inductive coupling between the waveguides.

[0074] FIG. 14 is a schematic diagram illustrating a network diagram of another exemplary network 1400 of interconnected multi-branch coplanar waveguide flux qubits. As shown in FIG. 14, the total number of interconnected qubits can be expanded by coupling a first fully-connected network of qubits 1410 to a second fully-connected network of qubits 1420. A "fully-connected qubit network" is a network in which each qubit is arranged such that it can mutually couple with other qubits in the network during operation of the network. In each qubit 1402 of the network 1410, a corresponding double-branch coplanar waveguide includes a first branch 1404 of the waveguide that couples to a first branch of each of the other qubits 1402 of the network 1410 at point 1406. Similarly, in the corresponding double-branched coplanar waveguide of each qubit 1402 of network 1420, a first branch 1404 of the waveguide couples to a first branch of each of the other qubits 1402 of network 1420 at point 1406. Both networks 1410, 1420 are then arranged such that a second branch 1408 of each waveguide from the first network 1410 couples to a second branch 1408 of each waveguide from the second network 1420 at coupling point 1412. Again, separate superconducting thin-film couplers are fabricated adjacent to each waveguide to enable inductive coupling between the waveguides. In addition, each qubit may include a corresponding qubit bias control device and a SQUID bias control device (not shown in FIG. 14), such as those described herein. Each flux qubit may also include a corresponding readout device (not shown) inductively coupled to the first waveguide branch of the qubit. Although the portions of the quantum processor illustrated in Figures 12-14 include only a limited number of quantum bits, a quantum processor may include any desired number of quantum bits that may be appropriately fabricated and disposed on a selected substrate surface.

[0075] FIG. 15A is a computer-aided design schematic showing a top view of an exemplary quantum processor layout 1500 utilizing an interconnected network of coplanar waveguide flux qubits. The quantum processor 1500 includes a ground plane 1520 that covers a large area of ​​the substrate surface and may be divided into several different regions. For example, the processor 1500 may include a control region 1501 that contains an array of qubit bias control devices and SQUID bias control devices. Each coplanar waveguide in the processor layout is adjacently positioned to couple to a corresponding qubit bias control device and SQUID bias control device from the control region 1501. A single coplanar waveguide 1506, shown in a close-up view of FIG. 15B, is positioned such that it may be inductively coupled to the qubit bias control device 1502 and is in electrical contact with the DC-SQUID 1504. The DC-SQUID 1504 is positioned such that it may be inductively coupled to the SQUID bias control device 1507. Waveguide 1506 is separated on either side of its elongated surface from ground plane 1520 by gap 1521. Waveguide 1506, DC-SQUID 1504, qubit bias control device 1502 and SQUID bias control device 1507 may be designed and fabricated in accordance with this disclosure.

[0076] The processor 1500 may also include a readout device region 1503. A close-up view of a portion of the readout device region 1503 including the readout devices 1508 is shown in FIG. 15C. Each of the multiple readout devices 1508 included in the readout device region 1503 is disposed adjacent to a corresponding coplanar waveguide 1506 such that it may be inductively coupled to the waveguide 1506. Each readout device 1508 is, in turn, disposed such that it may be inductively coupled to a readout line 1510. The readout line 1510 is separated from a ground plane 1520 on either side of its elongated surface by a small gap (e.g., about 1-5 microns).

[0077] The processor 1500 may also include a coupling region 1505, which corresponds to a region where the coplanar waveguides of each flux qubit are arranged to couple to one another. A close-up of a portion of the coupling region 1505 is shown in FIG. 15D. At each intersection of the coplanar waveguides, a superconducting thin film coupler 1512 is disposed adjacent the waveguides. The superconducting thin film coupler 1512 includes a loop of superconducting material with a first portion of the loop extending in a first direction 1514 along the first waveguide and a second portion of the loop extending in a second orthogonal direction 1516 along the second waveguide, with a right-angle bend where the first and second waveguides intersect. The first and second waveguides are not in electrical contact at the intersection. Rather, a crossover air bridge 1516 may be used as a jumper for a first waveguide to pass over a second waveguide at the intersection. The loop 1512 is separated from each waveguide by a narrow gap 1518 (e.g., on the order of a few microns). During processor operation, energy from one waveguide couples into the superconducting thin film coupler 1512 and then into a second waveguide located near the coupler 1512. The coupler 1512 is also separated from the ground plane 1520 by a larger gap 1522. The coupler 1512 may be defined with three parameters: trace width W, loop arm length L, and gap distance G (i.e., the inner distance between the loop arms). The trace width W may range from about 1 to 5 microns in some implementations. The loop arm length L may be about hundreds of microns in some implementations depending on the number of qubits in the network. The gap distance G may be about tens of microns in some implementations. Other ranges may be used depending on design criteria.

[0078] The digital and quantum subject matter and digital functional and quantum operation embodiments described herein may be implemented in digital electronic circuitry, suitable quantum circuitry, or more generally in a quantum computing system, in tangibly embodied digital or quantum computer software or firmware, in digital or quantum computer hardware including the structures disclosed herein and equivalents of those structures, or in one or more combinations thereof. The term "quantum computing system" may include, but is not limited to, a quantum computer, a quantum information processing system, a quantum cryptography system, or a quantum simulator.

[0079] Embodiments of the digital and quantum subject matter described herein may be implemented as one or more digital or quantum computer programs, i.e., one or more modules of digital or quantum computer program instructions encoded on a tangible, non-transitory storage medium for execution by or to control the operation of a data processing device. The digital or quantum computer storage medium may be a machine-readable storage device, a machine-readable storage substrate, a random or serial access storage device, one or more quantum bits, or a combination of one or more thereof. Alternatively, or in addition, the program instructions may be encoded on an artificially generated, propagating signal capable of encoding digital or quantum information, such as a machine-generated electrical, optical, or electromagnetic signal to encode the digital or quantum information, for example, for transmission to an appropriate receiver device for execution by a data processing device.

[0080] The terms quantum information and quantum data refer to information or data carried by, held in, or stored in a quantum system, with the smallest nontrivial system being a qubit, i.e., a system that defines a unit of quantum information. The term "qubit" is understood to encompass all quantum systems that can be adequately approximated as a two-level system in the corresponding context. Such quantum systems may include multilevel systems, for example, having more than two levels. By way of example, such systems may include atoms, electrons, photons, ions, or superconducting qubits. In many implementations, the computational base states are associated with ground and a first excited state, however, it is understood that other configurations are possible in which computational states are associated with higher-level excited states. The term "data processing apparatus" refers to digital or quantum data processing hardware and encompasses all kinds of apparatus, devices, and machines for processing digital or quantum data, including by way of 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 special-purpose logic circuitry, such as an FPGA (field programmable gate array), an ASIC (application specific integrated circuit), or a quantum simulator, i.e., a quantum data processing device designed to simulate or generate information about a particular 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 hardware, the device may optionally include code that creates an execution environment for a digital or quantum computer program, such as code constituting a processor firmware, a protocol stack, a database management system, an operating system, or a combination of one or more of these.

[0081] A digital 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 may be arranged in any form, whether as a stand-alone program or included as a module, component, subroutine, or other unit suitable for use in a digital computer 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 may be converted into a suitable quantum programming language, or written in a quantum programming language, such as QCL or Quipper.

[0082] A digital or quantum computer program may, but need not, correspond to a file in a file system. A program may be stored in a portion of a file holding other programs or data, e.g. one or more scripts stored in a markup language document, in a single file dedicated to the program, or in multiple integrated files, e.g. files storing one or more modules, subprograms, or code portions. A digital or quantum computer program may be arranged to be executed on one digital or quantum computer, or on multiple digital or quantum computers located at one site or distributed across multiple sites and interconnected by a digital or quantum data communication network. A quantum data communication network is understood to be a network that may transmit quantum data using quantum systems, e.g. qubits. In general, a digital data communication network cannot transmit quantum data, but a quantum data communication network may transmit both quantum data and digital data.

[0083] One or more programmable digital or quantum computers that may perform the process and logic flows described herein operate using one or more digital or quantum processors, and execute one or more digital or quantum computer programs as needed to perform functions by operating on input digital and quantum data and generating output. The process and logic flows may also be performed by, and devices may be implemented as, special purpose logic circuitry, e.g., an FPGA or ASIC or quantum simulator, or by a combination of special purpose logic circuitry or quantum simulator and one or more programmed digital or quantum computers.

[0084] With respect to one or more digital or quantum computer systems, "configured" to perform a particular operation or act means that the system has installed thereon software, firmware, hardware or a combination thereof that, in operation, causes the system to perform the operation or act. With respect to one or more digital or quantum computer programs, "configured" to perform a particular operation or act means that instructions contained in the one or more programs, when executed by a digital or quantum data processing device, cause the device to perform the operation or act. Instructions that a quantum computer may receive from a digital computer, when executed by a quantum computing device, cause the device to perform an operation or act.

[0085] A digital or quantum computer suitable for executing a digital or quantum computer program may be based on a general purpose or dedicated digital or quantum processor or both, or on any other kind of central digital or quantum processing unit. In general, the central digital or quantum processing unit will receive instructions and digital or quantum data from a read-only memory, a random access memory, or a quantum system, e.g. photons, suitable for transmitting quantum data, or a combination thereof.

[0086] The essential elements of a digital or quantum computer are a central processing unit for executing or executing instructions, and one or more storage devices for storing instructions and digital or quantum data. The central processing unit and storage devices may be supplemented by or incorporated into dedicated logic circuits or quantum simulators. In general, a digital or quantum computer will also include one or more mass storage devices for storing digital or quantum data, such as magnetic disks, magneto-optical disks, optical disks, or quantum systems suitable for storing quantum information, or will be operatively coupled to mass storage devices for receiving digital or quantum data, transferring digital or quantum data, or both. However, a digital or quantum computer may not have such devices.

[0087] Digital or quantum computer-readable media suitable for storing digital or quantum computer program instructions and digital or quantum data include all forms of non-volatile digital or quantum memories, media and storage devices, including, by way of example, semiconductor memory elements, such as EPROM, EEPROM, and flash memory elements, 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 trapped electrons. Quantum memory is understood to be a device capable of storing quantum data with high fidelity and efficiency for long periods of time, such as light-matter interfaces, where light is used for transmission and for storing and preserving quantum properties of quantum data, such as superposition or quantum coherence.

[0088] Control of the various systems or portions thereof described herein may be embodied in a digital or quantum computer program product that includes instructions stored on one or more non-transitory machine-readable storage media and executable on one or more digital or quantum processing devices. The systems or portions thereof described herein may be embodied as an apparatus, method, or system, each of which may include one or more digital or quantum processing devices and a memory device for storing executable instructions to perform the operations described herein.

[0089] Although this specification contains many specific implementation details, these should not be construed as limitations on the scope of what may be claimed, but as descriptions of features that may be specific to a particular embodiment. Certain features described in the context of individual embodiments herein may also be implemented in combination in a single embodiment. Conversely, various features described in the context of a single embodiment may also be implemented separately in multiple embodiments or in any suitable subcombination. Moreover, although each feature may be described above as operating in a particular combination and may even be initially claimed as such, one or more features from a claimed combination may in some cases be deleted from the combination, and the claimed combination may be directed to a subcombination or a variation of the subcombination.

[0090] Similarly, although operations are depicted in a particular order in the figures, this should not be understood as requiring that such operations be performed in the particular order or sequence shown, or that all of the operations depicted be performed, to achieve desirable results. In certain environments, multitasking and parallel processing may be advantageous. Moreover, the separation of various system modules and components in the foregoing embodiments should not be understood as requiring such separation in all embodiments, and it should be understood that the program components and systems described may be integrated together in a single software product or packaged into multiple software products.

[0091] Specific embodiments of the subject matter have been described. Other embodiments 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 desirable results. By way of example, the processes depicted in the accompanying figures do not necessarily require the particular order or sequence shown to achieve desirable results. In some cases, multitasking and parallel processing may be advantageous. [Explanation of symbols]

[0092] 100 Persistent Current Flux Qubits 102 Superconducting material loop 104 Josephson Junction 106 Josephson Junction 108 Josephson Junction 110 Source 112 Well 114 Well 200 Coplanar Waveguide Flux Qubits 202 Coplanar Waveguide 204 Quantum Devices 205 Gap 206 Ground plane 208 One end of the thin film 210 Opposite end of membrane 212 Superconducting material loop 214 Josephson Junction 215 Contact Pad 216 Circuit Diagram 218 Capacitance 220 Inductance 222 Grounding 300 Control System 302 Quantum bit bias control device 304 qubits 306 SQUID Bias Control Device 400 qubit bias control device 401 Current source 402 Waveguide 403 where the outer thin film trace 408 makes electrical contact with the waveguide 402 404 Current Drive Line 405 Current source 406 Flow divider 407 Bias shunt 408 outer thin film traces 410 Ground plane 412 Non-conducting gap 414 Air Bridge 600 Height 602 Width 800 SQUID bias control device 802 DC-SQUID 803 Coplanar Waveguide 804 Inner Membrane Loop 805 Ground plane 806 Outer membrane loop 808 Outer gap area 810 Inner gap area 812 Drive Line 814 Current source 816 Distance between the inner membrane loop and the outer loop 818 is the distance that the inner membrane loop 804 extends horizontally from the drive line 812 820 Distance between the top and bottom of the inner membrane loop 804 1000 Multiple Coplanar Waveguide Flux Qubits 1002a coplanar waveguide 1002b coplanar waveguide 1004 DC-SQUID 1006 Common points 1008 Ground plane 1010 Curved Region 1100 Multi-branch flux qubit 1102a First coplanar waveguide 1102b Second coplanar waveguide 1104 DC-SQUID 1110 qubit bias control device 1114 Readout device 1200 Network 1202 Flux Qubit 1204 Coplanar Waveguide 1206 Intersection Point 1300 Network 1302 Flux Qubit 1304 Coplanar Waveguide 1306 Points 1308 points 1400 Network 1402 qubit 1404 First branch of the waveguide 1406 Points 1408 Second branch of the waveguide 1410 Network 1412 Binding Points 1420 Network 1500 Quantum Processor 1501 Control Region 1502 Quantum bit bias control device 1503 Read Device Area 1504 DC-SQUID 1505 Combined area 1506 Waveguide 1507 SQUID bias control device 1508 Readout Device 1510 read line 1512 Superconducting thin film coupler 1514 First Direction 1516 Second orthogonal direction 1518 Gap 1520 Ground plane 1521 Gap 1522 Gap

Claims

1. a plurality of qubits arranged in a fully connected quantum network, the plurality of qubits including a first group of qubits and a second group of qubits; each qubit of the plurality of qubits comprises a plurality of coupling structures; For each qubit of the first group of qubits, a first coupling structure of the qubit is arranged to be coupled to a corresponding first coupling structure of each of a plurality of other qubits of the first group of qubits; the second coupling structure of the qubits is arranged to be coupled to a corresponding second coupling structure of each qubit of the second group of qubits.

2. For each qubit of the second group of qubits, 10. The apparatus of claim 1, wherein the first coupling structure of the quantum bit is arranged to be coupled to a corresponding first coupling structure of each of the other quantum bits in the second group of quantum bits.

3. The apparatus of claim 1 , wherein each coupling structure of the plurality of coupling structures comprises a coplanar waveguide.

4. 10. The apparatus of claim 1 , wherein the multiple coupling structures for each qubit comprise a double-branched coplanar waveguide.

5. 10. The apparatus of claim 1 , wherein each qubit of the plurality of qubits is a coplanar waveguide flux qubit.

6. 2. The apparatus of claim 1, wherein the first group of qubits are arranged in a first array and the second group of qubits are arranged in a second array, the first array being aligned along a first direction and the second array being aligned along a second direction different from the first direction.

7. The apparatus of claim 6 , wherein the first direction is orthogonal to the second direction.

8. For each qubit of the first group of qubits, the first coupling structure of the qubit is arranged to be coupled to the corresponding first coupling structure of each of the other qubits of the first group of qubits at each coupling position; The device of claim 1 , wherein each binding location includes a corresponding binding element that is separated from both first binding structures at the binding location.

9. 9. The apparatus of claim 8, wherein at each coupling location, a crossover bridge enables one of the first coupling structures at the coupling location to pass over another first coupling structure at the coupling location.

10. The apparatus of claim 8 , wherein each coupling element comprises a thin film coupler.

11. The apparatus of claim 8 , wherein each coupling element comprises a coupler loop.

12. 10. The apparatus of claim 1, wherein each qubit of the plurality of qubits comprises a corresponding readout device.

13. 10. The apparatus of claim 1, wherein each qubit of the plurality of qubits comprises a bias control device.

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