Quantum processing unit with one or more superconducting qubits based on phase-biased linear and nonlinear inductive energy elements

Abstract

The present invention generally relates to the field of quantum computing, and in particular to a quantum processing unit comprising at least one superconducting qubit based on phase-biased linear and nonlinear inductive energy elements. The superconducting phase difference between the linear inductive energy element and the nonlinear inductive energy element is biased, for example, by an external magnetic field, so that the quadratic potential energy terms of the linear and nonlinear inductive energy elements are at least partially cancelled. In a preferred embodiment, such cancellation is at least 30%. By doing so, it is possible to implement the design of a superconducting qubit with high coherence and high anharmonicity.

Description

[Technical Field]

[0001] The present invention generally relates to the field of quantum computing. In particular, the present invention relates to a quantum processing unit comprising at least one superconducting qubit based on phase-biased linear and nonlinear inductive energy elements, and to a quantum computer using one or more such quantum processing units. [Background technology]

[0002] Quantum computing devices, also known as quantum computers, use quantum mechanical phenomena such as superposition and entanglement to solve requested computational tasks. Unlike conventional computers that manipulate information in the form of bits (e.g., "1" or "0"), quantum computers manipulate information using qubits. A qubit refers not only to the basic unit of quantum information, but also to a quantum device used to store information of one or more qubits (e.g., a superposition of "0" and "1").

[0003] Quantum computers can be implemented based on superconducting circuits equipped with superconducting qubits and resonators. For example, there are several types of superconducting qubits, including charge qubits, transmons, persistent current flux qubits, C-shunt flux qubits, phase qubits, fluxonium, and 0-π qubits. Each of these qubit types has both its advantages and disadvantages. For example, charge qubits have high anharmonicity, which is ideal for fast single-qubit operation, but they also suffer from very short coherence times due to harmful phase dissipation resulting from charge noise. Due to their poor coherence characteristics, charge qubits, persistent current flux qubits, and phase qubits are not used in current quantum computers.

[0004] The longest measured relaxation and coherence times of superconducting qubits have been achieved with fluxonium. In fluxonium, Josephson junctions are shunted by a superinductor with large inductance but small capacitance. This inductive shunt renders fluxonium-based circuits immune to low-frequency charge noise. The superinductor of a fluxonium qubit is typically implemented by using a Josephson junction array or a superconducting nanowire with high kinetic inductance. Fluxonium is also well protected from magnetic flux noise that couples to fluxonium-based circuits mainly through the superinductor.

[0005] However, fluxonium can be difficult to implement and operate. The latter, for example, hinders the application of fluxonium in high-speed and accurate quantum logic gates. Furthermore, so-called heavy fluxonium, which is implemented by shunting normal fluxonium with a large geometry capacitor, may require several photon Raman processes to excite the qubit from its ground state to its excited state. Again, the same drawback is inherent to 0-π qubits.

Summary of the Invention

Problems to be Solved by the Invention

[0006] This summary is provided to introduce, in a simplified form, a selection of concepts that are further described in detail below. This summary is not intended to identify key features or essential features of the present invention, nor is it intended to be used to limit the scope of the present invention.

[0007] An object of the present invention is to provide a design of a superconducting qubit having high coherence and high anharmonicity.

Means for Solving the Problems

[0008] The above object is achieved by the features of the independent claims of the appended patent claims. Further embodiments and examples will be apparent from their dependent claims, the detailed description, and the appended drawings.

[0009] According to a first aspect, a quantum processing unit is provided. The quantum processing unit includes a dielectric substrate and at least one superconducting qubit provided on the dielectric substrate. Each of the at least one superconducting qubit includes a linear inductive energy element and a nonlinear inductive energy element. The linear inductive energy element is superconducting. Each of the at least one superconducting qubit further includes a phase bias element configured to bias a superconducting phase difference between the linear inductive energy element and the nonlinear inductive energy element, such that second-order potential energy terms of the linear inductive energy element and the nonlinear inductive energy element are at least partially canceled by each other. Such a configuration of the quantum processing unit has the following advantages. - By (at least partially) mutually canceling the second-order potential energy terms of the nonlinear and linear inductive energy elements, the anharmonicity of the superconducting qubit can be increased. - Often (but perhaps not always), maximum cancellation can occur at a flux insensitive sweet spot, where the superconducting qubit is not primarily affected by phase dissipation induced by flux noise.

[0010] In an embodiment of the first aspect, the phase bias element is configured to bias the superconducting phase difference such that the second-order potential energy terms of the linear inductive energy element and the nonlinear inductive energy element are canceled by at least 30%. Such cancellation can significantly increase the anharmonicity of the superconducting qubit.

[0011] In some embodiments of the first embodiment, the linear inductive energy element comprises one or more geometric inductors, and the nonlinear inductive energy element comprises one or more Josephson junctions or kinetic inductors. This makes the processing unit according to the first embodiment more flexible in use.

[0012] In one embodiment of the first aspect, each of at least one superconducting qubit further comprises a capacitive energy element. By using the capacitive energy element, it is possible to change the energy spectrum of the qubit and its sensitivity to different noise sources.

[0013] In one embodiment of the first aspect, the capacitive energy element comprises one or more interdigitated capacitors, gap capacitors, parallel plate capacitors, or junction capacitors. This allows for greater flexibility in the use of the processing unit according to the first aspect.

[0014] In one embodiment of the first aspect, the phase bias element is configured to bias the superconducting phase difference by generating and passing a magnetic field through at least one superconducting qubit, or by applying a predetermined voltage to a nonlinear inductive energy element. In this way, it is possible to bias the superconducting phase difference more effectively.

[0015] In one embodiment of the first aspect, the phase bias element comprises one or more coils and / or flux bias lines. By using coils and / or flux lines, it is possible to achieve magnetic flux control.

[0016] In one embodiment of the first aspect, at least one superconducting qubit comprises two or more superconducting qubits capacitively and / or inductively coupled to one another on a dielectric substrate. By doing so, it is possible to store and manipulate multiple qubits, thereby making the quantum processing unit according to the first aspect more flexible in use.

[0017] In one embodiment of the first aspect, at least one superconducting qubit comprises two or more superconducting qubits. In this embodiment, the quantum processing unit further comprises one or more coupled resonators and / or tunable couplers for coupling superconducting qubits on a dielectric substrate. By doing so, it is possible to store and manipulate multiple qubits, thereby making the quantum processing unit according to the first aspect more flexible in use.

[0018] In one embodiment of the first aspect, the quantum processing unit further comprises signal lines provided on a dielectric substrate. The signal lines are configured to provide control signals to a superconducting qubit (for example, from an external control unit). The signal lines may comprise radio frequency lines, and the control signals may include microwave pulses. The control signals may enable the superconducting qubit to be controlled in a desired manner.

[0019] In one embodiment of the first aspect, the quantum processing unit further comprises a readout line provided on a dielectric substrate. The readout line is configured to measure the state of a superconducting qubit. The readout line can be coupled to the superconducting qubit via a readout resonator. By using the readout line, it is possible to provide a state measurement of the superconducting qubit, thereby making the quantum processing unit according to the first aspect more flexible in use.

[0020] In one embodiment of the first aspect, at least one qubit is configured as a dispersion element resonator comprising at least two conductors separated by at least one gap. In this embodiment, at least one of the conductors acts as a linear inductive energy element, and the nonlinear inductive energy element comprises at least one Josephson element incorporated into the dispersion element resonator. Furthermore, a phase bias element is configured to bias the superconducting phase difference by generating and passing a magnetic field through at least one gap of the dispersion element resonator. In doing so, it is possible to increase the anharmonicity of the superconducting qubit.

[0021] In one embodiment of the first aspect, the dispersion element resonator is configured as a coplanar waveguide (CPW) resonator. In this embodiment, at least two conductors are represented by a central superconductor and a superconducting ground plane separated from each other by a gap in the CPW resonator. The central superconductor acts as a linear inductive energy element. Furthermore, in this embodiment, at least one Josephson junction is incorporated into the CPW resonator so that there are no isolated superconducting islands in the quantum processing unit. By using such a CPW resonator, the following advantages can be obtained: - The inductance and capacitance of the CPW resonator shunt the Josephson junction, thereby providing protection against low-frequency charge noise. - The geometry of the CPW resonator exhibits low dielectric loss. - Due to the aforementioned protection against charge noise, it is possible to avoid severe phase dissipation of superconducting qubits, thereby achieving long coherence times. - By making the potential energies of the Josephson junction and the central superconductor of the CPW resonator nearly equal to each other, it is possible to use external magnetic flux to (at least partially) cancel out the second-order energy term in the total potential energy of the superconducting qubit, thereby resulting in high anharmonicity of the superconducting qubit, and - Such a structure of a superconducting qubit makes it possible to incorporate a relatively small number (e.g., just one or a few) of Josephson junctions into the superconducting qubit (compared to conventional superconducting qubits), which in turn makes the manufacturing process of the superconducting qubit, and therefore the all-quantum processing unit according to the first embodiment, relatively simple and inexpensive.

[0022] In one embodiment of the first aspect, the central superconductor of the CPW resonator has first and second pairs of opposing sides. The superconducting ground plane is formed on the dielectric substrate, and as a result, the central superconductor is electrically (galvanically) connected to the superconducting ground plane on the first pair of opposing sides and separated from the superconducting ground plane by a gap on the second pair of opposing sides. Such a configuration of the superconducting qubit has the following advantages: - The central superconductor grounded (on the opposing sides of the first pair) of the resonator ensures that there are no isolated superconducting islands in the qubit circuit, thereby making the qubit immune to low-frequency charge noise. - The central superconductor grounded (on the opposing sides of the first pair) of the resonator can transform the superconducting qubit into a gradient circuit protected against magnetic flux noise, with a spatial scale exceeding the characteristic width of the resonator. - (In addition to the aforementioned protection against charge noise) protection against magnetic flux noise allows for more effective avoidance of severe phase dissipation in qubit devices, thereby enabling the achievement of longer coherence times.

[0023] In one embodiment of the first aspect, the ground plane comprises opposing portions physically separated from each other by a central superconductor and a gap. In this embodiment, the opposing portions are connected to each other via an air bridge extending across the gap and the central superconductor. By doing so, it is possible to suppress parasitic slot line modes of the resonator.

[0024] In one embodiment of the first aspect, the Josephson junction is incorporated into the central superconductor of the CPW resonator. In this embodiment, the central superconductor is blocked by the Josephson junction, which acts as a nonlinear inductive energy element that increases the anharmonicity of the modes of the superconducting qubit.

[0025] In one embodiment of the first aspect, the central superconductor of the CPW resonator has a parallel connection of two Josephson junctions incorporated therein. This allows for greater flexibility in the use of the superconducting qubit. For example, this makes it possible to implement a superconducting quantum interference device (SQUID) loop within the superconducting qubit.

[0026] In one embodiment of the first aspect, the Josephson junction is centrally located in the central superconductor of the CPW resonator. By placing the Josephson junction in the middle or in the center of the central superconductor, it is possible to increase the mode anharmonicity of the superconducting qubit by at least twofold.

[0027] In one embodiment of the first aspect, the superconducting qubit comprises a first Josephson junction incorporated in the central superconductor of a CPW resonator, and at least one second Josephson junction located in one or more of the gaps in the vicinity of the first Josephson junction. Each of the at least one second Josephson junction connects the central superconductor to the superconducting ground plane via the corresponding gap. This configuration of the superconducting qubit allows for a more flexible mode structure and a more flexible energy spectrum for each mode.

[0028] In one embodiment of the first aspect, at least one second Josephson junction comprises an even number of second Josephson junctions arranged symmetrically with respect to the first Josephson junction. Doing so makes it possible to achieve better operating behavior of the superconducting qubit.

[0029] In one embodiment of the first aspect, the central superconductor of the CPW resonator has a linear or curved shape. This allows for various configurations of the superconducting qubit depending on the specific application.

[0030] In one embodiment of the first aspect, the quantum processing unit further comprises at least one 3D cavity. In this embodiment, the dielectric substrate having at least one superconducting qubit comprises at least one 3D cavity internally. Placing the superconducting qubit inside at least one 3D cavity makes it possible to achieve longer relaxation and coherence times due to a reduction in surface participation rate.

[0031] According to a second embodiment, a quantum computer is provided. The quantum computer comprises at least one qubit device according to the first embodiment and a control unit configured to perform computational operations by using at least one quantum processing unit. By using such a quantum processing unit, the efficiency, functionality, and processing speed of the quantum computer can be improved.

[0032] Other features and advantages of the present invention will become apparent upon reading the detailed description below and examining the accompanying drawings.

[0033] The present invention is described below with reference to the accompanying drawings. [Brief explanation of the drawing]

[0034] [Figure 1] This is a schematic top view of a quantum processing unit (QPU) according to a first exemplary embodiment. [Figure 2] This figure shows the circuit model used to derive the Hamiltonian of a superconducting qubit when the superconducting qubit contained in the QPU shown in Figure 1 is exposed to an external magnetic flux. [Figure 3] This figure shows the DC Josephson phase as a function of the external magnetic flux. [Figure 4]This figure shows the frequencies of the four lowest-frequency normal modes as a function of the external magnetic flux. [Figure 5] This figure shows the anharmonics of the four lowest frequency normal modes as a function of external magnetic flux. [Figure 6] This figure shows the potential energy landscape and phase-based wavefunction for the four lowest energy states of the lowest frequency normal mode. [Figure 7] This is an enlarged view of the anharmonics and qubit frequencies associated with the lowest frequency normal modes around the sweet spot Φdiff / Φ0 = 0.5. [Figure 8A] This figure shows the schematic capacitive coupling between superconducting qubits according to the first exemplary embodiment. [Figure 8B] This figure shows a schematic inductive coupling between superconducting qubits according to a first exemplary embodiment. [Figure 9] This is a schematic top view showing a QPU according to a second exemplary embodiment. [Figure 10] This is a schematic top view showing a QPU according to a third exemplary embodiment. [Figure 11] This is a schematic top view showing a QPU according to a fourth exemplary embodiment. [Modes for carrying out the invention]

[0035] Various embodiments of the present invention are described in more detail with reference to the accompanying drawings. However, the present invention can be embodied in many other forms and should not be considered as limitations to any particular structure or function discussed in the following description. On the contrary, these embodiments are provided to make the description of the present invention more detailed and complete.

[0036] As will become apparent to those skilled in the art from the detailed description, the scope of the present invention encompasses any embodiment disclosed herein, whether this embodiment is carried out independently or in conjunction with any other embodiment of the present invention. For example, the devices disclosed herein can be put into practice by using any number of embodiments provided herein. Furthermore, it should be understood that any embodiment of the present invention can be carried out by using one or more of the elements presented in the appended claims.

[0037] The term “exemplary” is used herein to mean “used for illustrative purposes only.” Unless otherwise specified, any embodiment described herein as “exemplary” should not be considered preferred or superior to other embodiments.

[0038] Any positional terms such as “left,” “right,” “up,” “down,” “above,” “downward,” “top,” and “bottom” may be used herein, in accordance with the drawings, for convenience in describing the relationship of one element or feature to one or more other elements or features. It should be clear that the positional terms are intended to encompass different orientations of the device disclosed herein, in addition to the orientations depicted in the drawings. For example, if the device is imaginarily rotated 90 degrees clockwise in the drawings, the elements or features described as “left” and “right” relative to other elements or features would be oriented “above” and “downward,” respectively, relative to the other elements or features. Therefore, the positional terms used herein should not be considered as any limitation of the invention.

[0039] While classifiers such as "first" and "second" may be used in this specification to describe various embodiments, it should be understood that these embodiments should not be limited by these classifiers. These classifiers are used in this specification solely to distinguish one embodiment from another. Thus, the first embodiment discussed below may be referred to as the second embodiment without departing from the teachings of the invention.

[0040] A superconducting qubit as used in the embodiments disclosed herein can be referred to as a superconducting quantum device configured to store information (or simply qubits) of one or more qubits. In this sense, a superconducting qubit functions as a quantum information storage and processing device.

[0041] According to embodiments disclosed herein, a quantum processing unit (QPU), also called a quantum processor or quantum chip, may relate to a physical (fabricated) chip containing at least one superconducting qubit, or several superconducting qubits interconnected in some way (for example, to form a quantum logic gate). For example, this interconnection may be implemented as capacitive and / or inductive coupling, or by using any suitable coupling means such as a coupled resonator, a tunable coupler, etc. A QPU is a fundamental component of a quantum computing device, also called a quantum computer, and a quantum computing device may further include a housing for the QPU, control electronics, and many other components. Generally, by using superconducting qubits, quantum computing devices can perform different qubit operations, including reading the state of a qubit, initializing the state of a qubit, and entangling the state of a qubit with the state of other qubits in the quantum computing device. Existing implementations of such quantum computing devices include superconducting quantum computers, trapped ion quantum computers, spin-based quantum computers in semiconductors, cavity quantum electrodynamics-based quantum computers, optical quantum computers, and defect-center-based quantum computers in diamonds.

[0042] It should be noted that anharmonicity and coherence can be considered two of the most important properties of a single superconducting qubit. Anharmonicity is given by α / (2π)=(E 12 -E 01 ) / h can be defined as, where E 12 E is the energy difference between states 1 and 2. 01is the energy difference between states 0 and 1, and h is Planck's constant. In practice, anharmonicity affects the shortest possible duration of a single-qubit gate, and the anharmonicity should be high enough to implement fast single-qubit gates with small leakage errors for non-computational states. On the other hand, the coherence of a qubit can be quantitatively described by the relaxation time T1 and coherence time T2. Generally, a large ratio between coherence / relaxation time and gate duration is desirable, because this determines the number of quantum gates that can be applied before quantum information is lost to the environment.

[0043] The exemplary embodiments disclosed herein provide a superconducting qubit design with high coherence and high anharmonicity for use in QPUs. This design is realized by combining a phase-biased linear inductive energy element with a nonlinear inductive energy element in the superconducting qubit. As used herein, the term “phase bias” refers to biasing the superconducting phase difference between the ends of the linear inductive energy element and the nonlinear inductive energy element. To the knowledge of the authors herein, such a combination of phase-biased linear inductive energy elements with a nonlinear inductive energy element has not yet been used in superconducting qubits known from the prior art. It is important to note that the superconducting phase difference is biased such that the second-order potential energy terms of the linear and nonlinear inductive energy elements cancel each other out at least partially. More quantitative metrics for measuring the cancellation are discussed below. In preferred embodiments, such cancellation is at least 30%.

[0044] In the exemplary embodiments disclosed herein, the superconducting phase difference of a circuit element can be referred to as the physical magnitude defined by the following equation:

[0045]

number

[0046] Here,

[0047]

number

[0048] Here, is the superconducting phase difference at time t, V(t) is the voltage difference across the circuit element, Φ0 = h / (2e) is the magnetic flux quantum, and e is the charge of the electron. Note that the superconducting phase difference is related to the corresponding branched flux via a scale transformation.

[0049] Linear inductive energy elements can be represented by geometric or linear inductors. In the exemplary embodiments disclosed herein, a geometric or linear inductor may refer to a superconducting inductor having a geometric inductance that can be defined as follows: L = Φ / I Here, I represents the current flowing through the inductor, and Φ represents the magnetic flux generated by the current. Geometric inductance depends on the geometry of the inductor. For example, a geometric inductor can be implemented as a wire, coil, or the central conductor of a dispersion element resonator (especially a CPW resonator), depending on the specific application.

[0050] A nonlinear inductive energy element can be represented by one or more Josephson junctions or kinetic inductors. In the exemplary embodiments disclosed herein, a kinetic inductor can be defined as a nonlinear superconducting inductor whose inductance largely arises from the inertia of charge carriers in the inductor. The term “Josephson junction” is used herein in its usual sense and can refer to a quantum mechanical device made of two superconducting electrodes separated by a barrier (e.g., a thin-film insulating tunnel barrier, a conventional metal, a semiconductor, a ferromagnetic material, etc.).

[0051] Here, we will explain how the aforementioned mutual cancellation of the second-order potential energy terms of the linear and nonlinear inductive energy elements affects the anharmonicity of the superconducting qubit. Assuming that the superconducting qubit is represented as a simple circuit model with a linear (geometric) inductor shunting a Josephson junction (or multiple Josephson junctions), the total potential energy of the circuit model is given by the following equation:

[0052]

number

[0053] Here,

[0054]

number

[0055] This shows the superconducting phase difference between the ends of a linear inductor.

[0056]

number

[0057] E is the dielectric energy of a linear inductor, J This is the Josephson energy of the Josephson junction.

[0058]

number

[0059] This is the phase bias of the Josephson junction. Such a phase bias is, for example, the external magnetic flux through the loop formed by the Josephson junction and the linear inductor.

[0060]

number

[0061] It should be noted that this can be achieved. In this case, the flux quantization condition relates the superconducting phase difference between the ends of the linear inductor and the Josephson junction, as shown in the following equation.

[0062]

number

[0063] Here,

[0064]

number

[0065] m is the superconducting phase difference between the two ends of the Josephson junction, and m is an integer.

[0066] Phase bias,

[0067]

number

[0068] If equal to , the second-order potential energy terms associated with the linear inductor and the Josephson junction have different signs, and therefore they cancel each other out at least partially. In other words, the total potential energy can be approximated by a fourth-order equation as follows:

[0069]

number

[0070] Here, we can clearly see the cancellation of the second-order potential energy term.

[0071]

number

[0072] In this case, the fourth-order potential energy term may be larger than the second-order potential energy term, which leads to the high anharmonicity of the superconducting qubit corresponding to the circuit model assumed above.

[0073] Note that in order to quantitatively estimate the amount of cancellation for the total potential energy U, the potential energy of a phase-biased Josephson junction can be extended to a Taylor series as shown in the following equation.

[0074]

number

[0075] Here,

[0076]

number

[0077] This represents the coefficient of the k-th Taylor series of the potential energy of a phase-biased Josephson junction. This makes it possible to measure the cancellation efficiency present in the total potential energy U by using the following ratio.

[0078]

number

[0079] Here,

[0080]

number

[0081] Here, is the coefficient of the quadratic Taylor series of the potential energy of a phase-biased Josephson junction, and β is the amount of cancellation. At least 30% cancellation means that β ≥ 0.3. For example, if the phase bias is,

[0082]

number

[0083] If equal to E J,2 =-E J This means the following equation.

[0084]

number

[0085] In this case, the requirement β≧0.3 means that the Josephson energy and dielectric energy are,

[0086]

number

[0087] This means that the following conditions must be met.

[0088] In some embodiments, the circuit model assumed above may be further aided by capacitive energy elements positioned to shunt the Josephson junction. Such capacitive energy elements can be implemented as one or more interlocking capacitors, gap capacitors, parallel plate capacitors, or junction capacitors.

[0089] In some embodiments, one or more superconducting qubits, each represented by a combination of phase-biased linear inductive energy elements and nonlinear inductive energy elements, can be provided on a dielectric substrate. In some embodiments, the superconducting qubits can be further arranged inside one or more 3D cavities (together with the dielectric substrate).

[0090] Figure 1 shows a schematic top view of a QPU 100 according to a first exemplary embodiment. As shown in Figure 1, the QPU 100 comprises a dielectric substrate 102 and a superconducting qubit 104 provided on the dielectric substrate 102. In the first embodiment, the superconducting qubit 104 is configured as a CPW resonator comprising a central superconductor 106 and a superconducting ground plane 108. The superconductor 106 is electrically connected to the superconducting ground plane 108 on opposing sides of a first pair (i.e., the left and right sides as shown in Figure 1). At the same time, the superconductor 106 is separated from the superconducting ground plane 108 by equal gaps 110 and 112 on opposing sides of a second pair (i.e., the upper and lower sides as shown in Figure 1). In this case, the superconductor 106 acts as a linear inductive energy element of the superconducting qubit 104. In the case of a nonlinear inductive energy element, it is represented by a single Josephson junction 114 incorporated into the superconductor 106, such that the QPU 100 does not have a superconducting island. Here, the superconducting island is sometimes called a Cooper pair box, connected to the central superconductor 106 via a tunnel junction. In another example, the superconducting island is formed between two Josephson junctions incorporated in series within the central conductor. Note that all the structural elements of the QPU 100 in Figure 1 are not proportional to the actual size for convenience. Furthermore, the shapes of the central superconductor 106 and the superconducting ground plane 108 are also illustrative and can be modified according to the specific application.

[0091] Although the superconducting qubit 104 is configured as a CPW resonator, this should not be considered any limitation of the present invention. In other embodiments, the superconducting qubit 104 can be configured as any type of dispersion element resonator (one example being a CPW resonator), or as any other combination of linear inductive energy elements and nonlinear inductive energy elements configured to be phase-biased such that their second-order potential energy terms cancel each other out at least partially.

[0092] In the case of Josephson junction 114, it may interrupt the central superconductor 106, as shown in FIG. 1. In one embodiment, Josephson junction 114 can be incorporated into central superconductor 106 such that the current flowing through central superconductor 106 is equal on both sides of Josephson junction 114. In another embodiment, Josephson junction 114 is centrally located within central superconductor 106.

[0093] To achieve the above cancellation, QPU 100 should also include a phase bias element (not shown in FIG. 1). In a first embodiment, the phase bias element is configured to generate and pass magnetic fluxes Φ ext,1 and Φ ext,2 through gaps or loops 110 and 112, thereby intending to achieve phase bias in a suitable manner. Thanks to the two parallel loops, the superconducting qubit 104 is gradient and its spatial scale is protected against magnetic flux noise exceeding the width of the superconducting qubit 104. This phase bias results in at least partial mutual cancellation of the second potential energy terms of the superconductor 106 and Josephson junction 114, thereby improving the anharmonicity of the superconducting qubit 104. The phase bias element can include one or more coils and / or one or more magnetic flux bias lines to achieve magnetic flux control. The magnetic flux bias line can be implemented as a superconducting wire on the dielectric substrate 102, and the magnetic field can be generated by turning the current flowing through the wire. In some other embodiments, such a phase bias element can be configured to achieve phase bias by applying a voltage suitable for Josephson junction 114 instead of or in addition to passing a magnetic field through gaps 110 and 112.

[0094] Because the Josephson junction 114 is incorporated into the CPW resonator in such a way that a separate superconducting island is not formed, the inductance and capacitance of the CPW resonator shunt the Josephson junction 114, providing protection against phase dissipation caused by low-frequency charge noise. Unlike conventionally employed transmon qubits, where only a few lowest energy levels are well protected against charge noise, the superconducting qubit 104 should be completely unaffected by low-frequency charge noise due to its topology, thanks to the inductive shunt.

[0095] As can be seen in Figure 1, the superconducting ground plane 108 comprises opposing upper 108-1 and lower 108-2 that are physically separated from each other by a central superconductor 106 and gaps 110, 112. In one embodiment, these opposing portions can be connected to each other via an air bridge extending across the central superconductor 106 and gaps 110, 112 to suppress parasitic slot line modes of the CPW resonator.

[0096] Figure 2 shows a circuit model 200 used to derive the Hamiltonian of the superconducting qubit 104 contained in QPU 100 when exposed to an external magnetic flux. According to circuit model 200, a CPW resonator of length 2l is modeled by using N lumped element inductors and capacitors. In addition, it is assumed that a Josephson junction 114 is placed between capacitors 202 and 204 with subscripts J and J+1. Due to the gradient nature of the two loops, the external magnetic flux in the following calculation formula is considered to be the (scaled) difference of the external magnetic flux on the two sides of the central superconductor 106, i.e., Φ diff =(Φ ext,2 -Φ ext,1 ) / 2. By using circuit model 200, the classical kinetic energy term T and potential energy term U for the circuit can be written as follows:

[0097]

number

[0098] Here,

[0099]

number

[0100] is the voltage V i The nodal magnetic flux between the ends of the i-th capacitor is Φ. diff,i is the external magnetic flux across the i-th loop, Δx = 2l / N is the length scale for discretization, and c tot l is the total capacitance per unit length of the CPW resonator. tot This is the total inductance per unit length of the CPW resonator, and E J This is the Josephson energy, and C J Φ is the capacitance of the Josephson junction 114, and Φ0 is the magnetic flux quantum as shown above. In addition, the dot above the symbol indicates the time derivative.

[0101] Using the Lagrangian form, we can then derive the classical equation of motion for the nodal flux in the CPW resonator. In the continuum limit Δx→0, we obtain the following result:

[0102]

number

[0103] Here, Ψ i →ψ(x i ) is at position x i Corresponding to the continuum limit of the nodal magnetic flux in Φ diff,i / (sΔx)→B diff represents the effective magnetic field difference, and s is the distance between the central superconductor 106 and the superconducting ground plane 108. Using the Lagrangian form, the position corresponding to the left electrode of the Josephson junction 114 is expressed.

[0104]

number

[0105] Boundary conditions for the nodal magnetic flux at this point can also be derived.

[0106]

number

[0107] Here, Δψ=Ψ J+1 -Ψ J This is the branched magnetic flux across the Josephson junction 114, and I c =2πE J / Φ0 is the critical current of the Josephson junction 114, and Φ diff =Σ i Φ diff,i Φ is the total external magnetic flux difference. In the above equation, Φ diff,J / Δx→Φ diff The assumption of a uniform magnetic field is used to write / (2l), where 2l is the length of the central superconductor 106. Note that similar boundary conditions can be derived for the right electrode of the Josephson junction 114. The further boundary conditions ψ(-l)=0 and ψ(l)=0 arise from the grounding of the central superconductor 106.

[0108] Based on the classical equations of motion and boundary conditions, the (classical) generated flux can be described as a linear combination of DC superconducting current and countless oscillatory normal modes. That is, the following equation:

[0109]

number

[0110] Here, φ0 is the time-independent coefficient of the "DC mode," and u0(x) is the corresponding envelope function. In intuitive terms, the DC superconducting current biases the Josephson junction 114, thereby changing the effective Josephson inductance observed by the oscillatory (AC) normal mode. Here, {u n (x) is the envelope function of the oscillatory ac mode, and {ψn (t) is the corresponding time-dependent coefficient. Importantly, the envelope function and the corresponding mode frequencies can be derived using the equations of motion and boundary conditions above.

[0111] Since we are using a CPW resonator with a Josephson junction 114 incorporated as a superconducting qubit 104, we will observe that the nonlinearity of the Josephson junction 114 converts some of the normal modes into an anharmonic oscillator. Below, we assume that we want to focus on the m-th mode and operate it as a qubit. With this in mind, it is possible to derive a single-mode approximation for the quantum Hamiltonian given by the following equation.

[0112]

number

[0113] Here,

[0114]

number

[0115] This is the effective charge energy associated with the m-th mode,

[0116]

number

[0117] is the charge operator for the m-th mode,

[0118]

number

[0119] This is the effective dielectric energy of the m-th mode,

[0120]

number

[0121] This is the phase operator corresponding to the mth mode,

[0122]

number

[0123] This is the dielectric energy associated with the total linear inductance of the CPW resonator,

[0124]

number

[0125] This is the phase bias corresponding to the DC current,

[0126]

number

[0127] This indicates the phase associated with the external magnetic flux. The phase operator and charge operator are related to the rectification relation.

[0128]

number

[0129] The conjugate operator satisfies the following condition, where i is the imaginary unit.

[0130] The m-th mode of the superconducting qubit 104 is treated quantum mechanically in the Hamiltonian above, but with a DC Josephson phase.

[0131]

number

[0132] It should be noted that this is treated as a static variable calculated based on semiclassical theory. According to semiclassical theory, the DC Josephson phase is given by the following flux quantization condition.

[0133]

number

[0134] Here,

[0135]

number

[0136] This is the branched flux associated with the DC Josephson phase.

[0137] Generally, the anharmonicity α of a given mode m / (2π) can be calculated numerically by following these steps. - First, determine the DC Josephson phase using the flux quantization conditions given above. Next, we solve for the (classical) normal mode frequency using the following equation derived from the above equations of motion and boundary conditions.

[0138]

number

[0139] Here,

[0140]

number

[0141] L is the wavenumber of the m-th mode. J =Φ0 / (2πI c ) is the effective Josephson inductance, and - Finally, to obtain the quantized energy spectrum of the target mode for a given external magnetic flux, we use the single-mode Hamiltonian.

[0142]

number

[0143] We numerically diagonalize the qubit frequency ω using the energy spectrum of the m-th mode. q / (2π) and the corresponding anharmonic α m It's easier to understand by evaluating / (2π).

[0144] Due to the large capacitance per unit length of the CPW resonator, the anharmonicity of the superconducting qubit 104 is simply small unless the parameters of the circuit model 200 are suitably selected, and a suitable external magnetic flux is applied. However, if the external magnetic flux is equal to half of the magnetic flux quantum, i.e., Φ diff If / Φ0 = ±0.5, and assuming the Josephson inductance is greater than the total inductance of the CPW resonator, the DC Josephson phase is:

[0145]

number

[0146] It is equal to. If the linear inductance of the CPW resonator is only slightly smaller than the Josephson inductance, the inductive energy

[0147]

number

[0148] and Josephson energy E J The associated second-order potential energy terms almost completely cancel each other out, which can result in large anharmonics. Using experimentally achievable values ​​for the parameters of circuit model 200, the authors have shown that the external magnetic flux is Φ diffWhen / Φ0 is adjusted to ±0.5, we found that the anharmonicity of the lowest frequency mode exceeds 500 MHz (significantly) for a qubit frequency of approximately 5 GHz. It is important to note that this also corresponds to the flux-response-free sweet spot that protects the superconducting qubit 104 from phase dissipation induced by flux noise. Some numerical results are illustrated in Figures 3 to 7.

[0149] More specifically, Figure 3 shows one possible inductance ratio 2ll tot / L J =L CPW / L J Regarding =0.77, the external magnetic flux difference Φ diff DC Josephson phase as a function of

[0150]

number

[0151] Figure 4 shows the external magnetic flux Φ. diff As a function of the four lowest frequency normal modes, the frequency f m =ω m Figure 5 shows the external magnetic flux Φ diff The anharmonic α of the four lowest frequency normal modes as a function of m This represents / (2π). Φ diff Note the large anharmonicity (>500MHz) of the lowest frequency mode at / Φ0=0.5. Figure 6 shows Φ diff Potential energy landscape for the four lowest energy states of the lowest frequency normal mode at / Φ0=0.5

[0152]

number

[0153] And the phase-based wavefunction is shown. Figure 7 shows,

[0154]

number

[0155] The anharmonic α1 / (2π) and qubit frequency ω associated with the lowest frequency normal mode around it. q An enlarged view of / (2π) is shown. Φ diff Note that / Φ0=0.5 corresponds to the flux-response-free sweet spot with these parameter values. The parameters used to obtain the numerical results shown in Figures 3 to 7 correspond to the parameter set given in Table 1 below. Table 1. Exemplary parameters used to estimate the normal mode frequency and anharmonics in a superconducting qubit 104 exposed to an external magnetic flux.

[0156] [Table 1]

[0157] In Table 1, x J / l∈[-1,1] is the (relative) position of the Josephson junction 114 in the central superconductor 106 (x J / l=0 corresponds to the Josephson junction 114 located at the center of the central superconductor 106), k0=w / (w+2s) is a ratio describing the geometry of the CPW resonator, where w is the width of the central superconductor 106, s is the gap between the central superconductor 106 and the superconducting ground plane (i.e., gap 110 or 112), and ε eff l is the effective permittivity of the CPW resonator, k l is the kinetic inductance per unit length of the resonator, g This is the geometric inductance per unit length of the resonator. Furthermore,

[0158]

number

[0159] This is the characteristic impedance of the CPW resonator.

[0160] To further improve anharmonicity, the central superconductor 106 of the CPW resonator can be fabricated from a superconducting material with high kinetic inductance, such as a superconducting thin film. This increases the inductance of the CPW resonator relative to its capacitance. As a result, the total capacitance of the CPW resonator can be reduced, thereby improving the anharmonicity of the superconducting qubit 104. In such a circuit model, the anharmonicity can exceed 200 MHz even without external flux and well over 1 GHz with external flux. However, superconducting thin films tend to be relatively lossy, and therefore, an increase in anharmonicity may be accompanied by a significant decrease in relaxation time and coherence time. For this reason, the external flux-based approach without superconducting thin films appears to be the most promising path toward high-coherence, high-anharmonic superconducting qubits.

[0161] Figures 8A and 8B show schematic capacitive and inductive coupling between superconducting qubits according to a first exemplary embodiment. More specifically, Figure 8A shows a schematic top view of QPU800, which comprises a combination of two superconducting qubits 104 capacitively coupled to one another. Figure 8B shows a schematic top view of QPU802, which comprises a combination of three superconducting qubits 104 inductively coupled to one another. In Figures 8A and 8B, white represents the central superconductor 106, superconducting ground plane 108, and Josephson junction 114 within each superconducting qubit 104, while black represents the gaps 110 and 112 within each superconducting qubit 104. It will be apparent to those skilled in the art that the number of superconducting qubits 104 shown in Figures 8A and 8B is for illustrative purposes only and should not be considered as any limitation of the present invention. Furthermore, it should be noted again that the sizes of QPU800 and 802 and their constituent elements are not proportional to actual size for convenience.

[0162] Figure 9 shows a schematic top view of QPU900 according to a second exemplary embodiment. Similar to QPU100 in the first exemplary embodiment, QPU900 comprises a dielectric substrate 902 and a superconducting qubit 904 provided on the dielectric substrate 902. In the second embodiment, the superconducting qubit 904 is also configured as a CPW resonator comprising a central superconductor 906 and a superconducting ground plane 908. The superconductor 906 is electrically connected to the superconducting ground plane 908 on opposing sides of the first pair (i.e., left and right sides as shown in Figure 9). At the same time, the superconductor 906 is separated from the superconducting ground plane 908 by equal gaps 910 and 912 on opposing sides of the second pair (i.e., upper and lower sides as shown in Figure 9). The superconductor 906 acts as a linear inductive energy element of the superconducting qubit 904. In contrast to the first embodiment, the nonlinear inductive energy element in the second embodiment is represented by a combination of two parallel Josephson junctions 914 and 916 incorporated into the superconductor 906, such that there are no superconducting islands in the QPU900. Such an arrangement of Josephson junctions 914 and 916 forms a SQUID loop. Here, a phase bias can be achieved by passing a magnetic field through the gaps 910 and 912 and the SQUID loop. It should also be noted that all the structural elements of the QPU900 are shown in Figure 9 not to scale for convenience. Furthermore, the shapes of the central superconductor 906 and the superconducting ground plane 908 are also illustrative and can be modified according to the specific application.

[0163] Figure 10 shows a schematic top view of QPU 1000 according to a third exemplary embodiment. Similar to QPU 100 in the first exemplary embodiment and QPU 900 in the second embodiment, QPU 1000 comprises a dielectric substrate 1002 and a superconducting qubit 1004 provided on the dielectric substrate 1002. In the third embodiment, the superconducting qubit 1004 is also configured as a CPW resonator comprising a central superconductor 1006 and a superconducting ground plane 1008. The superconductor 1006 is electrically connected to the superconducting ground plane 1008 on opposing sides of a first pair (i.e., left and right sides as shown in Figure 10). At the same time, the superconductor 1006 is separated from the superconducting ground plane 1008 by equal gaps 1010 and 1012 on opposing sides of a second pair (i.e., upper and lower sides as shown in Figure 10). The superconductor 1006 acts as a linear inductive energy element of the superconducting qubit 1004. In contrast to the first and second embodiments, the nonlinear inductive energy element in the third embodiment is represented by a combination of three Josephson junctions 1014, 1016, and 1018. While the Josephson junction 1014 is incorporated into the central superconductor 1006, the Josephson junctions 1016 and 1018 are positioned in the upper gap 1010 near the Josephson junction 1014 such that the Josephson junctions 1016 and 1018 connect the central superconductor 1006 to the ground plane 1008. The shown arrangement of the Josephson junctions 1014, 1016, and 1018 is not limiting and can be modified depending on the specific application. For example, one of the Josephson junctions 1016 and 1018 can be omitted or positioned in the other lower gap 1012 near the Josephson junction 1014. Importantly, the Josephson junctions 1014, 1016, and 1018 are also incorporated into the superconducting qubit 1004, so that the QPU 1000 does not have a superconducting island. Meanwhile, the phase bias can be achieved in the same manner as in the first embodiment, namely by passing a magnetic field through the gaps 1010 and 1012. It should also be noted that all the structural elements of the QPU 1000 in Figure 10 are not scaled to actual size for convenience.Furthermore, the shapes of the central superconductor 1006 and the superconducting ground plane 1008 are also illustrative examples and can be modified according to specific applications.

[0164] Figure 11 shows a schematic top view of the QPU 1100 according to a fourth exemplary embodiment. Similar to the QPU 100 in the first embodiment, the QPU 900 in the second embodiment, and the QPU 1000 in the third embodiment, the QPU 1100 comprises a dielectric substrate 1102 and a superconducting qubit 1104 provided on the dielectric substrate 1102. In the fourth embodiment, the superconducting qubit 1104 is also configured as a CPW resonator comprising a central superconductor 1106 and a superconducting ground plane 1108. The superconductor 1106 is electrically connected to the superconducting ground plane 1108 on opposing sides of a first pair (i.e., left and right sides as shown in Figure 11). At the same time, the superconductor 1106 is separated from the superconducting ground plane 1108 by equal gaps 1110 and 1112 on opposing sides of a second pair (i.e., upper and lower sides as shown in Figure 11). The superconductor 1106 acts as a linear inductive energy element of the superconducting qubit 1104. In contrast to the first, second, and third embodiments, the nonlinear inductive energy element in the fourth embodiment is represented by a combination of five Josephson junctions 1114, 1116, 1118, 1120, and 1122. While the Josephson junction 1114 is incorporated into the central superconductor 1106, the Josephson junctions 1116-1122 are positioned in the gaps 1110 and 1112 near the Josephson junction 1114, such that the Josephson junctions 1116 and 1118 connect the central superconductor 1106 to the ground plane 1108 via the upper gap 1110, and the Josephson junctions 1120 and 1122 connect the central superconductor 1106 to the ground plane 1108 via the lower gap 1112. The shown arrangement of Josephson junctions 1114-1122 is not limiting and can be modified depending on the specific application. For example, one or more of Josephson junctions 1116-1122 can be omitted. Importantly, the Josephson junctions 1114-1122 are still incorporated into the superconducting qubit 1104 so that there are no superconducting islands in the QPU 1100. Meanwhile, phase bias can be achieved in the same manner as in the first and third embodiments, namely by passing a magnetic field through the gaps 1110 and 1112.It should also be noted that, for convenience, all structural elements of the QPU1100 are shown in Figure 11, not in proportion to their actual size. Furthermore, the shapes of the central superconductor 1106 and the superconducting ground plane 1108 are illustrative examples and can be modified according to specific applications.

[0165] In the third and fourth embodiments, if an even number of Josephson junctions exist in the gap between the central superconductor and the superconducting ground plane, these Josephson junctions can be arranged symmetrically or asymmetrically with respect to the Josephson junctions incorporated into the central superconductor, depending on the specific application.

[0166] In some other embodiments, the QPU (e.g., any of QPU100, 900-1100) further comprises signal lines provided on a dielectric substrate. The signal lines can be used to provide control signals to the superconducting qubit (e.g., from an external control unit or from control electronics if the QPU is used in a quantum computer). The signal lines may comprise radio frequency lines, and the control signals may include microwave pulses. The control signals can enable the superconducting qubit to be controlled in a desired manner.

[0167] In some other embodiments, the QPU (e.g., any of QPU100, 900-1100) further comprises readout lines provided on a dielectric substrate. The readout lines may be included in the QPU in combination with signal lines. The readout lines can be coupled to superconducting qubits via readout resonators. The readout lines may be used to take state measurements of the superconducting qubits if necessary.

[0168] While exemplary embodiments of the present invention are described herein, it should be noted that various modifications and changes can be made to these embodiments without departing from the scope of legal protection provided for by the appended claims. In the appended claims, the word “comprising” does not exclude other elements or actions, and the indefinite article “a” or “an” does not exclude the plural form. The mere fact that certain treatments are mentioned in different dependent claims does not imply that combinations of these treatments cannot be used to one's advantage. [Explanation of symbols]

[0169] 100 QPUs 102 Dielectric substrate 10⁴ Superconducting Qubits 106 Central Superconductor 108 Superconducting Ground Plane 108-1 Upper part 108-2 Lower part 110 Gap 112 Gap 114 Josephson junction 200 circuit models 202 Capacitors 204 Capacitor 800 QPUs 802 QPUs 900 QPUs 902 Dielectric Substrate 904 Superconducting Qubits 906 Central Superconductor 908 Superconducting Ground Plane 910 Gap 912 Gap 914 Josephson junction 916 Josephson junction 1000 QPUs 1002 Dielectric Substrate 1004 Superconducting Qubit 1006 Central Superconductor 1008 Superconducting Ground Plane 1010 Upper gap 1012 Lower gap 1014 Josephson junction 1016 Josephson junction 1018 Josephson junction 1100 QPUs 1102 Dielectric substrate 1104 Superconducting Qubit 1106 Central Superconductor 1108 Superconducting Ground Plane 1110 Upper gap 1112 Lower gap 1114 Josephson junction 1116 Josephson junction 1118 Josephson junction 1120 Josephson junction 1122 Josephson junction

Claims

1. Dielectric substrate and A superconducting qubit provided on the dielectric substrate, wherein each of the at least one superconducting qubits is A linear inductive energy element that is superconducting, and Nonlinear inductive energy element A superconducting qubit comprising at least one superconducting qubit and Equipped with, A quantum processing unit in which the linear inductive energy element and the nonlinear inductive energy element are configured such that the second-order potential energy terms related to the linear inductive energy element and the nonlinear inductive energy element cancel each other out at least partially by applying a bias to the superconducting phase difference between the linear inductive energy element and the nonlinear inductive energy element using a phase bias element.

2. The unit according to claim 1, wherein the linear inductive energy element and the nonlinear inductive energy element are configured such that the second-order potential energy terms related to the linear inductive energy element and the nonlinear inductive energy element cancel each other out by at least 30% by the phase bias element applied to the superconducting phase difference.

3. The unit according to claim 1 or 2, wherein the linear inductive energy element comprises one or more geometric inductors.

4. The unit according to any one of claims 1 to 3, wherein the nonlinear inductive energy element comprises one or more Josephson junctions or motion inductors.

5. The unit according to any one of claims 1 to 4, wherein each of the at least one superconducting qubits further comprises a capacitive energy element.

6. The unit according to claim 5, wherein the capacitive energy element comprises one or more interlocking capacitors, gap capacitors, parallel plate capacitors, or junction capacitors.

7. The unit according to any one of claims 1 to 6, wherein the linear inductive energy element and the nonlinear inductive energy element are configured such that the superconducting phase difference is biased by the phase bias element by generating and passing a magnetic field through the at least one superconducting qubit, or by applying a predetermined voltage to the nonlinear inductive energy element.

8. The unit according to any one of claims 1 to 7, wherein the at least one superconducting qubit comprises two or more superconducting qubits capacitively and / or inductively coupled to one another on the dielectric substrate.

9. The unit according to any one of claims 1 to 8, wherein the at least one superconducting qubit is two or more superconducting qubits, and the unit further comprises one or more coupling resonators and / or adjustable couplers on the dielectric substrate for coupling the superconducting qubits.

10. The unit according to any one of claims 1 to 9, further comprising signal lines provided on the dielectric substrate, wherein the signal lines are configured to provide control signals to the at least one superconducting qubit.

11. The unit according to claim 10, wherein the signal line comprises a radio frequency line and the control signal includes a microwave pulse.

12. The unit according to any one of claims 1 to 11, further comprising a readout line provided on the dielectric substrate, wherein the readout line is configured to measure the state of the at least one superconducting qubit.

13. The unit according to claim 12, further comprising a readout resonator provided on the dielectric substrate, wherein the readout line is coupled to the at least one superconducting qubit via the readout resonator.

14. At least one qubit is configured as a dispersed element resonator comprising at least two conductors separated by at least one gap, At least one of the two conductors acts as the linear inductive energy element, and the nonlinear inductive energy element comprises at least one Josephson element incorporated into the dispersion element resonator. The unit according to any one of claims 1 to 13, wherein the linear inductive energy element and the nonlinear inductive energy element are configured such that the superconducting phase difference is biased by the phase bias element by generating and passing a magnetic field through the at least one gap of the dispersion element resonator.

15. The unit according to claim 14, wherein the dispersion element resonator is configured as a coplanar waveguide (CPW) resonator, the at least two conductors comprising a central superconductor and a superconducting ground plane, the central superconductor acting as the linear inductive energy element, and at least one Josephson junction incorporated in the CPW resonator such that the quantum processing unit does not have isolated superconducting islands.

16. The unit according to claim 15, wherein the central superconductor of the CPW resonator has a first pair of opposing sides and a second pair of opposing sides, and the superconducting ground plane is formed on the dielectric substrate such that the central superconductor is electrically connected to the superconducting ground plane on the first pair of opposing sides and separated from the superconducting ground plane by the gap on the second pair of opposing sides.

17. The unit according to claim 15 or 16, wherein the superconducting ground plane comprises opposing portions physically separated from each other by the central superconductor and the gap, and the opposing portions are connected to each other via an air bridge extending across the gap and the central superconductor.

18. The unit according to any one of claims 15 to 17, wherein the at least one Josephson junction is incorporated into the central superconductor.

19. The unit according to claim 18, wherein the at least one Josephson junction is two Josephson junctions connected in parallel.

20. The unit according to claim 18 or 19, wherein the at least one Josephson junction is located at the center of the central superconductor.

21. The at least one Josephson junction is The first Josephson junction incorporated in the central superconductor, At least one second Josephson junction located in one or more of the gaps in the vicinity of the first Josephson junction, wherein each of the at least one second Josephson junction connects the central superconductor to the superconducting ground plane via the corresponding gap. The unit according to any one of claims 15 to 17, comprising:

22. The unit according to claim 21, wherein the at least one second Josephson junction comprises an even number of second Josephson junctions arranged symmetrically with respect to the first Josephson junction.

23. The unit according to claim 21 or 22, wherein the first Josephson junction is located at the center of the central superconductor.

24. The unit according to any one of claims 15 to 23, wherein the central superconductor has a linear or curved shape.

25. The unit according to any one of claims 1 to 24, further comprising at least one 3D cavity, wherein the dielectric substrate having at least one superconducting qubit is provided within the at least one 3D cavity.

26. A quantum computer comprising at least one quantum processing unit according to any one of claims 1 to 25, and a control unit configured to perform computational operations by using the at least one quantum processing unit.

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