Multi-mode coupler for controlling interaction between qubits

Abstract

An apparatus includes a first qubit and a second qubit, and a qubit coupler coupled between the first qubit and the second qubit. The second qubit includes a first pattern and a second pattern, wherein the first pattern is configured to store data. The qubit coupler includes a first mode and a second mode, and operates in a first state or a second state. In a first state, the first qubit swaps a first pattern coupled to the qubit coupler and the second pattern of the second qubit swaps a second pattern coupled to the qubit coupler to suppress interaction between the first qubit and the second qubit. In the second state, the first pattern of the first qubit and the second qubit exchanges both the first pattern and the second pattern coupled to the qubit coupler to effect interaction between the first qubit and the second qubit for entanglement gate operation in response to a control signal applied to the qubit coupler.

Description

Background Art

[0001] The present disclosure generally relates to superconducting quantum computing, and specifically to superconducting quantum systems and devices implemented using superconducting quantum bits (qubits). Superconducting quantum computing systems are implemented using circuit quantum electrodynamics (QED) devices that utilize quantum dynamics of electromagnetic fields in superconducting circuits including superconducting qubits to generate and process quantum information. Typically, a superconducting qubit is an electronic circuit that is implemented using components such as superconducting tunnel junctions (e.g., Josephson junctions), inductors, and / or capacitors, and when cooled to cryogenic temperatures, behaves as a quantum mechanical anharmonic (nonlinear) oscillator with a quantized state. Due to the anharmonicity imparted by the nonlinear inductor element (e.g., Josephson inductance) of the qubit, the qubit can be effectively operated as a two-level system using the ground state and the first excited state of the qubit, which allows the ground state and the first excited state to be uniquely addressed at the transition frequency of the qubit without significantly interfering with the higher excited states of the qubit.

[0002] Various types of quantum information processing operations can be implemented using a superconducting quantum processor including multiple superconducting qubits, in which the superconducting qubits can be coherently controlled, placed in a quantum superposition state (via, for example, a single gate operation), exhibit quantum interference effects, and become entangled with each other (via, for example, an entanglement gate operation). The fidelity of the quantum gate operation may be adversely affected by unwanted crosstalk (e.g., residual static ZZ interactions) between adjacent superconducting qubits. For example, unwanted crosstalk between superconducting qubits can cause the transition frequency of one superconducting qubit to depend on the state of one or more adjacent superconducting qubits. As quantum processors scale with increasing numbers of superconducting qubits and increasing integration density, this unwanted crosstalk becomes increasingly problematic. Summary of the invention

[0003] Exemplary embodiments of the present disclosure include a quantum device configured to control interactions (eg, ZZ interactions) between coupled superconducting qubits.

[0004] An exemplary embodiment includes a device including a first superconducting qubit, a second superconducting qubit, and a superconducting qubit coupler. The second superconducting qubit includes a first mode and a second mode, wherein the first mode is configured to store quantum data. The superconducting qubit coupler is coupled between the first superconducting qubit and the second superconducting qubit. The superconducting qubit coupler includes a first mode and a second mode, and is configured to operate in one of a first state and a second state in response to a control signal applied to the superconducting qubit coupler. In the first state of the superconducting qubit coupler, the first superconducting qubit is exchange coupled to the first mode of the superconducting qubit coupler, and the second mode of the second superconducting qubit is exchange coupled to the second mode of the superconducting qubit coupler to suppress interaction between the first mode of the first superconducting qubit and the second superconducting qubit. In a second state of the superconducting qubit coupler, the first modes of the first superconducting qubit and the second superconducting qubit are exchange-coupled to both the first mode and the second mode of the superconducting qubit coupler to enable interaction between the first superconducting qubit and the first mode of the second superconducting qubit, and an entanglement gate operation is performed in response to a control signal applied to the superconducting qubit coupler.

[0005] Advantageously, coupling the first and second superconducting qubits (which include two different excitation modes) using a superconducting qubit coupler allows for simultaneous suppression of static ZZ interactions and exchange interactions between the first and second superconducting qubits when the superconducting qubit coupler is in a state in which mode-selective exchange coupling is implemented, wherein the first and second superconducting qubits are exchange coupled to different modes of the superconducting qubit coupler. Such mode-selective exchange coupling results in substantially zero interaction between the first and second superconducting qubits. Furthermore, the mode-selective exchange coupling is used to suppress observer effects between the superconducting qubit coupler and the remote superconducting qubit.

[0006] Another exemplary embodiment includes a system including a quantum processor and a control system. The quantum processor includes a superconducting qubit array. The control system is configured to generate a control signal to control the quantum processor. The superconducting qubit array includes a first superconducting qubit, a second superconducting qubit, and a superconducting qubit coupler. The second superconducting qubit includes a first mode and a second mode, wherein the first mode is configured to store quantum data. The superconducting qubit coupler is coupled between the first superconducting qubit and the second superconducting qubit. The superconducting qubit coupler includes a first mode and a second mode, and is configured to operate in one of a first state and a second state in response to a control signal applied to the superconducting qubit coupler. In the first state of the superconducting qubit coupler, the first superconducting qubit is exchange-coupled to the first mode of the superconducting qubit coupler, and the second mode of the second superconducting qubit is exchange-coupled to the second mode of the superconducting qubit coupler to suppress the interaction between the first mode of the first superconducting qubit and the second superconducting qubit. In a second state of the superconducting qubit coupler, the first modes of the first superconducting qubit and the second superconducting qubit are exchange-coupled to both the first mode and the second mode of the superconducting qubit coupler to enable interaction between the first superconducting qubit and the first mode of the second superconducting qubit, and an entanglement gate operation is performed in response to a control signal applied to the superconducting qubit coupler.

[0007] Another exemplary embodiment includes a computer program product for calibrating an entanglement gate process. The computer program product includes one or more computer-readable storage media, and program instructions stored together on the one or more computer-readable storage media. The program instructions include program instructions for calibrating parameters of a control pulse, the control pulse being configured to control the operation of a superconducting qubit coupler to perform an entanglement gate operation between a first superconducting qubit and a second superconducting qubit, the first superconducting qubit and the second superconducting qubit being coupled to the superconducting qubit coupler. The program instructions for calibrating the parameters of the control pulse include program instructions for performing an iterative process. The iterative process includes one or more iterations of performing an amplitude calibration process and performing a frequency detuning calibration process. In response to applying a control pulse having a calibrated amplitude to the superconducting qubit coupler, an amplitude calibration process is performed to calibrate the amplitude of the control pulse so as to rotate the superconducting qubit coupler from a ground state to a first excited state and back to a ground state. In response to applying a control pulse having a calibrated amplitude and a calibrated frequency detuning to the superconducting qubit coupler, a frequency detuning calibration process is performed to calibrate the detuning of the frequency of the control pulse relative to the operating frequency of the superconducting qubit coupler to achieve a target conditional rotation of the first superconducting qubit and the second superconducting qubit.

[0008] Advantageously, an exemplary entanglement gate calibration process provides an accurate and efficient method for calibrating control pulses for two-qubit conditional gate operations, wherein the calibration process can be configured to individually calibrate the control pulse shape to cause a superconducting qubit coupler to rotate by a full 2π X axis with high precision, regardless of the detuning between the control pulse and the mode frequency of the superconducting qubit coupler. The pulse detuning is then individually calibrated to achieve the desired conditional Z rotation of the first and second superconducting qubits. The process of iteratively repeating the individual detuning and amplitude calibration stages allows the entanglement gate calibration process to achieve progressively higher fidelity.

[0009] Other embodiments are described in the following detailed description of exemplary embodiments, which is to be read in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 A Bloch sphere is depicted, graphically representing the various states of a qubit.

[0011] Figure 2A and Figure 2B A multi-mode double-junction superconducting qubit for realizing a superconducting multi-mode qubit coupler according to an exemplary embodiment of the present disclosure is schematically shown.

[0012] Figure 2C Two different excitation modes of a multi-mode double-junction superconducting qubit according to an exemplary embodiment of the present disclosure are schematically shown.

[0013] Figure 3 A quantum device including superconducting qubits coupled by a superconducting multimode coupler circuit according to an exemplary embodiment of the present disclosure is schematically shown.

[0014] Figure 4 A circuit diagram of a quantum device including superconducting qubits coupled by a superconducting multimode coupler circuit according to an exemplary embodiment of the present disclosure is schematically shown.

[0015] Figure 5 Schematically shows an exemplary embodiment according to the present disclosure Figure 4 Planar circuit configuration of superconducting quantum circuits.

[0016] Figure 6 Schematically illustrates another exemplary embodiment of the present disclosure. Figure 4 Planar circuit configuration of superconducting quantum circuits.

[0017] Figure 7 A quantum device including an array of superconducting qubits and a multimode coupler according to an exemplary embodiment of the present disclosure is schematically shown, the quantum device being configured to suppress crosstalk with an observer qubit.

[0018] Figure 8 Schematically illustrates an array of superconducting qubits coupled by a superconducting multi-mode qubit coupler according to an exemplary embodiment of the present disclosure.

[0019] Fig. 9 A flow chart of a method for calibrating entanglement gate operations of superconducting qubits coupled by a superconducting multi-mode qubit coupler according to an exemplary embodiment of the present disclosure is shown.

[0020] Fig. 10A , Fig. 10B , Fig. 10C , Fig. 10D , Fig. 10E , Fig.10F , Figure 10G , Fig. 10H and Fig.10I Describes the use of an exemplary embodiment according to the present disclosure Fig. 9 Time-dependent numerical simulation results of an exemplary entanglement gate calibration process performed with a control pulse of the process calibration, where:

[0021] Fig. 10A A waveform diagram including calibration control pulses generated using an entanglement gate calibration process according to an exemplary embodiment of the present disclosure;

[0022] Fig. 10B is a timing diagram showing a state projection of a superconducting multimode coupler when the superconducting multimode coupler is driven by a calibration control pulse and a control qubit is in a ground state according to an exemplary embodiment of the present disclosure;

[0023] Fig. 10C is a timing diagram showing a state projection of a superconducting multimode coupler when the superconducting multimode coupler is driven by a calibration control pulse and a control qubit is in an excited state according to an exemplary embodiment of the present disclosure;

[0024] Fig. 10D is a timing diagram showing a state projection of a target qubit when a superconducting multimode qubit coupler is driven by a calibration control pulse and a control qubit is in a ground state according to an exemplary embodiment of the present disclosure;

[0025] Fig. 10E is a timing diagram showing a state projection of a target qubit when a superconducting multimode qubit coupler is driven by a calibration control pulse and a control qubit is in an excited state according to an exemplary embodiment of the present disclosure;

[0026] Fig.10F is a timing diagram showing a state projection of a control qubit when a superconducting multimode qubit coupler is driven by a calibration control pulse and the control qubit is in a ground state according to an exemplary embodiment of the present disclosure;

[0027] Figure 10G is a timing diagram showing a state projection of a control qubit when a superconducting multimode qubit coupler is driven by a calibration control pulse and the control qubit is in an excited state according to an exemplary embodiment of the present disclosure;

[0028] Fig. 10H is a timing diagram showing a conditional rotation obtained for a target qubit in response to driving a superconducting multimode qubit coupler by a calibration control pulse according to an exemplary embodiment of the present disclosure; and

[0029] Fig.10I is a timing diagram showing concurrency of entanglement amounts obtained when a superconducting multimode qubit coupler is driven by a calibration control pulse to perform an entanglement gate operation according to an exemplary embodiment of the present disclosure.

[0030] Fig.11 A quantum computing system according to an exemplary embodiment of the present disclosure is schematically illustrated.

[0031] Fig.12 An exemplary architecture of a computing node that can host a quantum computing platform according to an exemplary embodiment of the present disclosure is schematically illustrated.

[0032] Fig.13 A cloud computing environment according to an exemplary embodiment of the present disclosure is depicted.

[0033] Fig.14 Abstract model layers according to an exemplary embodiment of the present disclosure are depicted. Specific embodiments

[0034] Exemplary embodiments of the present disclosure will now be described in more detail with respect to quantum devices configured to control interactions (e.g., ZZ interactions) between coupled superconducting qubits. It should be understood that the various features shown in the accompanying drawings are schematic diagrams that are not drawn to scale. In addition, the same or similar reference numerals are used throughout the accompanying drawings to represent the same or similar features, elements, or structures, and therefore, a detailed explanation of the same or similar features, elements, or structures will not be repeated for each drawing. In addition, the term "exemplary" as used herein means "used as an example, instance, or illustration." Any embodiment or design described herein as "exemplary" should not be construed as being preferred or advantageous over other embodiments or designs.

[0035] In addition, it should be understood that the phrase "configured to" as used in conjunction with circuits, structures, elements, components, etc. that perform one or more functions or otherwise provide some functions is intended to cover embodiments in which the circuits, structures, elements, components, etc. are implemented in hardware, software, and / or a combination thereof, as well as embodiments including hardware, where the hardware may include quantum circuit elements (e.g., qubits, coupler circuits, etc.). In some embodiments, the processor may include discrete circuit elements (e.g., transistors, inverters, etc.), programmable elements (e.g., application specific integrated circuit (ASIC) chips, field programmable gate array (FPGA) chips, etc.), processing devices (e.g., central processing units (CPUs), graphics processing units (GPUs), etc.), one or more integrated circuits, and / or a combination thereof. Therefore, by way of example only, when circuits, structures, elements, components, etc. are configured to implement the present invention, they may be configured to implement the present invention. For example, although defined as being configured to provide a specific function, it is intended to cover but not be limited to embodiments in which circuits, structures, elements, components, etc. are configured to provide a specific function. When circuits, structures, elements, components, etc. are in a non-operating state (e.g., not connected or otherwise deployed in a system, not powered, not receiving input and / or not generating output) or in a partially operating state, this includes elements, processing devices and / or integrated circuits that enable the circuits, structures, elements, components, etc. to perform specific functions, as well as embodiments covering circuits, structures, elements, components, etc. that are in a non-operating state (e.g., not connected or otherwise deployed in a system, not powered, not receiving input and / or not generating output) or in a partially operating state.

[0036] As is known in the art, quantum computing provides a computing paradigm that uses the basic principles of quantum mechanics to perform calculations. Quantum computing algorithms and applications are defined using quantum circuits. Quantum circuits are computing routines that define coherent quantum operations performed on quantum data stored in qubits in combination with operations performed using classical computing. Quantum circuits are used to define complex algorithms and applications in an abstract way that can be executed on quantum computers. In a quantum computer, primitive operations include gate operations (e.g., single-qubit gate operations, double-qubit gate operations, multi-qubit gate operations (e.g., 3 or more qubits)) applied to qubits to perform quantum computing operations for a given application. Quantum circuits allow quantum computers to receive classical data, perform quantum operations based on the received data, and output classical solutions.

[0037] A single qubit can have a basis state of |0> or |1>, or a linear combination of such basis states, which is called a superposition state. As is known in the art, the state of a qubit can be graphically represented as a point on a unit sphere (radius = 1), which is called a Bloch sphere, such as Figure 1 In particular, Figure 1An exemplary Bloch sphere 100 is shown, where the ground state of a qubit |0> or |1> is represented along the Z-axis of the Bloch sphere 100, where a point 101 on the positive Z-axis represents the ground state |0> of the qubit, and a point 102 on the negative Z-axis represents the first excited state |1> of the qubit. The superposition state |ψ> of a qubit can be represented as a point on the Bloch sphere as follows:

[0038]

[0039] Among them and corresponds to the magnitude probabilities associated with the respective states |0> and |1>, and where the term e iφ Corresponds to the relative phase between states |0> and |1>. The position of point 103 (representing the superposition state of the qubit) is determined based on angles θ and φ. Angle θ affects the probability of observing the qubit state |0> or |1> when the qubit is read, wherein the probability of reading the qubit state |1> increases as θ increases. Angle φ affects the relative phase between states |0> and |1>. For example, when θ=0, when the qubit state is read, the qubit is in the ground state |0>, which provides a 100% probability of observing the qubit state |0>. In addition, when θ=π, when the qubit state is read, the qubit is in the first excited state |1>, which provides a 100% probability of observing the qubit state |1>. On the other hand, when and φ = 0, the qubit is in the state at point 104, and when and When the qubit is in a superposition state represented by, for example, points 104 and 105, when the qubit state is read, there is a 50% probability of observing a qubit state of |1> and a 50% probability of observing a qubit state of |0>.

[0040] The state of a qubit can be changed by applying a single-qubit gate operation to the qubit, which causes the current state of the qubit to rotate about, for example, the X-axis, the Y-axis, and / or the Z-axis, depending on the given gate operation. Rotation about the Z-axis results in a change in the angle φ. In addition, entanglement gate operations can be used to control qubits to entangle the states of two or more qubits and thereby produce a combined state of the two or more qubits that contains more information than the individual states of the qubits.

[0041] As described above, superconducting quantum computing systems can be implemented using superconducting qubits. For example, a superconducting transmon (transmission line shunted plasma oscillation) qubit is a superconducting qubit that includes a superconducting tunnel junction device (e.g., a Josephson junction) connected in parallel with a capacitor. The Josephson junction acts as a nonlinear inductor that, when shunted with a capacitor, forms a non-harmonic oscillator with individually addressable energy levels (e.g., corresponding to the two lowest energy levels of the ground state |0> and the first excited state |1>). Transmon qubits are widely used in superconducting quantum computing because transmon qubits provide good coherence times and have a relatively simple structure that facilitates coupling with other superconducting circuit elements, as well as qubit readout, etc. In order to control and read out qubits, structures can be designed to capacitively or inductively couple transmon qubits to other circuit elements, including microwave and flux drive lines, readout resonators, and couplers.

[0042] In addition, transmon qubits can be designed to have a relatively high anharmonic spectrum, in which the frequency separation between the computational state and the non-computational state is relatively high, thereby allowing the superconducting transmon qubit to be effectively used as a two-level quantum system. In particular, as is known in the art, the operating frequency (alternatively, the transition frequency) of a superconducting qubit is the frequency corresponding to the energy difference between the ground state |1> and the first excited state |1> of the qubit. With superconducting qubits, although higher energy levels are available for a given qubit (e.g., |2>, |3>, etc.), the quantum system is designed to isolate the two lowest energy levels of the superconducting qubit (i.e., the ground state |0> and the first excited state |1>), thereby utilizing each superconducting qubit as a basic two-level system for quantum computation while ignoring the higher energy states. As used herein, the term "anharmonicity" refers to the frequency (f) at which a qubit (i) transitions from the ground state |0> to the first excited state |1>. 01 ) and (ii) the frequency (f 12 )

[0043] Another type of superconducting qubit that can be used to realize quantum systems includes multi-mode double-junction superconducting qubit architectures such as Figure 2A and Figure 2B More specifically, Figure 2Ais a schematic lumped element circuit representation of a multi-mode dual-junction superconducting qubit 200, which is alternatively referred to as a superconducting tunable coupler qubit (TCQ). The multi-mode dual-junction superconducting qubit 200 includes a shunt capacitor 221 and two capacitive shunt superconducting tunnel junctions (e.g., Josephson junctions) connected in series between a first node N1 and a second node N2 of the multi-mode dual-junction superconducting qubit 200, wherein the first capacitive shunt Josephson junction includes a first Josephson junction 222 and a first capacitor 223, and wherein the second capacitive shunt Josephson junction includes a second Josephson junction 224 and a second capacitor 225. The shunt capacitor 221 has a capacitance C S , the first Josephson junction 222 has a Josephson energy E J1 , the second Josephson junction 224 has a Josephson energy E J2 , the first capacitor 223 has a capacitance C1, and the second capacitor 225 has a capacitance C2. The two capacitive shunt superconducting Josephson junctions are coupled to the middle node N3.

[0044] Next, Figure 2B Schematically shows an exemplary embodiment according to the present disclosure Figure 2A The planar circuit configuration of the multi-mode double-junction superconducting quantum bit 200. More specifically, Figure 2B A planar multimode double-junction superconducting qubit 201 is schematically shown, which includes a first superconducting pad 201-1, a second superconducting pad 201-2, and a third (middle) superconducting pad 201-3, wherein a first Josephson junction 222 is coupled between the first superconducting pad 201-1 and the third superconducting pad 201-3, and a second Josephson junction 224 is coupled between the second superconducting pad 201-2 and the third superconducting pad 201-3.

[0045] In this configuration, superconducting pads 201-1, 201-2, and 201-3 include planar capacitor electrodes that form a coplanar parallel plate capacitor structure. Figure 2B In the exemplary configuration of the first superconducting pad 201-1 and the second superconducting pad 201-2 include Figure 2A The planar capacitor electrode of the shunt capacitor 221. In addition, the first and third superconducting pads 201-1 and 201-3 include Figure 2A The planar capacitor electrode of the first capacitor 223, and the second and third superconducting pads 201-2 and 201-3 include Figure 2A The first superconducting pad 201-1, the second superconducting pad 201-2 and the third superconducting pad 201-3 correspond to the planar capacitor electrodes of the second capacitor 225. Figure 2A The first node N1, the second node N2 and the third node N3 in.

[0046] The multi-mode dual-junction superconducting qubit 201 includes two excitation modes with different frequencies and spatial symmetries. More specifically, the multi-mode dual-junction superconducting qubit 201 includes two different excitation modes corresponding to symmetric and antisymmetric combinations of excitations associated with the two junctions, wherein the two different normal modes include (i) a low-frequency "bright" mode (referred to herein as the A mode) including a non-zero dipole moment, and (ii) a high-frequency "dark" mode (referred to herein as the B mode) that lacks a dipole moment and is not coupled to an external field. Figure 2C Schematically shows Figure 2B FIG. 2 shows two different excitation modes of a multi-mode double-junction superconducting quantum bit 201 , where the “bright” mode is depicted as A mode 202 , and the “dark” mode is depicted as B mode 204 .

[0047] like Figure 2C As schematically shown in FIG. 2 , the A mode 202 includes a charge pattern in which, at any given point in time, the first and second superconducting pads 201-1 and 201-2 have opposite charges, and the third (middle) superconducting pad 201-3 has a net zero charge. On the other hand, the B mode 204 includes a charge pattern in which, at any given point in time, the first and second superconducting pads 201-1 and 201-2 have the same charge, and the third (middle) superconducting pad 201-3 has a charge opposite to the charge on the first and second superconducting pads 201-1 and 201-2. The A mode and the B mode have different frequencies, for example, the mode frequency f of the B mode 204 is B Greater than the mode frequency f of the A mode 202 A , which allows the separate excitation of one mode relative to another.

[0048] In order to realize a scalable quantum computing system (e.g., a quantum processor) using superconducting qubits, it is important to minimize or eliminate crosstalk and unwanted ZZ interactions between coupling or adjacent qubits, for example, to achieve independent qubit control of high-fidelity single-qubit gate operations and to achieve high-fidelity entanglement gates (e.g., two-qubit gates) between superconducting qubits. As described above, an entanglement gate is an operation in which an external field (e.g., a microwave signal) is applied to a quantum processor to produce an entangled state between two or more individual qubits. For example, a controlled phase gate (referred to herein as a CPHASE gate) between two qubits is a type of entanglement gate in which one qubit (e.g., a target qubit) acquires a phase shift if and only if both qubits are in their first excited state.

[0049] The ZZ interaction is a type of longitudinal interaction between two qubits or modes, in which the excitation of one qubit or mode causes a shift in the transition frequency of the other qubit or mode. In some cases, the ZZ interaction provides a way to entangle two different qubits and create, for example, a CPHASE gate, since the state-dependent shift in the qubit frequency can be equivalent to a state-dependent phase shift. The ZZ interaction is sometimes referred to as longitudinal coupling or denoted as chi or 2-chi coupling. On the other hand, in some instances, undesired ZZ interactions between two superconducting qubits are a source of crosstalk, which can reduce the fidelity of the gate operation.

[0050] For example, static ZZ interaction is a type of ZZ interaction that exists between two qubits or modes in the absence of any external RF drive. This "always on" interaction includes unwanted crosstalk that can be detrimental to the quantum system of qubits by inhibiting the independent control of each qubit and by creating unwanted entanglement. In particular, static ZZ coupling can occur between adjacent qubits, where the state of one qubit affects the qubit frequency of an adjacent qubit, where the static ZZ coupling can lead to gate errors. In this regard, static ZZ interaction is a type of unwanted crosstalk between adjacent qubits that can adversely affect the fidelity of single-qubit gate operations, which are calibrated under the assumption that the qubit frequency is fixed.

[0051] Another source of crosstalk between adjacent qubits includes the exchange interaction that occurs when a microwave pulse is applied to one qubit (such as for a single-qubit gate operation), which could potentially affect another adjacent qubit if there is an exchange interaction between such adjacent qubits. For example, if there is an exchange interaction between two qubits, applying a microwave pulse to one qubit could conceivably excite the other qubit, which is a form of potentially harmful crosstalk.

[0052] In addition, another type of crosstalk is called the "observer effect", which represents a condition in which the state of an uninvolved qubit (e.g., an "observer") affects the fidelity / performance of a gate operation between two other qubits. For example, a two-qubit gate operation can be achieved by driving a coupling element that connects two qubits. In this case, the coupling element can have its own operating frequency (e.g., transition frequency) that is calibrated to achieve high-fidelity two-qubit gate operations. If there is static ZZ coupling between the coupling element and the observer qubit, the state of the observer qubit can affect the transition frequency of the coupling element in a way that reduces the fidelity of the calibrated two-qubit gate operation.

[0053] Exemplary embodiments of the present disclosure will now be discussed with respect to techniques for implementing a scalable quantum computing architecture with superconducting qubits coupled using a multimode qubit coupler to achieve high-fidelity entangled gate operations. The exemplary qubit coupling techniques as described herein are configured to suppress unwanted crosstalk between coupled superconducting qubits (e.g., suppress static ZZ interactions between coupled superconducting qubits, and suppress exchange interactions between coupled superconducting qubits when a single gate operation is performed on one of the coupled qubits), as well as suppress observer effects between a multimode qubit coupler and an adjacent qubit (e.g., an observer qubit).

[0054] Figure 3 Schematically illustrates a quantum device including superconducting qubits coupled by a multimode coupler circuit according to an exemplary embodiment of the present disclosure. In particular, Figure 3 A quantum device 300 is schematically shown, which includes a first superconducting qubit 310 (or first qubit 310), a second superconducting qubit 320 (or second qubit 320), and a superconducting multimode coupler circuit 330 (or multimode coupler circuit 330). In an exemplary configuration, first qubit 310 and second qubit 320 include computational qubits, and multimode coupler circuit 330 is configured to mediate interactions (e.g., ZZ interactions) between first qubit 310 and second qubit 320 under different gate operations. In some embodiments, first qubit 310 and second qubit 320 include different types of superconducting qubits. For example, in some embodiments, first qubit 310 includes a transmon qubit, and second qubit 320 includes a gate having a gate structure such as Figure 3 The multi-mode double-junction superconducting qubit of the circuit architecture shown. In some embodiments, the first qubit 310 can be implemented using other types of superconducting qubits (such as superconducting fluxonium qubits). In some embodiments, the first qubit 310 and the second qubit 320 include fixed frequency qubits (non-tunable), while in other embodiments, the first qubit 310 and the second qubit 320 can be tunable qubits, for example, tunable transition frequencies.

[0055] In addition, in some embodiments, the multimode coupler circuit 330 includes a Figure 3The multi-mode double-junction superconducting qubit of the circuit architecture shown is capacitively coupled to the first qubit 310 and the second qubit 320. The multi-mode coupler circuit 330 is configured to control the exchange interaction between the first qubit 310 and the second qubit 320 to implement the entanglement gate operation, and suppress the crosstalk (e.g., suppress the ZZ interaction) between the first qubit 310 and the second qubit 320 during the idle time or when the single-qubit gate operation is performed on one or both of the first qubit 310 and the second qubit 320. In other embodiments, the multi-mode coupler circuit 330 can be implemented using any suitable superconducting multi-mode qubit framework, which includes a combination of two strongly interacting anharmonic oscillators, wherein the composite quantum system is characterized by multiple excitation modes that exhibit strong longitudinal coupling between them, that is, the excitation of one mode can strongly shift the transition frequency of another mode.

[0056] Quantum device 300 also includes a plurality of control lines (e.g., transmission line resonators), including but not limited to qubit drive lines 312 and 322, qubit readout lines 314 and 324, and coupler drive line 332. In some embodiments, qubit drive lines 312 and 322 are coupled (e.g., capacitively coupled) to first qubit 310 and second qubit 320, respectively. In some embodiments, qubit drive lines 312 and 322 are configured to apply control signals (e.g., microwave control pulse signals) to independently change the states of corresponding first qubit 310 and second qubit 320 (e.g., single qubit gate operation). As is known in the art, the state of the qubit can be changed by applying a control signal having a transition frequency (expressed as f) equal to the qubit. 01 ) to change the state of the quantum bit, where the transition frequency f 01 Corresponding to the energy difference between the ground state |0> and the excited state |1> of the qubit. In addition, the rotation axis about a given axis of the Bloch sphere 100 (e.g., the X-axis, the Y-axis, or any axis in the XY plane) and the amount (angle) of such rotation are based on the phase of the microwave control signal and the amplitude and duration of the microwave control signal, respectively.

[0057] Additionally, in some embodiments, readout lines 314 and 324 are coupled to first qubit 310 and second qubit 320, respectively, using known techniques (e.g., dispersive readout). In some embodiments, readout lines 314 and 324 include transmission line readout resonators (e.g., coplanar transmission lines) configured to have resonant frequencies that are detuned from the respective transition frequencies of the respective first qubit 310 and second qubit 320. As readout lines 314 and 324 are coupled to the respective first qubit 310 and second qubit 320, there is a shift in the resonant frequency of the transmission line readout resonator depending on the state of the respective first qubit 310 and second qubit 320. The change in the resonant frequency of the transmission line readout resonator coupled to a given qubit is used to determine the readout state of the given qubit, e.g., a ground state |0> or an excited state |1>, where for readout, the superposition state of the given qubit is projected onto one of the ground state or excited state of the qubit, as is known in the art.

[0058] Coupler drive line 332 is coupled (e.g., capacitively coupled) to multimode coupler circuit 330. In some embodiments, multimode coupler circuit 330 includes two different normal excitation modes (e.g., different A and B excitation modes with different frequencies and spatial symmetries, such as Figure 2C ), wherein the coupler drive line 332 is configured to apply a control signal to the multimode coupler circuit 330 to control the mode-selective exchange coupling between the first quantum bit 310 and the second quantum bit 320 and the different excitation modes of the multimode coupler circuit 330.

[0059] For example, as explained in further detail below, the multimode coupler circuit 330 includes a first mode and a second mode, and is configured to operate in the first state or the second state in response to a driving control signal applied to the multimode coupler circuit 330. In the first state of the multimode coupler circuit 330 (e.g., the ground state |0>, in which no control pulse is applied to the coupler driving line 332), the first qubit 310 is exchange-coupled to the first mode of the multimode coupler circuit 330 (e.g., the A mode), and the second qubit 320 is exchange-coupled to the second mode of the multimode coupler circuit 330 (e.g., the B mode), which suppresses the interaction between the first qubit 310 and the second qubit 320.

[0060] On the other hand, in the second state of the multimode coupler circuit 330, an appropriately calibrated control pulse is applied to the coupler drive line 332 to drive the second mode (e.g., B mode) of the multimode coupler circuit 330 through a complete 2π mode (e.g., from the ground state |0> to the first excited state |1>, and back to the ground state |0>), which causes the first quantum bit 310 and the second quantum bit 320 to be exchange coupled to both the first mode and the second mode of the multimode coupler circuit 330 to achieve interaction between the first quantum bit 310 and the second quantum bit 320 and perform an entanglement gate operation.

[0061] It should be noted that in embodiments where the first qubit 310 and / or the second qubit 320 include frequency tunable qubits (e.g., flux tunable transmon qubits or fluxonium qubits, etc.), the quantum device 300 will include a flux bias control line coupled (e.g., inductively coupled) to the corresponding tunable qubit. In such embodiments, the flux bias control line will be configured to apply a flux bias control signal to the tuning structure of the qubit to tune the operating frequency of the tunable qubit as required by a given application. For example, a flux tunable transmon qubit can be implemented by replacing a transmon Josephson junction with a superconducting quantum interference device (SQUID), which forms a superconducting loop (referred to as a SQUID loop) through an external magnetic flux, which can pass through the external magnetic flux to change the effective Josephson energy of the transmon qubit, thereby changing the transition frequency of the transmon qubit. In this regard, the flux bias control line would be configured to apply an external magnetic flux to the SQUID loop of the transmon qubit to tune the transition frequency of the transmon qubit.

[0062] Figure 3 The quantum device 300 can be implemented using different circuit architectures according to exemplary embodiments, which will now be combined with Figure 4 , Figure 5 and Figure 6 These circuit architectures are further described in detail. For example, Figure 4 Schematically shows a circuit diagram of a quantum device including superconducting qubits coupled by a superconducting multimode coupler circuit according to an exemplary embodiment of the present disclosure. More specifically, Figure 44 is a schematic circuit diagram (e.g., a lumped element circuit representation) of a superconducting quantum circuit 400, which includes a superconducting transmon qubit (or a first data qubit 410), a superconducting multimode qubit 420 (or a second data qubit 420), a superconducting multimode qubit coupler 430, a first coupling capacitor 440, a second coupling capacitor 442, and a third coupling capacitor 450. The superconducting multimode qubit coupler 430 and the coupling capacitors 440 and 442 collectively include Figure 3 An exemplary embodiment of a multi-mode coupler circuit 330 is shown.

[0063] The superconducting transmon qubit 410 includes a superconducting Josephson tunnel junction 412 (having a critical current I CT1 ) and shunt capacitor 414 (having capacitance C T1 ), which are connected in parallel between the first node N1 and the second node N2 of the superconducting transmon quantum bit 410. The Josephson tunnel junction 412 includes a small junction capacitor. For ease of explanation, Figure 4 The junction capacitance is omitted in FIG. 4. The capacitance C of the shunt capacitor 414 T1 The junction capacitance of the Josephson tunnel junction 412 is relatively large.

[0064] In some embodiments, Figure 4 As shown, the superconducting multi-mode quantum bit 420 and the superconducting multi-mode quantum bit coupler 430 each include a multi-mode double-junction superconducting quantum bit architecture, which is similar to Figure 2A The multi-mode double-junction superconducting qubit 200. Specifically, the superconducting multi-mode qubit coupler 430 includes a shunt capacitor 431, and two capacitive shunt superconducting tunnel junctions (e.g., Josephson junctions) connected in series between a first node N1 and a second node N2 of the superconducting multi-mode qubit coupler 430, wherein the first capacitive shunt Josephson junction includes a Josephson junction 432 and a capacitor 433, and wherein the second capacitive shunt Josephson junction includes a Josephson junction 434 and a capacitor 435. The shunt capacitor 431 has a capacitance C S1 , the Josephson junction 432 has a critical current I C1 , the Josephson junction 434 has a critical current I C2 , capacitor 433 has a capacitance C1, and capacitor 435 has a capacitance C2. The two capacitive shunt superconducting Josephson junctions are coupled to the middle node N3 of the superconducting multimode qubit coupler 430.

[0065] Similarly, the superconducting multimode qubit 420 includes a shunt capacitor 421, and two capacitance shunt superconducting tunnel junctions (e.g., Josephson junctions) connected in series between a first node N1 and a second node N2 of the superconducting multimode qubit 420, wherein the first capacitance shunt Josephson junction includes a Josephson junction 422 and a capacitor 423, and wherein the second capacitance shunt Josephson junction includes a Josephson junction 424 and a capacitor 425. The shunt capacitor 421 has a capacitance C S2 , the Josephson junction 422 has a critical current I C3 , the Josephson junction 424 has a critical current I C4 , capacitor 423 has a capacitance C3, and capacitor 425 has a capacitance C4. Two capacitive shunt superconducting Josephson junctions are coupled to the middle node N3 of the superconducting multimode qubit 420.

[0066] like Figure 4 As further shown in FIG. 4 , the first coupling capacitor 440 is configured to capacitively couple the first node N1 of the superconducting transmon qubit 410 to the first node N1 of the superconducting multimode qubit coupler 430. In addition, the second coupling capacitor 442 is configured to capacitively couple the second node N2 of the superconducting transmon qubit 410 to the second node N2 of the superconducting multimode qubit coupler 430. In addition, the third coupling capacitor 450 is configured to capacitively couple the third node N3 of the superconducting multimode qubit 420 to the third node N3 of the superconducting multimode qubit coupler 430.

[0067] exist Figure 4 In the exemplary circuit configuration of , superconducting transmon qubit 410 and superconducting multimode qubit 420 are configured as "data qubits" to store quantum data, and superconducting multimode qubit coupler 430 includes a multimode qubit configured as a "coupler qubit" to couple data qubits and control the interaction between data qubits. As described above, due to the multimode double-junction superconducting qubit architecture, superconducting multimode qubit 420 and superconducting multimode qubit coupler 430 each include two different excitation modes, such as A mode and B mode, such as Figure 2C As shown, the superconducting transmon qubit 410 and the superconducting multimode qubit 420 are directly coupled to different modes of the superconducting multimode qubit coupler 430 .

[0068] For example, in some embodiments, the superconducting transmon qubit 410 is directly coupled to the A mode of the superconducting multimode qubit coupler 430 via the capacitive coupling of the corresponding first node N1 through the first coupling capacitor 440, and via the capacitive coupling of the corresponding second node N2 through the second coupling capacitor 442. In addition, the superconducting multimode qubit 420 is directly coupled to the B mode of the superconducting multimode qubit coupler 430 via the capacitive coupling of the corresponding third node N3 through the coupling capacitor 450. More specifically, in Figure 4 In the exemplary embodiment shown, the B mode of the superconducting multimode qubit 420 is directly coupled to the B mode of the superconducting multimode qubit coupler 430 by means of capacitive coupling of the corresponding third node N3 through the third coupling capacitor 450. In addition, the A mode of the superconducting multimode qubit 420 is configured as a data mode for storing quantum data, thereby Figure 4 In the exemplary configuration of , the A mode is not directly coupled to the superconducting multimode qubit coupler 430 .

[0069] In addition, Figure 4 In an exemplary configuration of , superconducting multimode qubit coupler 430 is configured to operate in a first state (referred to herein as a “closed” state) and a second state (referred to herein as an “on” state) to control the interaction between coupled data qubits (e.g., superconducting transmon qubit 410 and superconducting multimode qubit 420). In some embodiments, the operating state of superconducting multimode qubit coupler 430 is controlled by applying microwave control pulses to superconducting multimode qubit coupler 430 (via coupler drive line 332, Figure 3 , Figure 4 (not specifically shown) to control the state of the B mode of the superconducting multi-mode quantum bit coupler 430.

[0070] For example, in the “off” state, the B mode of the superconducting multimode qubit coupler 430 is in the ground state |0>, and no microwave control pulse is applied to the superconducting multimode qubit coupler 430. In the “off” state, the superconducting multimode qubit coupler 430 implements mode-selective exchange coupling between the first data qubit 410 and the second data qubit 420 and different excitation modes of the superconducting multimode qubit coupler 430 to produce a condition of essentially zero interaction (e.g., suppressed static ZZ interaction) between the first data qubit 410 and the second data qubit 420. More specifically, when the superconducting multimode qubit coupler 430 is in the “off” state, due to the different charge patterns of the A mode and the B mode of the superconducting multimode qubit coupler 430, the superconducting transmon qubit 410 is only exchange-coupled to the A mode of the superconducting multimode qubit coupler 430, and the B mode of the superconducting multimode qubit 420 is only exchange-coupled to the B mode of the superconducting multimode qubit coupler 430 (e.g., as Figure 3 C). In this regard, in the “off” state, residual longitudinal interactions (e.g., static ZZ interactions) between first data qubit 410 and second data qubit 420 are substantially suppressed because first data qubit 410 and second data qubit 420 are exchange coupled to different modes of superconducting multimode qubit coupler 430.

[0071] On the other hand, to perform an entanglement gate operation, superconducting multimode qubit coupler 430 is temporarily driven to an “on” state by applying a microwave control pulse (with appropriately calibrated frequency, duration, envelope amplitude, etc.) to drive the B mode of superconducting multimode qubit coupler 430 through a full 2π rotation about the X-axis of the Bloch sphere (e.g., from the ground state |0> to the first excited state |1>, and back to the ground state |0>). The microwave control pulse drives the B mode of superconducting multimode qubit coupler 430 in a manner that changes the energies of the A and B modes of superconducting multimode qubit coupler 430, and essentially destroys the mode-selective coupling of the first data qubit 410 and the second data qubit 420 to the corresponding A and B modes of superconducting multimode qubit coupler 430, thereby allowing a ZZ interaction between the first data qubit 410 and the second data qubit 420 to perform an entanglement gate operation (e.g., a CPHASE operation).

[0072] More specifically, driving the B-mode of the superconducting multimode qubit coupler 430 causes a state-dependent Stark shift in the data modes of both the first data qubit 410 and the second data qubit 420 (e.g., the plasma mode of the superconducting transmon qubit 410, and the A-mode of the superconducting multimode qubit 420), which causes the data modes of the first data qubit 410 and the second data qubit 420 to have a longitudinal coupling (e.g., ZZ coupling) to the B-mode of the superconducting multimode qubit coupler 430. The state-dependent Stark shift in the data modes is equivalent to a microwave-activated ZZ coupling between the data modes of the first data qubit 410 and the second data qubit 420, which mediates an entanglement gate operation between the first data qubit 410 and the second data qubit 420. For example, for a CPHASE gate operation, when the data modes of the first data qubit 410 and the second data qubit 420 are both in an excited state (e.g., a ket|1> state), a conditional Z rotation can be achieved.

[0073] It should be noted that the state-dependent Stark shift is an AC Stark shift that Figure 4 The coupling configuration is used to mediate the longitudinal interaction (e.g., ZZ interaction) between the first data qubit 410 and the second data qubit 420 to achieve an entanglement gate operation. In general, the AC Stark shift is based on the AC Stark effect, where the transition frequency of a qubit can be shifted by a certain amount by applying an electromagnetic (EM) tone to the qubit. The amount of AC Stark shift of the transition frequency of the qubit is based on, for example, the intensity (e.g., amplitude) of the EM tone and the amount of detuning between the frequency of the EM tone and the transition frequency of the qubit. Figure 4 In an exemplary embodiment of the present invention, a state-dependent Stark shift is achieved by applying a microwave pulse with a given frequency to drive the B mode of superconducting multimode qubit coupler 430 (which has a given transition frequency), which results in exchange coupling of energy between superconducting multimode qubit coupler 430 and first data qubit 410 and second data qubit 420. Depending on the state of first data qubit 410 and second data qubit 420, a shift in the transition frequency of superconducting multimode qubit coupler 430 may occur depending on the data qubit state, wherein such a state-based shift in the transition frequency of superconducting multimode qubit coupler 430 in turn modifies the strength of the AC Stark shift felt by first data qubit 410 and second data qubit 420. The resulting state-dependent Stark shift is utilized to achieve a controlled Z-gate between first data qubit 410 and second data qubit 420.

[0074] Figure 4The exemplary superconducting quantum circuit 400 shown in can be implemented using planar microwave circuit elements, which are formed on a substrate (e.g., a silicon substrate) using prior art semiconductor manufacturing techniques and materials. For example, various components of superconducting quantum bits (e.g., Josephson tunnel junction devices, inductors, capacitors), interconnects, coupling circuits, coupler drive lines, quantum bit drive lines, and state readout lines, etc. include lithographically defined patterns of superconducting materials formed on semiconductor substrates. Circuit elements can be formed using various types of superconductor materials suitable for a given application, including but not limited to single metals such as niobium (Nb), aluminum (Al), and tantalum (Ta), and compounds such as titanium nitride (TiN), niobium nitride (NbN), and niobium titanium nitride (NbTiN). The Josephson tunnel junction device includes two superconducting electrodes separated by a thin insulating barrier layer. For example, a Josephson tunnel junction device for a superconducting quantum bit can include an Al-AlOx-Al three-layer tunnel junction manufactured using a double-angle evaporation technique or other suitable manufacturing techniques.

[0075] Figure 5 Schematically shows an exemplary embodiment according to the present disclosure Figure 4 The planar circuit configuration of the superconducting quantum circuit 400. More specifically, Figure 5 A planar superconducting quantum circuit 500 is schematically shown, which includes a superconducting transmon qubit 510 (or a first data qubit 510), a superconducting multimode qubit 520 (or a second data qubit 520), a superconducting multimode qubit coupler 530, a first superconducting coupling capacitor 540, a second superconducting coupling capacitor 542 and a third superconducting coupling capacitor 550.

[0076] Superconducting transmon qubit 510 includes a Josephson tunnel junction device 512 and a shunt capacitor 514. In some embodiments, shunt capacitor 514 includes a coplanar parallel plate capacitor structure including a first superconducting pad 514-1 (or first electrode) and a second superconducting pad 514-2 (or second electrode), which corresponds to having a shunt capacitance C T1 The shunt capacitor 414 (at Figure 4 ). The Josephson tunnel junction device 512 includes a first superconducting electrode and a second superconducting electrode coupled to a first superconducting pad 514-1 and a second superconducting pad 514-2 of a shunt capacitor 514, respectively. In some embodiments, as Figure 5 As schematically shown in FIG. 5 , the Josephson tunnel junction device 512 is disposed between a first superconducting pad 514 - 1 and a second superconducting pad 514 - 2 of a shunt capacitor 514 .

[0077] The superconducting multimode qubit 520 includes a first superconducting pad 521-1, a second superconducting pad 521-2, a third superconducting pad 521-3, a fourth superconducting pad 521-4, a fifth superconducting pad 521-5, a first Josephson tunnel junction device 522, and a second Josephson tunnel junction device 524. The first superconducting pad 521-1 and the second superconducting pad 521-2 include electrodes of a coplanar parallel plate capacitor structure, which corresponds to a capacitor having a capacitance C S2 The shunt capacitor 421 ( Figure 4 ). The first Josephson tunnel junction device 522 is coupled to the first superconducting pad 521-1 and the third superconducting pad 521-3 and is disposed between the first superconducting pad 521-1 and the third superconducting pad 521-3. The second Josephson tunnel junction device 524 is coupled to the second superconducting pad 521-2 and the third superconducting pad 521-3 and is disposed between the second superconducting pad 521-2 and the third superconducting pad 521-3.

[0078] The first superconducting pad 521-1 and the third superconducting pad 521-3 include electrodes of a coplanar parallel plate capacitor structure corresponding to the shunt capacitor 423 ( Figure 4 ), the shunt capacitor 423 provides a capacitance C3 on the Josephson tunnel junction device 522. Similarly, the second superconducting pad 521-2 and the third superconducting pad 521-3 include capacitors corresponding to the shunt capacitors 425 ( Figure 4 ) of the coplanar parallel plate capacitor structure, the shunt capacitor 425 provides a shunt capacitance C4 across the Josephson tunnel junction device 524. In addition, in some embodiments, as Figure 5 As shown, the fourth superconducting pad 521-4 and the fifth superconducting pad 521-5 are connected to opposite ends of the third superconducting pad 521-3, and the third superconducting pad 521-3 corresponds to the third node N3 of the superconducting multimode qubit 520. The fourth superconducting pad 521-4 and the fifth superconducting pad 521-5 are configured to mediate capacitive coupling to the B mode of the superconducting multimode qubit 520, as described above.

[0079] The superconducting multimode qubit coupler 530 includes a first superconducting pad 531-1, a second superconducting pad 531-2, a third superconducting pad 531-3, a fourth superconducting pad 531-4, a first Josephson tunnel junction device 532, and a second Josephson tunnel junction device 534. The first superconducting pad 531-1 and the second superconducting pad 531-2 include electrodes of a coplanar parallel plate capacitor structure corresponding to a capacitor having a capacitance C S1 The shunt capacitor 431 ( Figure 4). The first Josephson tunnel junction device 532 is coupled to the first superconducting pad 531-1 and the third superconducting pad 531-3 and is disposed between the first superconducting pad 531-1 and the third superconducting pad 531-3. The second Josephson tunnel junction device 534 is coupled to the second superconducting pad 531-2 and the third superconducting pad 531-3 and is disposed between the second superconducting pad 531-2 and the third superconducting pad 531-3.

[0080] The first superconducting pad 531-1 and the third superconducting pad 531-3 include electrodes of a coplanar parallel plate capacitor structure corresponding to the shunt capacitor 433 ( Figure 4 ), the shunt capacitor 433 provides a shunt capacitance C1 across the Josephson tunnel junction device 532. Similarly, the second superconducting pad 531-2 and the third superconducting pad 531-3 include a shunt capacitor 435 ( Figure 4 ), the shunt capacitor 435 provides a shunt capacitance C2 across the Josephson tunnel junction device 534. In addition, in some embodiments, as Figure 5 As shown, the fourth superconducting pad 531-4 is connected to an end of the third superconducting pad 531-3, which corresponds to the third node N3 of the superconducting multimode qubit coupler 530. The fourth superconducting pad 521-4 is configured to enable and mediate capacitive coupling to the B mode of the superconducting multimode qubit coupler 530, as described above.

[0081] The first superconducting coupling capacitor 540 and the second superconducting coupling capacitor 542 are configured to enable and mediate capacitive coupling of the first data qubit 510 to the A mode of the superconducting multimode qubit coupler 530, and the third superconducting coupling capacitor 550 is configured to enable and mediate capacitive coupling of the B mode of the second data qubit 520 to the B mode of the superconducting multimode qubit coupler 530. More specifically, as Figure 5 As shown in the exemplary embodiment of the first superconducting coupling capacitor 540 (which corresponds to Figure 4 The first coupling capacitor 440 of the superconducting transmon qubit 510 includes a superconducting planar transmission line, such as a coplanar waveguide, which is configured to capacitively couple the first superconducting pad 514-1 of the shunt capacitor 514 of the superconducting transmon qubit 510 to the first superconducting pad 531-1 (e.g., node N1) of the superconducting multimode qubit coupler 530. The first superconducting coupling capacitor 540 includes (i) a first end portion overlapping a portion of the first superconducting pad 514-1 of the shunt capacitor 514 of the superconducting transmon qubit 510, and (ii) a second end portion overlapping a portion of the first superconducting pad 531-1 of the superconducting multimode qubit coupler 530. The coupling capacitance (e.g., C C1) depends at least in part on the amount of overlap and spacing between the ends of the first superconducting coupling capacitor 540 and the first superconducting pads 514-1 and 531-1.

[0082] Similarly, the second superconducting coupling capacitor 542 (which corresponds to Figure 4 The second coupling capacitor 442 of the superconducting transmon qubit 510 includes a superconducting planar transmission line, such as a coplanar waveguide, which is configured to capacitively couple the second superconducting pad 514-2 of the shunt capacitor 514 of the superconducting transmon qubit 510 to the second superconducting pad 531-2 (e.g., node N2) of the superconducting multimode qubit coupler 530. The second superconducting coupling capacitor 542 includes (i) a first end portion overlapping a portion of the second superconducting pad 514-2 of the shunt capacitor 514 of the superconducting transmon qubit 510, and (ii) a second end portion overlapping a portion of the second superconducting pad 531-2 of the superconducting multimode qubit coupler 530. The coupling capacitance (e.g., C C2 ) depends at least in part on the amount of overlap and spacing between the ends of the second superconducting coupling capacitor 542 and the second superconducting pads 514-2 and 531-2.

[0083] In addition, the third superconducting coupling capacitor 550 (which corresponds to Figure 4 The third coupling capacitor 450 includes a first superconducting pad 552 (or a first coupling electrode), a second superconducting pad 554 (or a second coupling electrode), which are connected by a superconducting planar transmission line 556 (e.g., a coplanar waveguide). The first superconducting pad 552 is capacitively coupled to the fourth superconducting pad 521-4 of the superconducting multimode qubit 520. The second superconducting pad 554 is capacitively coupled to the fourth superconducting pad 531-4 of the superconducting multimode qubit coupler 530. In this exemplary configuration, the third node N3 of the superconducting multimode qubit 520 is capacitively coupled to the third node N3 of the superconducting multimode qubit coupler 530 (e.g., direct coupling of the second data qubit 520 and the B mode of the superconducting multimode qubit coupler 530). The coupling capacitance (e.g., C C3 ) depends at least in part on (i) the amount of capacitive coupling between superconducting pads 552 and 524-1, and (ii) the amount of capacitive coupling between superconducting pads 554 and 531-4.

[0084] Figure 6 Schematically shows another exemplary embodiment according to the present disclosure Figure 4 The planar circuit configuration of the superconducting quantum circuit 400. More specifically, Figure 6A planar superconducting quantum circuit 600 is schematically shown, which includes a superconducting transmon quantum bit 610 (or a first data quantum bit 610), a superconducting multimode quantum bit 620 (or a second data quantum bit 620), and a superconducting multimode quantum bit coupler 630. Figure 5 In contrast to the exemplary embodiments, Figure 6 Planar superconducting quantum circuit 600 is configured to provide direct capacitive coupling of first data qubit 610 and second data qubit 620 to superconducting multimode qubit coupler 630 without the need for a separate superconducting coupling capacitor.

[0085] The superconducting transmon qubit 610 includes a Josephson tunnel junction device 612 and a shunt capacitor 614. In some embodiments, the shunt capacitor 614 includes a coplanar parallel plate capacitor structure including a first superconducting pad 614-1 (or first electrode) and a second superconducting pad 614-2 (or second electrode), which corresponds to a shunt capacitor having a capacitance C T1 The shunt capacitor 414 (at Figure 4 ). The Josephson tunnel junction device 612 includes a first superconducting electrode and a second superconducting electrode coupled to a first superconducting pad 614-1 and a second superconducting pad 614-2 of a shunt capacitor 614, respectively. In some embodiments, as Figure 6 As schematically shown in FIG. 6 , the Josephson tunnel junction device 612 is disposed between a first superconducting pad 614 - 1 and a second superconducting pad 614 - 2 of a shunt capacitor 614 .

[0086] The superconducting multimode quantum bit 620 includes a first superconducting pad 621-1, a second superconducting pad 621-2, a third superconducting pad 621-3, a fourth superconducting pad 621-4, a fifth superconducting pad 621-5, a first Josephson tunnel junction device 622, and a second Josephson tunnel junction device 624. The first superconducting pad 621-1 and the second superconducting pad 621-2 include a capacitor C S2 The shunt capacitor 421 ( Figure 4 ). The first Josephson tunnel junction device 622 is coupled to the first superconducting pad 621-1 and the third superconducting pad 621-3 and is disposed between the first superconducting pad 621-1 and the third superconducting pad 621-3. The second Josephson tunnel junction device 624 is coupled to the second superconducting pad 621-2 and the third superconducting pad 621-3 and is disposed between the second superconducting pad 621-2 and the third superconducting pad 621-3.

[0087] The first superconducting pad 621-1 and the third superconducting pad 621-3 include electrodes of a coplanar parallel plate capacitor structure corresponding to the shunt capacitor 423 ( Figure 4), the shunt capacitor 423 provides a shunt capacitance C3 on the Josephson tunnel junction device 622. Similarly, the second superconducting pad 621-2 and the third superconducting pad 621-3 include a shunt capacitor 425 ( Figure 4 ) of the coplanar parallel plate capacitor structure, the shunt capacitor 425 provides a shunt capacitance C4 across the Josephson tunnel junction device 624. In addition, in some embodiments, such as Figure 6 As shown, the fourth superconducting pad 621-4 and the fifth superconducting pad 621-5 are connected to opposite ends of the third superconducting pad 621-3, and the third superconducting pad 621-3 corresponds to the third node N3 of the superconducting multimode qubit 620. The fourth superconducting pad 621-4 and the fifth superconducting pad 621-5 are configured to mediate capacitive coupling with the B mode of the superconducting multimode qubit 620, as described above.

[0088] The superconducting multimode qubit coupler 630 includes a first superconducting pad 631-1, a second superconducting pad 631-2, a third superconducting pad 631-3, a fourth superconducting pad 631-4, a first Josephson tunnel junction device 632, and a second Josephson tunnel junction device 634. The first superconducting pad 631-1 and the second superconducting pad 631-2 include electrodes of a coplanar parallel plate capacitor structure corresponding to a shunt capacitor 431 ( Figure 4 ). The first Josephson tunnel junction device 632 is coupled to the first superconducting pad 631-1 and the third superconducting pad 631-3 and is disposed between the first superconducting pad 631-1 and the third superconducting pad 631-3. The second Josephson tunnel junction device 634 is coupled to the second superconducting pad 631-2 and the third superconducting pad 631-3 and is disposed between the second superconducting pad 631-2 and the third superconducting pad 631-3.

[0089] The first superconducting pad 631-1 and the third superconducting pad 631-3 include electrodes of a coplanar parallel plate capacitor structure corresponding to the shunt capacitor 433 ( Figure 4 ), the shunt capacitor 433 provides a shunt capacitance C1 across the Josephson tunnel junction device 632. Similarly, the second superconducting pad 631-2 and the third superconducting pad 631-3 include a shunt capacitor 435 ( Figure 4 ) of the coplanar parallel plate capacitor structure, the shunt capacitor 435 provides a shunt capacitance C2 across the Josephson tunnel junction device 634.

[0090] Furthermore, in some embodiments, Figure 6As shown, the fourth superconducting pad 631-4 is connected to the end of the third superconducting pad 631-3, which corresponds to the third node N3 of the superconducting multimode qubit coupler 430. The fourth superconducting pads 621-4 and 631-4 are configured to enable and mediate direct capacitive coupling of the B mode of the superconducting multimode qubit 620 to the B mode of the superconducting multimode qubit coupler 630. In addition, as Figure 6 As further shown in , due to the direct capacitive coupling of (i) the corresponding first superconducting pads 614-1 and 631-1 and (ii) the direct capacitive coupling of the corresponding second superconducting pads 614-2 and 631-2 of the superconducting transmon qubit 610 and the superconducting multimode qubit coupler 630, the superconducting transmon qubit 610 is directly capacitively coupled to the A mode of the superconducting multimode qubit coupler 630.

[0091] Figure 4 , Figure 5 and Figure 6 The various superconducting circuit elements of the superconducting quantum circuits 400, 500 and 600 in the embodiment can be configured to achieve the desired operating characteristics. In some embodiments, the superconducting multimode qubit coupler that couples the first data qubit and the second data qubit will be configured with an A mode and a B mode, and the A mode and the B mode have frequencies close to the transition frequencies of the first data qubit and the second data qubit. In addition, the transition frequencies of the first and second data qubits will be slightly different. In order to realize the entanglement gate, the superconducting multimode qubit coupler will be driven with a microwave control signal having a frequency close to the transition frequencies of the first and second data qubits.

[0092] For example, refer to Figure 4 In a non-limiting exemplary embodiment, superconducting transmon qubit 410 comprises a fixed frequency transmon qubit, which may be configured to have a transition frequency f Q = 4.29 GHz and given anharmonicity, where the critical current I of the Josephson tunnel junction device 412 is based on, for example, CT1 and the capacitance C of the shunt capacitor 414 T1 The selection of a specific value of f to achieve such an operating parameter. In addition, in a non-limiting exemplary embodiment, the superconducting multimode qubit 420 can be configured to have f A =4.2GHz and f B =5.54 GHz mode frequency (f A ) and B-mode frequency (f B ) and the corresponding anharmonicity, where the critical current I of the Josephson tunnel junction devices 422 and 424 is based on, for example, C3 and I C4The selection of specific values ​​of and the capacitance C of the corresponding capacitors 421, 423 and 425 S2 , C3 and C4 to achieve such operating parameters.

[0093] Furthermore, in a non-limiting exemplary embodiment, the superconducting multimode qubit coupler 430 may be configured to have f A =4.1GHz and f B =5.82GHz mode frequency (f A ) and B-mode frequency (f B ) and the corresponding anharmonicity, where the critical current I of the Josephson tunnel junction devices 432 and 434 is based on, for example, C1 and I C2 and the capacitance C of the corresponding capacitors 431, 433 and 435 S1 , C1 and C2 are selected to achieve such operating parameters. In addition, the coupling capacitors are selected to achieve the desired level of exchange coupling between the first data qubit 410 and the superconducting multimode qubit coupler 430 and between the second data qubit 420 and the superconducting multimode qubit coupler 430.

[0094] Using these exemplary parameters, computer simulations were performed that indicated that with superconducting multimode qubit coupler 430 in the “off” state, significantly low static ZZ coupling (e.g., as low as 1.6 kHz) can be achieved between superconducting transmon qubit 410 and the A mode (data mode) of superconducting multimode qubit 420. Furthermore, computer simulations indicated that when superconducting multimode qubit coupler 430 was driven to the “on” state via a calibrated microwave pulse, (i) relatively high longitudinal coupling (e.g., up to 22.4 MHz) can be achieved between superconducting transmon qubit 410 and the B mode of superconducting multimode qubit coupler 430, and (ii) relatively high longitudinal coupling (e.g., up to 29.6 MHz) can be achieved between the A mode (data mode) of superconducting multimode qubit 420 and the B mode of superconducting multimode qubit coupler 430. In this regard, the longitudinal coupling (e.g., ZZ coupling) between the B mode of superconducting multimode qubit coupler 430 and the data modes of first data qubit 410 and second data qubit 420 is approximately 10,000 times greater than the static ZZ coupling between the data modes of first data qubit 410 and second data qubit 420.

[0095] Furthermore, as described above, the exemplary quantum circuits as discussed herein are configured to suppress the effects of observer qubits. For example, Figure 7A quantum device 700 including an array of superconducting qubits and multimode qubit couplers according to an exemplary embodiment of the present disclosure is schematically shown, which is configured to suppress crosstalk between an observer qubit and an adjacent multimode qubit coupler. More specifically, the quantum device 700 includes a first superconducting multimode qubit 710, a superconducting transmon qubit 720, a second superconducting multimode qubit 730, a first superconducting multimode qubit coupler 740, and a second superconducting multimode qubit coupler 750. The first superconducting multimode qubit 710 and the superconducting transmon qubit 720 are coupled together by the first superconducting multimode qubit coupler 740. In addition, the superconducting transmon qubit 720 and the second superconducting multimode qubit 730 are coupled together by the second superconducting multimode qubit coupler 750.

[0096] exist Figure 7 In the exemplary configuration of , the second superconducting multimode qubit 730 can act as an observer qubit, which can potentially adversely affect the transition frequency of the first superconducting multimode qubit coupler 740 through static ZZ coupling 760, and thus adversely affect the fidelity of the entanglement gate operation performed between the first superconducting multimode qubit 710 and the superconducting transmon qubit 720. Similarly, the first superconducting multimode qubit 710 can act as an observer qubit, which can adversely affect the transition frequency of the second superconducting multimode qubit coupler 750 through static ZZ coupling, and thus adversely affect the fidelity of the entanglement gate operation performed between the second superconducting multimode qubit 730 and the superconducting transmon qubit 720. However, the exemplary quantum device 700 is configured to suppress crosstalk between a given superconducting multimode qubit and an adjacent multimode qubit coupler that is not directly coupled to the given superconducting multimode qubit.

[0097] For example, assuming that the superconducting transmon qubit 720, the second superconducting multimode qubit coupler 750 and the second superconducting multimode qubit 730 have the same characteristics as the superconducting transmon qubit 410, the superconducting multimode qubit coupler 430 and the second superconducting multimode qubit 420 ( Figure 4 ) have the same operating characteristics as described above. It is further assumed that the first superconducting multimode qubit coupler 740 is configured to have an A-mode frequency f A =4.0GHz and B-mode frequency f B =5.72 GHz. Using these exemplary operating parameters, computer simulations have indicated that the longitudinal coupling between the A mode (data mode) of the second superconducting multimode qubit 730 and the B mode of the first superconducting multimode qubit coupler 740 is as low as 0.004 kHz, which is so small as to vanish, thereby significantly suppressing the observer effect.

[0098] It should be understood that the exemplary quantum devices discussed herein (e.g., Figure 7 ) is configured to suppress observer effects, for example, suppressing static ZZ between a multimode qubit and a remote multimode qubit coupler. In essence, suppression of the observer effect is achieved due to mode-selective exchange coupling between the multimode qubit coupler and the transmon qubit. Only the A-mode of the multimode qubit coupler has exchange coupling with the transmon qubit, which prevents any exchange or longitudinal (ZZ) coupling between the B-modes of the multimode qubit coupler connected to a particular transmon. This isolation subsequently prevents any exchange or longitudinal coupling between the B-mode of a given multimode qubit coupler and any mode of an observer multimode qubit connected to another multimode qubit coupler.

[0099] Although Figure 5 and Figure 6 Planar superconducting quantum circuits 500 and 600 are schematically shown including two superconducting data qubits coupled by a superconducting multimode qubit coupler, but it should be understood that, depending on the application, superconducting quantum devices such as quantum processors can be implemented using superconducting qubit arrays including tens, hundreds, or thousands or more coupled superconducting qubits. For example, Figure 8 Schematically illustrates an array of superconducting qubits coupled by a superconducting multimode qubit coupler circuit according to an exemplary embodiment of the present disclosure. More specifically, Figure 8 A multi-qubit array 800 is schematically shown, which includes a plurality of data qubits, including superconducting multimode qubits 810-1, 810-2, 810-3, 810-4, and 810-5, superconducting quadrupole transmon qubits 820-1 and 820-2, and a plurality of superconducting multimode qubit couplers 830-1, 830-2, 830-3, 830-4, 830-5, and 830-6. Figure 8 In the exemplary configuration of , the data qubits are capacitively coupled directly to superconducting multimode qubit couplers 830-1, 830-2, 830-3, 830-4, 830-5, and 830-6 (without using separate superconducting coupling capacitors).

[0100] Figure 8 An exemplary layout of a unit cell including a heavy hexagonal lattice structure as known in the art is shown. The heavy hexagonal lattice layout is particularly suitable for superconducting qubit architectures to minimize frequency collisions and crosstalk between qubits (the term "heavy" describes the exemplary layout in which qubits are placed at both the vertices and edges of the hexagonal lattice). Figure 8In an exemplary embodiment of the present invention, a heavy hexagonal lattice structure is facilitated by using superconducting quadrupole transmon qubits 820-1 and 820-2, each of which allows dipole-dipole interaction and coupling with at least three superconducting multimode qubit couplers, such as shown.

[0101] like Figure 8 As schematically shown in FIG. 1 , each of superconducting multimode quantum bits 810-1, 810-2, 810-3, 810-4 and 810-5 includes a superconducting multimode quantum bit 810-1, 810-2, 810-3, 810-4 and 810-5 as shown in FIG. Figure 5 and Figure 6 The exemplary layouts of the discussed superconducting multimode qubits 520 and 620 are similar to the layouts. Figure 8 As specifically shown in FIG. 8 , superconducting multimode qubit 810-1 includes a first superconducting pad 811-1, a second superconducting pad 811-2, a third superconducting pad 811-3, a fourth superconducting pad 811-4, a fifth superconducting pad 811-5, a first Josephson tunnel junction device 812, and a second Josephson tunnel junction device 814. Superconducting pads 811-1, 811-2, 811-3, 811-4, and 811-5 include capacitor electrodes of a coplanar parallel plate capacitor structure, which form a shunt capacitor of superconducting multimode qubit 810-1, as described above.

[0102] In addition, each of the superconducting multimode quantum bit couplers 830-1, 830-2, 830-3, 830-4, 830-5 and 830-6 includes a Figure 5 and Figure 6 The superconducting multimode qubit couplers 530 and 630 discussed above have similar layouts. Figure 8 As specifically shown in FIG. 8 , the superconducting multimode qubit coupler 830-1 includes a first superconducting pad 831-1, a second superconducting pad 831-2, a third superconducting pad 831-3, a first Josephson tunnel junction device 832, and a second Josephson tunnel junction device 834. Superconducting pads 831-1, 831-2, and 831-3 include capacitor electrodes of a coplanar parallel plate capacitor structure, which form a shunt capacitor of the superconducting multimode qubit coupler 830-1, as described above. In addition, Figure 8 Schematically illustrates an exemplary embodiment of a superconducting multimode qubit coupler 830-1, wherein the end of the superconducting pad 831-3 is directly capacitively coupled to the fourth superconducting pad 811-4 of the superconducting multimode qubit 810-1 without using an additional extended superconducting pad, such as Figure 6 The fourth superconducting pad 631 - 4 is shown in FIG.

[0103] exist Figure 8In the exemplary layout of , the B-mode of superconducting multimode qubit 810-1 is directly capacitively coupled to the B-mode of superconducting multimode qubit coupler 830-1. The B-mode of superconducting multimode qubit 810-2 is directly capacitively coupled to the B-mode of superconducting multimode qubit coupler 830-2. The B-mode of superconducting multimode qubit 810-3 is directly capacitively coupled to the B-mode of superconducting multimode qubit coupler 830-3. The B-mode of superconducting multimode qubit 810-4 is directly capacitively coupled to the B-mode of superconducting multimode qubit coupler 830-4. The B-mode of superconducting multimode qubit 810-5 is directly capacitively coupled to the B-mode of superconducting multimode qubit coupler 830-5 and the B-mode of superconducting multimode qubit coupler 830-6.

[0104] As mentioned above, in Figure 8 In the exemplary layout shown, each superconducting quadrupole transmon qubit 820-1 and 820-2 is configured to implement dipole-dipole interaction with three superconducting tunable coupler qubits. Figure 4 , Figure 5 and Figure 6 The superconducting transmon qubits shown operate in a similar manner, except that superconducting quadrupole transmon qubits 820-1 and 820-2 each include a different arrangement of parallel capacitor pads that have a quadrupole charge pattern when energized. Figure 8 As shown, the superconducting quadrupole transmon qubit 820-1 includes a single Josephson tunnel junction device 822, which has a Manhattan Josephson junction framework, and a first superconducting pad 824-1, a second superconducting pad 824-2, a third superconducting pad 824-3 and a fourth superconducting pad 824-4, which together include capacitor electrode pads forming a shunt capacitor of the superconducting quadrupole transmon qubit 820-1.

[0105] The first superconducting pad 824-1, the second superconducting pad 824-2, the third superconducting pad 824-3, and the fourth superconducting pad 824-4 of the superconducting quadrupole transmon qubit 820-1 are arranged in a rectangular array. The first superconducting pad 824-1 and the second superconducting pad 824-2 are configured to implement a first capacitor electrode of a shunt capacitor and are commonly connected to a first electrode of a single Josephson tunnel junction device 822. The third superconducting pad 824-3 and the fourth superconducting pad 824-4 are configured to implement a second capacitor electrode of a shunt capacitor and are commonly connected to a second electrode of a single Josephson tunnel junction device 822. Using an exemplary quadrupole configuration, as shown in FIG. Figure 8As shown, the superconducting quadrupole transmon qubit 820-1 is configured to be directly capacitively coupled to each of the three superconducting multimode qubit couplers 830-1, 830-3, and 830-5. For example, the first superconducting pad 831-1 and the second superconducting pad 832-2 of the superconducting multimode qubit coupler 830-1 are directly capacitively coupled to the first superconducting pad 824-1 and the fourth superconducting pad 824-4 of the superconducting quadrupole transmon qubit 820-1, respectively.

[0106] As described above, the use of superconducting quadrupole transmon qubits 820-1 and 820-2 facilitates Figure 8 , because each superconducting quadrupole transmon qubit can be coupled to three superconducting tunable coupler qubits to achieve a unit cell layout of the multi-qubit array 800 including seven (7) superconducting data qubits. It should be understood that Figure 8 The array shown adds one more heavy hexagonal unit cell to achieve a larger multi-qubit array. For example, in some embodiments, the multi-qubit array 800 can be expanded by coupling (B-mode coupling) one or more of the superconducting multimode qubits 810-1, 810-2, 810-3, and 810-4 to corresponding superconducting multimode qubit couplers to expand the heavy hexagonal lattice structure. In other exemplary embodiments, the multi-qubit array 800 can be expanded by coupling (mode coupling) additional superconducting multimode qubit couplers to each of the superconducting quadrupole transmon qubits 820-1 and 820-2 to expand the lattice structure, in which case each superconducting quadrupole transmon qubit 820-1 and 820-2 will be coupled to four (4) superconducting multimode qubit couplers to achieve a heavy square lattice.

[0107] As is known in the art, calibration procedures are periodically performed on a quantum system such as a quantum processor to calibrate various quantum elements such as a readout resonator, data qubits, and coupler circuits to achieve high-fidelity gate operations (e.g., single-qubit gate operations and entangled gate operations). For example, various types of in-situ calibration procedures are periodically performed to, for example, determine the resonant frequency of the readout resonator, determine the transition frequency of the qubit, determine the coherence time (T1) of the qubit (where the coherence time T1 of a given qubit represents the time it takes for the qubit state to decay from an excited state to a ground state), determine the transverse relaxation time (T2) of the qubit (or the decoherence time of the qubit along the XY plane of the Bloch sphere), calibrate the control pulses applied to the qubit to perform a single-qubit gate operation, calibrate the control pulses applied to the active coupler circuit to perform an entangled gate operation, etc. The calibration process results in the determination of various control parameters that are maintained in a calibration database and updated periodically as needed on the order of seconds, minutes, hours, days, etc., depending on the type of quantum element and the operating characteristics of the quantum computing system, as well as other factors understood by those of ordinary skill in the art.

[0108] Exemplary embodiments of the present disclosure include techniques for calibrating a two-qubit gate operation of a superconducting qubit coupled by a superconducting multimode qubit coupler. For example, in some embodiments, as described above, a two-qubit entanglement gate operation (e.g., a CPHASE gate) is performed on a data qubit coupled to a superconducting multimode qubit coupler by driving the B-mode of the superconducting multimode qubit coupler using a control pulse that is appropriately calibrated to cause the data qubit to undergo a state-dependent Stark shift (which is equivalent to microwave-activated ZZ), thereby causing a conditional Z-axis rotation of the data qubit according to the state of the data qubit.

[0109] As part of the two-qubit gate calibration process, the shape and amplitude of the control pulses are calibrated to drive the B mode of the superconducting multimode qubit coupler through a full 2π rotation (e.g., from the ground state 0|0> to the first excited state |1>, and back to the ground state |0>). In addition, the calibration process includes iteratively adjusting the detuning of the control pulses to ensure that the desired conditional Z rotation is achieved for the data qubit while obtaining a full 2π rotation of the B mode of the superconducting multimode qubit coupler. When calibrating the control pulses, it is desirable to utilize control pulses with a short duration and sufficient amplitude in order to perform gate operations that are fast enough than the finite coherence time of the qubit. However, short pulses (e.g., square wave pulses) that are turned on and off too quickly often include unwanted spectral components that can excite higher qubit states, such as the second excited state |2> and higher, which can result in low-fidelity gate operations. For example, the increased spectral width of the fast pulses can excite f12 jump, resulting in errors.

[0110] In this regard, various pulse shaping techniques may be utilized to calibrate a precise pulse shape that provides the desired spectral components that drive transitions between the ground state |0> and the first excited state |1> while suppressing undesirable spectral components that drive transitions to and between higher states. For example, shaped pulses such as Gaussian pulses, cosine pulses (e.g., the sum of half cosines), or hyperbolic secant pulses may be used to drive f 01 transition, while suppressing f 12 and higher transitions. Essentially, this pulse shaping technique suppresses / reduces transients associated with turning on and off control pulses. Additionally, pulse shaping techniques include DRAG (Derivative Removal by Adiabatic Heat) correction pulses, which can be used in conjunction with shaped pulses (e.g., Gaussian, cosine, or hyperbolic secant pulses) to further suppress unwanted state transitions while maintaining the same pulse envelope area (or integral of the pulse envelope). The DRAG correction technique essentially superimposes a finely tuned out-of-phase component with the main control pulse, which has an envelope that is a derivative of the main control pulse and is configured to further suppress f 12 and higher jumps.

[0111] Now combine Fig. 9 and FIG. 10A to FIG. 10I An exemplary technique for calibrating a two-qubit gate operation of a superconducting qubit coupled by a superconducting multimode qubit coupler is discussed in further detail. In some embodiments, the two-qubit gate calibration process includes calibrating a hyperbolic secant pulse with DRAG correction to drive a superconducting coupler (e.g., a superconducting multimode qubit coupler) to perform an entanglement gate operation (e.g., a CPHASE gate) between two superconducting qubits (e.g., a superconducting transmon qubit and a superconducting multimode qubit) coupled to the superconducting coupler.

[0112] More specifically, in an exemplary embodiment, an analog control pulse, A(t), having a DRAG-corrected hyperbolic secant pulse shape is defined as follows:

[0113]

[0114] Where A0 represents the amplitude of the hyperbolic secant pulse envelope, where σ is a measure of the transition time of the pulse, and where A1 represents the amplitude of the DRAG correction pulse. In this embodiment, the DRAG correction pulse includes a pulse envelope proportional to the time derivative of the hyperbolic secant pulse, which is superimposed on the hyperbolic secant pulse to suppress unwanted transitions. In some embodiments, hyperbolic secant pulses are utilized because such pulse shapes can produce high-fidelity 2π rotations of qubits for a wide range of detuning between the pulse frequency and the qubit frequency. In other embodiments, control pulses can be implemented using a pulse envelope generated using a sum of half cosines, which is robust over a wide range of detuning and works best for longer gate times. In other embodiments, standard Gaussian pulses with DRAG correction can be utilized in the presence of sufficiently strong coupling between the data qubit and the coupler mode.

[0115] Reference now Fig. 9 , a flow chart illustrating a method for calibrating an entanglement gate operation of a superconducting qubit coupled by a superconducting multimode qubit coupler according to an exemplary embodiment of the present disclosure. An initial step includes starting an entanglement gate calibration process (box 900) at an appropriate stage in the overall calibration process. For example, as described above, the calibration process involves different calibration stages with respect to, for example, calibrating a readout resonator, a qubit, a coupler, etc. In some embodiments, the entanglement gate calibration process begins after, for example, a calibration stage that is performed to determine the resonant frequency of a readout resonator coupled to a data qubit and a qubit coupler, and to determine the transition frequencies of the data qubit and the qubit coupler, etc. It should be noted that the entanglement gate calibration process is performed for each two-qubit gate circuit within the quantum system. Fig. 9 The entanglement gate calibration process is described in the context of a single two-qubit gate circuit because each two-qubit gate circuit has different operating frequencies and characteristics, so the control parameters will vary between different two-qubit gate circuits. For ease of explanation, Fig. 9 , but it should be understood that the same entanglement gate calibration process will be applied to each two-qubit gate circuit within the quantum system.

[0116] The initial step of the entanglement gate calibration process includes initializing the parameters of the control pulse, and generating an initial control pulse and applying it to the target multi-mode qubit coupler (box 901). For example, in an exemplary embodiment where the control pulse includes a hyperbolic secant pulse with DRAG correction, the parameters A0, σ, A1, pulse duration, and frequency are set to initial values. It should be noted that the control pulses for a given superconducting multi-mode qubit coupler can be generated using known arbitrary waveform generation (AWG) techniques that implement IQ amplitude modulation. In particular, the exemplary AWG system includes a baseband signal generator, a digital-to-analog converter (DAC) stage, an IQ modulation stage, and a phase-locked loop system to generate a local oscillator (LO) signal (e.g., orthogonal LO signals LO_I and LO_Q) for the IQ modulation stage.

[0117] The baseband signal generator generates a digital baseband signal (e.g., a digital IQ signal) under software control of a gate calibration process, wherein the digital baseband signal is generated based on target parameters for generating analog control pulses. The DAC stage converts the digital baseband signal into an analog baseband signal having a baseband frequency (e.g., analog baseband signals I(t) and Q(t)). In particular, the DAC stage operates as an envelope generator of analog IQ envelope pulses (e.g., I(t) and Q(t)) including a hyperbolic secant pulse shape and a superimposed DRAG correction pulse shape. The analog IQ signal is filtered and applied to the IQ signal modulation stage. The IQ modulation stage performs amplitude modulation by modulating an orthogonal LO signal (e.g., an in-phase LO signal (LO_I) and an orthogonal phase LO signal (LO_Q)) with the analog IQ signal to generate a modulated analog control signal, which includes an analog control pulse for driving a superconducting multimode quantum bit coupler.

[0118] For a first calibration procedure in which no previous calibration pulses are generated, the amplitude parameter A1 (for the drag correction pulse envelope) can be initialized to A1=0, and the amplitude parameter A0 (for the hyperbolic secant pulse envelope) can be selected based on the known operating characteristics of the hardware circuits that generate and apply the control pulses to the superconducting multimode qubit coupler (e.g., the amount of signal attenuation applied to the control input of the superconducting multimode qubit coupler along the RF path, the operating characteristics of the IQ mixer of the IQ modulation stage, the amplitude / strength of the LO signal, etc.). In addition, the parameters σ and the pulse duration are initially set to target values ​​that define the initial control pulse length. In addition, the LO frequency is set to a frequency close to the B-mode frequency of the superconducting multimode qubit coupler for a given two-qubit gate to be calibrated. It should be noted that for a current calibration procedure that performs a previous calibration procedure to calibrate the gate pulse, the current calibration procedure can utilize some or all of the previously calibrated control pulse parameters as initial parameters.

[0119] A current control pulse is applied to drive the B mode of a given superconducting multimode qubit coupler, and the state of the B mode of the given superconducting multimode qubit coupler is measured to determine the amount of X rotation obtained in response to the applied control pulse (block 902). At this stage of the entanglement gate calibration process, it is desirable to achieve a full 2π rotation of the B mode around the X axis of the Bloch sphere (i.e., a transition from the ground state |0> to the first excited state |1> and back to the ground state |0>). In some embodiments, the process (block 902) is performed hundreds or thousands of times for the current control pulse to determine whether a full 2π rotation of the B mode is achieved with high probability based on probability information derived from a set of measured states. For each iteration, the B mode of the superconducting multimode qubit coupler is initialized to the ground state |0>, a current control pulse is applied to drive the B mode, and the B mode state is measured via, for example, a readout system.

[0120] If it is determined that a full 2π rotation of the B mode is not obtained for the current control pulse (a negative result in block 903), the software calibration control process continues to recalibrate the control pulse by adjusting the amplitude A0 of the hyperbolic secant pulse envelope as needed to obtain a full 2π rotation (block 904). The iterative process (blocks 902, 903, and 904) is then repeated for each recalibrated control pulse within the range of amplitude A0 values ​​until a full 2π rotation of the B mode of a given superconducting multimode qubit coupling is obtained in response to a given control pulse with a given amplitude A0 value (a positive result in block 903).

[0121] Once the amplitude A0 of the control pulse is properly calibrated to obtain a full 2π rotation of the state of the B mode of the given superconducting multimode qubit coupler (affirmative result in box 903), the B mode of the given superconducting multimode qubit coupler is driven using a current control pulse, a conditional Z-rotation operation is performed on the data qubit coupled to the given superconducting multimode qubit coupler (box 905), and the resulting state of the data qubit is measured to determine whether the target conditional Z-rotation is obtained in response to the current control pulse (box 906).

[0122] In some embodiments, a process for performing a conditional Z-rotation gate operation and measuring a conditional Z-rotation of a data qubit is performed by a process comprising multiple iterations of: (i) selecting one data qubit (e.g., a superconducting multimode qubit) as a "target" qubit Q0, and selecting other data qubits (e.g., superconducting transmon qubits) as "control" qubits Q1; (ii) placing the target qubit Q0 in a ground state |0>, a first excited state |1>, or an even superposition state, (iii) placing the control qubit Q1 in a ground state |0> or a first excited state |1>, (iv) applying a control pulse to drive the B-mode of the superconducting multimode qubit coupler, and (v) performing, for example, a Ramsey experiment to measure the result of the conditional Z-rotation achieved. For an appropriate CPPHASE gate operation, if both data qubits are in an excited state, both data qubits will have a Z-rotation (e.g., a π-rotation) in response to the CPPHASE gate operation. Otherwise, as a result of the CPHASE gate operation, both data qubits will have no Z-rotation.

[0123] Upon completion of the process in boxes 905 and 906, if it is determined that the target conditional Z rotation of the data qubit is not achieved due to driving the B-mode of the superconducting multimode qubit coupler with the current control pulse (a negative result in box 906), the calibration control process continues to adjust the "detuning" of the control pulse (box 907). In particular, the term "detuning" refers to the difference between the frequency of the control pulse and the B-mode frequency of the superconducting multimode qubit coupler. In some embodiments, detuning is performed by incrementally adjusting the LO frequency applied to the IQ modulation stage to generate control pulses with a recalibrated frequency that is detuned from the B-mode frequency of the superconducting multimode qubit coupler. The iterative process (boxes 905, 906, and 907) is then repeated for each recalibrated control pulse within the detuning range until the desired conditional Z rotation of the data qubit is achieved due to driving the B-mode of the superconducting multimode qubit coupler with a sufficiently detuned control pulse (a positive result in box 906).

[0124] Once the detuning of the control pulses is sufficiently calibrated to obtain the target condition Z rotation of the data qubit, a current control pulse is applied to drive the B mode of the given superconducting multimode qubit coupler, and the state of the B mode of the given superconducting multimode qubit coupler is measured to determine the amount of X-axis rotation obtained in response to the applied control pulse (block 908). At this stage of the entanglement gate calibration process, it is expected to achieve a full 2π rotation about the X axis of the Bloch sphere using the newly detuned control pulse. If it is determined that a full 2πX rotation axis of the B mode is not obtained using the current detuned control pulse (a negative result in block 909), Software calibration controlThe process continues to recalibrate the control pulses and amplitudes by adjusting the amplitude A0 of the hyperbolic secant pulse envelope and the amplitude A1 of the DRAG correction pulse as needed to achieve a full 2π X-axis rotation with the currently detuned control pulse (block 910). The iterative process (blocks 908, 909, and 910) is repeated for each recalibrated control pulse over the range of A0 and A1 amplitude values ​​until a full 2π X-axis rotation of the B mode of the given superconducting multimode qubit coupler is obtained using control pulses with recalibrated A0 and A1 amplitudes and the current detuning (affirmative result in block 909).

[0125] Once the amplitudes A0 and A1 of the control pulses are properly calibrated at the current detuning to obtain a full 2π rotation of the B mode of the given superconducting multimode qubit coupler, a new amplitude calibration control pulse is used to drive the B mode of the given superconducting multimode qubit coupler to perform a conditional Z rotation operation, and the resulting state of the data qubit is measured to determine whether the target conditional Z rotation is obtained in response to the new amplitude calibration control pulse using the current detuning (box 911). At this point in the entanglement gate calibration process, if the target conditional Z rotation is obtained in response to the new amplitude calibration control pulse using the current detuning (a positive result in box 911), the entanglement gate calibration process is considered complete and terminated (box 912).

[0126] On the other hand, if the target conditional Z rotation is not obtained in response to the new amplitude calibration control pulse using the current detuning (negative result in block 911), and if obtaining the target conditional Z rotation is deemed achievable by further iterations of recalibrating the detuning and amplitude of the control pulse (affirmative determination in block 913), then the gate calibration process continues to recalibrate the detuning of the control pulse (returning to block 907). Thereafter, the iterative process of blocks 905, 906, 907, 908, 909, 910, and 911 is repeated with the goal of obtaining a sufficiently calibrated control pulse in which both (i) a full 2π X-axis rotation of the B mode of the superconducting multimode qubit coupler and (ii) the target conditional Z rotation of the data qubit are obtained with an error below a predetermined error threshold.

[0127] At some point in the entanglement gate calibration process, if it is determined that the target conditional Z rotation of the data qubit is not achievable (negative determination in block 913), the gate calibration control process proceeds to recalibrate the control pulses by adjusting the pulse duration and / or the pulse transition time σ (block 914), and repeat the entanglement gate calibration process (returning to block 901). For example, in some embodiments, it may be determined (in block 913) that the target conditional Z rotation of the data qubit is not achievable after completing a number of iterations of adjusting the amplitudes A0 and A1 of the control pulses and detuning without sufficient convergence to minimize the error below a predetermined error threshold.

[0128] It should be understood that Fig. 9 The entanglement gate calibration process provides an accurate and efficient method for calibrating control pulses for two-qubit conditional gate operations. In fact, since the superconducting multimode qubit coupler includes anharmonic modes (e.g., anharmonic B modes), the calibration process can be configured to individually calibrate the control pulse shape to rotate the multimode qubit coupler through a full 2πX axis with high precision, without considering the detuning between the control pulse and the mode frequency (e.g., B mode frequency) of the multimode qubit coupler. The pulse detuning is then individually calibrated to achieve the desired conditional Z rotation of the data qubit. The process of iteratively repeating the individual detuning and amplitude calibration stages allows the entanglement gate calibration process to gradually achieve higher fidelity.

[0129] Fig. 10A , Fig. 10B , Fig. 10C , Fig. 10D , Fig. 10E , Fig.10F , Figure 10G , Fig. 10H and Fig.10I Describes the use of an exemplary embodiment according to the present disclosure based on Fig. 9 The time-dependent numerical simulation results of an exemplary entanglement gate calibration process are evaluated by the control pulses of the process calibration. In particular, Figures 10A-10I The computer simulation results of the entanglement gate calibration process (e.g., two-qubit gate) of an exemplary system including a superconducting transmon qubit and a superconducting multimode qubit coupled by a superconducting multimode qubit coupler (such as Figure 4 For the simulation results, the transmon qubit was designated as the control qubit. In addition, computer simulations were performed using the exemplary parameters described above, in which the superconducting transmon qubit was set to have a transition frequency f Q = 4.29 GHz, the superconducting multimode qubit is set to have an A-mode frequency f A=4.2GHz and B-mode frequency f B =5.54 GHz, and the superconducting multimode qubit coupler is set to have an A-mode frequency f A =4.1GHz and B-mode frequency f B =5.82GHz. It should be understood that Figures 10A-10I The computer simulation results shown in are presented for the purpose of illustrating aspects of an exemplary entanglement gate calibration process and should not be construed in any limiting manner as to the scope of the claimed subject matter.

[0130] Fig. 10A A waveform diagram 1000 of calibration control pulses generated using an entanglement gate calibration process according to an exemplary embodiment of the present disclosure is included. In particular, Fig. 10A An exemplary pulse envelope 1002 of a calibration control pulse is shown, the calibration control pulse having a pulse duration of 90 nanoseconds (ns), an amplitude A0 = 0.13342 (arb units), a DRAG correction A1 = -3 (no units), σ = 15 ns, and a detuning = -5.2 MHz. For ease of illustration, Fig. 10A A pulse envelope representing the amplitude modulation envelope of the Rabi oscillation (Y-axis) over a time period from 0 ns to 90 ns (X-axis) is shown, omitting the actual illustration of the Rabi oscillation which is otherwise indiscernible at the pulse frequency of the calibration control pulse. Fig. 10A Exemplary calibration control pulses for driving the B-mode of a superconducting multimode qubit coupler to perform a two-qubit entangled gate operation (e.g., a CPHASE gate) are shown.

[0131] Fig. 10B and Fig. 10C is a timing diagram showing the state projection (along the Z axis of the Bloch sphere) of the B mode of a superconducting multimode qubit coupler for controlling different states of a qubit according to an exemplary embodiment of the present disclosure. In particular, Fig. 10B 1 is a timing diagram 1010 showing a curve 1012 representing a state projection of the B-mode of a superconducting multimode qubit coupler over the duration (0 ns to 90 ns) of a calibration control pulse driving the B-mode of the superconducting multimode qubit coupler, wherein the control qubit (e.g., a superconducting transmon qubit) is in the ground state |0>. In addition, Fig. 10C is a timing diagram 1020 showing curve 1022, which represents the state projection of the B-mode of the superconducting multimode qubit coupler within the duration (0ns to 90ns) of the calibration control pulse that drives the B-mode of the superconducting multimode qubit coupler, wherein the control qubit (e.g., a superconducting transmon qubit) is in a first excited state |1>.

[0132] exist Fig. 10B and Fig. 10C In the figure, the y-axis represents the value of the state projection (along the Z-axis of the Bloch sphere) of the B mode of the superconducting multimode quantum bit coupler, where state projection = 1.0 represents the ground state of the B mode, where state projection = -1.0 represents the first excited state of the B mode, and where state projection = 0 represents an even superposition state of the ground state and the first excited state. Fig. 10B and Fig. 10C The simulation results shown in are performed by placing a target qubit (e.g., a superconducting multimode qubit) in a uniform superposition of the ground state and the first excited state, and placing a control qubit (e.g., a superconducting transmon qubit) in the ground state |0> or the first excited state |1>, and applying a calibration control pulse to the B mode of the superconducting multimode qubit coupler to evaluate the ability of the calibration control pulse to drive the B mode of the coupler through a full 2π rotation (e.g., from the ground state |0> to the first excited state |1>, and back to the ground state |0>). Fig. 10B and Fig. 10C It shows that when the superconducting multimode qubit coupler transitions through different paths depending on the state of the control qubit, the B mode returns to the ground state.

[0133] Next, Fig. 10D , Fig. 10E , Fig.10F and Figure 10G is a timing diagram showing the state projection (along the Z-axis of the Bloch sphere) of a data qubit coupled to a superconducting multimode qubit coupler according to an exemplary embodiment of the present disclosure, which is produced by driving the B-mode of the superconducting multimode qubit coupler with calibrated control pulses for different states of the control qubit. In particular, Fig. 10D is a timing diagram 1030 showing a curve 1032 representing the state projection (along the Z-axis of the Bloch sphere) of the target qubit Q0 (e.g., a superconducting multimode qubit) over the duration (0 ns to 90 ns) of a calibration control pulse driving the B-mode of the superconducting multimode qubit coupler, wherein the control qubit Q1 (e.g., a superconducting transmon qubit) is in the ground state |0>. In addition, Fig. 10E is a timing diagram 1040 showing curve 1042, which represents the state projection (along the Z-axis of the Bloch sphere) of the target quantum bit Q0 within the duration (0ns to 90ns) of the calibration control pulse that drives the B-mode of the superconducting multimode quantum bit coupler, where the control quantum bit Q1 is in the first excited state |1>.

[0134] Similarly, Fig.10Fis a timing diagram 1050 showing a curve 1052 representing the state projection (along the Z-axis of the Bloch sphere) of the control qubit Q1 over the duration (0 ns to 90 ns) of the calibration control pulse driving the B-mode of the superconducting multimode qubit coupler, wherein the control qubit Q1 is in the ground state |0>. In addition, Figure 10G is a timing diagram 1060 showing curve 1062, which represents the state projection (along the Z-axis of the Bloch sphere) of the control quantum bit Q1 within the duration (0ns to 90ns) of the calibration control pulse that drives the B-mode of the superconducting multimode quantum bit coupler, where the control quantum bit Q1 is in the first excited state |1>.

[0135] like Fig. 10D , Fig. 10E , Fig.10F and Figure 10G The simulation results of the state projection shown show that in each case, when the B mode of the superconducting multimode qubit coupler is driven with a calibrated control pulse, the data qubits Q0 and Q1 eventually approach their starting states, which is the desired result. In fact, when the conditional Z-gate operation is performed, there should be no X or Y rotation of the data qubits, because the phase of the data qubits should only be changed when both data qubits are in an excited state.

[0136] Next, Fig. 10H is a timing diagram 1070 according to an exemplary embodiment of the present disclosure, which shows a curve 1072 representing the conditional Z rotation obtained for the target qubit in response to driving the B-mode of the superconducting multimode qubit coupler with a calibrated control pulse. The conditional Z rotation can be measured by calculating the X and Y state projections of the target qubit Q0 over time, which allows one to determine how the phase of the target qubit Q0 evolves over time as it undergoes precession around the equator of the Bloch sphere (e.g., the XY plane). We subtract the phase of the target qubit Q0 during the gate operation with the control qubit Q1 in its ground state or first excited state. The difference is the conditional Z rotation, which is Fig. 10H The figure shows the 90 nanosecond period of the control pulse. Fig. 10H The simulation results in show that a conditional Z rotation of π radians can be achieved within the 90 nanosecond time period of the calibration control pulse, which is sufficient for a maximally entangled gate.

[0137] Next, Fig.10I1 is a timing diagram 1080 showing a curve 1082 representing the concurrency of the amount of entanglement obtained when a superconducting multimode qubit coupler is driven with a calibration control pulse to perform an entanglement gate operation according to an exemplary embodiment of the present disclosure. The concurrency of the system is calculated to evaluate the amount of entanglement and obtain an upper limit on the gate fidelity. A concurrency value of 1 indicates maximum entanglement, while deviations from a concurrency value of 1 indicate incomplete entanglement or leakage of the computational basis. For the simulation, the target qubit Q0 and the control qubit Q1 are placed in a uniform superposition of their ground state and the first excited state, and the concurrency is determined over the time period of the calibration control pulse. Fig.10I The simulation results shown in show a final concurrency of 0.9998, indicating high-fidelity entanglement gate operation.

[0138] Fig.11 A quantum computing system according to an exemplary embodiment of the present disclosure is schematically shown. In particular, Fig.11 The quantum computing system 1100 is schematically shown, which includes a quantum computing platform 1110, a control system 1120, and a quantum processor 1130. In some embodiments, the quantum computing platform 1110 implements a software control program, such as a gate calibration process 1112, which is configured to perform, for example, an entanglement gate calibration process to calibrate the two-qubit gate system implemented by the quantum processor 1130, and to perform the above-mentioned combined Fig. 9 Other calibration operations discussed. Additionally, in some embodiments, control system 1120 includes a multi-channel arbitrary waveform generator 1122 and a qubit readout control system 1124. Quantum processor 1130 includes a solid-state semiconductor chip having a superconducting qubit array 1132 and a network 1134 of qubit drive lines, coupler drive lines, and qubit state readout lines, as well as other circuit QED components that may be required for a given application or quantum system configuration.

[0139] In some embodiments, the control system 1120 and the quantum processor 1130 are disposed in a dilution refrigeration system 1140, which can generate cryogenic temperatures sufficient to operate components of the control system 1120 for quantum computing applications. For example, the quantum processor 1130 may need to be cooled to near absolute zero, such as 10-15 millikelvin (mK), to allow superconducting qubits to exhibit quantum behavior. In some embodiments, the dilution refrigeration system 1140 includes a multi-stage dilution refrigerator, in which components of the control system 1120 can be maintained at different cryogenic temperatures as needed. For example, while the quantum processor 1130 may need to be cooled to, for example, 10-15 mK, the circuit components of the control system 1120 can be operated at cryogenic temperatures greater than 10-15 mK (e.g., cryogenic temperatures in the range of 3K-4K), depending on the configuration of the quantum computing system.

[0140] In some embodiments, superconducting qubit array 1132 includes a plurality of superconducting transmon qubits and superconducting tunable coupler qubits, wherein each pair of superconducting qubits is connected via a corresponding superconducting qubit coupler using techniques as discussed herein. For example, in some embodiments, superconducting qubit array 1132 implements Figure 8 The multi-qubit array 800 of FIG. As described above, the superconducting qubit coupler is configured to control the interaction between the spatially separated superconducting qubit pairs to implement the entanglement gate operation. The number of superconducting qubits in the qubit array 1132 can be in the order of tens, hundreds, thousands, or more.

[0141] The network 1134 of qubit drive lines, coupler drive lines, qubit state readout lines, etc. is configured to apply microwave control signals to the superconducting qubits and coupler circuits in the superconducting qubit array 1132 to perform various types of gate operations, such as single gate operations, entanglement gate operations (e.g., CPHASE gate operations), etc., and to read the quantum state of the superconducting qubits. More specifically, as described above, microwave control pulses are applied to the qubit drive lines of the corresponding superconducting qubits to change the quantum state of the superconducting qubits (e.g., to change the quantum state of a given qubit between a ground state and an excited state, or to a superposition state). In particular, as described above, the qubit drive line for a given superconducting qubit is used to modify the state of a given superconducting qubit by applying a microwave drive pulse having a center frequency that matches the operating frequency of the given superconducting qubit. In addition, when certain quantum information processing algorithms are executed, calibration control pulses are applied to the coupler drive lines to perform entanglement gate operations between coupled superconducting qubit pairs.

[0142] In addition, as described above, the state readout line includes a readout resonator coupled to the corresponding superconducting qubit. The state of a given superconducting qubit can be determined by microwave transmission measurements performed between the readout ports of the readout resonator. The state of the superconducting qubit is read out after executing the quantum algorithm. In some embodiments, a dispersive readout operation is performed, in which the state (e.g., ground state or excited state) of a given superconducting qubit is read out using a change in the resonant frequency of a given readout resonator coupled to a given superconducting qubit.

[0143] A network 1134 of qubit drive lines, coupler drive lines, qubit state readout lines, etc. is coupled to the control system 1120 via a suitable hardware input / output (I / O) interface that couples I / O signals between the control system 1120 and the quantum processor 1130. For example, the hardware I / O interface may include various types of hardware and components, such as RF cables, wiring, RF elements, optical fibers, heat exchangers, filters, amplifiers, isolators, etc.

[0144] In some embodiments, a multi-channel arbitrary waveform generator (AWG) 1122 and other suitable microwave pulse signal generators are configured to generate microwave control pulses that are applied to the qubit drive lines and coupler drive lines to control the operation of the superconducting qubits and associated qubit coupler circuits when performing various gate operations to perform a given specific quantum information processing algorithm. In some embodiments, the multi-channel AWG 1122 includes a plurality of AWG channels that control corresponding superconducting qubits within the superconducting qubit array 1132 of the quantum processor 1130. In some embodiments, each AWG channel includes a baseband signal generator, a digital-to-analog converter (DAC) stage, a filter stage, a modulation stage, an impedance matching network, and a phase-locked loop system to generate a local oscillator (LO) signal (e.g., orthogonal LO signals LO_I and LO_Q) for the corresponding modulation stage of the corresponding AWG channel.

[0145] In some embodiments, the multi-channel AWG 1122 includes an orthogonal AWG system configured to process orthogonal signals, wherein the orthogonal signals include an in-phase (I) signal component and a quadrature phase (Q) signal component. In each AWG channel, a baseband signal generator is configured to receive baseband data as input (e.g., from a quantum computing platform) and generate digital quadrature signals I and Q representing the input baseband data. In this process, the baseband data input to the baseband signal generator of a given AWG channel is separated into two orthogonal digital components, including an in-phase (I) baseband component and a quadrature phase (Q) baseband component. The baseband signal generator for a given AWG channel will generate the necessary digital quadrature baseband IQ signals required to generate an analog waveform (e.g., a sinusoidal voltage waveform) having a target center frequency that is configured to operate or otherwise control a given quantum bit coupled to the output of the given AWG channel.

[0146] The DAC stage of a given AWG channel is configured to convert a digital baseband signal (e.g., a digital IQ signal output from a baseband signal generator) into an analog baseband signal having a baseband frequency (e.g., analog baseband signals I(t) and Q(t)). The filter stage for a given AWG channel is configured to filter the IQ analog signal components output from the DAC stage, thereby generating a filtered analog IQ signal. The modulation stage for a given AWG channel is configured to perform analog IQ signal modulation (e.g., single sideband (SSB) modulation) by mixing the filtered analog signals I(t) and Q(t) output from the filter stage with quadrature LO signals (e.g., in-phase LO signal (LO_I) and quadrature phase LO signal (LO_Q)) to generate and output an analog RF signal (e.g., a single sideband modulated RF output signal).

[0147] In some embodiments, the qubit readout control system 1124 includes a microwave pulse signal generator configured to apply a microwave tone to a given readout resonator line of a given superconducting qubit to perform a readout operation to read out the state of the given superconducting qubit, and a circuit configured to process the readout signal generated by the readout resonator line to determine the state of the given superconducting qubit using techniques known to those of ordinary skill in the art.

[0148] The quantum computing platform 1110 includes a software and hardware platform, which includes various software layers configured to perform various functions, including but not limited to generating and implementing various quantum applications using a suitable quantum programming language, configuring and implementing various quantum gate operations, compiling quantum programs into quantum assembly languages, implementing and utilizing a suitable quantum instruction set architecture (ISA), performing calibration operations to calibrate quantum circuit elements and gate operations, etc. In addition, the quantum computing platform 1110 includes a hardware architecture of processors, memories, etc., which are configured to control the execution of quantum applications and interface with the control system 1120 to (i) generate digital control signals, which are converted by the control system 1120 into analog microwave control signals to control the operation of the quantum processor 1130 when executing a given quantum application, and (ii) obtain and process digital signals received from the control system 1120, which represent processing results generated by the quantum processor 1130 when executing various gate operations of a given quantum application.

[0149] In some exemplary embodiments, the quantum computing platform 1110 of the quantum computing system 1100 may use any suitable computing system architecture (e.g., Fig.12 The computing system architecture is implemented by executing computer-readable program instructions embodied on a computer program product to implement a method of supporting quantum computing operations, the computer program product including a computer-readable storage medium (or medium) having such computer-readable program instructions thereon, for causing a processor to execute a control method as discussed herein.

[0150] A computer-readable storage medium may be a tangible device that can retain and store instructions used by an instruction execution device. A computer-readable storage medium may be, for example, but not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. A non-exhaustive list of more specific examples of computer-readable storage media includes the following: a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a static random access memory (SRAM), a portable compact disk read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanical encoding device (such as a punched card or a raised structure in a groove on which instructions are recorded), and any suitable combination of the foregoing. As used herein, a computer-readable storage medium should not be interpreted as a temporary signal itself, such as a radio wave or other freely propagating electromagnetic wave, an electromagnetic wave propagated through a waveguide or other transmission medium (e.g., a light pulse through a fiber optic cable), or an electrical signal transmitted through a wire.

[0151] The computer-readable program instructions described herein can be downloaded from a computer-readable storage medium to a corresponding computing / processing device, or downloaded to an external computer or external storage device via a network (e.g., the Internet, a local area network, a wide area network, and / or a wireless network). The network can include copper transmission cables, optical transmission fibers, wireless transmissions, routers, firewalls, switches, gateway computers, and / or edge servers. The network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards the computer-readable program instructions to be stored in a computer-readable storage medium in the corresponding computing / processing device.

[0152] The computer-readable program instructions for performing the operations discussed herein may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-related instructions, microcode, firmware instructions, state setting data, configuration data for integrated circuits, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, and procedural programming languages ​​such as "C" programming language or similar programming languages. The computer-readable program instructions may be executed entirely on the user's computer, partially on the user's computer, as an independent software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the latter case, the remote computer may be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., by using the Internet of an Internet service provider). In some embodiments, an electronic circuit including, for example, a programmable logic circuit, a field programmable gate array (FPGA), or a programmable logic array (PLA) may execute computer-readable program instructions to personalize the electronic circuit by utilizing the state information of the computer-readable program instructions, so as to perform various operations as discussed herein.

[0153] Computer-readable program instructions may be provided to a processor of a computer or other programmable data processing apparatus to produce a machine, such that the instructions executed via the processor of the computer or other programmable data processing apparatus create a device for implementing the functions / actions as discussed herein. These computer-readable program instructions may also be stored in a computer-readable storage medium, which may instruct a computer, a programmable data processing apparatus, and / or other device to function in a particular manner, such that the computer-readable storage medium having the instructions stored therein comprises an article of manufacture, which comprises instructions for implementing the exemplary computing operations as discussed herein.

[0154] Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus, or other device to produce a computer-implemented process, so that the instructions executed on the computer, other programmable apparatus, or other device implement the functions / actions discussed herein.

[0155] The block diagrams in the accompanying drawings illustrate the architecture, functions and operations of possible implementations of the system, method and computer program product according to various embodiments of the present invention. In this regard, each block diagram may represent a module, segment or portion of an instruction, which includes one or more executable instructions for implementing a specified logical function. In some alternative embodiments, the functions annotated in the box may not occur in the order annotated in the figure. For example, the two boxes shown in succession can actually be completed as a step, executed simultaneously, substantially simultaneously, in a partially or completely time-overlapping manner, or these boxes can sometimes be executed in reverse order, depending on the functions involved. It will also be noted that each box of the block diagram and the combination of the boxes in the block diagram can be implemented by a dedicated hardware-based system that performs a specified function or action or performs a combination of dedicated hardware and computer instructions.

[0156] refer to Fig.12 These concepts are shown, Fig.12 Schematically illustrates an exemplary architecture of a computing node that can host a quantum computing platform according to an exemplary embodiment of the present disclosure. For example, Fig.12 Schematically shows a quantum computing platform 1110 ( Fig.11 ) is an exemplary architecture of a computing node 1200. More specifically, Fig.12 The computing node 1200 is shown to include a computer system / server 1212 that can operate with numerous other general purpose or special purpose computing system environments or configurations. Examples of well-known computing systems, environments, and / or configurations that may be suitable for use with the computer system / server 1212 include, but are not limited to, personal computer systems, server computer systems, thin clients, fat clients, handheld or laptop devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputer systems, mainframe computer systems, and distributed cloud computing environments including any of the above systems or devices, and the like.

[0157] Computer system / server 1212 can be described in the general context of computer system executable instructions (such as program modules) executed by a computer system. In general, program modules can include routines, programs, objects, components, logic, data structures, etc. that perform specific tasks or implement specific abstract data types. Computer system / server 1212 can be practiced in a distributed cloud computing environment, where tasks are performed by remote processing devices linked through a communication network. In a distributed cloud computing environment, program modules can be located in both local and remote computer system storage media including memory storage devices.

[0158] exist Fig.1212, the computer system / server 1212 in the computing node 1200 is shown in the form of a general-purpose computing device. The components of the computer system / server 1212 may include, but are not limited to, one or more processors or processing units 1216, a system memory 1228, and a bus 1218 that couples various system components including the system memory 1228 to the processor 1216.

[0159] Bus 1218 represents any one or more of several types of bus structures, including a memory bus or memory controller, a peripheral bus, an accelerated graphics port, and a processor or local bus using any of a variety of bus architectures. By way of example and not limitation, such architectures include an Industry Standard Architecture (ISA) bus, a Micro Channel Architecture (MCA) bus, an Enhanced ISA (EISA) bus, a Video Electronics Standards Association (VESA) local bus, and a Peripheral Component Interconnect (PCI) bus.

[0160] Computer system / server 1212 typically includes a variety of computer system readable media. Such media can be any available media that can be accessed by computer system / server 1212, and it includes volatile and nonvolatile media, removable and non-removable media.

[0161] System memory 1228 may include computer system readable media in the form of volatile memory, such as random access memory (RAM) 1230 and / or cache memory 1232. Computer system / server 1212 may also include other removable / non-removable, volatile / non-volatile computer system storage media. By way of example only, a storage system 1234 may be provided for reading and writing from a non-removable non-volatile magnetic medium (not shown and generally referred to as a "hard drive"). Although not shown, a disk drive for reading and writing from a removable non-volatile disk (e.g., a "floppy disk") may be provided, as well as an optical drive for reading or writing from a removable non-volatile optical disk (e.g., a CD-ROM, DVD-ROM, or other optical media). In this case, each may be connected to bus 1218 via one or more data media interfaces. As depicted and described herein, memory 1228 may include at least one program product having a set (e.g., at least one) of program modules configured to perform the functions of an embodiment of the present invention.

[0162] By way of example and not limitation, a program / utility 1240 having a set (at least one) of program modules 1242, as well as an operating system, one or more application programs, other program modules, and program data, may be stored in memory 1228. Each or some combination of the operating system, one or more application programs, other program modules, and program data may include an implementation of a networking environment. Program modules 1242 generally perform the functions and / or methods of embodiments of the present disclosure as described herein.

[0163] The computer system / server 1212 may also communicate with one or more external devices 1214 (such as a keyboard, a pointing device, a display 1224, etc.), one or more devices that enable a user to interact with the computer system / server 1212, and / or any device that enables the computer system / server 1212 to communicate with one or more other computing devices (e.g., a network card, a modem, etc.). Such communication may occur via an input / output (I / O) interface 1222. In addition, the computer system / server 1212 may communicate with one or more networks such as a local area network (LAN), a general wide area network (WAN), and / or a public network (e.g., the Internet) via a network adapter 1220. As shown, the network adapter 1220 communicates with other components of the computer system / server 1212 via a bus 1218. It should be understood that, although not shown, other hardware and / or software components may be used in conjunction with the computer system / server 1212. Examples include, but are not limited to, microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, SSD drives, and data archiving storage systems, etc.

[0164] In some embodiments, Fig.11 The quantum computing system 1100 can be implemented in the cloud (Quantum Computing as a Service (QaaS)) to provide quantum computing facilities as an on-demand service. Although the present disclosure includes a detailed description of cloud computing, the implementation of the teachings recorded herein is not limited to a cloud computing environment. Instead, the embodiments of the present disclosure can be implemented in conjunction with any other type of computing environment now known or later developed.

[0165] Cloud computing is a service delivery model for enabling convenient, on-demand network access to a shared pool of configurable computing resources (e.g., networks, network bandwidth, servers, processing, memory, storage, applications, virtual machines, and services) that can be quickly provisioned and released with minimal management effort or interaction with a service provider. The cloud model can include at least five characteristics, at least three service models, and at least four deployment models.

[0166] Features are as follows:

[0167] On-demand self-service: Cloud consumers can automatically and unilaterally provision computing capabilities, such as server time and network storage, as needed, without requiring human interaction with the service provider.

[0168] Broad Network Access: Functionality is available over the network and accessed through standard mechanisms that facilitate use of heterogeneous thin-client platforms or thick-client platforms (e.g., mobile phones, laptops, and PDAs).

[0169] Resource pooling: A provider's computing resources are pooled to serve multiple consumers using a multi-tenant model, where different physical and virtual resources are dynamically allocated and reallocated based on demand. There is a sense of location independence, as consumers generally have no control or knowledge of the exact location of the resources provided, but may be able to specify a location at a higher level of abstraction (e.g., country, state, or data center).

[0170] Rapid elasticity: Capabilities can be provisioned quickly and elastically (in some cases automatically) to scale out quickly and released quickly to scale in quickly. To the consumer, the capabilities available for provisioning often appear to be unlimited and can be purchased in any quantity at any time.

[0171] Metered Services: Cloud systems automatically control and optimize resource usage by leveraging metering capabilities at some level of abstraction appropriate to the type of service (e.g., storage, processing, bandwidth, and active user accounts). Resource usage can be monitored, controlled, and reported, providing transparency to both providers and consumers of the utilized services.

[0172] The service model is as follows:

[0173] Software as a Service (SaaS): The functionality provided to the consumer is to use the provider's applications running on the cloud infrastructure. The applications can be accessed from a variety of client devices through a thin client interface such as a web browser (e.g., web-based email). The consumer does not manage or control the underlying cloud infrastructure, including the network, servers, operating systems, storage, or even individual application functions, with the possible exception of limited user-specific application configuration settings.

[0174] Platform as a Service (PaaS): The functionality provided to consumers is to deploy applications created or acquired by consumers onto the cloud infrastructure. Applications created or acquired by consumers are created using programming languages ​​and tools supported by the provider. Consumers do not manage or control the underlying cloud infrastructure, including networks, servers, operating systems, or storage, but have control over deployed applications and possibly the configuration of the application hosting environment.

[0175] Infrastructure as a Service (IaaS): The functionality provided to consumers is the provisioning of processing, storage, networking, and other basic computing resources, where consumers can deploy and run arbitrary software, which may include operating systems and applications. Consumers do not manage or control the underlying cloud infrastructure, but have control over the operating system, storage, deployed applications, and may have limited control over select networking components (e.g., host firewalls).

[0176] The deployment model is as follows:

[0177] Private cloud: Cloud infrastructure is operated only for an organization. It can be managed by the organization or a third party and can exist on-premises or off-premises.

[0178] Community cloud: The cloud infrastructure is shared by several organizations and supports a specific community with common concerns (e.g., mission, security requirements, policies, and compliance considerations). It can be managed by the organization or a third party and can exist on-premises or off-premises.

[0179] Public cloud: Cloud infrastructure is available to the general public or large industry groups and is owned by an organization that sells cloud services.

[0180] Hybrid cloud: A cloud infrastructure is a combination of two or more clouds (private, community, or public) that remain distinct entities but are bound together by standardized or proprietary technologies that enable data and application portability (e.g., cloud bursting for load balancing between clouds).

[0181] The cloud computing environment is service-oriented, with characteristics centered on statelessness, low coupling, modularity, and semantic interoperability. The core of cloud computing is the infrastructure consisting of a network of interconnected nodes.

[0182] Reference now Fig.13 , depicts an illustrative cloud computing environment 1300. As shown, the cloud computing environment 1300 includes one or more cloud computing nodes 1350 with which a local computing device used by a cloud consumer (e.g., a personal digital assistant (PDA) or cellular phone 1354A, a desktop computer 1354B, a laptop computer 1354C, and / or an automobile computer system 1354N) can communicate. The nodes 1350 can communicate with each other. They can be physically or virtually grouped in one or more networks (not shown), such as a private cloud, community cloud, public cloud, or hybrid cloud as described above, or a combination thereof. This allows the cloud computing environment 1300 to provide infrastructure, platform, and / or software as a service that cloud consumers do not need to maintain resources on local computing devices. It should be understood that Fig.13The types of computing devices 1354A-N shown in are intended to be illustrative only, and computing node 1350 and cloud computing environment 1300 may communicate with any type of computerized device over any type of network and / or network addressable connection (eg, using a web browser).

[0183] Reference now Fig.14 , showing a cloud computing environment 1300 ( Fig.13 ) provides a set of functional abstraction layers. It should be understood in advance that Fig.14 The components, layers and functions shown in are intended to be illustrative only, and embodiments of the present invention are not limited thereto. As shown, the following layers and corresponding functions are provided:

[0184] The hardware and software layer 1460 includes hardware and software components. Examples of hardware components include: host 1461; server 1462 based on RISC (Reduced Instruction Set Computer) architecture; server 1463; blade server 1464; storage device 1465; and network and networking components 1466. In some embodiments, software components include network application server software 1467 and database software 1468.

[0185] Virtualization layer 1470 provides an abstraction layer from which the following examples of virtual entities can be provided: virtual servers 1471 ; virtual storage 1472 ; virtual networks 1473 , including virtual private networks; virtual applications and operating systems 1474 ; and virtual clients 1475 .

[0186] In one example, the management layer 1480 may provide the functionality described below. Resource provisioning 1481 provides dynamic procurement of computing resources and other resources for performing tasks within a cloud computing environment. Metering and pricing 1482 provides cost tracking when utilizing resources within a cloud computing environment, as well as billing or invoicing for the consumption of these resources. In one example, these resources may include application software licenses. Security provides authentication for cloud consumers and tasks, as well as protection for data and other resources. User portal 1483 provides access to the cloud computing environment for consumers and system administrators. Service level management 1484 provides cloud computing resource allocation and management so that the required service levels are met. Service level agreement (SLA) planning and fulfillment 1485 provides pre-scheduling and procurement of cloud computing resources for future demand for cloud computing resources in accordance with the SLA.

[0187] Workload layer 1490 provides examples of functionality that can take advantage of a cloud computing environment. Examples of workloads and functionality that can be provided from this layer include: mapping and navigation 1491; software development and lifecycle management 1492; virtual classroom education delivery 1493; data analytics processing 1494; transaction processing 1495; and various functions of a quantum computing platform for implementing a quantum computing system 1496, such as those described herein in conjunction with Fig.11 In some embodiments, the hardware and software layer 1460 will include, for example, a quantum computing system 1100 ( Fig.11 ) to implement or otherwise support various workloads and functions 1496 for performing, for example, quantum computing operations and executing quantum computing applications.

[0188] The description of various embodiments of the present disclosure has been presented for illustrative purposes, but is not intended to be exhaustive or limited to the disclosed embodiments. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is selected to best explain the principles of the embodiments, practical applications, or technical improvements to technologies found in the marketplace, or to enable those of ordinary skill in the art to understand the embodiments disclosed herein.

Claims

1. A device comprising: The first superconducting qubit; a second superconducting qubit comprising a first mode and a second mode, wherein the first mode is configured to store quantum data; and A superconducting qubit coupler coupled between the first superconducting qubit and the second superconducting qubit; wherein the superconducting qubit coupler comprises a first mode and a second mode, and is configured to operate in one of a first state and a second state in response to a control signal applied to the superconducting qubit coupler; wherein, in the first state of the superconducting qubit coupler, the first superconducting qubit is exchange-coupled to the first mode of the superconducting qubit coupler, and the second mode of the second superconducting qubit is exchange-coupled to the second mode of the superconducting qubit coupler to suppress interaction between the first modes of the first superconducting qubit and the second superconducting qubit; and Wherein, in the second state of the superconducting qubit coupler, the first modes of the first superconducting qubit and the second superconducting qubit are exchange-coupled to both the first mode and the second mode of the superconducting qubit coupler to achieve interaction between the first mode of the first superconducting qubit and the second superconducting qubit, and an entanglement gate operation is performed in response to the control signal applied to the superconducting qubit coupler.

2. The device according to the preceding claim, wherein: The control signal is configured to drive the second mode of the superconducting qubit coupler to perform the entanglement gate operation.

3. The device according to any one of the preceding claims, wherein: The control signal is configured to drive the second mode of the superconducting qubit coupler through a rotation from a ground state to a first excited state and back to the ground state to perform the entanglement gate operation.

4. The device according to any one of the preceding claims, wherein: In the first state, the second mode of the superconducting qubit coupler is in a ground state without a control signal applied to the superconducting qubit coupler.

5. Apparatus according to any one of the preceding claims, wherein: The first superconducting qubit comprises a superconducting transmon qubit.

6. The device according to the preceding claim, wherein: The superconducting transmon qubit includes a superconducting quadrupole transmon qubit.

7. Apparatus according to any one of the preceding claims, wherein: The superconducting quantum bit coupler comprises: First superconducting pad; a second superconducting pad; a third superconducting pad disposed between the first superconducting pad and the second superconducting pad; a first superconducting tunnel junction device coupled to and between the first superconducting mat and the third superconducting mat; and A second superconducting tunnel junction device is coupled to and between the second superconducting pad and the third superconducting pad.

8. Apparatus according to the preceding claim, wherein: The first superconducting quantum bit comprises: a first node coupled to the first superconducting pad of the superconducting qubit coupler; and a second node coupled to the second superconducting pad of the superconducting qubit coupler; and The second superconducting quantum bit comprises: First superconducting pad; a second superconducting pad; a third superconducting pad disposed between the first superconducting pad and the second superconducting pad; a first superconducting tunnel junction device coupled to and between the first superconducting mat and the third superconducting mat; and a second superconducting tunnel junction device coupled to and between the second superconducting mat and the third superconducting mat; Wherein, the third superconducting pad of the second superconducting qubit is coupled to the third superconducting pad of the superconducting qubit coupler.

9. A system comprising: A quantum processor comprising a superconducting qubit array; as well as a control system configured to generate control signals to control the quantum processor; Wherein, the superconducting quantum bit array comprises: The first superconducting qubit; a second superconducting qubit comprising a first mode and a second mode, wherein the first mode is configured to store quantum data; and A superconducting qubit coupler coupled between the first superconducting qubit and the second superconducting qubit; wherein the superconducting qubit coupler comprises a first mode and a second mode, and is configured to operate in one of a first state and a second state in response to a control signal applied to the superconducting qubit coupler; wherein, in the first state of the superconducting qubit coupler, the first superconducting qubit is exchange-coupled to the first mode of the superconducting qubit coupler, and the second mode of the second superconducting qubit is exchange-coupled to the second mode of the superconducting qubit coupler to suppress interaction between the first modes of the first superconducting qubit and the second superconducting qubit; and Wherein, in the second state of the superconducting qubit coupler, the first modes of the first superconducting qubit and the second superconducting qubit are exchange-coupled to both the first mode and the second mode of the superconducting qubit coupler to achieve interaction between the first mode of the first superconducting qubit and the second superconducting qubit, and an entanglement gate operation is performed in response to the control signal applied to the superconducting qubit coupler.

10. A system according to the preceding claim, wherein: The control signal is configured to drive the second mode of the superconducting qubit coupler to perform the entanglement gate operation by rotating from a ground state to a first excited state and back to the ground state; and In the first state, the second mode of the superconducting qubit coupler is in a ground state without a control signal applied to the superconducting qubit coupler.

11. A system according to any one of the two preceding claims, wherein: The first superconducting qubit comprises a superconducting transmon qubit.

12. A system according to any one of the three preceding claims, wherein: The first superconducting qubit comprises a superconducting quadrupole transmon qubit; and The superconducting quantum bit array further comprises: A second superconducting qubit coupler coupled to the superconducting quadrupole transmon qubit; A third superconducting qubit coupler coupled to the superconducting quadrupole transmon qubit; a third superconducting qubit coupled to the second superconducting qubit coupler; and A fourth superconducting qubit is coupled to the third superconducting qubit coupler.

13. A system according to any one of the preceding four claims, wherein: The superconducting quantum bit array includes a hexagonal lattice structure.

14. A system according to any one of the five preceding claims, wherein: The superconducting quantum bit coupler comprises: First superconducting pad; a second superconducting pad; a third superconducting pad disposed between the first superconducting pad and the second superconducting pad; a first superconducting tunnel junction device coupled to and between the first superconducting mat and the third superconducting mat; and A second superconducting tunnel junction device is coupled to and between the second superconducting pad and the third superconducting pad.

15. A system according to the preceding claim, wherein: The first superconducting quantum bit comprises: a first node coupled to the first superconducting pad of the superconducting qubit coupler; and a second node coupled to the second superconducting pad of the superconducting qubit coupler; and The second superconducting quantum bit comprises: First superconducting pad; a second superconducting pad; a third superconducting pad disposed between the first superconducting pad and the second superconducting pad; a first superconducting tunnel junction device coupled to and between the first superconducting mat and the third superconducting mat; and a second superconducting tunnel junction device coupled to and between the second superconducting mat and the third superconducting mat; Wherein, the third superconducting pad of the second superconducting qubit is coupled to the third superconducting pad of the superconducting qubit coupler.

16. A computer program product for calibrating an entanglement gate process, the computer program product comprising: One or more computer-readable storage media, and program instructions stored together on the one or more computer-readable storage media, the program instructions comprising: program instructions for calibrating parameters of a control pulse configured to control operation of a superconducting qubit coupler to perform an entanglement gate operation between a first superconducting qubit and a second superconducting qubit coupled to the superconducting qubit coupler; Wherein, the program instructions for calibrating the parameters of the control pulses include program instructions for performing an iterative process, wherein the iterative process includes one or more iterations of: In response to applying a control pulse having a calibrated amplitude to the superconducting qubit coupler, performing an amplitude calibration process to calibrate the amplitude of the control pulse to rotate the superconducting qubit coupler from a ground state to a first excited state and back to the ground state; and In response to applying a control pulse having the calibrated amplitude and the calibrated frequency detuning to the superconducting qubit coupler, a frequency detuning calibration process is performed to calibrate the detuning of the frequency of the control pulse relative to the operating frequency of the superconducting qubit coupler to achieve a target conditional rotation of the first superconducting qubit and the second superconducting qubit.

17. A computer program product according to the preceding claim, wherein: The program instructions for performing an amplitude calibration procedure include program instructions for calibrating the amplitude of a hyperbolic secant pulse.

18. Computer program product according to any one of the two preceding claims, wherein: The program instructions for performing the amplitude calibration procedure include program instructions for calibrating the amplitude of a hyperbolic secant pulse and the amplitude of a derivate-removed pulse by an adiabatic thermal correction pulse superimposed on the hyperbolic secant pulse.

19. A computer program product according to any one of the three preceding claims, wherein: The superconducting qubit coupler comprises a first mode and a second mode, and wherein the calibration control pulse is applied to the second mode of the superconducting qubit coupler to calibrate the entanglement gate operation.

20. A computer program product according to any one of the preceding claims, wherein: The program instructions for calibrating the parameters of the control pulses further include: Program instructions for determining whether the target conditional rotation of the first superconducting qubit and the second superconducting qubit can be achieved through further iterations of the amplitude calibration process and the frequency detuning calibration process; and Program instructions for adjusting at least one of a pulse duration and a pulse transition time of the control pulses, and in response to determining that the target conditional rotation is not achievable, repeating the iterative process.

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