Coupling data qubits to auxiliary qubits

Abstract

An apparatus includes a data qubit, a first qubit coupler, a second qubit coupler, and an auxiliary qubit. A first qubit coupler is coupled to a data qubit. The second qubit coupler is coupled to the first qubit coupler. The auxiliary qubit is coupled to the second qubit coupler. The first qubit coupler is configured to operate in a state that suppresses interaction between the data qubit and the auxiliary qubit. The first qubit coupler and the second qubit coupler are each configured to operate in respective states to cause interaction between a data qubit and an auxiliary qubit and entanglement of a state of the data qubit with a state of the auxiliary qubit.

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, where the superconducting qubits can be coherently controlled, placed in a quantum superposition state (via, for example, single gate operations), exhibit quantum interference effects, and become entangled with each other (via, for example, entanglement gate operations). The fidelity of quantum gate operations can 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, such unwanted crosstalk becomes increasingly problematic. Summary of the invention

[0003] Exemplary embodiments of the present disclosure include techniques for coupling data qubits to auxiliary qubits to facilitate operations such as quantum error correction.

[0004] An exemplary embodiment includes an apparatus including a first data qubit, a first qubit coupler, a second qubit coupler, and an auxiliary qubit. The first qubit coupler is coupled to the first data qubit. The second qubit coupler is coupled to the first qubit coupler. The auxiliary qubit is coupled to the second qubit coupler. The first qubit coupler is configured to operate in a state that inhibits interaction between the first data qubit and the auxiliary qubit. The first qubit coupler and the second qubit coupler are each configured to operate in a respective state to enable interaction between the first data qubit and the auxiliary qubit and to entangle the state of the first data qubit with the state of the auxiliary qubit.

[0005] Advantageously, when at least the first qubit coupler is configured to operate in a given state, controlling the interaction between the data qubit and the auxiliary qubit using the first qubit coupler and the second qubit coupler enables suppression of crosstalk between the first data qubit and the auxiliary qubit, as well as suppression of crosstalk between the first data qubit and other data qubits coupled to the same auxiliary qubit. Furthermore, controlling the interaction between the first data qubit and the auxiliary qubit using the first qubit coupler and the second qubit coupler allows strong exchange coupling between the first data qubit and the auxiliary qubit when the first qubit coupler and the second qubit coupler are each configured in a respective operating state to entangle the state of the first data qubit with the state of the auxiliary qubit.

[0006] Another exemplary embodiment includes a system including a quantum processor and a control system, the quantum processor including a qubit array, the control system being configured to generate a control signal to control the quantum processor. The qubit array includes a first data qubit, a first qubit coupler, a second qubit coupler, and an auxiliary qubit. The first qubit coupler is coupled to the first data qubit and is configured to operate in one of a first state and a second state in response to a first control signal applied to the first qubit coupler by the control system. The second qubit coupler is coupled to the first qubit coupler and is configured to operate in one of a first state and a second state in response to a second control signal applied to the second qubit coupler by the control system. The auxiliary qubit is coupled to the second qubit coupler. The first qubit coupler is configured to operate in the first state to suppress interaction between the first data qubit and the auxiliary qubit. The first qubit coupler and the second qubit coupler are each configured to operate in the second state to enable interaction between the first data qubit and the auxiliary qubit and to entangle the state of the first data qubit with the state of the auxiliary qubit.

[0007] In another exemplary embodiment, as may be combined with the preceding paragraph, the first qubit coupler and the second qubit coupler each comprise a flux tunable transmon qubit.

[0008] In another exemplary embodiment, as may be combined with the preceding paragraph, the first qubit coupler comprises a first multimode qubit comprising a first mode and a second mode, and the second qubit coupler comprises a second multimode qubit comprising a first mode and a second mode.

[0009] In another exemplary embodiment, as may be combined with the preceding paragraph, the first data qubit is capacitively coupled to the first mode of the first multimode qubit, the auxiliary qubit is capacitively coupled to the first mode of the second multimode qubit, the second mode of the first multimode qubit is capacitively coupled to the second mode of the second multimode qubit, the first qubit coupler is configured to operate in a state in which the first data qubit is exchange coupled only to the first mode of the first multimode qubit, the first qubit coupler is configured to operate in a state in which the first data qubit is exchange coupled to both the first mode and the second mode of the first multimode qubit, and the second qubit coupler is configured to operate in a state in which the auxiliary qubit is capacitively coupled to the first mode of the first multimode qubit. The second qubit coupler is configured to operate in a state in which the auxiliary qubit is exchange coupled only to the first mode of the second multimode qubit, and the second qubit coupler is configured to operate in a state in which the auxiliary qubit is exchange coupled only to the first mode of the second multimode qubit, and the second qubit coupler is configured to operate in a state in which the auxiliary qubit is exchange coupled to the second mode of the second multimode qubit, and the second qubit coupler is configured to operate in a state in which the auxiliary qubit is exchange coupled to the second mode of the second multimode qubit, and the second multimode qubit coupler is configured to operate in a state in which the auxiliary qubit is exchange coupled to both the first mode and the second mode of the second multimode qubit.

[0010] Another exemplary embodiment includes an apparatus including a data qubit, a qubit coupler, a transmission line resonator, and an auxiliary qubit. The qubit coupler is coupled to the data qubit. The transmission line resonator is coupled to the qubit coupler. The auxiliary qubit is coupled to the transmission line resonator. The qubit coupler is configured to operate in a state that inhibits interaction between the data qubit and the auxiliary qubit. The qubit coupler is configured to operate in a state to enable interaction between the data qubit and the auxiliary qubit through the qubit coupler and the transmission line resonator to entangle the state of the data qubit with the state of the auxiliary qubit.

[0011] Advantageously, when at least a first qubit coupler is configured in a given operational state, utilizing the qubit coupler and the transmission line resonator to control the interaction between the data qubit and the auxiliary qubit enables suppression of crosstalk between the data qubit and the auxiliary qubit, as well as suppression of crosstalk between the data qubit and other data qubits coupled to the same auxiliary qubit. The transmission line resonator allows for relatively long distance coupling of the data qubit and the auxiliary qubit. Furthermore, the transmission line resonator eliminates the need for coupling a dedicated qubit coupler to the auxiliary qubit because the transmission line resonator has a relatively large capacitance to ground, which serves to reduce crosstalk between data qubits coupled to the same auxiliary qubit.

[0012] Another exemplary embodiment includes a system including a quantum processor and a control system, the quantum processor including a qubit array, the control system configured to generate a control signal to control the quantum processor. The qubit array includes a data qubit, a qubit coupler, a transmission line resonator, and an auxiliary qubit. The qubit coupler is coupled to the data qubit. The transmission line resonator is coupled to the qubit coupler. The auxiliary qubit is coupled to the transmission line resonator. The qubit coupler is configured to operate in a state that inhibits interaction between the data qubit and the auxiliary qubit. The qubit coupler is configured to operate in a state to enable interaction between the data qubit and the auxiliary qubit through the qubit coupler and the transmission line resonator to entangle the state of the data qubit with the state of the auxiliary qubit.

[0013] In another exemplary embodiment, as may be combined with the preceding paragraph, the qubit coupler includes a multimode qubit including a first mode and a second mode, a data qubit is capacitively coupled to the first mode of the multimode qubit, a transmission line resonator is capacitively coupled to the second mode of the multimode qubit, the qubit coupler is configured to operate in a state in which the data qubit is exchange coupled only to the first mode of the multimode qubit, and the qubit coupler is configured to operate in a state in which the data qubit is exchange coupled to both the first mode and the second mode of the multimode qubit.

[0014] Another exemplary embodiment includes a method, the method comprising: initializing a state of an auxiliary qubit; placing a first qubit coupler coupled to the auxiliary qubit in an activated state; placing a second qubit coupler coupled to a data qubit in an activated state to enable interaction between the data qubit and the auxiliary qubit, and entangle the state of the first data qubit with the state of the auxiliary qubit through the first qubit coupler and the second qubit coupler in the activated state; placing each of the first qubit coupler and the second qubit coupler in a deactivated state; reading the state of the auxiliary qubit after each of the first qubit coupler and the second qubit coupler is placed in the deactivated state; and determining the presence of a quantum error based on the readout of the auxiliary qubit.

[0015] Other embodiments will be 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

[0016] Figure 1 A Bloch sphere is depicted that graphically represents the various states of a qubit.

[0017] Figure 2A and Figure 2B Schematically illustrates a superconducting transport sub-qubit for realizing a data qubit and an auxiliary qubit according to an exemplary embodiment of the present disclosure.

[0018] Figure 3A and Figure 3B A superconducting multimode qubit according to an exemplary embodiment of the present disclosure is schematically shown, which can be configured to implement a superconducting multimode qubit coupler for coupling a data qubit to an auxiliary qubit.

[0019] Figure 3C Schematically shows an exemplary embodiment according to the present disclosure Figure 3A and Figure 3B Two different excitation modes of a superconducting multimode qubit.

[0020] Figure 4A and 4B A tunable superconducting multi-mode qubit coupler for coupling superconducting data qubits and superconducting auxiliary qubits according to an exemplary embodiment of the present disclosure is schematically shown.

[0021] Figure 5 A quantum device according to an exemplary embodiment of the present disclosure is schematically shown, the quantum device comprising a superconducting data qubit coupled to a superconducting auxiliary qubit using a tunable superconducting multimode qubit coupler.

[0022] Figure 6 A quantum device according to an exemplary embodiment of the present disclosure is schematically shown, the quantum device comprising a superconducting data qubit coupled to a superconducting auxiliary qubit using a tunable superconducting multimode qubit coupler and a superconducting transmission line resonator.

[0023] Fig. 7A A method for controlling the interaction between a superconducting data qubit and a superconducting auxiliary qubit using a tunable superconducting multimode qubit coupler according to an exemplary embodiment of the present disclosure is schematically illustrated.

[0024] Figure 7B and Figure 7C A method for controlling the interaction between a superconducting data qubit and a superconducting auxiliary qubit using a tunable superconducting multimode qubit coupler according to an exemplary embodiment of the present disclosure is graphically illustrated.

[0025] Figure 8 A quantum device according to an exemplary embodiment of the present disclosure is schematically shown, the quantum device comprising a superconducting qubit array including a superconducting data qubit coupled to a superconducting auxiliary qubit using a superconducting qubit coupler.

[0026] Fig. 9A quantum device according to an exemplary embodiment of the present disclosure is schematically shown, the quantum device comprising a superconducting qubit array including a superconducting data qubit coupled to a superconducting auxiliary qubit using a superconducting qubit coupler and a transmission line resonator.

[0027] Fig.10 A quantum device according to another exemplary embodiment of the present disclosure is schematically shown, the quantum device comprising a superconducting qubit array including a superconducting data qubit coupled to a superconducting auxiliary qubit using a superconducting qubit coupler.

[0028] Fig.11 A quantum device according to another exemplary embodiment of the present disclosure is schematically shown, the quantum device comprising a superconducting qubit array including a superconducting data qubit coupled to a superconducting auxiliary qubit using a superconducting qubit coupler.

[0029] Fig.12 is a flow chart of a method for performing a quantum error correction process according to an exemplary embodiment of the present disclosure.

[0030] Fig.13 A quantum computing system according to an exemplary embodiment of the present disclosure is schematically illustrated.

[0031] Fig.14 An exemplary architecture of a computing environment for hosting a quantum computing platform and performing quantum information processing according to an exemplary embodiment of the present disclosure is schematically shown. DETAILED DESCRIPTION

[0032] An exemplary embodiment of the present disclosure will now be described in more detail with respect to a quantum device that implements a superconducting qubit coupler for coupling a superconducting data qubit (data qubit) to a superconducting auxiliary qubit (auxiliary qubit) to facilitate quantum operations, such as parity checks for quantum error correction, while suppressing crosstalk between data 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 figure. 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.

[0033] 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 implementations 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 the 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 the circuits, structures, elements, components, etc. A circuit, structure, element, component, etc., when 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 operational state, includes elements, processing devices and / or integrated circuits that enable it to perform specific functions.

[0034] As 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. A quantum circuit is a computing routine that defines 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 a quantum computer. 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.

[0035] A single qubit can have a ground state of |0> or |1>, or a linear combination of these ground 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 |0> or |1> of a qubit is represented along the Z-axis of the Bloch sphere 100, where point 101 on the positive Z-axis represents the ground state |0>, and 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:

[0036]

[0037] 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. When the qubit is read, angle θ affects the probability of observing a qubit state of |0> or |1>, where the probability of reading a qubit state of |1> increases as θ increases. Angle φ affects the relative phase between states |0> and |1>. For example, when θ=0, the qubit is in the ground state |0>, which provides a 100% probability of observing a qubit state of |0> when the qubit state is read. In addition, when θ=π, the qubit is in the first excited state |1>, which provides a 100% probability of observing a qubit state of |1> when the qubit state is read. On the other hand, when When and φ = 0, the qubit is in the state of point 104. 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>.

[0038] The state of a given qubit can be changed by applying a single-qubit gate operation to the given 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, qubits can be controlled using entanglement gate operations to entangle the states of two or more qubits and thereby generate a combined state of the two or more qubits that contains more information than the individual states of the qubits. In this regard, qubit-based quantum computing operates on two key principles of quantum physics: superposition and entanglement, where superposition essentially allows a given qubit to represent both 1 and 0 simultaneously, and where entanglement allows multiple qubits in a superposition to be related to each other in a way that the state of one qubit can depend on the state of another qubit, so that more information can be encoded with multiple entangled qubits than if the qubits were encoded individually. Therefore, quantum information processing based on the principles of superposition and entanglement phases of qubits allows quantum computers to solve difficult problems that are difficult to solve using conventional computers.

[0039] A major challenge in the development of quantum computers is the sensitivity of the quantum state of the qubit to noise and errors. For example, a quantum system can interact with the environment in a way that causes decoherence of the qubit state. As is known in the art, quantum error correction (QEC) techniques are used to protect quantum information from errors caused by decoherence of the qubit state and other quantum noise. Typically, QEC techniques are based on quantum error correction codes, which store quantum information and protect quantum states from a set of errors. In order to perform reliable quantum computing, we must use qubits encoded with error correction codes.

[0040] Quantum error correction codes are used to encode quantum systems into a subspace of the entire qubit space (called the code space) so that errors caused by the decoherence of the quantum system can be detected and corrected based on the quantum error correction code. In general, quantum error correction codes provide a way to store (or transmit) M bits of quantum information using N qubits (where N>M) so that the quantum information can be recovered if any subset of the N qubits experiences an arbitrary error. In order for a quantum error code to properly protect a quantum state from a set of errors, the code space is chosen so that each error transforms the state in a way that enables a quantum error correction system to perform a suitable measurement to determine which error occurred without actually acquiring any information about the state of the qubit stored in the code, which necessarily perturbs the state of the qubit.

[0041] In the context of quantum computing, superconducting auxiliary qubits can be used for various purposes, such as quantum error correction. The term "superconducting auxiliary quantum bit" or "auxiliary qubit" generally refers to a superconducting qubit used to facilitate one or more quantum operations associated with one or more other superconducting qubits. For example, as used in connection with one or more illustrative embodiments, a superconducting auxiliary qubit is used to facilitate one or more error detection / correction operations associated with one or more superconducting data qubits.

[0042] As explained in further detail below, a superconducting auxiliary qubit is coupled to one or more superconducting data qubits using a superconducting multimode qubit coupler. As used herein, the term "superconducting data qubit" or "data qubit" refers to a superconducting qubit used to store the computational state of a quantum system. In addition, the data qubit is used to encode a logical qubit in a quantum error correction code. In the context of quantum error correction, the auxiliary qubit is entangled with the state of multiple data qubits, which encode the logical qubit state for quantum error correction, and the state of the auxiliary qubit is directly measured and used to detect errors in the data qubit in the quantum error code. In other words, in the context of quantum error correction, the logical qubit is composed of physical data qubits, where each logical qubit is encoded with several physical data qubits having an entangled state.

[0043] Quantum error correction systems utilize auxiliary qubits to determine error syndromes. For example, error syndromes may be determined by a process that includes performing a series of operations in which an auxiliary qubit is entangled with multiple data qubits, and then measuring the auxiliary qubit to determine whether there is an error in the encoded state of the data qubit. This process allows information about the data qubit to be inferred without directly reading the data qubit, which would cause the state of the data qubit to collapse. Symptom measurements provide information about errors that have occurred, but not the quantum information stored in the logical qubit, since the measurement would destroy any quantum superposition of the logical qubit with other qubits in the quantum system.

[0044] As described above, a superconducting quantum computing system can be implemented using superconducting qubits. For example, a superconducting transmission (transmission line shunt 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. Figure 2A and Figure 2B Schematically illustrates a superconducting transport sub-qubit according to an exemplary embodiment of the present disclosure, which can be used to implement data qubits and auxiliary qubits. More specifically, Figure 2A is a schematic lumped element circuit representation of superconducting transport sub-qubit 200, and Figure 2B Schematically shows an exemplary embodiment according to the present disclosure Figure 2A A planar circuit configuration 201 of a superconducting transport sub-qubit 200 is shown.

[0045] like Figure 2A As shown, the superconducting transmission sub-qubit 200 includes a superconducting tunnel junction device 210 and a capacitor 220 connected in parallel. In some embodiments, the superconducting tunnel junction device 210 has a Josephson energy E J and critical current I C The Josephson tunnel junction device 210 includes a capacitor 220. The Josephson tunnel junction device 210 includes a small junction capacitor. For ease of description, Figure 2A The junction capacitance is omitted in FIG. 2 . The capacitance C of capacitor 220 is large relative to the junction capacitance of Josephson tunnel junction device 210. Josephson tunnel junction 210 acts as a nonlinear inductor and, when shunted with capacitor 220, forms a non-harmonic LC oscillator having individually addressable energy levels (e.g., corresponding to the two lowest energy levels of the ground state |0> and the first excited state |1>).

[0046] like Figure 2B As shown, the planar circuit configuration 201 of the superconducting transmission sub-qubit 200 includes a first superconducting pad 220-1, a second superconducting pad 220-2, and a Josephson tunnel junction device 210, the Josephson tunnel junction device 210 is coupled to the first superconducting pad 220-1 and the second superconducting pad 220-2 and is disposed between the first superconducting pad 220-1 and the second superconducting pad 220-2. The first superconducting pad 220-1 and the second superconducting pad 220-2 include electrodes of a coplanar parallel plate capacitor structure, which corresponds to the capacitor 220 (having a capacitance C) of the superconducting transmission sub-qubit 200.

[0047] Typically, superconducting transport qubits are often used in superconducting quantum computing systems because transport qubits provide good coherence times and have relatively simple structures that facilitate coupling with other superconducting circuit elements and qubit readout resonators, etc. In order to control and read out the state of the transport qubit, such structures can be designed to capacitively or inductively couple the transport qubit to other circuit elements, including microwave and flux drive lines, readout resonators, and couplers. In addition, the transport qubit can be designed to have a relatively high anharmonic spectrum, where the frequency separation between the computational state and the non-computational state is relatively high, allowing the superconducting transport qubit to be effectively used as a two-level quantum system.

[0048] In particular, as is known in the art, the operating frequency (alternatively, transition frequency) of a superconducting qubit is the frequency corresponding to the energy difference between the ground state |0> and the first excited state |1> of the qubit. With superconducting qubits, although higher energy states 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 fundamental two-level system for quantum computation while ignoring the higher energy states. As used herein, the term "anharmonicity" refers to the frequency (f) of a qubit's (i) transition from the ground state |0> to the first excited state |1>. 01 ) and (ii) the frequency (f 12 )

[0049] The Josephson tunnel junction device 210 of the superconducting transport sub-qubit 200 can be designed to have a target critical current I c and the Josephson energy E J , to achieve a given anharmonicity of the quantum potential. For a Josephson tunnel junction, the resulting superconducting current I flowing through the tunnel junction and the junction voltage V across the tunnel junction are related to the superconducting phase difference Related, as follows: and Among them, I c represents the critical current of the tunnel junction, and where The junction critical current is given by Determine, where the junction critical current I c The maximum amount of current that can coherently tunnel through a junction (showing no dissipation). c is the Josephson energy E of the Josephson junction J The function of Where L J represents the Josephson inductance of a Josephson junction. Based on the standard relationship for inductance Josephson inductor L J Determined as: This shows that L J Relative to It is nonlinear.

[0050] Another type of superconducting qubit that can be used to implement quantum systems includes superconducting multimode qubits, which include multimode dual-junction qubit architectures such as Figure 3A and Figure 3B More specifically, Figure 3Ais a schematic lumped element circuit representation of a superconducting multimode qubit 300, which is alternatively referred to as a superconducting tunable coupler qubit (TCQ). The superconducting multimode qubit 300 includes a shunt capacitor 321, and two capacitive shunt superconducting Josephson tunnel junctions connected in series between a first node N1 and a second node N2 of the superconducting multimode qubit 300. The first capacitive shunt Josephson tunnel junction includes a first Josephson tunnel junction device 322 connected in parallel with a first capacitor 323. The second capacitive shunt Josephson tunnel junction includes a second Josephson tunnel junction device 324 connected in parallel with a second capacitor 325. The shunt capacitor 321 has a capacitance C S , the first Josephson tunnel junction device 322 has a Josephson energy E J1 , the second Josephson tunnel junction device 324 has a Josephson energy E J2 , the first capacitor 323 has a capacitance C1, and the second capacitor 325 has a capacitance C2. The first capacitance-shunt superconducting Josephson tunnel junction and the second capacitance-shunt superconducting Josephson tunnel junction are coupled to the intermediate node N3.

[0051] Next, Figure 3B Schematically shows an exemplary embodiment according to the present disclosure Figure 3A The planar circuit configuration of the superconducting multimode qubit 300. More specifically, Figure 3B A planar superconducting multimode qubit 301 is schematically shown, which includes a first superconducting pad 301-1, a second superconducting pad 301-2, a third (middle) superconducting pad 301-3, wherein a first Josephson tunnel junction device 322 is coupled to and located between the first superconducting pad 301-1 and the third superconducting pad 301-3, and a second Josephson tunnel junction device 324 is coupled to and located between the second superconducting pad 301-2 and the third superconducting pad 301-3. In this configuration, the superconducting pads 301-1, 301-2, and 301-3 include planar capacitor electrodes that form a coplanar parallel plate capacitor structure. For example, in Figure 3B In the exemplary configuration of the first superconducting pad 301-1 and the second superconducting pad 301-2 include Figure 3A The planar capacitor electrode of the shunt capacitor 321. In addition, the first superconducting pad 301-1 and the third superconducting pad 301-3 include Figure 3A The planar capacitor electrode of the first capacitor 323, and the second superconducting pad 301-2 and the third superconducting pad 301-3 include Figure 3A The first superconducting pad 301-1, the second superconducting pad 301-2 and the third superconducting pad 301-3 correspond to the planar capacitor electrode of the second capacitor 325. Figure 3AThe first node N1, the second node N2 and the third node N3 in.

[0052] Planar superconducting multimode qubit 301 includes two excitation modes with different frequencies and different spatial symmetries. More specifically, planar superconducting multimode qubit 301 includes two different excitation modes corresponding to symmetric and antisymmetric combinations of excitations associated with two junctions, where the two different normal modes include (i) a low-frequency "bright" mode (referred to herein as the A mode) that includes 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 does not couple to an external field. Figure 3C Schematically shows Figure 3B Two different excitation modes of a planar superconducting multimode qubit 301 , where the “bright” mode is depicted as A mode 302 , and the “dark” mode is depicted as B mode 304 .

[0053] like Figure 3C As schematically shown in FIG. 3 , the A mode 302 includes a charge pattern where, at any given point in time, the first superconducting pad 301-1 and the second superconducting pad 301-2 have opposite charges, and the third (middle) superconducting pad 301-3 has a net zero charge. On the other hand, the B mode 304 includes a charge pattern where, at any given point in time, the first superconducting pad 301-1 and the second superconducting pad 301-2 have the same charge, and the third (middle) superconducting pad 301-3 has a charge opposite to the charge on the first superconducting pad 301-1 and the second superconducting pad 301-2. The A mode and the B mode have different frequencies, for example, the mode frequency f of the B mode 304 is B Greater than the mode frequency f of the A mode 302 A , which allows the separate excitation of one mode relative to another.

[0054] 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 entangled gates (e.g., two-qubit gates) between superconducting qubits. As described above, an entangled 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 between two qubits (referred to herein as a C-phase (CPHASE) gate) is a type of entangled 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.

[0055] 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 C-phase gate, since the state-dependent shift of the qubit frequency can be equivalent to the 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.

[0056] For example, static ZZ interaction is a type of ZZ interaction that exists between two qubits or patterns 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.

[0057] 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 can potentially affect another adjacent qubit if there is an exchange interaction between such adjacent qubits. For example, if there is an exchange interaction between the two qubits, applying a microwave pulse to one qubit can potentially excite the other qubit, which is a form of crosstalk that can be harmful.

[0058] In the context of quantum error correction where multiple data qubits are coupled to the same auxiliary qubit, it is desirable to selectively control the interaction between the data qubits and the auxiliary bits while suppressing crosstalk (e.g., ZZ interaction) between the data qubits when performing consecutive entanglement gate operations to entangle the auxiliary qubit with each data qubit. In addition, it is desirable to suppress crosstalk between the auxiliary qubit and the data qubit when performing non-destructive measurements of the auxiliary qubit to determine error syndromes without changing the state of the data qubit coupled to the auxiliary qubit. In this regard, exemplary embodiments of the present disclosure will now be described in more detail with respect to techniques for controlling interactions between superconducting data qubits and superconducting auxiliary qubits to facilitate quantum error correction (e.g., parity check) while suppressing crosstalk between data qubits.

[0059] In some embodiments, a superconducting multimode qubit coupler is used to couple a superconducting data qubit with a superconducting auxiliary qubit to control the exchange interaction for entangled data qubits and auxiliary qubits, while suppressing crosstalk between superconducting data qubits. For example, in some embodiments, a flux-tunable superconducting multimode qubit coupler is implemented to couple a superconducting data qubit with a superconducting auxiliary qubit. In some embodiments, the flux-tunable superconducting multimode qubit coupler is based on the above combined FIG. 3A to FIG. 3C The multimode double-junction superconducting qubit architecture discussed.

[0060] For example, Figure 4A and Figure 4B Schematically shows a tunable superconducting multimode qubit coupler according to an exemplary embodiment of the present disclosure, which is used to couple a superconducting data qubit with a superconducting auxiliary qubit. More specifically, according to an exemplary embodiment of the present disclosure, Figure 4A is a schematic lumped element circuit representation of the flux tunable superconducting multimode qubit coupler 400, and Figure 4B Schematically shows Figure 4A A planar circuit configuration 401 of a tunable superconducting multimode qubit coupler 400. The tunable superconducting multimode qubit coupler 400 includes a multimode double-junction superconducting qubit architecture similar to the superconducting multimode qubit 300 ( Figure 3A ), except that the superconducting multimode qubits are configured to be flux tunable by replacing the Josephson tunnel junction device with a superconducting quantum interference device (SQUID). As explained in further detail below, the SQUID forms a superconducting loop (referred to as a SQUID loop) through which an external magnetic flux can pass to control the interaction between the superconducting qubits (e.g., to promote exchange interaction or suppress crosstalk), and the superconducting qubits are coupled to each other through a tunable superconducting multimode qubit coupler 400.

[0061] More specifically, if Figure 4A As shown, the tunable superconducting multi-mode qubit coupler 400 includes a shunt capacitor 421 (having a capacitance C S ), and two capacitance-shunt superconducting Josephson tunnel junctions connected in series between the first node N1 and the second node N2 of the tunable superconducting multimode qubit coupler 400. The first capacitance-shunt Josephson tunnel junction includes a first Josephson tunnel junction device 422 connected in parallel with a first capacitor 423 (having capacitance C1). The first Josephson tunnel junction device 422 includes a critical current I C1 and the Josephson energy E J1The second capacitive shunt Josephson tunnel junction includes a SQUID 424 connected in parallel with a second capacitor 425 (having a capacitance C2). The SQUID 424 includes a first Josephson tunnel junction device 424-1 and a second Josephson tunnel junction device 424-2, which are connected in parallel between the first node N1 and the third node N3 of the tunable superconducting multimode qubit coupler 400 and form a superconducting loop.

[0062] The SQUID 424 effectively acts as a CS and the Josephson energy E JS The Josephson energy E JS By applying an external magnetic field Φ ext In this regard, SQUID 424 allows the superconducting loop formed by the parallel-connected Josephson tunnel junctions 424-1 and 424-2 to be regulated by applying a target external magnetic field Φ ext To tune the tunable superconducting multimode qubit coupler 400, the target external magnetic field Φ ext The external magnetic field Φ is applied by a flux bias control wire disposed near the SQUID 424 and passing through the superconducting loop. The flux bias control wire feeds a current (e.g., a DC current) into an inductor element placed adjacent to the superconducting loop of the SQUID 424, which causes the external magnetic field Φ to ext is applied to the superconducting loop of SQUID424. ext modulates the critical current ICS and thus the Josephson energy E of the SQUID 424 in a very specific way JS .

[0063] The flux tuning of the tunable superconducting multimode qubit coupler 400 is used to control the exchange interaction (e.g., promote the exchange interaction or suppress the crosstalk) between the first superconducting qubit and the second superconducting qubit that are capacitively coupled to the A mode and the B mode of the tunable superconducting multimode qubit coupler 400, respectively. In particular, Figure 4A , coupling capacitors 430 and 432 (connected to respective nodes N1 and N2) enable superconducting qubits to be capacitively coupled to the A mode of tunable superconducting multimode qubit coupler 400. Additionally, coupling capacitor 434 (connected to node N3) enables superconducting qubits to be capacitively coupled to the B mode of tunable superconducting multimode qubit coupler 400. Coupling capacitors 430, 432, and 434 may be implemented by direct capacitive coupling (via gap capacitance) or by superconducting planar transmission lines such as coplanar waveguides.

[0064] The critical current I is adjusted by varying the amount of external magnetic flux applied to the superconducting loop of the SQUID 424. CSand thus adjust the Josephson energy E of the SQUID 424 JS , tunable superconducting multimode qubit coupler 400 can be tuned to operate in a first state (e.g., an “off” state or a “deactivated” state) or a second state (e.g., an “on” state or an “activated” state). For example, tunable superconducting multimode qubit coupler 400 can be tuned to operate in the “off” state by applying a certain amount of external magnetic flux to the superconducting loop of SQUID 424 so that the critical current I of SQUID 424 is CS is equal to or substantially equal to the critical current I of the Josephson tunnel junction device 422 C1 , which results in the corresponding Josephson energy E of the Josephson tunnel junction device 422 and the SQUID 424 J1 and E JS balance.

[0065] In the “off” state, tunable superconducting multimode qubit coupler 400 implements mode selective coupling and produces a substantially zero interaction condition between superconducting qubits capacitively coupled to respective A and B modes. More specifically, in the “off” state of tunable superconducting multimode qubit coupler 400, superconducting qubits capacitively coupled to nodes N1 and N2 of tunable superconducting multimode qubit coupler 400 are exchange coupled only to the A mode of tunable superconducting multimode qubit coupler 400, and superconducting qubits capacitively coupled to node N3 of tunable superconducting multimode qubit coupler 400 are exchange coupled only to the B mode of tunable superconducting multimode qubit coupler 400. In the “off” state of tunable superconducting multimode qubit coupler 400, the A mode and the B mode have different and separate charge patterns, such as Figure 3C As shown, this results in suppressing crosstalk (e.g., static ZZ interactions) between superconducting qubits coupled by tunable superconducting multimode qubit coupler 400.

[0066] On the other hand, a certain amount of external magnetic flux can be applied to the superconducting loop of SQUID 424 to increase the critical current I CS is not equal to (eg, greater than) the critical current I of the Josephson tunnel junction device 422 C1 (This results in the corresponding Josephson energy E of the Josephson tunnel junction device 422 and the SQUID 424 J1 and E JS The Josephson energy E is used to tune the tunable superconducting multimode qubit coupler 400 to operate in the "on" state. J1 and E JS The imbalance modifies the different charge patterns of A mode and B mode, so that the charge pattern becomes Figure 3C, which destroys the mode selective coupling of tunable superconducting multimode qubit coupler 400 and causes the superconducting qubit to have exchange coupling with both the A mode and the B mode of tunable superconducting multimode qubit coupler 400. In the “on” state of tunable superconducting multimode qubit coupler 400, the exchange coupling of the two superconducting qubits to the A mode and the B mode results in exchange coupling (e.g., ZZ interaction) between the superconducting qubits capacitively coupled to the A mode and the B mode of tunable superconducting multimode qubit coupler 400.

[0067] like Figure 4B As schematically shown in Figure 4A The exemplary planar circuit configuration 401 of the tunable superconducting multimode qubit coupler 400 includes a first superconducting pad 401-1, a second superconducting pad 401-2, and a third superconducting pad 401-3. The first superconducting pad 401-1 and the second superconducting pad 401-2 include electrodes of a coplanar parallel plate capacitor structure corresponding to a shunt capacitance C S The shunt capacitor 421 ( Figure 4A ). The Josephson tunnel junction device 422 is coupled to the first superconducting pad 401-1 and the third superconducting pad 401-3 and is coupled between the first superconducting pad 401-1 and the third superconducting pad 401-3. The first superconducting pad 401-1 and the third superconducting pad 401-3 include a first capacitor 423 ( Figure 4A ) of the coplanar parallel plate capacitor structure. SQUID 424 is coupled to and between second superconducting pad 401-2 and third superconducting pad 401-3. Second superconducting pad 401-2 and third superconducting pad 401-3 include electrodes corresponding to second capacitor 425 ( Figure 4A ) are electrodes of a coplanar parallel plate capacitor structure.

[0068] For purposes of illustration, exemplary embodiments of quantum systems and devices as discussed herein are based on Figure 4A and Figure 4B The tunable multimode qubit framework implements a flux-tunable superconducting multimode qubit coupler to control the interaction between the superconducting data qubit and the superconducting auxiliary qubit. However, it should be noted that other suitable tunable multimode qubit architectures can be used as a coupler to control the interaction between the superconducting data qubit and the superconducting auxiliary qubit. Such a tunable multimode qubit will realize the combination of two strongly interacting anharmonic oscillators with a composite quantum system characterized by multiple excitation modes that exhibit strong longitudinal coupling between them, i.e., the excitation of one mode can strongly shift the transition frequency of another mode.

[0069] Figure 5Schematically illustrates a quantum device according to an exemplary embodiment of the present disclosure, the quantum device comprising a superconducting data qubit coupled to a superconducting auxiliary qubit using a tunable superconducting multimode qubit coupler. In particular, Figure 5 Quantum device 500 is schematically shown and includes superconducting data qubit 510, first superconducting multimode qubit coupler 520, second superconducting multimode qubit coupler 530, and superconducting auxiliary qubit 540. Quantum device 500 also includes a plurality of control lines, including but not limited to qubit drive lines 512 and 542, qubit readout lines 514 and 544, and flux bias control lines 522 and 532.

[0070] In some embodiments, superconducting data qubit 510 and superconducting auxiliary qubit 540 each include a superconducting transport sub-qubit such as Figure 2A and Figure 2B As shown. In other embodiments, superconducting data qubit 510 and superconducting auxiliary qubit 540 can be implemented using other types of superconducting qubits such as superconducting fluxonium qubits. In some embodiments, superconducting data qubit 510 and superconducting auxiliary qubit 540 include fixed frequency qubits (non-tunable), while in other embodiments, superconducting data qubit 510 and / or superconducting auxiliary qubit 540 can be tunable qubits, for example, tunable transition frequencies.

[0071] In some embodiments, qubit drive lines 512 and 542 are coupled (e.g., capacitively coupled) to superconducting data qubit 510 and superconducting auxiliary qubit 540, respectively. In some embodiments, qubit drive lines 512 and 542 are configured to apply control signals (e.g., microwave control pulse signals) to independently change the states of the corresponding superconducting data qubit 510 and superconducting auxiliary qubit 540. For example, microwave control pulses may be applied to qubit drive line 512 to perform single-qubit gate operations on superconducting data qubit 510, or to otherwise modify the computational state of superconducting data qubit 510 as desired when executing a quantum algorithm. In addition, microwave control pulses may be applied to qubit drive line 542 to initialize superconducting auxiliary qubit 540 to a ground state |0> at the initial stage of a quantum error correction cycle. As is known in the art, a quantum error correction cycle may be performed by applying a microwave control pulse having a transition frequency equal to the qubit (denoted as f 01 ) to change the state of the qubit, where the transition frequency f 01 corresponds to the energy difference between the ground state |0> and the excited state |1> of the qubit. In addition, the axis of rotation 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.

[0072] Additionally, in some embodiments, qubit readout lines 514 and 544 are coupled to superconducting data qubit 510 and superconducting auxiliary qubit 540, respectively, using known techniques to perform dispersive readout. In some embodiments, qubit readout lines 514 and 544 include transmission line readout resonators (e.g., coplanar waveguide resonators) configured to have a resonant frequency that is detuned from the respective transition frequencies of superconducting data qubit 510 and superconducting auxiliary qubit 540. Since qubit readout lines 514 and 544 are coupled to respective superconducting data qubit 510 and superconducting auxiliary qubit 540, there is a shift in the resonant frequency of the transmission line readout resonator depending on the state of the respective superconducting data qubit 510 and superconducting auxiliary qubit 540. The change in the resonant frequency of a transmission line readout resonator coupled to a given qubit is used to determine the readout state of the given qubit, e.g., the ground state |0> or the first excited state |1>, where for readout the superposition state of the given qubit is projected onto the ground state or the first excited state, as is known in the art.

[0073] In some embodiments, first superconducting multimode qubit coupler 520 and second superconducting multimode qubit coupler 530 each comprise a flux tunable superconducting multimode qubit coupler, such as the one described above in conjunction with Figure 4A and Figure 4B As described above, the tunable superconducting multimode qubit coupler 400 ( Figure 4A ) includes two different normal excitation modes (e.g., different A and B excitation modes with different frequencies and spatial symmetries, such as Figure 3C ). Flux bias control lines 522 and 532 are used to apply flux bias control signals to the corresponding first superconducting multimode qubit coupler 520 and second superconducting multimode qubit coupler 530 to control (implement or interrupt) mode selective exchange coupling between superconducting data qubit 510 and first superconducting multimode qubit coupler 520, between first superconducting multimode qubit coupler 520 and second superconducting multimode qubit coupler 530, and between superconducting auxiliary qubit 540 and second superconducting multimode qubit coupler 530 as needed, depending on a given operation.

[0074] More specifically, in some embodiments, superconducting data qubit 510 is capacitively coupled to a first mode (e.g., A mode) of first superconducting multimode qubit coupler 520, and superconducting auxiliary qubit 540 is capacitively coupled to a first mode (e.g., A mode) of second superconducting multimode qubit coupler 530. In addition, a second mode (e.g., B mode) of first superconducting multimode qubit coupler 520 is capacitively coupled to a second mode (e.g., B mode) of second superconducting multimode qubit coupler 530. First superconducting multimode qubit coupler 520 and second superconducting multimode qubit coupler 530 are configured to mediate interactions (e.g., ZZ interactions) with superconducting data qubit 510 and superconducting auxiliary qubit 540 and between superconducting data qubit 510 and superconducting auxiliary qubit 540, respectively, for different operation modes.

[0075] Advantageously, mediating the coupling between superconducting data qubit 510 and superconducting auxiliary qubit 540 through superconducting multimode qubit couplers 520 and 530 allows for simultaneous suppression of both static ZZ interactions and exchange interactions between superconducting data qubit 510 and superconducting auxiliary qubit 540 when at least one of superconducting multimode qubit couplers 520 and 530 is in an off state, wherein each of superconducting multimode qubit couplers 520 and 530 includes two different excitation modes. Superconducting multimode qubit couplers 520 and 530 can be flux tuned to be in an off state to implement mode-selective exchange coupling, wherein superconducting data qubit 510 is exchange-coupled only to the first mode (A-mode) of the first superconducting multimode qubit coupler 520, and superconducting auxiliary qubit 540 is exchange-coupled only to the first mode (A-mode) of the second superconducting multimode qubit coupler 530. In this configuration, despite the capacitive coupling of the second mode (B mode) of first superconducting multimode qubit coupler 520 and second superconducting multimode qubit coupler 530 , there is essentially zero interaction between superconducting data qubit 510 and superconducting auxiliary qubit 540 .

[0076] Figure 6 A quantum device according to an exemplary embodiment of the present disclosure is schematically shown, the quantum device comprising a superconducting data qubit coupled to a superconducting auxiliary qubit using a tunable superconducting multimode qubit coupler and a superconducting transmission line resonator. Specifically, Figure 6 A quantum device 600 is schematically shown, which is similar to Figure 5 The quantum device 500 is a quantum device 500, except that the first superconducting multimode qubit coupler 520 is coupled to the superconducting auxiliary qubit 540 via a superconducting transmission line resonator 630 (instead of Figure 5510). This configuration can be used for remote coupling in the case where the superconducting auxiliary qubit 540 is disposed relatively far from the superconducting data qubit 510. Advantageously, the superconducting transmission line resonator 630 eliminates the need to utilize a dedicated superconducting multimode qubit coupler (e.g., the second superconducting multimode qubit coupler 530) for the superconducting auxiliary qubit 540 because the superconducting transmission line resonator 630 is used to reduce crosstalk between the superconducting data qubit 510 and other superconducting data qubits coupled to the same superconducting auxiliary qubit 540. In particular, the superconducting transmission line resonator 630 has a relatively large capacitance to ground, which acts as a distributor to reduce ZZ coupling between superconducting data qubits coupled to the same superconducting auxiliary qubit.

[0077] In some embodiments, superconducting transmission line resonator 630 comprises a coplanar waveguide resonator having a given resonant frequency that is selected (e.g., detuned) based on the transition frequencies of superconducting data qubit 510 and superconducting auxiliary qubit 540. In some embodiments, a first end of superconducting transmission line resonator 630 is capacitively coupled to the B mode of superconducting multimode qubit coupler 520, and a second end of superconducting transmission line resonator 630 is capacitively coupled to superconducting auxiliary qubit 540.

[0078] Fig. 7A Schematically illustrates a method for controlling the interaction between a superconducting data qubit and a superconducting auxiliary qubit using a tunable superconducting multimode qubit coupler according to an exemplary embodiment of the present disclosure. In particular, Fig. 7A Schematically illustrates a process 700 for controlling the interaction between a data qubit 701 and an auxiliary qubit 702 by utilizing a first tunable superconducting multimode qubit coupler 703 and a second tunable superconducting multimode qubit coupler 704 (similar to Figure 5 500). Fig. 7A As schematically shown in FIG. 7 , when both the first tunable superconducting multimode qubit coupler 703 and the second tunable superconducting multimode qubit coupler 704 are flux tuned in the closed state 700-1, the superconducting data qubit 701 has exchange coupling only with the A mode of the first tunable superconducting multimode qubit coupler 703, and the superconducting auxiliary qubit 702 has exchange coupling only with the A mode of the second tunable superconducting multimode qubit coupler 704. In addition, the B modes of the first tunable superconducting multimode qubit coupler 703 and the second tunable superconducting multimode qubit coupler 704 are exchange coupled with each other. In the closed state 700-1, there is substantially no interaction (static ZZ or exchange interaction) between the superconducting data qubit 701 and the superconducting auxiliary qubit 702.

[0079] On the other hand, Fig. 7AAs schematically shown in FIG. 7 , when both the first tunable superconducting multimode qubit coupler 703 and the second tunable superconducting multimode qubit coupler 704 are flux tuned in the “on” state 700-2, the superconducting data qubit 701 has exchange coupling with both the A mode and the B mode of the first tunable superconducting multimode qubit coupler 703, and the superconducting auxiliary qubit 702 has exchange coupling with both the A mode and the B mode of the second tunable superconducting multimode qubit coupler 704. In addition, the B mode of the first tunable superconducting multimode qubit coupler 703 has exchange coupling with both the A mode and the B mode of the second tunable superconducting multimode qubit coupler 704, and similarly, the B mode of the second tunable superconducting multimode qubit coupler 704 has exchange coupling with both the B mode and the A mode of the first tunable superconducting multimode qubit coupler 703. In addition, the A mode of the first tunable superconducting multimode coupler 703 has exchange coupling with the A mode and the B mode of the second tunable superconducting multimode qubit coupler 704, and vice versa. In the on state 700-2, there is a large amount of exchange interaction between the superconducting data qubit 701 and the superconducting auxiliary qubit 702.

[0080] It should be noted that Fig. 7A Schematically illustrates different energy levels (e.g., frequencies) of the A mode and the B mode of the superconducting data qubit 701, the superconducting auxiliary qubit 702, and the first tunable superconducting multimode qubit coupler 703 and the second tunable superconducting multimode qubit coupler 704. In an exemplary non-limiting embodiment, the superconducting data qubit 701 is configured to have a transition frequency f Q1 , and the superconducting auxiliary qubit 702 is configured to have a transition frequency f Q1 Detuned transition frequency f Q2 In addition, in some embodiments, in the closed state, the first tunable superconducting multimode qubit coupler 703 and the second tunable superconducting multimode qubit coupler 704 are configured to have a normal A-mode frequency (f A ) and the normal B-mode frequency (f B ) corresponding to the normal A and B modes, which are detuned by the desired amount. Fig. 7A As schematically shown in FIG. 1 , the normal A-mode frequency (f A ) and the normal B-mode frequency (f B ) is less than the transition frequency of the superconducting data qubit 701 and the superconducting auxiliary qubit 702. In addition, the normal A mode frequency (f A ) is less than the normal B-mode frequency (f ) of the first tunable superconducting multimode qubit coupler 703 and the second tunable superconducting multimode qubit coupler 704 B ).

[0081] In addition, if Fig. 7A As schematically shown in FIG. 7 , when both first tunable superconducting multimode qubit coupler 703 and second tunable superconducting multimode qubit coupler 704 are flux tuned in the “on” state 700-2, the energies (frequencies) of the A and B modes of first tunable superconducting multimode qubit coupler 703 and second tunable superconducting multimode qubit coupler 704 increase to be closer to the transition frequencies of superconducting data qubit 701 and superconducting auxiliary qubit 702. This results in a breakdown of the mode-selective coupling due to a transformation of the charge patterns of the A and B modes, with the B mode generating a net dipole moment (and no longer being in a fully “dark” mode). This transformation of the A mode and the B mode (e.g., an increase in mode frequency, a change in charge pattern, etc.) causes superconducting data qubit 701 and superconducting auxiliary qubit 702 to have exchange coupling with both the A mode and the B mode of the corresponding first tunable superconducting multimode qubit coupler 703 and second tunable superconducting multimode qubit coupler 704, which enables and mediates the ZZ interaction between superconducting data qubit 701 and superconducting auxiliary qubit 702 so that the state of superconducting data qubit 701 is entangled with the state of superconducting auxiliary qubit 702.

[0082] It should be noted that in other embodiments, mode coupling of superconducting data qubit 701 and superconducting auxiliary qubit 702 with corresponding first tunable superconducting multimode qubit coupler 703 and second tunable superconducting multimode qubit coupler 704 may be implemented differently, wherein superconducting data qubit 701 and superconducting auxiliary qubit 702 are capacitively coupled to the B modes of corresponding first tunable superconducting multimode qubit coupler 703 and second tunable superconducting multimode qubit coupler 704, and wherein the A modes of first tunable superconducting multimode qubit coupler 703 and second tunable superconducting multimode qubit coupler 704 are capacitively coupled. In this configuration, in the off state of first tunable superconducting multimode qubit coupler 703 and second tunable superconducting multimode qubit coupler 704, mode selective coupling is implemented so that superconducting data qubit 701 has only exchange coupling to the B mode of first superconducting multimode qubit coupler 703, and superconducting auxiliary qubit 702 has only exchange coupling to the B mode of second superconducting multimode qubit coupler 704. Depending on a given mode coupling configuration, the coupling capacitances of superconducting data qubit 701 and superconducting auxiliary qubit 702 to the respective first tunable superconducting multimode qubit coupler 703 and second tunable superconducting multimode qubit coupler 704 can be fine-tuned to achieve sufficient exchange coupling for a given mode coupling configuration.

[0083] Figure 7B and Figure 7CA method for controlling the interaction between a superconducting data qubit and a superconducting auxiliary qubit using a tunable superconducting multimode qubit coupler according to an exemplary embodiment of the present disclosure is graphically illustrated. Figure 7B and Figure 7C The graphic illustrations in the figure are based on computer simulations, which show Figure 5 The quantum system shown and Figure 6 The exchange interaction (e.g., ZZ interaction) characteristics of the quantum system shown.

[0084] In particular, Figure 7B A graph 710 is depicted showing the Josephson energy E of a SQUID as a first superconducting multimode qubit coupler and a second superconducting multimode qubit coupler. JS (X-axis) is a function of the first superconducting multimode qubit coupler and the second superconducting multimode qubit coupler (configured as Figure 5 The amount of ZZ interaction (Y axis) between the coupled superconducting transporter data qubit and the superconducting transporter auxiliary qubit (shown). More specifically, Figure 7B A curve 712 is shown, which depicts the amount of static ZZ interaction between the superconducting transporton data qubit and the superconducting transporton auxiliary qubit, where the first superconducting multimode qubit coupler and the second superconducting multimode qubit coupler are coupled at SQUID Josephson energies E from about 10 GHz to about 30 GHz. JS is flux tuned in the range of Figure 7B In the simulation, the first superconducting multimode qubit coupler and the second superconducting multimode qubit coupler are modeled with the same or similar operating parameters, and the Josephson energy E of the SQUIDs of the first superconducting multimode qubit coupler and the second superconducting multimode qubit coupler is JS At the same time, it changes and Figure 7B The energy ranges shown remain the same or nearly the same as each other.

[0085] Curve 712 shows the amount of ZZ interaction between a superconducting transporter data qubit and a superconducting transporter auxiliary qubit, where the superconducting multimode qubit coupler is flux tuned in different states (e.g., an on state and an off state). Figure 7B As shown, in the off state, there is essentially no ZZ coupling between the superconducting transporter data qubit and the superconducting transporter auxiliary qubit (e.g., the ZZ interaction is close to 1x 10 -5 kHz). In addition, in the on state, there is a relatively large amount of ZZ interaction (e.g., close to 1x 10 4 kHz).

[0086] Next, Figure 7CA graph 720 is depicted showing the Josephson energy E of a SQUID as a superconducting multimode qubit coupler. JS (x-axis) is a function of the number of channels through a single superconducting multimode qubit coupler and a superconducting transmission line resonator (e.g. Figure 6 The amount of ZZ interaction (Y-axis) between the superconducting transporter data qubit and the superconducting transporter auxiliary qubit coupled in the configuration shown in FIG. Figure 7C A curve 722 is shown, which depicts the amount of ZZ interaction between a superconducting transporton data qubit and a superconducting transporton auxiliary qubit, where the superconducting multimode qubit coupler is at a SQUID Josephson energy E from about 7.5 GHz to about 25 GHz. JS Curve 722 shows the amount of ZZ interaction between the superconducting transport sub-data qubit and the superconducting transport sub-assist qubit, where the superconducting multimode qubit coupler flux is tuned in different states (e.g., on state and off state). Figure 7C As shown, in the off state, there is a relatively low amount of ZZ coupling (e.g., close to 1 x 10 -1 kHz). In addition, in the on state, there is a relatively large amount of ZZ coupling (e.g., close to 1x10 3 kHz).

[0087] Although Figure 5 and Figure 6 Quantum devices 500 and 600 are schematically shown including one superconducting data qubit coupled to one superconducting auxiliary qubit, but it should be understood that superconducting quantum devices (such as quantum processors) can be implemented using superconducting qubit arrays including tens, hundreds, thousands, or more superconducting qubits, including data qubits and auxiliary qubits, which are coupled together using techniques as discussed herein to facilitate error correction and suppress crosstalk, depending on the application. For example, Figure 8 A quantum device according to an exemplary embodiment of the present disclosure is schematically shown, the quantum device comprising a superconducting qubit array including a superconducting data qubit coupled to a superconducting auxiliary qubit using a superconducting qubit coupler.

[0088] Specifically, Figure 8Schematically illustrates a quantum device including a superconducting qubit array 800, which includes superconducting data qubits 810-1, 810-2, and 810-3 and tunable superconducting multimode qubit couplers 820-1, 820-2, and 820-3, which are capacitively coupled to superconducting data qubits 810-1, 810-2, and 810-3, respectively. Superconducting qubit array 800 also includes a tunable superconducting multimode qubit coupler 830 and a superconducting auxiliary qubit 840, which is capacitively coupled to tunable superconducting multimode qubit coupler 830. In some embodiments, as Figure 8 As schematically shown in FIG. 1 , superconducting data qubits 810-1, 810-2, and 810-3 and superconducting auxiliary qubit 840 each include a superconducting transmission sub-qubit having the same structure as that in the above combination. Figure 2A and Figure 2B The circuit configuration and layout are similar to the exemplary embodiments shown and discussed, and the details will not be repeated. In addition, the tunable superconducting multimode qubit couplers 820-1, 820-2, 820-3 and 830 each include a circuit similar to the above combined circuit. Figure 4A and Figure 4B The circuit configuration and layout of the exemplary embodiments are shown and discussed, and the details will not be repeated.

[0089] like Figure 8 As further shown in FIG. 8 , each superconducting data qubit 810-1, 810-2, and 810-3 is capacitively coupled to the A mode of a corresponding tunable superconducting multimode qubit coupler 820-1, 820-2, and 820-3. More specifically, in Figure 8 In the exemplary embodiment of FIG. 8 , A-mode coupling is achieved by direct capacitive coupling (gap capacitance) of first superconducting pad 220-1 and second superconducting pad 220-2 of superconducting data qubit 810-1 to corresponding first superconducting pad 401-1 and second superconducting pad 401-2 of tunable superconducting multimode qubit coupler 820-1. Similarly, superconducting auxiliary qubit 840 is capacitively coupled (via direct capacitive coupling) to the A-mode of tunable superconducting multimode qubit coupler 830.

[0090] The superconducting qubit array 800 also includes a capacitive bus 850 configured to capacitively couple the tunable superconducting multimode qubit couplers 820-1, 820-2, and 820-3 to the tunable superconducting multimode qubit coupler 830. The capacitive bus 850 includes (i) a first capacitor pad 851 connected to the first tunable superconducting multimode qubit coupler 820-1 through a first superconducting transmission line 851-1, (ii) a second capacitor pad 852 connected to the second tunable superconducting multimode qubit coupler 820-2 through a second superconducting transmission line 852-1, (iii) a third capacitor pad 853 connected to the third tunable superconducting multimode qubit coupler 820-3 through a third superconducting transmission line 853-1, and (iv) a fourth capacitor pad 854 connected to the tunable superconducting multimode qubit coupler 830 through a fourth superconducting transmission line 854-1. The first capacitor pad 851, the second capacitor pad 852, and the third capacitor pad 853 are arranged adjacent to different edges of the fourth capacitor pad 854. The fourth capacitor pad 854 has a size larger than the corresponding sizes of the first capacitor pad 851, the second capacitor pad 852, and the third capacitor pad 853. In some embodiments, the superconducting transmission lines 851-1, 852-1, 853-1, and 854-1 are implemented as superconducting coplanar waveguides.

[0091] exist Figure 8 In the exemplary embodiment of FIG. 8 , capacitive bus 850 is coupled to the B modes of the corresponding tunable superconducting multimode qubit couplers 820-1, 820-2, 820-3, and 830. In this configuration, the B modes of tunable superconducting multimode qubit couplers 820-1, 820-2, 820-3, and 830 are commonly coupled together through capacitive bus 850. Capacitive bus 850 is structurally configured to ensure that the amount of capacitive coupling between tunable superconducting multimode qubit coupler 830 (of superconducting auxiliary qubit 840) and each of tunable superconducting multimode qubit couplers 820-1, 820-2, and 820-3 (of superconducting data qubits 810-1, 810-2, and 810-3) is greater than the amount of capacitive coupling between tunable superconducting multimode qubit couplers 820-1, 820-2, and 820-3. This is achieved by, for example, making the size of the fourth capacitor pad 854 larger than the corresponding sizes of the first capacitor pad 851 , the second capacitor pad 852 , and the third capacitor pad 853 .

[0092] As described above, suppression of crosstalk (e.g., exchange interaction or static ZZ interaction) between superconducting data qubits 810-1, 810-2, and 810-3 and between superconducting auxiliary qubit 840 and superconducting data qubits 810-1, 810-2, and 810-3 is achieved by deactivating tunable superconducting multimode qubit couplers 820-1, 820-2, 820-3, and 830, wherein corresponding flux control signals are applied to corresponding SQUIDs 424 of tunable superconducting multimode qubit couplers 820-1, 820-2, 820-3, and 830 to tune SQUIDs 424 to have the same Josephson energy as corresponding single Josephson tunnel junction devices 422 of tunable superconducting multimode qubit couplers 820-1, 820-2, 820-3, and 830. When tunable superconducting multimode qubit couplers 820-1, 820-2, 820-3, and 830 are in a deactivated state, superconducting data qubits 810-1, 810-2, and 810-3 and superconducting auxiliary qubit 840 will only couple to the A-mode of the corresponding tunable superconducting multimode qubit couplers 820-1, 820-2, 820-3, and 830, thereby inhibiting or otherwise shutting down the interaction between superconducting data qubits 810-1, 810-2, and 810-3 and superconducting auxiliary qubit 840.

[0093] On the other hand, to turn on the ZZ coupling between superconducting auxiliary qubit 840 and a given one of superconducting data qubits 810-1, 810-2, and 810-3, a corresponding flux control signal is applied to the corresponding SQUID of tunable superconducting multimode qubit coupler 830 and the associated tunable superconducting multimode qubit couplers 820-1, 820-2, 820-3 of the given superconducting data qubit to tune the SQUID to have a different Josephson energy from the corresponding single Josephson tunnel junction device of the superconducting multimode qubit coupler, which destroys the mode selective coupling and causes superconducting auxiliary qubit 840 and the given superconducting data qubit to couple to the B mode of the superconducting multimode qubit coupler and thus to couple to each other.

[0094] Although Figure 8 The exemplary embodiment of shows three superconducting data qubits 810-1, 810-2, and 810-3 selectively coupled to a single superconducting auxiliary qubit 840 via respective superconducting multimode qubit couplers, but in other embodiments, more than three superconducting data qubits may be coupled to superconducting auxiliary qubit 840. For example, Figure 8Fourth capacitor pad 854 of capacitor bus 850 is shown as being rectangular in shape, providing three edges for coupling to three capacitor pads 851, 852, and 853. In other embodiments, fourth capacitor pad 854 may have other shapes to provide additional edges for coupling additional data qubit pairs and associated multi-mode qubit couplers. For example, fourth capacitor pad 854 may be hexagonal to provide five (5) edges for coupling to five (5) capacitor pads (e.g., allowing five (5) superconducting data qubits to couple to a single ancillary qubit), or octagonal to provide seven (7) edges for coupling to seven (7) capacitor pads (e.g., allowing seven (7) superconducting data qubits to couple to a single ancillary qubit), etc.

[0095] In some embodiments, superconducting data qubits 810-1, 810-2, and 810-3 and superconducting auxiliary qubit 840 have transition frequencies that are detuned from one another. For example, in an exemplary non-limiting embodiment, superconducting data qubits 810-1, 810-2, and 810-3 and superconducting auxiliary qubit 840 have transition frequencies of ~5.5 GHz, but are detuned by plus / minus 100 MHz. For example, a superconducting data qubit may have a transition frequency of 5.45 GHz, while superconducting auxiliary qubit 840 has a transition frequency of 5.55 GHz. Furthermore, in some embodiments, each tunable superconducting multimode qubit coupler 820-1, 820-2, 820-3, and 830 is substantially identical, e.g., the same normal A-mode frequency and B-mode frequency. For example, in an exemplary non-limiting embodiment, in the off state, each tunable superconducting multimode qubit coupler 820-1, 820-2, 820-3, and 830 has a normal A-mode frequency of ˜2.5 GHz, and a normal B-mode frequency of ˜4.0 GHz. Furthermore, in some embodiments, the coupling capacitance between the superconducting transport sub-qubit and the corresponding superconducting multimode qubit coupler is on the order of about 10 femtofarads (fF) to about 20 fF.

[0096] Figure 8 Schematically illustrates a superconducting qubit array including superconducting data qubits coupled to ancillary qubits using superconducting multimode qubit couplers, which is effective for controlling relatively short-range coupled interactions across a given qubit chip or between stacked qubit chips, where the ancillary bits are disposed relatively close to the superconducting data qubits. In other embodiments, for long-range coupling between superconducting data qubits and superconducting ancillary qubits, long coplanar waveguide resonators may be utilized to couple superconducting multimode qubit couplers (associated with superconducting data qubits) to superconducting ancillary qubits, while eliminating the need to couple the superconducting ancillary qubits to associated superconducting multimode qubit couplers.

[0097] For example, Fig. 9 A quantum device according to an exemplary embodiment of the present disclosure is schematically shown, the quantum device comprising a superconducting qubit array, the superconducting qubit array comprising a superconducting data qubit coupled to a superconducting auxiliary qubit using a superconducting qubit coupler and a transmission line resonator. Specifically, Fig. 9 A quantum device is schematically shown, which includes a superconducting qubit array 900, which includes superconducting data qubits 910-1, 910-2, and 910-3, and tunable superconducting multimode qubit couplers 920-1, 920-2, and 920-3, which are capacitively coupled to superconducting data qubits 910-1, 910-2, and 910-3, respectively. Superconducting qubit array 900 also includes superconducting auxiliary qubit 940, which is coupled to tunable superconducting multimode qubit couplers 920-1, 920-2, and 920-3 through superconducting transmission line resonator 950.

[0098] In some embodiments, Fig. 9 As schematically shown in FIG. 1 , each of superconducting data qubits 910-1, 910-2, and 910-3 and superconducting auxiliary qubit 940 includes a superconducting transmission sub-qubit having the same structure as that in the above combination. Figure 2A and Figure 2B The circuit configuration and layout are similar to the exemplary embodiments shown and discussed, and the details will not be repeated. In addition, the tunable superconducting multimode qubit couplers 920-1, 920-2 and 920-3 each include the above combined Figure 4A and Figure 4B The circuit configuration and layout are similar to the exemplary embodiments shown and discussed, and the details will not be repeated.

[0099] In some embodiments, superconducting transmission line resonator 950 comprises a coplanar waveguide resonator bus with a given resonant frequency (e.g., close to 5 GHz). Superconducting transmission line resonator 950 can be several millimeters in length across the same qubit chip, or extend from a first qubit chip to a second qubit chip, which are vertically stacked and coupled together via indium bump bonding using known structures and manufacturing techniques. In some embodiments, superconducting data qubits 910-1, 910-2, and 910-3 and associated tunable superconducting multimode qubit couplers 920-1, 920-2, and 920-3 are disposed on the first qubit chip, while superconducting auxiliary qubit 940 (and other auxiliary qubits) are disposed on the second qubit chip.

[0100] In addition, if Fig. 9As schematically shown in FIG. 1 , a first end of superconducting transmission line resonator 950 is capacitively coupled to corresponding B modes of tunable superconducting multimode qubit couplers 920-1, 920-2, and 920-3 via corresponding coupling capacitors 951, 952, and 953, and a second end of superconducting transmission line resonator 950 is capacitively coupled to superconducting auxiliary qubit 940 via coupling capacitor 954. Coupling capacitors 951, 952, 953, and 954 may be implemented using suitable capacitive coupling structures and techniques known to those of ordinary skill in the art.

[0101] It should be noted that, depending on the length of the superconducting transmission line resonator 950, the tunable superconducting multimode qubit couplers 920-1, 920-2, and 920-3 can be coupled to the superconducting transmission line resonator 950 at the fundamental mode of the superconducting transmission line resonator 950 (e.g., close to 5 GHz) or at the higher modes at longer lengths of the superconducting transmission line resonator 950, in which case the length of the transmission line resonator is adjusted so that the higher modes are also close to 5 GHz, where the lower frequency modes will not play a role. For example, in some embodiments, the superconducting transmission line resonator 950 includes an open circuit half-wavelength (λ / 2) transmission line that behaves as a parallel resonant circuit with a length l = (n×λ) / 2, where n represents the number of resonant modes (n = 1, 2, 3, ...). Thus, for a target resonance of about 5 GHz, the superconducting transmission line resonator 950 may have (i) a length l = λ / 2 (n = 1), which corresponds to a fundamental mode frequency of f0 ≈ 5 GHz, or (ii) a length l = (n×λ) / 2, which corresponds to f n =n×f0≈higher mode frequency of 5 GHz.

[0102] exist Fig. 9 In the exemplary embodiment of , coupling superconducting auxiliary qubit 940 directly to superconducting transmission line resonator 950 ensures that superconducting data qubits 910-1, 910-2, and 910-3 will be more strongly coupled to superconducting auxiliary qubit 940 than they are to each other. In fact, as described above, superconducting transmission line resonator 950 eliminates the need to couple a dedicated superconducting multimode qubit coupler to superconducting auxiliary qubit 940 because superconducting transmission line resonator 950 has a relatively large capacitance to ground, which serves to reduce crosstalk between superconducting data qubits 910-1, 910-2, and 910-3 coupled to superconducting auxiliary qubit 940.

[0103] In some embodiments, superconducting data qubits 910-1, 910-2, and 910-3 and superconducting auxiliary qubit 940 have transition frequencies that are detuned from one another and that depend in part on the resonance of superconducting transmission line resonator 950. For example, in an exemplary non-limiting embodiment, superconducting auxiliary qubit 940 has a transition frequency that is about 200 MHz to about 300 MHz lower than the resonance of superconducting transmission line resonator 950. For example, superconducting transmission line resonator 950 may be designed to have a resonance of ~5 GHz, and superconducting auxiliary qubit 940 has a transition frequency of about 4.7 GHz to 4.8 GHz. Furthermore, in an exemplary non-limiting embodiment, superconducting data qubits 910-1, 910-2, and 910-3 and superconducting auxiliary qubit 940 have transition frequencies of 4.7-4.8 GHz, but are detuned by plus / minus 100 MHz.

[0104] In addition, in some embodiments, each tunable superconducting multimode qubit coupler 920-1, 920-2, and 920-3 is substantially identical, e.g., the same normal A-mode frequency and B-mode frequency. For example, in an exemplary non-limiting embodiment, in the closed state, each tunable superconducting multimode qubit coupler 920-1, 920-2, and 920-3 has a normal A-mode frequency of ˜2.0 GHz, and a normal B-mode frequency of ˜3.5 GHz. The exemplary operating frequencies can all be adjusted up or down in unison to accommodate other design issues. In addition, in some embodiments, the coupling capacitance between the superconducting transport sub-data qubit and the corresponding superconducting multimode qubit coupler is on the order of about 10 fF to about 20 fF.

[0105] Fig.10 A quantum device according to another exemplary embodiment of the present disclosure is schematically shown, the quantum device comprising a superconducting qubit array, the superconducting qubit array comprising a superconducting data qubit coupled to a superconducting auxiliary qubit using a superconducting qubit coupler. Specifically, Fig.10 Schematically illustrates a quantum device including a superconducting qubit array 1000, which includes superconducting data qubits 1010-1 and 1010-2 and associated tunable superconducting multimode qubit couplers 1020-1 and 1020-2, which are capacitively coupled to superconducting data qubits 1010-1 and 1010-2, respectively. Superconducting qubit array 1000 also includes superconducting auxiliary qubit 1040, which is coupled to a plurality of tunable superconducting multimode qubit couplers 1030-1, 1030-2, and 1030-3. Superconducting qubit array 1000 also includes a plurality of capacitive buses 1050-1, 1050-2, and 1050-3.

[0106] The superconducting qubit array 1000 is similar in configuration to Figure 8 The superconducting qubit array 800 is different in that the superconducting auxiliary qubit 1040 includes a superconducting quadrupole transmission sub-qubit that allows dipole-dipole interaction and coupling with at least three tunable superconducting multimode qubit couplers 1030-1, 1030-2, and 1030-3, such as shown in the figure. The superconducting quadrupole transmission sub-qubit 1040 is coupled to the superconducting auxiliary qubit 1040. Figure 2A and Figure 2B The illustrated superconducting transport sub-qubit operates in a similar manner, except that superconducting quadrupole transport sub-qubit 1040 includes a different arrangement of parallel capacitor pads that have a quadrupole charge pattern when energized.

[0107] For example, Fig.10 As shown, the superconducting quadrupole transport sub-qubit 1040 includes a single Josephson tunnel junction device 1045 having a Manhattan Josephson junction framework, and a first superconducting pad 1041, a second superconducting pad 1042, a third superconducting pad 1043, and a fourth superconducting pad 1044, which together comprise a capacitor electrode pad forming a shunt capacitor of the superconducting quadrupole transport sub-qubit 1040. The first superconducting pad 1041, the second superconducting pad 1042, the third superconducting pad 1043, and the fourth superconducting pad 1044 of the superconducting quadrupole transport sub-qubit 1040 are arranged in a rectangular array. The first superconducting pad 1041 and the second superconducting pad 1042 are configured to implement a first capacitor electrode of the shunt capacitor and are commonly connected to a first electrode of the single Josephson tunnel junction device 1045. The third superconducting pad 1043 and the fourth superconducting pad 1044 are configured to implement a second capacitor electrode of the shunt capacitor and are commonly connected to a second electrode of the single Josephson tunnel junction device 1045. Using an exemplary quadrupole configuration, as shown in FIG. Fig.10 As shown, superconducting quadrupole transport sub-qubit 1040 is configured to be capacitively coupled directly to the A-mode of each of three tunable superconducting multimode qubit couplers 1030-1, 1030-2, and 1030-3.

[0108] Similar to Figure 8 An exemplary array layout of Fig.10 Each of the capacitive buses 1050-1, 1050-2, and 1050-3 in is configured to couple to three pairs of superconducting data qubits and associated superconducting multimode qubit couplers. For ease of illustration, Fig.10Two superconducting data qubits and associated superconducting multimode qubit couplers coupled to capacitive bus 1050-1 are depicted. Capacitive bus 1050-1 includes (i) a first capacitor pad 1051 connected to first superconducting multimode qubit coupler 1020-1 via a first superconducting transmission line 1051-1, (ii) a second capacitor pad 1052 connected to second superconducting multimode qubit coupler 1020-2 via a second superconducting transmission line 1052-1, (iii) a third capacitor pad 1053 connected to a third superconducting multimode qubit coupler (not shown) via a third superconducting transmission line 1053-1, and (iv) a fourth capacitor pad 1054 connected to tunable superconducting multimode qubit coupler 1030-1 via a fourth superconducting transmission line 1054-1. Fig.10 The exemplary array layout shown in allows nine (9) superconducting data qubits to be selectively coupled to superconducting auxiliary qubit 1040 by selectively activating / deactivating appropriate superconducting multimode qubit couplers.

[0109] Fig.11 A quantum device according to another exemplary embodiment of the present disclosure is schematically shown, the quantum device comprising a superconducting qubit array, the superconducting qubit array comprising a superconducting data qubit coupled to a superconducting auxiliary qubit using a superconducting qubit coupler. In particular, Fig.11 Schematically illustrated is a superconducting qubit array 1100 that utilizes a tunable transmission sub-qubit coupler to selectively couple a superconducting data qubit to a superconducting auxiliary qubit. For example, superconducting qubit array 1100 includes superconducting data qubits 1110-1 and 1110-2 and tunable superconducting transmission sub-qubit couplers 1120-1 and 1120-2, which are capacitively coupled to superconducting data qubits 1110-1 and 1110-2, respectively. Superconducting qubit array 1100 also includes a tunable superconducting transmission sub-qubit coupler 1130 and a superconducting auxiliary qubit 1140, which is capacitively coupled to tunable superconducting transmission sub-qubit coupler 1130.

[0110] Superconducting data qubits 1110-1 and 1110-2 each include a corresponding planar capacitor including a first superconducting pad 1112-1 and a second superconducting pad 1112-2, and a Josephson tunnel junction device 1114, which is coupled to and disposed between the first superconducting pad 1112-1 and the second superconducting pad 1112-2. Similarly, superconducting auxiliary qubit 1140 includes a planar capacitor including a first superconducting pad 1142-1 and a second superconducting pad 1142-2, and a Josephson tunnel junction device 1144, which is coupled to and disposed between the first superconducting pad 1142-1 and the second superconducting pad 1142-2.

[0111] Tunable superconducting transport sub-qubit couplers 1120-1 and 1120-2 each include a corresponding planar capacitor including a first superconducting pad 1122-1 and a second superconducting pad 1122-2, and corresponding SQUIDs 1124-1 and 1124-2, wherein each SQUID 1124-1 and 1124-2 includes two Josephson tunnel junction devices coupled to the first superconducting pad 1122-1 and the second superconducting pad 1122-2 and connected in parallel between the first superconducting pad 1122-1 and the second superconducting pad 1122-2. Similarly, tunable superconducting transport sub-qubit coupler 1130 includes a planar capacitor including a first superconducting pad 1132-1 and a second superconducting pad 1132-2 and a SQUID 1134 including two Josephson tunnel junction devices coupled to the first superconducting pad 1132-1 and the second superconducting pad 1132-2 and connected in parallel between the first superconducting pad 1132-1 and the second superconducting pad 1132-2.

[0112] like Fig.11 Schematically shown in FIG. 1 , first superconducting pad 1132-1 of tunable superconducting transport sub-qubit coupler 1130 is directly capacitively coupled (via gap capacitance) to respective second superconducting pads 1122-2 of tunable superconducting transport sub-qubit couplers 1120-1 and 1120-2, and second superconducting pad 1132-2 of tunable superconducting transport sub-qubit coupler 1130 is directly capacitively coupled to first superconducting pad 1142-1 of superconducting auxiliary qubit 1140. Furthermore, respective second superconducting pads 1112-2 of superconducting data qubits 1110-1 and 1110-2 are directly capacitively coupled (via gap capacitance) to respective first superconducting pads 1122-1 of tunable superconducting transport sub-qubit couplers 1120-1 and 1120-2.

[0113] SQUIDs 1124-1, 1124-2, and 1134 of respective tunable superconducting transport sub-qubit couplers 1120-1, 1120-2, and 1130 provide a flux tunable control mechanism to tune respective transition frequencies of tunable superconducting transport sub-qubit couplers 1120-1, 1120-2, and 1130 using respective flux bias control signals applied to SQUIDs 1124-1, 1124-2, and 1134 to selectively control coupling (e.g., exchange interaction) between superconducting data qubits 1110-1 and 1110-2 and superconducting auxiliary qubit 1140. Each tunable superconducting transmission sub-qubit coupler 1120-1, 1120-2, and 1130 includes a superconducting qubit coupler configured to operate in a first state (e.g., an off state or a deactivated state) and a second state (e.g., an on state or an activated state) in response to a respective control signal applied thereto.

[0114] More specifically, in some embodiments, a given superconducting transport sub-qubit coupler is considered to be in an off-state when its corresponding SQUID and transition frequency are tuned so as to nullify any ZZ coupling between two superconducting transport sub-qubits (e.g., a data qubit and an auxiliary qubit) coupled (directly or indirectly) to the given superconducting transport sub-qubit coupler. In particular, the given superconducting transport sub-qubit coupler is considered to be in an off-state when its transition frequency (via the corresponding SQUID) is tuned away from the transition frequencies of superconducting data qubits 1110-1 and 1110-2 and the transition frequency of superconducting auxiliary qubit 1140. On the other hand, a given superconducting transport sub-qubit coupler is considered to be in the on state when its corresponding SQUID and transition frequency are tuned so as to be close in frequency to the transition frequencies of two superconducting transport sub-qubits (e.g., a data qubit and an auxiliary qubit) that are (directly or indirectly) coupled to the given superconducting transport sub-qubit coupler.

[0115] For example, in a non-limiting embodiment, where superconducting data qubits 1110-1 and 1110-2 and superconducting auxiliary qubit 1140 have respective transition frequencies in the range of about 5.0 GHz to about 5.5 GHz, when a given superconducting transport sub-qubit coupler is tuned (via a flux bias control signal applied to the associated SQUID) to have a transition frequency close to 5.0 GHz, the given superconducting transport sub-qubit coupler is considered to be in an on state, whereas when a given superconducting transport sub-qubit coupler is tuned (via a flux bias control signal applied to the associated SQUID) to have a transition frequency close to 3.5 GHz, the given superconducting transport sub-qubit coupler is considered to be in an off state.

[0116] Cancellation of ZZ coupling between superconducting data qubits and superconducting auxiliary qubits coupled (directly or indirectly) to a given superconducting transport sub-qubit coupler occurs because the superconducting data and auxiliary qubits interact not only through the given superconducting transport sub-qubit coupler, but also through direct capacitive coupling (e.g., stray capacitance, capacitance through the transport sub-coupler itself, or a separate bypass capacitor.) In this regard, when a given superconducting transport sub-qubit coupler is tuned to its off-state transition frequency, these two types of capacitive coupling become substantially equal in magnitude but opposite in sign, resulting in net zero ZZ coupling.

[0117] It should be noted that Figure 2B , Figure 3B , Figure 4B , Figure 8 , Fig. 9 , Fig.10 and Fig.11 The exemplary superconducting quantum device shown in can be implemented using planar microwave circuit elements formed on a substrate (e.g., a silicon substrate) using prior art semiconductor manufacturing techniques and materials. For example, various components of superconducting qubits (e.g., Josephson tunnel junction devices, inductors, capacitors), interconnects, coupling circuits, flux bias control lines, qubit drive lines, state readout lines, etc. include lithographically defined patterns of superconducting materials formed on a semiconductor substrate. Circuit elements can be formed using various types of superconductor materials suitable for a given application, including but not limited to elemental metals such as niobium (Nb), aluminum (Al), tantalum (Ta), and compounds such as titanium nitride (TiN), niobium nitride (NbN), niobium titanium nitride (NbTiN), etc. 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 qubit may include Al-AlO2 fabricated using a dual angle evaporation technique or other suitable manufacturing technique. x -Al triple-layer tunnel junction.

[0118] Fig.12 is a flow chart of a method for performing a quantum error correction process according to an exemplary embodiment of the present disclosure. Figure 8 discussed in the context of the exemplary quantum system shown in Fig.12 The quantum computing system starts the quantum error correction process (block 1200). As an initial step, the state of the auxiliary qubit is initialized to the ground state (block 1201). For example, Figure 8 In block 1202, a microwave control pulse is applied to superconducting auxiliary qubit 840 to initialize superconducting auxiliary qubit 840 to a ground state. The quantum error correction process continues by activating a superconducting qubit coupler coupled to the auxiliary qubit (block 1202). For example, in Figure 8 , a flux control signal is applied to the SQUID of the tunable superconducting multimode qubit coupler 830 to destroy the mode selective coupling of the tunable superconducting multimode qubit coupler 830 to allow the superconducting auxiliary qubit 840 to be exchange-coupled to the A mode and the B mode of the tunable superconducting multimode qubit coupler 830.

[0119] The quantum error correction process continues to selectively activate and deactivate the superconducting qubit couplers coupled to the superconducting data qubits in sequence to sequentially entangle the state of each data qubit with the state of the superconducting auxiliary qubit (block 1203). Figure 8 , a flux control signal is applied to SQUID 424 of tunable superconducting multimode qubit coupler 820-1 to interrupt the mode selective coupling of tunable superconducting multimode qubit coupler 820-1, which allows superconducting data qubit 810-1 to be exchange-coupled to the A mode and the B mode of tunable superconducting multimode qubit coupler 820-1. In this case, superconducting data qubit 810-1 is exchange-coupled to superconducting auxiliary qubit 840, and the state of superconducting data qubit 810-1 is entangled with the state of superconducting auxiliary qubit 840. A flux control signal is then applied to SQUID 424 of tunable superconducting multimode qubit coupler 820-1 to implement the mode selective coupling of tunable superconducting multimode qubit coupler 820-1, which causes superconducting data qubit 810-1 to be decoupled from the B mode and coupled only to the A mode of tunable superconducting multimode qubit coupler 820-1. This process is repeated in sequence for the remaining superconducting data qubits 810-2 and 810-3.

[0120] Once the state of each superconducting data qubit has been entangled with the superconducting auxiliary qubit, the quantum error correction process proceeds to deactivate the superconducting qubit coupler coupled to the auxiliary qubit (block 1204), and then perform a readout operation to read out the resulting state of the auxiliary qubit (block 1205). The quantum error correction process proceeds to determine whether an error exists in the quantum state of the superconducting data qubit based on the readout of the superconducting auxiliary qubit (block 1206), and if so, correct the determined error (block 1207).

[0121] It should be noted that although exemplary embodiments are described in the context of utilizing auxiliary qubits in the context of quantum error correction, one of ordinary skill in the art will appreciate that auxiliary qubits may be used for other purposes in quantum circuits. For example, one may implement Figure 5 , Figure 6 , Figure 8 , Fig. 9 , Fig.10 and Fig.11, to facilitate interactions between a large set of data qubits, some of which may be located relatively far from each other on the same qubit chip, wherein multimode qubit couplers, transmission line resonators, and auxiliary qubits essentially function as a "superconducting bus" to enable control and facilitation of interactions between the data qubits. For a conventional square or heavy hexagonal lattice, in order to perform a gate operation between a first data qubit and a second data qubit that are relatively far apart from each other, it would be necessary to perform multiple two-qubit gate operations to swap the quantum state of the first data qubit with an intermediate data qubit that is directly adjacent to the second qubit. On the other hand, by utilizing, for example, Figure 5 , Figure 6 , Figure 8 , Fig. 9 , Fig.10 and Fig.11 In the exemplary coupling configuration shown in , where a first data qubit and a second data qubit are coupled to the same ancillary qubit, an entanglement gate operation (e.g., a desired two-qubit gate operation) may be performed between the first and second data qubits by (i) performing a “swap” gate operation between the first data qubit and the ancillary qubit, (ii) performing a desired two-qubit gate between the ancillary qubit and the second qubit, and (iii) performing a “swap” gate operation between the ancillary qubit and the first data qubit. A “swap” gate is a two-qubit operation that is performed to swap the states of two qubits.

[0122] Fig.13 A quantum computing system according to an exemplary embodiment of the present disclosure is schematically shown. In particular, Fig.13 The quantum computing system 1300 is schematically shown and includes a quantum computing platform 1310, a control system 1320, and a quantum processor 1330. In some embodiments, the quantum computing platform 1310 implements a software control program, such as a software-based quantum error correction system 1312, to perform quantum error correction processes, such as those described above in conjunction with, for example, Fig.12 13 and 13. The control system 1320 may be used to control the quantum state of the quantum bit and the quantum processor 1330 ...

[0123] In some embodiments, the control system 1320 and the quantum processor 1330 are disposed in a dilution refrigeration system 1340, which can generate cryogenic temperatures sufficient to operate components of the control system 1320 for quantum computing applications. For example, the quantum processor 1330 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 1340 includes a multi-stage dilution refrigerator, in which components of the control system 1320 can be maintained at different cryogenic temperatures as needed. For example, while the quantum processor 1330 may need to be cooled to, for example, 10-15 mK, the circuit components of the control system 1320 may 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.

[0124] In some embodiments, superconducting qubit array 1332 includes a quantum system of superconducting data qubits, superconducting auxiliary qubits, and superconducting qubit couplers, such as Figure 8 , Fig. 9 , Fig.10 or Fig.11 etc. The number of superconducting qubits of the qubit array 1332 may be in the order of tens, hundreds, thousands, or more. The network 1334 of qubit drive lines, coupler flux bias control lines, and qubit state readout lines, etc., is configured to apply microwave control signals to the superconducting qubits and coupler circuits in the superconducting qubit array 1332 to perform various types of gate operations, such as single gate operations, entangled gate operations (e.g., C-phase gate operations), perform error correction operations, etc., and read the quantum state of the superconducting qubits. For example, 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., change the quantum state of a given qubit between a ground state and an excited state, or change to a superposition state) when executing a quantum information processing algorithm.

[0125] 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 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 the given superconducting qubit.

[0126] A network 1334 of qubit drive lines, coupler flux bias control lines, qubit state readout lines, and the like is coupled to control system 1320 via a suitable hardware input / output (I / O) interface that couples I / O signals between control system 1320 and quantum processor 1330. 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, and the like.

[0127] In some embodiments, a multi-channel arbitrary waveform generator (AWG) 1322 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 1322 includes multiple AWG channels that control corresponding superconducting qubits within the superconducting qubit array 1332 of the quantum processor 1330. 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.

[0128] In some embodiments, the multi-channel AWG 1322 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 qubit coupled to the output of the given AWG channel.

[0129] 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).

[0130] In some embodiments, qubit readout control system 1324 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 circuitry 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.

[0131] The quantum computing platform 1310 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 1310 includes a hardware architecture of processors, memories, etc., which are configured to control the execution of quantum applications and interface with the control system 1320 to (i) generate digital control signals, which are converted by the control system 1320 into analog microwave control signals to control the operation of the quantum processor 1330 when executing a given quantum application, and (ii) obtain and process digital signals received from the control system 1320, which represent processing results generated by the quantum processor 1330 when executing various gate operations of a given quantum application.

[0132] In some exemplary embodiments, the quantum computing platform 1310 of the quantum computing system 1300 may use any suitable computing system architecture (e.g., Fig.14The computing system architecture is implemented by executing computer-readable program instructions embodied in a computer program product to implement a method of supporting quantum computing operations, the computer program product including a computer-readable storage medium (or multiple media) having such computer-readable program instructions thereon, for causing a processor to execute a control method as discussed herein.

[0133] The quantum computing platform 1310 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 1310 includes a hardware architecture of processors, memories, etc., which is configured to control the execution of quantum applications and interface with the control system 1320 to (i) generate digital control signals, which are converted by the control system 1320 into analog microwave control signals to control the operation of the quantum processor 1330 when executing a given quantum application, and (ii) obtain and process digital signals received from the control system 1320, which represent processing results generated by the quantum processor 1330 when executing various gate operations of a given quantum application. In some exemplary embodiments, the quantum computing platform 1310 of the quantum computing system 1300 may use any suitable computing system architecture (e.g., such as Fig.14 The computing system architecture is implemented by executing computer-readable program instructions embodied in a computer program product to implement a method of supporting quantum computing operations, the computer program product including a computer-readable storage medium (or multiple media) having such computer-readable program instructions thereon, for causing a processor to execute a control method as discussed herein.

[0134] Various aspects of the present disclosure are described by narrative text, flow charts, block diagrams of computer systems, and / or block diagrams of machine logic included in computer program product (CPP) embodiments. With respect to any flow chart, depending on the technology involved, the operations may be performed in an order different from the order shown in a given flow chart. For example, again depending on the technology involved, two operations shown in successive flow chart blocks may be performed in reverse order, as a single integrated step, simultaneously, or in a manner that at least partially overlaps in time.

[0135] Computer program product embodiments ("CPP embodiments" or "CPP") are terms used in this disclosure to describe any collection of one or more storage media (also referred to as "media") collectively included in a set of one or more storage devices that collectively include machine-readable code corresponding to instructions and / or data for performing the computer operations specified in a given CPP claim. A "storage device" is any tangible device that can retain and store instructions for use by a computer processor. Without limitation, a computer-readable storage medium may be an electronic storage medium, a magnetic storage medium, an optical storage medium, an electromagnetic storage medium, a semiconductor storage medium, a mechanical storage medium, or any suitable combination of the foregoing. Some known types of storage devices that include these media include: magnetic disks, hard disks, random access memories (RAM), read-only memories (ROM), erasable programmable read-only memories (EPROM or flash memory), static random access memories (SRAM), compact disk read-only memories (CD-ROM), digital versatile disks (DVD), memory sticks, floppy disks, mechanical encoding devices (such as punch cards or pits / land formed in a major surface of a disk), or any suitable combination of the foregoing. The term computer-readable storage medium as used in this disclosure should not be interpreted as storage in the form of a transitory signal itself, such as a radio wave or other freely propagating electromagnetic wave, an electromagnetic wave propagating through a waveguide, a light pulse through a fiber optic cable, an electrical signal transmitted through an electric wire and / or other transmission medium. As will be understood by those skilled in the art, during normal operation of the storage device, such as during access, defragmentation, or garbage collection, data is typically moved at some occasional point in time, but this does not make the storage device transitory because the data is not transitory when it is stored.

[0136] Fig.14 The computing environment 1400 includes an example of an environment for executing at least some of the computer code involved in executing the method of the present invention, such as for controlling Fig.13The quantum error correction control code in the block 1426 of the quantum error correction function of the quantum error correction system 1312 of the embodiment of the present invention is shown in FIG. 1426. In addition to the block 1426, the computing environment 1400 also includes, for example, a computer 1401, a wide area network (WAN) 1402, an end user device (EUD) 1403, a remote server 1404, a public cloud 1405, and a private cloud 1406. In this embodiment, the computer 1401 includes a processor set 1410 (including a processing circuit 1420 and a cache 1421), a communication structure 1411, a volatile memory 1412, a persistent storage device 1413 (including an operating system 1422 and a block 1426, as identified above), a peripheral device set 1414 (including a user interface (UI), a device set 1423, a storage device 1424, and an Internet of Things (IoT) sensor set 1425) and a network module 1415. The remote server 1404 includes a remote database 1430. The public cloud 1405 includes a gateway 1440 , a cloud orchestration module 1441 , a host physical machine set 1442 , a virtual machine set 1443 , and a container set 1444 .

[0137] Computer 1401 may take the form of a desktop computer, laptop computer, tablet computer, smart phone, smart watch or other wearable computer, mainframe computer, quantum computer, or any other form of computer or mobile device now known or developed in the future that is capable of running programs, accessing a network, or querying a database (such as remote database 1430). As is well understood in the field of computer technology, and depending on the technology, the execution of the computer-implemented method may be distributed among multiple computers and / or among multiple locations. On the other hand, in this presentation of computing environment 1400, the detailed discussion focuses on a single computer, particularly computer 1401, to keep the presentation as simple as possible. Computer 1401 may be located in the cloud, even if it is not in the cloud. Fig.14 On the other hand, except to any extent that can be indicated with certainty, there is no requirement that computer 1401 be in the cloud.

[0138] Processor set 1410 includes one or more computer processors of any type known now or developed in the future. Processing circuit 1420 can be distributed over multiple packages, for example, multiple coordinated integrated circuit chips. Processing circuit 1420 can implement multiple processor threads and / or multiple processor cores. Cache 1421 is a memory located in (one or more) processor chip packages, and is generally used for data or code that should be available for rapid access by threads or cores running on processor set 1410. Cache memory is generally organized into multiple levels according to relative proximity to the processing circuit. Alternatively, some or all of the caches for the processor set may be located "off-chip". In some computing environments, processor set 1410 may be designed to work with qubits and perform quantum computing.

[0139] Computer readable program instructions are typically loaded onto computer 1401 to cause processor set 1410 of computer 1401 to perform a series of operating steps to implement a computer-implemented method, such that the instructions so executed will instantiate the method specified in the flowchart and / or the narrative description of the computer-implemented method included in this document (collectively referred to as "the method of the present invention"). These computer readable program instructions are stored in various types of computer readable storage media, such as cache 1421 and other storage media discussed below. The program instructions and associated data are accessed by processor set 1410 to control and direct the execution of the method of the present invention. In computing environment 1400, at least some of the instructions for performing the method of the present invention may be stored in persistent storage device 1413 in box 1426.

[0140] Communications fabric 1411 is the signaling pathways that allow the various components of computer 1401 to communicate with each other. Typically, the fabric is made of switches and conductive pathways, such as those that make up a bus, a bridge, physical input / output ports, etc. Other types of signal communication pathways may be used, such as fiber optic communication pathways and / or wireless communication pathways.

[0141] Volatile memory 1412 is any type of volatile memory now known or developed in the future. Examples include dynamic type random access memory (RAM) or static type RAM. Typically, volatile memory is characterized by random access, but this is not required unless affirmatively indicated. In computer 1401, volatile memory 1412 is located in a single package and internal to computer 1401, but alternatively or additionally, volatile memory can be distributed over multiple packages and / or located externally relative to computer 1401.

[0142] Persistent storage 1413 is any form of non-volatile storage for computers known now or developed in the future. The non-volatility of the storage means that the stored data is maintained regardless of whether the computer 1401 is powered and / or the persistent storage 1413 is powered directly. Persistent storage 1413 can be a read-only memory (ROM), but typically at least a portion of the persistent storage allows writing data, deleting data, and rewriting data. Some familiar forms of persistent storage include disks and solid-state storage devices. Operating system 1422 can take several forms, such as various known proprietary operating systems or operating systems of the open source portable operating system interface type using a kernel. The code included in box 1426 typically includes at least some of the computer code related to executing the method of the present invention.

[0143] The peripheral device set 1414 includes a peripheral device set of the computer 1401. The data communication connection between the peripheral device and other components of the computer 1401 can be implemented in various ways, such as a Bluetooth connection, a near field communication (NFC) connection, a connection by a cable (such as a universal serial bus (USB) type cable), a plug-in type connection (e.g., a secure digital (SD) card), a connection through a local area network, and even a connection through a wide area network (such as the Internet). In various embodiments, the UI device set 1423 may include components such as a display screen, a speaker, a microphone, a wearable device (such as goggles and smart watches), a keyboard, a mouse, a printer, a touchpad, a game controller, and a tactile device. The storage device 1424 is an external storage device, such as an external hard drive, or a pluggable storage device, such as an SD card. The storage device 1424 can be persistent and / or volatile. In some embodiments, the storage device 1424 can take the form of a quantum computing storage device for storing data in the form of quantum bits. In embodiments where it is necessary for computer 1401 to have a large amount of storage (e.g., where computer 1401 locally stores and manages a large database), the storage may be provided by a peripheral storage device designed to store very large amounts of data, such as a storage area network (SAN) shared by multiple geographically distributed computers. IoT sensor set 1425 consists of sensors that can be used in IoT applications. For example, one sensor may be a thermometer, while another sensor may be a motion detector.

[0144] The network module 1415 is a collection of computer software, hardware, and firmware that allows the computer 1401 to communicate with other computers via the WAN 1402. The network module 1415 may include hardware (such as a modem or a Wi-Fi signal transceiver), software for packetizing and / or depacketizing data for transmission over a communication network, and / or web browser software for communicating data over the Internet. In some embodiments, the network control function and the network forwarding function of the network module 1415 are executed on the same physical hardware device. In other embodiments (e.g., embodiments utilizing software defined networks (SDN)), the control function and the forwarding function of the network module 1415 are executed on physically separated devices, so that the control function manages several different network hardware devices. Computer-readable program instructions for executing the method of the present invention can typically be downloaded to the computer 1401 from an external computer or an external storage device via a network adapter card or a network interface included in the network module 1415.

[0145] WAN 1402 is any wide area network (e.g., the Internet) capable of transmitting computer data over non-local distances by any technology now known or developed in the future for transmitting computer data. In some embodiments, the WAN may be replaced and / or supplemented by a local area network (LAN) designed to transmit data between devices located in a local area (such as a Wi-Fi network). WANs and / or LANs typically include computer hardware such as copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers, and edge servers.

[0146] End-user device (EUD) 1403 is any computer system used and controlled by an end-user (e.g., a customer of an enterprise operating computer 1401), and may take any of the forms discussed above in connection with computer 1401. EUD 1403 typically receives helpful and useful data from the operation of computer 1401. For example, in the hypothetical case where computer 1401 is designed to provide recommendations to an end-user, the recommendations would typically be transmitted from network module 1415 of computer 1401 to EUD 1403 via WAN 1402. In this manner, EUD 1403 may display or otherwise present the recommendations to the end-user. In some embodiments, EUD 1403 may be a client device, such as a thin client, a heavy client, a mainframe computer, a desktop computer, etc.

[0147] Remote server 1404 is any computer system that provides at least some data and / or functionality to computer 1401. Remote server 1404 may be controlled and used by the same entity that operates computer 1401. Remote server 1404 represents a machine that collects and stores useful and useful data for use by other computers, such as computer 1401. For example, in the hypothetical case where computer 1401 is designed and programmed to provide recommendations based on historical data, then this historical data may be provided to computer 1401 from remote database 1430 of remote server 1404.

[0148] The public cloud 1405 is any computer system available for use by multiple entities that provides on-demand availability of computer system resources and / or other computer capabilities, particularly data storage (cloud storage) and computing capabilities, without direct active management by users. Cloud computing typically utilizes resource sharing to achieve consistency and economies of scale. The direct and active management of the computing resources of the public cloud 1405 is performed by computer hardware and / or software of the cloud orchestration module 1441. The computing resources provided by the public cloud 1405 are typically implemented by virtual computing environments that run on various computers that constitute the host physical machine set 1442, which is the totality of physical computers in and / or available for the public cloud 1405. The virtual computing environment typically takes the form of a virtual machine from a virtual machine set 1443 and / or a container from a container set 1444. It should be understood that these VCEs can be stored as images and can be transferred between and among various physical machine hosts as images or after instantiation of the VCEs. Cloud orchestration module 1441 manages the transfer and storage of images, deploys new instantiations of VCEs and manages active instantiations of VCE deployments. Gateway 1440 is a collection of computer software, hardware and firmware that allows public cloud 1405 to communicate over WAN 1402 .

[0149] Some further explanation of virtualized computing environments (VCEs) will now be provided. A VCE can be stored as an "image". A new active instance of a VCE can be instantiated from an image. Two common types of VCEs are virtual machines and containers. Containers are VCEs that use operating system-level virtualization. This refers to an operating system feature where the kernel allows the existence of multiple isolated user space instances (called containers). From the perspective of the programs running in them, these isolated user space instances typically behave like real computers. Computer programs running on a normal operating system can utilize all of the resources of that computer, such as connected devices, files and folders, network shares, CPU power, and quantifiable hardware capabilities. However, programs running within a container can only use the contents of the container and the devices assigned to the container, a feature known as containerization.

[0150] Private cloud 1406 is similar to public cloud 1405, except that the computing resources are only available to a single enterprise. Although private cloud 1406 is depicted as communicating with WAN 1402, in other embodiments, the private cloud can be completely disconnected from the Internet and accessible only through a local / private network. A hybrid cloud is a combination of multiple clouds of different types (e.g., private cloud, community cloud, or public cloud types), typically implemented by different vendors. Each of the multiple clouds remains a separate and discrete entity, but the larger hybrid cloud architecture is bound together by standardized or proprietary technologies that enable orchestration, management, and / or data / application portability between the multiple constituent clouds. In this embodiment, both public cloud 1405 and private cloud 1406 are part of a larger hybrid cloud.

[0151] 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: a first data qubit; a first qubit coupler coupled to the first data qubit; a second qubit coupler coupled to the first qubit coupler; and an auxiliary qubit coupled to the second qubit coupler; wherein the first qubit coupler is configured to operate in a state that inhibits interaction between the first data qubit and the auxiliary qubit; and The first qubit coupler and the second qubit coupler are each configured to operate in a corresponding state to enable interaction between the first data qubit and the auxiliary qubit and to entangle the state of the first data qubit with the state of the auxiliary qubit.

2. The device according to claim 1, wherein: The first data qubit and the auxiliary qubit each comprise a transmission sub-qubit.

3. The device according to any one of the preceding claims, further comprising: a second data qubit; as well as a third qubit coupler coupled to the second data qubit and the second qubit coupler; wherein the third qubit coupler is configured to operate in a state that inhibits interaction between the second data qubit and the first data qubit and inhibits interaction between the second data qubit and the auxiliary qubit; and The third qubit coupler and the second qubit coupler are each configured to operate in a corresponding state to enable interaction between the second data qubit and the auxiliary qubit and to entangle the state of the second data qubit with the state of the auxiliary qubit.

4. The apparatus according to claim 3, further comprising: a capacitive bus configured to capacitively couple the first qubit coupler and the third qubit coupler to the second qubit coupler, wherein the capacitive bus comprises: a first capacitor pad connected to the first qubit coupler via a first transmission line; a second capacitor pad connected to the second qubit coupler via a second transmission line; and a third capacitor pad connected to the third qubit coupler via a third transmission line; wherein the first capacitor pad and the third capacitor pad are arranged adjacent to a first edge and a second edge of the second capacitor pad, respectively, and The second capacitor pad has a size greater than that of the first capacitor pad and that of the third capacitor pad.

5. A device according to any one of the preceding claims, wherein: The first qubit coupler and the second qubit coupler each include a flux tunable transmission sub-qubit.

6. A device according to any one of the preceding claims, wherein: The auxiliary qubits include quadrupole transport sub-qubits.

7. A device according to any one of the preceding claims, wherein: The first qubit coupler includes a first multimode qubit, the first multimode qubit including a first mode and a second mode; The second qubit coupler includes a second multi-mode qubit including a first mode and a second mode.

8. The device according to claim 7, wherein: The first data qubit is capacitively coupled to a first mode of the first multimode qubit; The auxiliary qubit is capacitively coupled to the first mode of the second multimode qubit; The second mode of the first multimode qubit is capacitively coupled to the second mode of the second multimode qubit; The first qubit coupler is configured to operate in a state in which the first data qubit is exchange coupled only to a first mode of the first multimode qubit; the first qubit coupler being configured to operate in a state in which the first data qubit is exchange coupled to both the first mode and the second mode of the first multimode qubit; the second qubit coupler being configured to operate in a state in which the auxiliary qubit is exchange coupled only to the first mode of the second multimode qubit; and The second qubit coupler is configured to operate in a state in which the auxiliary qubit is exchange coupled to both the first mode and the second mode of the second multimode qubit.

9. A system comprising: a quantum processor comprising an array of qubits; as well as a control system configured to generate control signals to control the quantum processor; Wherein, the quantum bit array comprises: a first data qubit; a first qubit coupler coupled to the first data qubit; a second qubit coupler coupled to the first qubit coupler; and an auxiliary qubit coupled to the second qubit coupler; wherein the first qubit coupler is configured to operate in a state that inhibits interaction between the first data qubit and the auxiliary qubit; and The first qubit coupler and the second qubit coupler are each configured to operate in a corresponding state to enable interaction between the first data qubit and the auxiliary qubit and to entangle the state of the first data qubit with the state of the auxiliary qubit.

10. The system according to claim 9, wherein: The first data qubit and the auxiliary qubit each comprise a transmission sub-qubit.

11. The system according to any one of claims 9 to 10, wherein: The qubit array further comprises: a second data qubit; and a third qubit coupler coupled to the second data qubit and the second qubit coupler; wherein the third qubit coupler is configured to operate in a state that inhibits interaction between the second data qubit and the first data qubit and inhibits interaction between the second data qubit and the auxiliary qubit; and The third qubit coupler and the second qubit coupler are each configured to operate in a corresponding state to enable interaction between the second data qubit and the auxiliary qubit and to entangle the state of the second data qubit with the state of the auxiliary qubit.

12. The system according to claim 11, further comprising: a capacitive bus configured to capacitively couple the first qubit coupler and the third qubit coupler to the second qubit coupler, wherein the capacitive bus comprises: a first capacitor pad connected to the first qubit coupler via a first transmission line; a second capacitor pad connected to the second qubit coupler via a second transmission line; and a third capacitor pad connected to the third qubit coupler via a third transmission line; wherein the first capacitor pad and the third capacitor pad are arranged adjacent to a first edge and a second edge of the second capacitor pad, respectively, and The second capacitor pad has a size greater than that of the first capacitor pad and that of the third capacitor pad.

13. A system according to any one of claims 9 to 12, wherein: The first qubit coupler and the second qubit coupler each include a flux tunable transmission sub-qubit.

14. A system according to any one of claims 9 to 13, wherein: The auxiliary qubits include quadrupole transport sub-qubits.

15. A system according to any one of claims 9 to 14, wherein: The first qubit coupler includes a first multimode qubit, the first multimode qubit including a first mode and a second mode; and The second qubit coupler includes a second multi-mode qubit including a first mode and a second mode.

16. The system of claim 15, wherein: The first data qubit is capacitively coupled to a first mode of the first multimode qubit; The auxiliary qubit is capacitively coupled to the first mode of the second multimode qubit; The second mode of the first multimode qubit is capacitively coupled to the second mode of the second multimode qubit; The first qubit coupler is configured to operate in a state in which the first data qubit is exchange coupled only to a first mode of the first multimode qubit; the first qubit coupler being configured to operate in a state in which the first data qubit is exchange coupled to both the first mode and the second mode of the first multimode qubit; the second qubit coupler being configured to operate in a state in which the auxiliary qubit is exchange coupled only to the first mode of the second multimode qubit; and The second qubit coupler is configured to operate in a state in which the auxiliary qubit is exchange coupled to both the first mode and the second mode of the second multimode qubit.

17. An apparatus comprising: Data qubits; a qubit coupler coupled to the data qubit; a transmission line resonator coupled to the qubit coupler; as well as an auxiliary qubit coupled to the transmission line resonator; wherein the qubit coupler is configured to operate in a state that inhibits interaction between the data qubit and the auxiliary qubit; and Wherein the qubit coupler is configured to operate in a state to enable interaction between the data qubit and the auxiliary qubit through the qubit coupler and the transmission line resonator to entangle the state of the data qubit with the state of the auxiliary qubit.

18. The device according to claim 17, wherein: The data qubit and the auxiliary qubit each include a transport sub-qubit.

19. The device according to any one of claims 17 to 18, wherein: The qubit coupler includes a multi-mode qubit, the multi-mode qubit including a first mode and a second mode; The data qubit is capacitively coupled to a first mode of the multimode qubit; The transmission line resonator is capacitively coupled to a second mode of the multi-mode qubit; The qubit coupler is configured to operate in a state in which the data qubit is exchange coupled only to the first mode of the multimode qubit; and The qubit coupler is configured to operate in a state in which a data qubit is exchange coupled to both a first mode and a second mode of a multi-mode qubit.

20. A system comprising: a quantum processor comprising an array of qubits; as well as a control system configured to generate control signals to control the quantum processor; Wherein, the quantum bit array comprises: Data qubits; a qubit coupler coupled to the data qubit; a transmission line resonator coupled to the qubit coupler; and an auxiliary qubit coupled to the transmission line resonator; wherein the qubit coupler is configured to operate in a state that inhibits interaction between the data qubit and the auxiliary qubit; and Wherein the qubit coupler is configured to operate in a state to enable interaction between the data qubit and the auxiliary qubit through the qubit coupler and the transmission line resonator to entangle the state of the data qubit with the state of the auxiliary qubit.

21. The system of claim 20, wherein: The data qubit and the auxiliary qubit each include a transport sub-qubit.

22. A system according to any one of claims 20 to 21, wherein: The qubit coupler includes a multi-mode qubit, the multi-mode qubit including a first mode and a second mode; The data qubit is capacitively coupled to a first mode of the multimode qubit; The transmission line resonator is capacitively coupled to a second mode of the multi-mode qubit; The qubit coupler is configured to operate in a state in which the data qubit is exchange coupled only to the first mode of the multimode qubit; and The qubit coupler is configured to operate in a state in which a data qubit is exchange coupled to both a first mode and a second mode of a multi-mode qubit.

23. A method comprising: Initialize the state of the auxiliary qubit; placing a first qubit coupler coupled to the auxiliary qubit in an activated state; placing a second qubit coupler coupled to a data qubit in an activated state to enable interaction between the data qubit and the auxiliary qubit, and entangle the state of the first data qubit with the state of the auxiliary qubit through the first qubit coupler and the second qubit coupler in the activated state; placing each of the first qubit coupler and the second qubit coupler in a deactivated state; After each of the first qubit coupler and the second qubit coupler is placed in the deactivated state, reading the state of the auxiliary qubit; and The presence of a quantum error is determined based on the readout of the auxiliary qubit.

24. The method of claim 23, wherein: Placing the first qubit coupler in the activated state includes applying a first flux control signal to a first superconducting loop of a first superconducting quantum interference device of the first qubit coupler to configure the first qubit coupler from the deactivated state to the activated state; and Placing the second qubit coupler in the activated state includes applying a second flux control signal to a second superconducting loop of a second superconducting quantum interference device of the second qubit coupler to configure the second qubit coupler from the deactivated state to the activated state.

25. A method according to any one of claims 23 to 24, wherein: The first qubit coupler includes a first multimode qubit, the first multimode qubit including a first mode and a second mode; The second qubit coupler includes a second multimode qubit, the second multimode qubit including a first mode and a second mode; The auxiliary qubit is capacitively coupled to a first mode of the first multimode qubit; The data qubit is capacitively coupled to a first mode of the second multimode qubit; The second mode of the first multimode qubit is capacitively coupled to the second mode of the second multimode qubit; Placing the first qubit coupler in the activated state comprises applying a first flux control signal to a first superconducting loop of a first superconducting quantum interference device of the first multimode qubit to exchange couple the auxiliary qubit to both the first mode and the second mode of the first multimode qubit; and Placing the second qubit coupler in the activated state includes applying a second flux control signal to a second superconducting loop of a second superconducting quantum interference device of the second multimode qubit to exchange couple the data qubit to both the first mode and the second mode of the second multimode qubit.

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