Improved J / ZZ operation for superconducting qubits

Abstract

A system, device, computer-implemented method, or computer program product, or combination thereof, that facilitates dynamic control of ZZ interaction for a quantum computing device. In one example, the quantum device can include a bias component operably coupled to first and second qubits via respective first and second drive lines. The bias component can facilitate dynamic control of the ZZ interaction between the first and second qubits using a continuous wave (CW) tone applied via the respective first and second drive lines.

Description

[Technical Field]

[0001] This disclosure relates to quantum computing, and more specifically to systems, devices, computer implementations, or computer program products, or combinations thereof, that facilitate the dynamic control of ZZ interactions for quantum computing devices. [Background technology]

[0002] Quantum computing devices can consist of superconducting qubits of various configurations. In various cases, qubits can have a fixed operating frequency (for example, a transmon qubit containing a single Josephson junction can have a fixed operating frequency) and can be arranged in a two-dimensional array on any suitable quantum computing substrate. In various embodiments, any qubit in such a two-dimensional array can be coupled to some or all or both of the nearest neighbor qubits, or to some or all or both of the next nearest neighbor qubits. Various techniques and systems or both exist for implementing or constructing two-qubit gates by driving qubits using microwave tones or microwave signals at the frequencies of one or more adjacent qubits. Two-qubit gates implemented using such microwave-driven tones can exhibit strong ZX interactions from high coherence or cross-resonance or both, which can improve the performance or functionality or both of quantum computing devices.

[0003] Multiple two-qubit gates implemented using microwave-driven tones, including cross-resonance, can have an entanglement rate that can be proportional to the exchange coupling strength J between the coupled qubits. Therefore, the speed of such two-qubit gates can be increased by increasing the exchange coupling strength J. However, increasing the exchange coupling strength J can also increase the known sources of idle gate error and non-fidelity in multi-qubit circuits (always-active pseudo-ZZ interaction between coupled qubits). Thus, there can be a conflict between obtaining the desired exchange coupling strength J and the always-active pseudo-ZZ interaction between coupled qubits, which degrades circuit performance. [Overview of the Initiative]

[0004] The following is an overview to enable a basic understanding of one or more embodiments of the present invention. This overview is not intended to identify major or important elements, nor is it intended to precisely describe the scope of any particular embodiment or claim. The sole purpose of this overview is to present the concepts in a simplified form as a prelude to the more detailed descriptions presented later. One or more embodiments described herein describe a system, device, computer implementation method, or computer program product, or combination thereof, that facilitates the dynamic control of ZZ interactions for quantum computing devices.

[0005] According to one embodiment, the quantum device may comprise a bias component operably coupled to the first and second qubits via each of the first and second drive lines. The bias component can facilitate dynamic control of the ZZ interaction between the first and second qubits using a continuous wave (CW) tone applied via each of the first and second drive lines. One embodiment of such a quantum device is that the quantum device can facilitate dynamic control of the ZZ interaction.

[0006] According to another embodiment, the computer implementation method may include operably coupling bias components to the first and second qubits via each first and second drive line by a system operably coupled to a processor. The computer implementation method may further include the system dynamically controlling the ZZ interaction between the first and second qubits with CW tones applied via each first and second drive line using the bias components. One aspect of such a computer implementation method is that the computer implementation method can facilitate the dynamic control of the ZZ interaction of the quantum device.

[0007] According to another embodiment, a computer program product may comprise a computer-readable storage medium on which program instructions are embodied. The program instructions are executable by the processor to cause the processor to perform operations. These operations may include the processor operably coupling bias components to first and second qubits via each first and second drive line. These operations may further include the processor facilitating dynamic control of the ZZ interaction between the first and second qubits using the bias components with CW tones applied via each first and second drive line. One embodiment of such a computer program product is that the computer program product can facilitate dynamic control of the ZZ interaction of a quantum device.

[0008] According to another embodiment, the quantum device may comprise a bias component operably coupled to the first and second qubits via each of the first and second drive lines. The bias component can facilitate the dynamic control of the ZZ interaction between the first and second qubits by dynamically adjusting the relative phase difference between the CW tones applied via each of the first and second drive lines. One aspect of such a quantum device is that the quantum device can facilitate the dynamic control of the ZZ interaction.

[0009] According to another embodiment, the quantum device may comprise a bias component operably coupled to the first and second qubits via first and second drive lines. The bias component can facilitate dynamic control of the ZZ interaction between the first and second qubits by dynamically adjusting the first amplitude of a first CW tone applied via the first drive line, by dynamically adjusting the second amplitude of a second CW tone applied via the second drive line, or by a combination thereof. One aspect of such a quantum device is that it facilitates dynamic control of the ZZ interaction. [Brief explanation of the drawing]

[0010] [Figure 1] This figure shows a block diagram of an exemplary non-restrictive device that can facilitate the dynamic control of ZZ interactions for quantum computing devices according to one or more embodiments described herein. [Figure 2] This figure shows an exemplary non-restrictive qubit driving tone (or driving signal) according to one or more embodiments described herein. [Figure 3] This figure shows an exemplary, non-limiting graph illustrating the relative phase difference between CW tones and the ZZ interaction strength with respect to the driving intensity (or amplitude) of the CW tone of the first qubit, according to one or more embodiments described herein. [Figure 4] This figure shows an exemplary, non-limiting graph that plots the ZX velocity as a function of cross-resonance drive strength (or amplitude) with respect to the amplitudes of different CW tones, according to one or more embodiments described herein. [Figure 5] This figure shows another exemplary, non-limiting graph illustrating the relative phase difference between CW tones and the ZZ interaction strength with respect to the amplitude of the CW tone of the first qubit, according to one or more embodiments described herein. [Figure 6] This figure shows another exemplary, non-limiting graph plotting the ZX velocity as a function of the cross-resonance drive intensity with respect to the amplitude of different CW tones, according to one or more embodiments described herein. [Figure 7] This figure shows an exemplary non-restrictive graph illustrating the reduction of static ZZ interaction facilitated by a CW tone during the operation of a single-qubit gate, according to one or more embodiments described herein. [Figure 8] This figure shows an exemplary non-restrictive graph illustrating the reduction of static ZZ interaction facilitated by a CW tone during the operation of a single-qubit gate, according to one or more embodiments described herein. [Figure 9] This figure shows an exemplary non-restrictive graph illustrating the reduction of static ZZ interaction facilitated by a CW tone during the operation of a single-qubit gate, according to one or more embodiments described herein. [Figure 10] This figure shows an exemplary non-restrictive graph illustrating the reduction of static ZZ interaction facilitated by a CW tone during the operation of a single-qubit gate, according to one or more embodiments described herein. [Figure 11] This figure shows an exemplary non-restrictive graph illustrating the reduction of static ZZ interaction facilitated by CW tones during the operation of a two-qubit gate, according to one or more embodiments described herein. [Figure 12] This figure shows an exemplary non-restrictive graph illustrating the reduction of static ZZ interaction facilitated by CW tones during the operation of a two-qubit gate, according to one or more embodiments described herein. [Figure 13] This figure shows an exemplary non-limiting graph that plots the ZZ interaction strength as a function of the cross-resonance driving strength according to one or more embodiments described herein. [Figure 14] This figure shows an exemplary non-limiting graph plotting the ZX velocity as a function of the cross-resonance drive intensity according to one or more embodiments described herein. [Figure 15] FIG. is another exemplary non-limiting graph depicting the ZZ interaction strength as a function of the cross resonance drive strength, according to one or more embodiments described herein. [Figure 16] FIG. is another exemplary non-limiting graph depicting the ZX velocity as a function of the cross resonance drive strength, according to one or more embodiments described herein. [Figure 17] FIG. is a flow diagram of an exemplary non-limiting computer implementation method for facilitating dynamic control of the ZZ interaction for a quantum computing device, according to one or more embodiments described herein. [Figure 18] FIG. is a block diagram of an exemplary non-limiting operating environment that can facilitate one or more embodiments described herein. DETAILED DESCRIPTION

[0011] The following detailed description is merely by way of example, and is not intended to limit embodiments, or the application or use of embodiments, or both. Further, there is no intention to be constrained by any information, whether explicitly or implicitly presented, in the preceding "Technical Field" or "Summary of the Invention" sections, or the "Detailed Description of the Invention" section.

[0012] Here, one or more embodiments are described with reference to the drawings, and throughout the drawings, like reference numerals are used to refer to like elements. In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of one or more embodiments. However, it is clear that one or more embodiments may be practiced in various instances without these specific details.

[0013] Unless otherwise specified, the following definitions are used throughout this disclosure: “CR” indicates a cross-resonance gate. “CW” indicates a continuous wave (e.g., always valid). “Anharmonicity” (α) indicates the difference between the energy levels of the second and first excited states and the transition of the qubit (e.g., the two lowest energy levels). “Resonant state” refers to the case where the driving magnetic field is at the same frequency as the transition frequency in the quantum system. “Hamiltonian” indicates the energy of the quantum system expressed with respect to quantum operations. “Stark shift” indicates a shift in the energy level of the quantum system due to a non-resonant driving magnetic field. “Stark drive” indicates a non-resonant drive that causes an AC Stark shift. “ZZ” indicates a shift in the energy of the state when two qubits are excited. “Gate” indicates an operation for a quantum system that transforms a quantum state. “Single-qubit gate” indicates a gate that transforms the state of a single qubit (e.g., usually using microwave drive). A "two-qubit gate" refers to a gate that transforms the coupled state of two qubits, involving some form of interaction between the two qubits.

[0014] Classical computers operate on binary numbers (or bits) that store or represent information as binary states, and perform computation and information processing functions. In contrast, quantum computing devices operate on quantum bits (or qubits) that store or represent information as both binary states and superpositions of binary states. Therefore, quantum computing devices utilize quantum mechanical phenomena such as entanglement and interference.

[0015] Quantum computing uses qubits as its basic unit instead of classical computing bits. A qubit (e.g., a quantum binary number) is a quantum mechanical analogue of a classical bit. While classical bits can use states based on only one of two (e.g., 0 or 1), qubits can use states based on superpositions of these states (e.g., α|0>+β|1>, where α and β are |α| 2 +|β|2 It is possible to use complex scalars (where α and β are such that = 1), and theoretically, multiple qubits can hold exponentially more information than the same number of classical bits. Therefore, quantum computers (e.g., computers that employ qubits rather than only classical bits) can theoretically solve problems that are extremely difficult for classical computers very quickly. A bit in a classical computer is simply a binary number with a value of either 0 or 1. Almost any device with two different states, such as switches, valves, magnets, and coins, can serve to represent a classical bit. A qubit operating according to the principles of quantum mechanics can occupy a superposition of states 0 and 1, as previously mentioned, using complex scalars α and β. However, while the result will be either 0 or 1 when the state of a qubit is measured, during the computation process, the qubit develops in a superposition state, and interference effects can exist between these complex coefficients. This is very different from strictly classical probabilistic computation. General quantum programs require coordination between the quantum mechanical and classical parts of the computation. One way to think about a typical quantum program is to identify the processes and abstractions involved in specifying a quantum algorithm, translating that algorithm into an executable form, performing experiments or simulations, and analyzing the results. By processing information using the laws of quantum mechanics, quantum computers offer new ways to perform computational tasks such as molecular calculations, financial risk calculations, and optimization.

[0016] One common type of quantum circuit implemented in quantum computing devices comprises a fixed-frequency transmon qubit with fixed coupling. Transmons can be considered prime candidates for creating quantum bits (or qubits) to improve the scalability of quantum computing devices. Each qubit in such a quantum circuit may include a microwave drive line that operably couples that qubit to a bias component. In embodiments, the Hamiltonian of such a quantum circuit can be approximated using the Hamiltonian defined by equation 1.

[0017]

number

[0018] According to equation 1 above, ω i This indicates the qubit frequency of transmon i (e.g., energy splitting between the two lowest levels), and α i This is the anharmonicity of transmon i (e.g., energy splitting between the first and second energy levels and ω i (The difference between them)

number

number

number

Number

Number

Number

[0019] In some cases, the application of a drive signal in a "resonant state" (e.g., ω d,i = ω i ) can facilitate a single qubit gate. That is, by applying a drive signal in a "resonant state", the manipulation of the state of a specific qubit can be facilitated. For example, a specific qubit can be modulated between the ground state |0> and the excited state |1>. In some cases, cross resonance can be performed by applying a drive signal that resonates with an adjacent qubit. For example, cross resonance can be performed when ω d,0 = ω1 or the reverse. By performing such cross resonance, a full microwave method for performing a two qubit gate can be facilitated.

[0020] One characteristic of the fixed-coupling Hamiltonian form defined by equation 1 is that there may be residual unwanted ZZ couplings within the "dressed frame" (e.g., the frame after diagonalizing the Hamiltonian to account for coupling terms). In embodiments, these residual unwanted ZZ couplings can be approximated using the equation defined by equation 2.

[0021]

number

[0022] A multi-microwave-only 2-qubit gate containing cross-resonance can have an entanglement rate that can be proportional to the exchange coupling J between the qubits. Therefore, the speed of the 2-qubit gate can be increased by increasing J. However, increasing J may also lead to an increase in ZZ, a known source of idle error and non-fidelity in multi-qubit circuits. This competition between the speed of the 2-qubit gate and pseudo-crosstalk can be mitigated by sophisticated coupling schemes that can utilize multiple coupling paths to design energy shifts that can lead to ZZ cancellation while maintaining a relatively large J coupling strength. However, in fixed-frequency architectures, improvements in the J / ZZ ratio can be sensitive to the arrangement of qubit frequencies in the straddling regime.

[0023] In some cases, a CW drive near-resonant to the sideband transition may be used to cancel out the ZZ. Furthermore, the drive may be used simultaneously at the same frequency for a pair of coupled qubits to drive a Stark-induced ZZ gate. In embodiments, a three-level model of the transmons that excludes the inverse rotation term in the coupled Hamiltonian may be approximated within high power limits using the equation defined by Equation 3.

[0024]

number

[0025] According to the equation above,

number

[0026] Equation 3 shows that the activation or cancellation of ZZ by Stark, or both, can be effectively set by the ratio of drive power to detune. Equation 3 further shows that Stark can be a function of the relative phase between drive tones and can also be proportional to the exchange coupling J between qubits. Equation 3 also shows that cancellation of ZZ can be achieved with respect to a wide range of operating parameters (e.g., frequency, drive amplitude, or phase difference, or a combination thereof) that satisfy the relationship defined by Equation 4.

[0027]

number

[0028] Unlike cases where a CW-driven near-resonance to the sideband transition is used to cancel out ZZ, double driving can facilitate a wide frequency range and generally does not involve a driven near-resonance to the sideband transition. Furthermore, double driving can introduce an additional parameter (phase difference) to facilitate ZZ cancellation.

[0029] Figure 1 shows a block diagram of an exemplary non-restrictive quantum device 100 that can facilitate the dynamic control of ZZ interactions for quantum computing devices according to one or more embodiments described herein. As illustrated by the embodiment shown in Figure 1, the quantum device 100 includes a bias component 110, a first qubit 120, and a second qubit 130. The first qubit 120 and the second qubit 130 can be operably coupled to the bias component 110 via a first drive line 125 and a second drive line 135, respectively. Examples of qubits suitable for implementing the first qubit 120 or the second qubit 130 or both include, but are not limited to, fixed-frequency qubits, tunable qubits, transmon qubits, fixed-frequency transmon qubits, tunable transmon qubits, and the like. In embodiments, the first qubit 120 or the second qubit 130 or both may be fixed-frequency, non-tunable qubits. As will be described in more detail below, the bias component 110 can facilitate dynamic control of the ZZ interaction between qubits (e.g., the first qubit 120 or the second qubit 130 or both) using a continuous wave (CW) tone applied through each drive line (e.g., the first drive line 125 or the second drive line 135 or both). By modifying the characteristics of such CW tones, embodiments of the bias component 110 can provide a tunable coupling 140 between the first qubit 120 and the second qubit 130.

[0030] Figure 2 shows exemplary non-restrictive qubit drive tones (or drive signals) according to one or more embodiments described herein. In particular, Figure 2 shows graphs 200 and 250 illustrating exemplary non-restrictive drive tones that a bias component 110 can apply to the first qubit 120 and the second qubit 130, respectively, via the corresponding drive lines. In embodiments, the drive tone applied by the bias component 110 may be a microwave drive tone. The Y-axis of each graph depicted in Figure 2 (e.g., the vertical axis of graph 200) represents the drive amplitude (or drive intensity), and the X-axis of each graph depicted in Figure 2 (e.g., the horizontal axis of graph 200) represents time.

[0031] As shown in Figure 2, the bias component 110 can apply single-qubit pulse tones (e.g., single-qubit pulse tones 204, 206, 210, 254, 256, or 258, or a combination thereof) to the first qubit 120 or the second qubit 130 or both via the first drive line 125 and the second drive line 135, respectively. The application of single-qubit pulse tones can cause a single-qubit gate operation on the first qubit 120 or the second qubit 130 or both. Figure 2 further illustrates that the bias component 110 can apply a two-qubit entangling pulse tone (e.g., two-qubit entangling pulse tone 208 or 212 or both) to one of the first qubit 120 and the second qubit 130 via the corresponding drive line. The application of a two-qubit entangling pulse tone to one of the first qubit 120 and the second qubit 130 can induce a two-qubit gate operation (e.g., a CNOT gate via cross resonance) between the first qubit 120 and the second qubit 130.

[0032] The bias component 110 can also add CW tones to the first qubit 120 and the second qubit 130 via the corresponding drive lines. For example, the bias component 110 can add CW tones 202 and 252 to the first qubit 120 and the second qubit 130, respectively. CW tone 202 includes a first frequency (e.g., f_stark), a first drive amplitude Ω0, and a first drive phase φ0. CW tone 252 includes a second frequency (e.g., f_stark), a second drive amplitude Ω1, and a second drive phase φ1. In the example in Figure 2, CW tones 202 and 252 can include a common frequency (e.g., f_stark). That is, the first frequency of CW tone 202 and the second frequency of CW tone 252 can be substantially similar. In embodiments, this common frequency may be defined using a frequency that is non-resonant from each transition of the first qubit 120 or the second qubit 130 or both. As will be described in more detail below, the bias component 110 can utilize CW tones (e.g., CW tone 202 or CW tone 252 or both) to facilitate dynamic control of the ZZ interaction between the qubits. That is, the bias component 110 can utilize such CW tones to facilitate tunable ZZ interaction between the qubits.

[0033] In this embodiment, the bias component 110 can facilitate the dynamic control of the ZZ interaction between the first qubit 120 and the second qubit 130 by dynamically adjusting (or controlling) the relative phase difference between the CW tone 202 or the CW tone 252 or both. In this embodiment, the bias component 110 can dynamically adjust the first drive phase φ0 or the second drive phase φ1 or both so that the phase difference between the first drive phase φ0 and the second drive phase φ1 changes. For example, the CW tone 202 and the CW tone 252 may have a phase difference of π / 2 radians. In this example, the bias component 110 can facilitate dynamic control of the ZZ interaction between the first qubit 120 and the second qubit 130 by dynamically adjusting the first drive phase φ0 or the second drive phase φ1 or both, such that the phase difference between the CW tone 202 and the CW tone 252 changes from π / 2 radians to another phase difference (e.g., π radians). The bias component 110 can cancel, mitigate, or significantly reduce the static ZZ interaction between the first qubit 120 and the second qubit 130 by dynamically adjusting the relative phase difference between the CW tone 202 and the CW tone 252.

[0034] In this embodiment, the bias component 110 can facilitate dynamic control of the ZZ interaction between the first qubit 120 and the second qubit 130 by calibrating (or adjusting) the ZZ interaction between the first qubit 120 and the second qubit 130 during a two-qubit gate operation. For example, the bias component 110 can dynamically adjust (or control) the relative phase difference between CW tone 202 and CW tone 252 while applying a two-qubit entangled pulse tone to one of the two qubits, the first qubit 120 and the second qubit 130. In this example, the bias component 110 can additionally or alternatively adjust the amplitude of at least one of the first drive amplitude Ω0 and the second drive amplitude Ω1 while applying the two-qubit entangled pulse tone.

[0035] Those skilled in the art will understand that during a corresponding two-qubit gate operation, independent of the static ZZ interaction term, a two-qubit entangled pulse tone (e.g., a cross-resonance pulse tone) can generate a ZZ interaction term. Such a ZZ interaction term generated during a two-qubit gate operation may be called a dynamic ZZ interaction. The bias component 110 can facilitate canceling, mitigating, or significantly reducing the net ZZ interaction during a two-qubit gate operation by dynamically calibrating the ZZ interaction (e.g., static ZZ interaction) between the first qubit 120 and the second qubit 130. In embodiments, the net ZZ interaction may have a magnitude based on the exchange coupling strength J between the first qubit 120 and the second qubit 130 during a two-qubit gate operation.

[0036] Figures 3-4 illustrate embodiments in which the bias component 110 can facilitate dynamic control of the ZZ interaction between the first qubit 120 and the second qubit 130 using CW tones 202 and 252. In the embodiments shown in Figures 3-4, the first qubit 120 and the second qubit 130 may have resonant frequencies of approximately 4841 megahertz (MHz) and 4964 MHz, respectively. The CW tones 202 and 252 may have a common frequency that can be defined using a non-resonant frequency from each transition of the first qubit 120 or the second qubit 130. In this embodiment, the CW tones 202 and 252 may have a common frequency of 5000 MHz. In Figures 3-4, the first qubit 120 and the second qubit 130 may also have a qubit anharmonic of -300 MHz and an exchange coupling strength J of 4.4 MHz, respectively.

[0037] The Y-axis of Graph 300 (e.g., the vertical axis of Graph 300) represents the relative phase difference between CW tone 202 and CW tone 252, and the X-axis of Graph 300 (e.g., the horizontal axis of Graph 300) represents the first driving amplitude Ω0 of CW tone 202 that the bias component 110 applies to the first qubit 120 and the second qubit 130. As shown by Graph 300, the static ZZ interaction between the first qubit 120 and the second qubit 130 can vary based on the relative phase difference between CW tone 202 and CW tone 252, which is consistent with equations 3 and 4. For example, Graph 300 includes a low static ZZ interaction region 310 in which the static ZZ interaction between the first qubit 120 and the second qubit 130 can be substantially zero. Graph 300 shows that the low static ZZ interaction region 310 is approximately centered on line 320, which corresponds to a relative phase difference of about π radians between CW tone 202 and CW tone 252. Therefore, the bias component 110 can easily cancel, mitigate, or significantly reduce the static ZZ interaction between the first qubit 120 and the second qubit 130 by dynamically adjusting the relative phase difference between CW tone 202 and CW tone 252 to about π radians. In embodiments, the first drive amplitude Ω0 of CW tone 202 and the second drive amplitude Ω1 of CW tone 252 can remain constant while the bias component 110 dynamically adjusts (or adjusts) the relative phase difference.

[0038] Graph 300, consistent with equations 3 and 4, further demonstrates that the static ZZ interaction between the first qubit 120 and the second qubit 130 can also be varied based on the first drive amplitude Ω0 of the CW tone 202 (or, in this embodiment, the second drive amplitude Ω1 of the CW tone 252, as long as the bias component maintains a constant ratio of approximately 1.24 between the first drive amplitude Ω0 of the CW tone 202 and the second drive amplitude Ω1 of the CW tone 252). For example, the low static ZZ interaction region 310 in Graph 300 corresponds to various values ​​of the first drive amplitude Ω0 of the CW tone 202. Thus, the bias component 110 can also facilitate canceling, mitigating, or significantly reducing the static ZZ interaction between the first qubit 120 and the second qubit 130 by dynamically adjusting the first drive amplitude Ω0 of the CW tone 202 or the second drive amplitude Ω1 of the CW tone 252 or both. In this embodiment, the relative phase difference between CW tone 202 and CW tone 252 can remain constant when (or while) the bias component 110 dynamically adjusts the first drive amplitude Ω0 of CW tone 202 or the second drive amplitude Ω1 of CW tone 252 or both.

[0039] Figure 4 shows an exemplary non-restrictive graph 400 plotting the ZX velocity as a function of the cross-resonance drive strength (or amplitude) according to one or more embodiments described herein. As shown by graph 400, relatively fast ZX velocities can be realized via cross-resonance, in addition to a 4.4 MHz exchange coupling strength J, because the bias component 110 facilitates such cancellation or significant reduction in the static interaction between the first qubit 120 and the second qubit 130. In particular, graph 400 shows the ZX velocities that can be realized when the bias component 110 dynamically adjusts the relative phase difference between CW tone 202 and CW tone 252 to π radians with respect to various values ​​of the first drive amplitude Ω0. For example, line 410 corresponds to a first drive amplitude Ω0 at 25 MHz, line 420 corresponds to a first drive amplitude Ω0 at 22 MHz, line 430 corresponds to a first drive amplitude Ω0 at 19 MHz, line 440 corresponds to a first drive amplitude Ω0 at 16 MHz, line 450 corresponds to a first drive amplitude Ω0 at 13 MHz, line 460 corresponds to a first drive amplitude Ω0 at 10 MHz, line 470 corresponds to a first drive amplitude Ω0 at 7 MHz, line 480 corresponds to a first drive amplitude Ω0 at 4 MHz, and line 490 corresponds to a first drive amplitude Ω0 at 1 MHz.

[0040] Figures 5-6 show another embodiment in which the bias component 110 can facilitate dynamic control of the ZZ interaction between the first qubit 120 and the second qubit 130 using CW tones 202 and 252. In the embodiment shown in Figures 5-6, the resonant frequencies and qubit anharmonics of the first qubit 120 and the second qubit 130 can remain unchanged from the embodiments shown in Figures 3-4. Furthermore, the frequencies of CW tones 202 and 252 can remain at 5000 MHz. In Figures 5-6, the first qubit 120 and the second qubit 130 can have an exchange coupling strength J of 8 MHz.

[0041] The Y-axis of Graph 500 (e.g., the vertical axis of Graph 500) represents the relative phase difference between CW tone 202 and CW tone 252, and the X-axis of Graph 500 (e.g., the horizontal axis of Graph 500) represents the first driving amplitude Ω0 of CW tone 202 that the bias component 110 applies to the first qubit 120 and the second qubit 130. As shown by Graph 300, the static ZZ interaction between the first qubit 120 and the second qubit 130 can vary based on the relative phase difference between CW tone 202 and CW tone 252, which is consistent with equations 3 and 4. For example, Graph 500 includes a low static ZZ interaction region 510 in which the static ZZ interaction between the first qubit 120 and the second qubit 130 can be substantially zero. Graph 500 shows that the low static ZZ interaction region 510 is approximately centered on line 520, which corresponds to a relative phase difference of about π radians between CW tone 202 and CW tone 252. Therefore, the bias component 110 can easily cancel, mitigate, or significantly reduce the static ZZ interaction between the first qubit 120 and the second qubit 130 by dynamically adjusting the relative phase difference between CW tone 202 and CW tone 252 to about π radians. In embodiments, the first drive amplitude Ω0 of CW tone 202 and the second drive amplitude Ω1 of CW tone 252 can remain constant when (or while) the bias component 110 is dynamically adjusting the relative phase difference.

[0042] Graph 500 further demonstrates, in agreement with equations 3 and 4, that the static ZZ interaction between the first qubit 120 and the second qubit 130 can also be varied based on the first drive amplitude Ω0 of the CW tone 202 (or, in this embodiment, the second drive amplitude Ω1 of the CW tone 252, insofar as the bias component maintains a constant ratio of approximately 3 between the first drive amplitude Ω0 of the CW tone 202 and the second drive amplitude Ω1 of the CW tone 252). For example, the low static ZZ interaction region 510 in Graph 500 corresponds to various values ​​of the first drive amplitude Ω0 of the CW tone 202. Thus, the bias component 110 can also facilitate canceling, mitigating, or significantly reducing the static ZZ interaction between the first qubit 120 and the second qubit 130 by dynamically adjusting the first drive amplitude Ω0 of the CW tone 202 or the second drive amplitude Ω1 of the CW tone 252 or both. In this embodiment, the relative phase difference between CW tone 202 and CW tone 252 can remain constant when (or while) the bias component 110 dynamically adjusts the first drive amplitude Ω0 of CW tone 202 or the second drive amplitude Ω1 of CW tone 252 or both. Graph 500 further includes the inverse rotation term in the coupled Hamiltonian. In this example, the static ZZ interaction between the first qubit 120 and the second qubit 130 may exceed 1 MHz.

[0043] Figure 6 shows an exemplary non-restrictive graph 600 plotting the ZX velocity as a function of the cross-resonance drive intensity (or amplitude) according to one or more embodiments described herein. As shown by graph 600, relatively fast ZX velocities can be realized via cross-resonance, in addition to an exchange coupling intensity J of 8 MHz, because the bias component 110 facilitates such cancellation or significant reduction in the static ZZ interaction between the first qubit 120 and the second qubit 130. In particular, graph 600 shows the ZX velocities that can be realized when the bias component 110 dynamically adjusts the relative phase difference between CW tone 202 and CW tone 252 to π radians with respect to various values ​​of the first drive amplitude Ω0. For example, line 610 corresponds to a first drive amplitude Ω0 at 25 MHz, line 620 corresponds to a first drive amplitude Ω0 at 22 MHz, line 630 corresponds to a first drive amplitude Ω0 at 19 MHz, line 640 corresponds to a first drive amplitude Ω0 at 16 MHz, line 650 corresponds to a first drive amplitude Ω0 at 13 MHz, line 660 corresponds to a first drive amplitude Ω0 at 10 MHz, line 670 corresponds to a first drive amplitude Ω0 at 7 MHz, line 680 corresponds to a first drive amplitude Ω0 at 4 MHz, and line 690 corresponds to a first drive amplitude Ω0 at 1 MHz.

[0044] Figures 7-10 illustrate examples of the reduction of static ZZ interaction facilitated by CW tones during the performance of randomized benchmarking (RB) of a single qubit, according to one or more embodiments described herein. In particular, Graph 700 in Figure 7 and Graph 900 in Figure 9 show the results of simultaneous single-qubit RB performances performed on a first qubit 120 and a second qubit 130, respectively, where the bias component 110 does not facilitate the control of static ZZ interaction using CW tones. Graph 800 in Figure 8 and Graph 1000 in Figure 10 show the results of simultaneous single-qubit RB performances performed on a first qubit 120 and a second qubit 130, respectively, where the bias component 110 facilitates the control of static ZZ interaction using CW tones. In Figures 7-10, the Y-axis of each graph (e.g., the vertical axis of graph 700) represents the excited state occupancy, and the X-axis of each graph (e.g., the horizontal axis of graph 700) represents the Clifford length or Clifford number. In the embodiment, the Y-axis of each graph in Figures 7-10 can correspond to a unitless decimal. In this example, the first qubit 120 and the second qubit 130 can have resonant frequencies of 4963.9 MHz and 4841.3 MHz, respectively. In this example, the first qubit 120 can have an average T1 coherence time of 158.1 microseconds (μs) and an average T2 coherence time of 144.6 μs. In this example, the second qubit 130 can have an average T1 coherence time of 123.9 μs and an average T2 coherence time of 126.7 μs.

[0045] To perform a simultaneous single-qubit RB on the first qubit 120 and the second qubit 130, the bias component 110 can simultaneously apply single-qubit pulse tones via the first drive line 125 and the second drive line 135, respectively. This simultaneous application of single-qubit pulse tones can induce a 72 nanosecond (ns) single-qubit gate operation on the first qubit 120 and the second qubit 130. In this example, the first qubit 120 and the second qubit 130 can have an exchange coupling strength J of approximately 4.4 MHz. If the bias component 110 does not facilitate control of the static ZZ interaction using a CW tone, a static ZZ interaction of approximately 312 kilohertz (kHz) between the first qubit 120 and the second qubit 130 may occur with this exchange coupling strength J of approximately 4.4 MHz. This static ZZ interaction of approximately 312 kHz can degrade circuit performance. For example, graphs 700 and 900 show that if the bias component 110 does not use CW tones to facilitate control of the static ZZ interaction, the first qubit 120 and the second qubit 130 will have an average error rate or error per Clifford (EPC) of approximately 0.08%, respectively.

[0046] If the bias component 110 facilitates the control of the static ZZ interaction using a CW tone, an exchange coupling strength J of approximately 4.4 MHz can be maintained between the first qubit 120 and the second qubit 130. However, if the bias component 110 facilitates the control of the static ZZ interaction using a CW tone, the static ZZ interaction between the first qubit 120 and the second qubit 130 can be reduced from approximately 312 kHz to approximately 8 kHz. Such a reduction in the static interaction between the first qubit 120 and the second qubit 130 can facilitate improvements in circuit performance. For example, graphs 800 and 1000 show that if the bias component 110 facilitates the control of the static ZZ interaction using a CW tone, the mean error rate or EPC of the first qubit 120 and the second qubit 130 improves from approximately 0.08% to approximately 0.03%, respectively. In this example, the bias component 110 can apply CW tones having frequencies of 5000 MHz, respectively, via the first drive line 125 and the second drive line 135, while simultaneously performing single-qubit RB on the first qubit 120 and the second qubit 130.

[0047] Figures 11-12 illustrate examples of the reduction of static ZZ interaction facilitated by CW tones during the execution of a two-qubit RB according to one or more embodiments described herein. In particular, graph 1100 in Figure 11 and graph 1200 in Figure 12 show the results of executions of a two-qubit RB performed on a first qubit 120 and a second qubit 130, respectively, where the bias component 110 facilitates the control of static ZZ interaction using CW tones. The Y-axis of each graph depicted in Figures 11-12 (e.g., the vertical axis of graph 1100) represents each |1>excited state occupancy, and the X-axis of each graph depicted in Figures 11-12 (e.g., the horizontal axis of graph 1100) represents the Clifford length or Clifford number. In embodiments, the Y-axis of each graph depicted in Figures 7-10 may correspond to a unitless decimal. In this example, the first qubit 120 and the second qubit 130 can have resonant frequencies of 4963.9 megahertz (MHz) and 4841.3 MHz, respectively. In this example, the first qubit 120 can have an average T1 coherence time of 158.1 microseconds (μs) and an average T2 coherence time of 144.6 μs. In this example, the second qubit 130 can have an average T1 coherence time of 123.9 μs and an average T2 coherence time of 126.7 μs.

[0048] To perform a simultaneous two-qubit RB on the first qubit 120 and the second qubit 130, the bias component 110 can apply a two-qubit entangled pulse tone to the first qubit 120 via the first drive line 125. This application of the two-qubit entangled pulse tone can induce a two-qubit gate operation (e.g., a CNOT gate via cross resonance) between the first qubit 120 and the second qubit 130. In this example, while performing a two-qubit RB on the first qubit 120 and the second qubit 130, the bias component 110 can also apply CW tones having frequencies of 5000 MHz, respectively, via the first drive line 125 and the second drive line 135. In this example, during the execution of the two-qubit RB, the static ZZ interaction between the first qubit 120 and the second qubit 130 can be approximately 8 kHz. Graphs 1100 and 1200 show that if the bias component 110 facilitates control of the static ZZ interaction using CW tones, the first qubit 120 and the second qubit 130 can have an average error rate per gate (EPC / 1.5) of approximately 0.8%, respectively.

[0049] Figure 13 shows an exemplary non-restrictive graph 1300 plotting the ZZ interaction intensity between the first qubit 120 and the second qubit 130 as a function of the cross-resonance drive intensity (or amplitude) according to one or more embodiments described herein. In graph 1300, line 1310 corresponds to the static ZZ interaction between the first qubit 120 and the second qubit 130, line 1320 corresponds to the ZZ interaction between the first qubit 120 and the second qubit 130 after a CW Stark drive tone, and line 1330 corresponds to the ZZ interaction between the first qubit 120 and the second qubit 130 after an additional cross-resonance drive tone. Figure 14 shows an exemplary non-restrictive graph 1400 plotting the ZX interaction intensity as a function of the cross-resonance drive intensity (or amplitude) according to one or more embodiments described herein. Figures 13-14 show another embodiment in which the bias component 110 can facilitate dynamic control of the ZZ interaction between the first qubit 120 and the second qubit 130 using CW tones 202 and 252.

[0050] In the embodiments shown in Figures 13-14, the first qubit 120 and the second qubit 130 can have resonant frequencies of approximately 4963.9 MHz and 4841.2 MHz, respectively. In Figures 13-14, the first qubit 120 and the second qubit 130 can also have a qubit anharmonic of -300 MHz and an exchange coupling strength J of 4.4 MHz, respectively. CW tones 202 and 252 can have a common frequency (e.g., 5000 MHz) that can be defined using a frequency that is non-resonant from each transition of the first qubit 120 or the second qubit 130. The bias component 110 can set a relative phase difference between CW tone 202 and CW tone 252 of approximately π radians. In Figures 13-14, the bias component 110 can calibrate the ZZ interaction between the first qubit 120 and the second qubit 130 to cancel out the net ZZ interaction during two-qubit gate operation. Thus, the bias component 110 can adjust the first drive amplitude Ω0 of the CW tone 202 and the second drive amplitude Ω1 of the CW tone 252 to 16.09 MHz and 17.35 MHz, respectively. In this case, as shown in Figures 13 and 14, the net ZZ interaction during two-qubit gate operation can be virtually zero for ZX operation with cross-resonance tone amplitudes of approximately 30 MHz.

[0051] Figure 15 shows an exemplary non-restrictive graph 1500 plotting the ZZ interaction intensity between the first qubit 120 and the second qubit 130 as a function of the cross-resonance drive intensity (or amplitude) according to one or more embodiments described herein. In graph 1500, line 1510 corresponds to the static ZZ interaction between the first qubit 120 and the second qubit 130, line 1520 corresponds to the ZZ interaction between the first qubit 120 and the second qubit 130 after a CW Stark drive tone, and line 1530 corresponds to the ZZ interaction between the first qubit 120 and the second qubit 130 after an additional cross-resonance drive tone. Figure 16 shows an exemplary non-restrictive graph 1600 plotting the ZX interaction intensity as a function of the cross-resonance drive intensity (or amplitude) according to one or more embodiments described herein. Figures 15-16 show another embodiment in which the bias component 110 can facilitate dynamic control of the ZZ interaction between the first qubit 120 and the second qubit 130 using CW tones 202 and 252.

[0052] In the embodiments shown in Figures 15-16, the resonant frequencies and qubit anharmonics of the first qubit 120 and the second qubit 130 can remain unchanged from those of the embodiments shown in Figures 13-14. Furthermore, the frequencies of CW tone 202 and CW tone 252 can remain at 5000 MHz. In Figures 15-16, the first qubit 120 and the second qubit 130 can also have an exchange coupling strength J of 4.4 MHz. The bias component 110 can set a relative phase difference between CW tone 202 and CW tone 252 of approximately π radians. In Figures 15-16, the bias component 110 can tune CW tone 202 and CW tone 252 to cancel out the static ZZ interaction between the first qubit 120 and the second qubit 130 during 2-qubit gate operation. Therefore, the bias component 110 can adjust the first drive amplitude Ω0 of the CW tone 202 and the second drive amplitude Ω1 of the CW tone 252 to 17 MHz and 21.8 MHz, respectively. In this case, as shown in Figures 15 and 16, the static ZZ interaction during the two-qubit gate operation can be substantially reduced to zero.

[0053] Figure 17 shows a flowchart of an exemplary non-limiting computer implementation method 1700 that facilitates dynamic control of ZZ interactions for quantum computing devices according to one or more embodiments described herein. For brevity, repetition of descriptions of similar elements employed in other embodiments described herein has been omitted. In 1710, the computer implementation method 1700 may include operably coupling a bias component (e.g., bias component 110 in Figure 1) to first and second qubits (e.g., first qubit 120 and second qubit 130) via first and second drive lines (e.g., first drive line 125 and second drive line 135) by a system coupled to a processor.

[0054] In 1720, the computer implementation method 1700 may include the system dynamically controlling the ZZ interaction between the first and second qubits with CW tones applied via each first and second drive line using a bias component. In an embodiment, the system can dynamically control the ZZ interaction between the first and second qubits by dynamically adjusting the relative phase difference between the CW tones using the bias component, and the dynamic adjustment of the relative phase difference cancels out the static ZZ interaction between the first and second qubits. In an embodiment, the system can dynamically control the ZZ interaction between the first and second qubits by dynamically adjusting the amplitude of at least one of the CW tones applied via each first and second drive line tone using the bias component. In an embodiment, the static ZZ interaction between the first and second qubits can be canceled out by dynamically adjusting the amplitude of at least one CW tone. In one embodiment, the system can dynamically control the ZZ interaction between the first and second qubits by using a bias component to calibrate the ZZ interaction between the first and second qubits in order to cancel out the net ZZ interaction between the first and second qubits during a two-qubit gate operation between the first and second qubits. In another embodiment, the system can dynamically control the ZZ interaction between the first and second qubits by using a bias component to tune the CW tone to cancel out the ZZ interaction between the first and second qubits.

[0055] In embodiments, the computer implementation method 1700 may further include the system recalibrating the operating frequencies of the first and second qubits while the CW tone is tuned to cancel out the ZZ interaction. In embodiments, the system may recalibrate the operating frequencies of the first and second qubits using Ramsey pulse sequences.

[0056] To provide background to the various aspects of the disclosed subject matter, Figure 18 and the following description are intended to outline a suitable environment in which the various aspects of the disclosed subject matter may be implemented. Since implementing the various aspects of this disclosure may also include a computer 1812, Figure 18 shows a suitable operating environment 1800. The computer 1812 may also include a processing unit 1814, system memory 1816, and a system bus 1818. The system bus 1818 connects system components, including but not limited to the system memory 1816, to the processing unit 1814. The processing unit 1814 can be any of the various available processors. Dual microprocessors and other multiprocessor architectures may also be employed as the processing unit 1814. System bus 1818 can be any of several types of bus structures, including memory buses or memory controllers, peripheral buses or external buses, or local buses, or combinations thereof, using any variety of available bus architectures, including but not limited to ISA (Industry Standard Architecture), MCA (Micro Channel Architecture), EISA (Enhanced ISA), IDE (Intelligent Drive Electronics), VESA Local Bus (VLB), PCI (Peripheral Component Interconnects), CardBus, Universal Serial Bus (USB), AGP (Advanced Graphics Port), Firewire (IEEE 1094), and Small Computer Systems Interface (SCSI). System memory 1816 may also include volatile memory 1820 and non-volatile memory 1822.A basic input / output system (BIOS), which includes basic routines for transferring information between elements within the computer 1812 during startup, is stored in the non-volatile memory 1822. Examples of non-volatile memory 1822 include, but are not limited to, read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), flash memory, or non-volatile random access memory (RAM) (e.g., ferroelectric RAM (FeRAM)). Volatile memory 1820 may also include random access memory (RAM) that functions as external cache memory. For example, RAM is available in many forms, including, but not limited to, static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchlink DRAM (SLDRAM), direct Rambus RAM (DRRAM), direct Rambus dynamic RAM (DRDRAM), and Rambus dynamic RAM.

[0057] Computer 1812 may also include removable / non-removable volatile / non-volatile computer storage media. For example, Figure 18 shows disk storage 1824. Disk storage 1824 may also include devices such as, but not limited to, magnetic disk drives, floppy(R) disk drives, tape drives, Jaz drives, Zip drives, LS-100 drives, flash memory cards, or memory sticks. Disk storage 1824 may also include, but not limited to, optical disk drives such as compact disk ROM (CD-ROM) devices, recordable CD (CD-R) drives, rewritable CD (CD-RW) drives, or digital versatile disk ROM (DVD-ROM) drives, either separately or in combination with other storage media. To facilitate connection of disk storage 1824 to system bus 1818, removable or non-removable interfaces, such as interface 1826, are typically used. Figure 18 also shows software that acts as an intermediary between the user and the basic computer resources described in a suitable operating environment 1800. Such software may include, for example, an operating system 1828. The operating system 1828, which can be stored in disk storage 1824, operates to control and allocate the resources of computer 1812. System applications 1830 utilize the management of resources by the operating system 1828, for example, through program modules 1832 and program data 1834 stored in either system memory 1816 or disk storage 1824. It should be understood that this disclosure can be implemented using various operating systems or combinations of operating systems.The user inputs commands or information to the computer 1812 via input device 1836. Input device 1836 includes, but is not limited to, pointing devices such as a mouse, trackball, stylus, touchpad, keyboard, microphone, joystick, gamepad, satellite receiver antenna, scanner, TV tuner card, digital camera, digital video camera, and webcam. These and other input devices connect to the processing unit 1814 via interface port 1838 and system bus 1818. Interface port 1838 includes, for example, serial ports, parallel ports, game ports, and Universal Serial Bus (USB). Output device 1840 uses some of the same types of ports as input device 1836. Thus, for example, a USB port can be used to provide input to computer 1812, and information can be output from computer 1812 to output device 1840. The output adapter 1842 is provided to indicate the presence of any output device 1840 that requires a special adapter, such as a monitor, speaker, and printer. Examples of the output adapter 1842 include, but are not limited to, video cards and sound cards that provide a means of connection between the output device 1840 and the system bus 1818. Other devices or systems of devices, or both, such as a remote computer 1844, can be said to provide both input and output functions.

[0058] Computer 1812 can operate within a network environment using logical connections to one or more remote computers, such as remote computer 1844. Remote computer 1844 can be a computer, server, router, network PC, workstation, microprocessor-based device, peer device, or other common network node, and can typically include many of the elements described in relation to computer 1812. For brevity, only the memory storage device 1846 is shown in conjunction with remote computer 1844. Remote computer 1844 is logically connected to computer 1812 via network interface 1848 and then physically connected via communication connection 1850. Network interface 1848 encompasses wired or wireless communication networks, or both, such as local-area networks (LANs), wide-area networks (WANs), and cellular networks. LAN technologies include Fiber Distributed Data Interface (FDDI), Copper Distributed Data Interface (CDDI), Ethernet(R), Token Ring, etc. WAN technologies include, but are not limited to, point-to-point links, circuit-switched networks such as Integrated Services Digital Networks (ISDN) and their variations, packet-switched networks, and Digital Subscriber Lines (DSL). Communication connection 1850 refers to the hardware / software employed to connect network interface 1848 to system bus 1818. Communication connection 1850 is shown within computer 1812 for clarity, but may also exist outside of computer 1812.Hardware / software for connecting to network interface 1848 may also include, for illustrative purposes only, internal and external technologies such as modems including standard telephone-grade modems, cable modems, and DSL modems, ISDN adapters, and Ethernet(R) cards.

[0059] The present invention may, at any possible level of technical detail of integration, be a system, method, apparatus, or computer program product, or a combination thereof. The computer program product may include a computer-readable storage medium containing computer-readable program instructions for causing a processor to perform aspects of the present invention. The computer-readable storage medium may be a tangible device capable of holding and storing instructions for use by an instruction execution device. The computer-readable storage medium may be, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination thereof. A non-exclusive list of more specific examples of computer-readable storage media may also include portable computer diskettes, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM) or flash memory, static random access memory (SRAM), compact disc read-only memory (CD-ROM), digital versatile disk (DVD), memory sticks, floppy(R) disks, mechanically encoded devices such as punch cards or raised structures in grooves on which instructions are recorded, and any appropriate combination thereof. When used herein, computer-readable storage media should not be construed as themselves being transient signals such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmitting media (e.g., light pulses passing through fiber optic cables), or electrical signals transmitted through wires.

[0060] The computer-readable program instructions described herein may be downloaded from a computer-readable storage medium to each computing device / processing device, or to an external computer or external storage device via a network (e.g., the Internet, a local area network, a wide area network, or a wireless network, or a combination thereof). This network may include copper transmission cables, optical transmission fibers, wireless transmitters, routers, firewalls, switches, gateway computers, or edge servers, or a combination thereof. A network adapter card or network interface within each computing device / processing device receives computer-readable program instructions from the network and transfers those computer-readable program instructions for storage on a computer-readable storage medium within each computing device / processing device. The computer-readable program instructions for performing the operation of the present invention may be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, state-setting data, configuration data for integrated circuits, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk(R) and C++, and procedural programming languages ​​such as the C programming language or similar programming languages. The computer-readable program instructions may be executed as a whole on the user's computer, partially as a standalone software package on the user's computer, partially on the user's computer and on a remote computer, or entirely on a remote computer or on a server.In the latter scenario, a remote computer can connect to a user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection can be made to an external computer (for example, via the Internet using an Internet service provider). In some embodiments, to carry out aspects of the present invention, electronic circuits, including, for example, programmable logic circuits, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), can execute computer-readable program instructions to customize the electronic circuits by utilizing state information of computer-readable program instructions.

[0061] Aspects of the present invention will be described herein with reference to flowcharts or block diagrams, or both, of methods, apparatus (systems), and computer program products, according to embodiments of the present invention. It will be understood that each block in a flowchart or block diagram, or both, and any combination of blocks contained in a flowchart or block diagram, or both, can be implemented by computer-readable program instructions. These computer-readable program instructions may be instructions that are provided to a general-purpose computer, a dedicated computer, or another programmable data processing device processor to create a machine, where instructions executed via the processor of a computer or other programmable data processing device create means to perform the functions / operations specified in the blocks of the flowchart or block diagram, or both. These computer-readable program instructions may also be stored on a computer-readable storage medium containing instructions that include instructions to perform the functions / operations specified in the blocks of the flowchart or block diagram, or both, and can instruct a computer, a programmable data processing device, or other device, or a combination thereof, to function in a particular manner. Computer-readable program instructions can also be instructions that are read into a computer, another programmable data processing device, or another device to generate a computer implementation process in which instructions executed on a computer, another programmable device, or another device perform functions / operations specified in a flowchart or block diagram, or both, and cause a series of operable operations to be performed on the computer, another programmable device, or another device.

[0062] The flowcharts and block diagrams in the figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagram may represent a module, segment, or portion of instructions containing one or more executable instructions for implementing a defined logical function. In some alternative implementations, the functions shown in the blocks may occur in an order different from the order shown in the figures. For example, two consecutively shown blocks may actually be executed substantially simultaneously or, in some cases, in reverse order, depending on the functions they contain. Note also that each block in the block diagram or flowchart diagram, or both, and any combination of blocks contained in the block diagram or flowchart diagram, or both, may be implemented by a dedicated hardware-based system that performs a defined function or operation, or a combination of dedicated hardware and computer instructions.

[0063] While the subject matter has been described above in general terms with computer executable instructions for computer program products running on one computer, multiple computers, or both, those skilled in the art will recognize that the disclosure may be combined with or implemented in conjunction with other program modules. Typically, a program module includes routines, programs, components, data structures, etc., that perform a specific task, implement a specific abstract data type, or both. Furthermore, those skilled in the art will understand that the computer implementation methods of the present invention may be practiced using other computer system configurations, including single-processor or multi-processor computer systems, minicomputing devices, mainframe computers, computers, handheld computing devices (e.g., PDAs, telephones), microprocessor-based or programmable consumer electronics or industrial electronics. The embodiments shown may also be practiced in a distributed computing environment where tasks are performed by remote processing devices linked via a communication network. However, some, if not all, of the embodiments of the disclosure may be practiced on a standalone computer. In a distributed computing environment, program modules may reside on both local and remote memory storage devices. For example, in one or more embodiments, a computer executable component may be executed from memory, which may include or consist of one or more distributed memory units. As used herein, “memory” and “memory units” are interchangeable. Furthermore, in one or more embodiments described herein, the code of the computer executable component may be executed in a distributed manner, for example, by multiple processors coupled or working in coordination to execute code from one or more distributed memory units.As used herein, the term “memory” may encompass a single memory or memory unit at one location, or multiple memories or memory units at one or more locations.

[0064] As used in this application, terms such as “component,” “system,” “platform,” and “interface” may refer to, or include, computer-related entities or entities related to operable machines that include one or more specific functions. Entities disclosed herein may be hardware, a combination of hardware and software, software, or running software. For example, a component may be, but is not limited to, a process running on a processor, a processor, an object, an executable file, a thread of execution, a program, or a computer, or a combination thereof. For example, both an application running on a server and the server itself may be components. One or more components may reside within a process or a thread of execution, or both, and components may be localized on one computer or distributed across two or more computers, or both. In another example, each component may be executed from various computer-readable media containing various data structures. A component can communicate via local, remote, or both processes according to signals containing one or more data packets (for example, data from one component exchanging information with another component within a local system or a distributed system, or with another system via signals over a network such as the Internet, or both). As another example, a component can be a device having a specific function provided by mechanical parts operated by electrical or electronic circuits, and operated by a software application or firmware application run by a processor. In such a case, the processor can reside inside or outside the device and can run at least part of the software application or firmware application.As yet another example, a component may be a device that provides a specific function through electronic components that do not include mechanical parts, and these electronic components may include a processor or other means for running software or firmware that gives at least some of the functionality of the electronic components. In one embodiment, a component may be emulated via a virtual machine, for example, within a cloud computing system.

[0065] In addition, the term “or” is intended to mean an inclusive OR, not an exclusive OR. That is, unless otherwise specified or evident from the context, “X adopts A or B” is intended to mean any of the natural inclusive permutations. That is, “X adopts A or B” is satisfied in any of the aforementioned cases if X adopts A, X adopts B, or X adopts both A and B. Furthermore, the articles “a” and “an” used herein and in the accompanying drawings should generally be interpreted as meaning “one or plural” unless otherwise specified or evident from the context. When used herein, the terms “example” or “exemplary” or both are used to mean an example, case, or instance. To avoid misunderstanding, the subject matter disclosed herein is not limited by such examples. In addition, any embodiment or design described herein as “example” or “exemplary” or both shall not necessarily be construed as being preferable or advantageous to other embodiments or designs, and is not intended to exclude equivalent exemplary structures and techniques known to those skilled in the art.

[0066] As used herein, the term “processor” can refer to substantially any computing unit or device, including but not limited to single-core processors, single processors with software multithreading capabilities, multi-core processors, multi-core processors with software multithreading capabilities, multi-core processors with hardware multithreading technology, parallel platforms, and parallel platforms with distributed shared memory. Furthermore, a processor can refer to integrated circuits, application-specific integrated circuits (ASICs), digital signal processors (DSPs), field-programmable gate arrays (FPGAs), programmable logic controllers (PLCs), complex programmable logic devices (CPLDs), individual gate or transistor logic, individual hardware components, or any combination thereof designed to perform the functions described herein. In addition, processors can utilize nanoscale architectures, including but not limited to molecular and quantum dot-based transistors, switches, and gates, to optimize space utilization and improve the performance of user equipment. A processor may be implemented as a combination of computing units. In this disclosure, terms such as “store,” “storage,” “data store,” “data storage,” “database,” and substantially any other information storage component related to the operation and functionality of a component are used to refer to an entity embodied in “memory component,” “memory,” or a component that contains memory.It should be understood that the memory or memory component described herein, or both, may be either volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. Examples of non-volatile memory include, but are not limited to, read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable ROM (EEPROM), flash memory, or non-volatile random access memory (RAM) (e.g., ferroelectric RAM (FeRAM)). Volatile memory may include RAM, which can function, for example, as external cache memory. For example, RAM is available in many forms, including, but not limited to, synchronous RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM), direct Rambus RAM (DRRAM), direct Rambus dynamic RAM (DRDRAM), and Rambus dynamic RAM (RDRAM). Furthermore, the memory components of the systems or computer implementations disclosed herein are intended to include, but not limited to, these and any other suitable types of memory.

[0067] The foregoing contains only examples of systems and computer implementations. Naturally, it is impossible to describe all possible combinations of components or computer implementations for the purpose of illustrating this disclosure, but those skilled in the art will recognize that many other combinations and arrangements of the disclosure are possible. Furthermore, where terms such as “includes,” “have,” and “own” are used in the modes for carrying out the invention, claims, appendices, and drawings, they are intended to be inclusive in the same way as the term “equipped,” as “equipped” is interpreted when used as a provisional term in the claims.

[0068] The descriptions of various embodiments are presented for illustrative purposes only and are not intended to be exhaustive, nor are they limited to the embodiments disclosed. Many changes and modifications that do not deviate from the scope and spirit of the embodiments described will be apparent to those skilled in the art. The terminology used herein has been chosen to best describe the principles, practical applications, or technical improvements beyond the technology available on the market, or to enable those else skilled in the art to understand the embodiments disclosed herein.

Claims

1. A quantum device comprising a bias component operably coupled to first and second qubits via each of first and second drive lines, wherein the bias component dynamically controls the ZZ interaction between the first and second qubits using a continuous wave (CW) tone applied via each of the first and second drive lines.

2. The quantum device according to claim 1, wherein the bias component dynamically controls the ZZ interaction between the first and second qubits by dynamically adjusting the relative phase difference between the CW tones.

3. The quantum device according to claim 2, wherein the static ZZ interaction between the first and second qubits is canceled out by dynamically adjusting the relative phase difference between the CW tones.

4. The quantum device according to claim 2 or 3, wherein the amplitude of each CW tone remains constant while the relative phase difference between the CW tones is dynamically adjusted.

5. The quantum device according to claim 1, wherein the CW tone applied via each of the first and second drive lines includes a common frequency.

6. The quantum device according to claim 5, wherein the common frequency is defined using frequencies that are non-resonant with each transition of the first or second qubit.

7. The quantum device according to claim 1, wherein the bias component dynamically controls the ZZ interaction between the first and second qubits by calibrating the ZZ interaction between the first and second qubits to cancel out the net ZZ interaction during a two-qubit gate operation between the first and second qubits.

8. The quantum device according to claim 7, wherein the net ZZ interaction has a magnitude based on the exchange coupling strength between the first and second qubits.

9. The quantum device according to claim 1, wherein the bias component dynamically controls the ZZ interaction between the first and second qubits by dynamically adjusting the amplitude of at least one of the CW tones applied via the respective first and second drive lines.

10. The quantum device according to claim 9, wherein the static ZZ interaction between the first and second qubits is canceled by dynamically adjusting the amplitude of the at least one CW tone.

11. The quantum device according to any one of claims 9 or 10, wherein the relative phase difference between the CW tones remains constant while the amplitude of at least one of the CW tones is dynamically adjusted.

12. The quantum device according to claim 1, wherein the bias component dynamically controls the ZZ interaction between the first and second qubits by tuning the CW tone to cancel out the ZZ interaction between the first and second qubits.

13. The quantum device according to claim 12, wherein the bias component further recalibrates the operating frequencies of the first and second qubits while the CW tone is tuned to cancel out the ZZ interaction.

14. A system operably coupled to the processor couples the bias components to the first and second qubits via the first and second drive lines, A method for dynamically controlling the ZZ interaction between the first and second qubits using continuous wave (CW) tones applied through the respective first and second drive lines in the bias component.

15. The method according to claim 14, wherein the system dynamically controls the ZZ interaction between the first and second qubits by dynamically adjusting the relative phase difference between the CW tones using the bias component, and the dynamic adjustment of the relative phase difference cancels out the static ZZ interaction between the first and second qubits.

16. The method according to any one of claims 14 or 15, wherein the system dynamically controls the ZZ interaction between the first and second qubits by dynamically adjusting the amplitude of at least one of the CW tones applied via the tones of each of the first and second drive lines using the bias component, and the dynamic adjustment of the amplitude of the at least one CW tone cancels out the static ZZ interaction between the first and second qubits.

17. The method according to claim 14, wherein the system dynamically controls the ZZ interaction between the first and second qubits by using the bias component to calibrate the ZZ interaction between the first and second qubits in order to cancel out the net ZZ interaction between the first and second qubits during a two-qubit gate operation between them.

18. The method according to claim 14, wherein the system dynamically controls the ZZ interaction between the first and second qubits by tuning the CW tone to cancel out the ZZ interaction between the first and second qubits using the bias component.

19. The method according to claim 18, further comprising recalibrating the operating frequencies of the first and second qubits while the CW tone is tuned by the system to cancel out the ZZ interaction.

20. On the computer, The bias components are operably coupled to the first and second qubits via the first and second drive lines, A computer program that causes the bias component to dynamically control the ZZ interaction between the first and second qubits using continuous wave (CW) tones applied through the respective first and second drive lines.

21. A computer program according to claim 20, which dynamically controls the ZZ interaction between the first and second qubits by using the bias component to dynamically adjust the relative phase difference between the CW tones, or by adjusting the amplitude of at least one of the CW tones, or by dynamically adjusting the amplitude of at least one of the CW tones applied via the tones of each of the first or second drive lines.

22. A quantum device comprising a bias component operably coupled to first and second qubits via each of first and second drive lines, wherein the bias component dynamically controls the ZZ interaction between the first and second qubits by dynamically adjusting the relative phase difference between continuous wave (CW) tones applied via each of the first and second drive lines, and the CW tones include frequencies that are non-resonant with each transition of the first or second qubit.

23. The quantum device according to claim 22, wherein the bias component dynamically controls the ZZ interaction between the first and second qubits by calibrating the ZZ interaction between the first and second qubits in order to cancel out the net ZZ interaction between the first and second qubits during a two-qubit gate operation between the first and second qubits.

24. A quantum device comprising a bias component operably coupled to first and second qubits via first and second drive lines, wherein the bias component dynamically controls the ZZ interaction between the first and second qubits by dynamically adjusting a first amplitude of a first continuous wave (CW) tone applied via the first drive line, dynamically adjusting a second amplitude of a second CW tone applied via the second drive line, or a combination thereof.

25. The quantum device according to claim 24, wherein the bias component dynamically controls the ZZ interaction between the first and second qubits by calibrating the ZZ interaction between the first and second qubits in order to cancel out the net ZZ interaction between the first and second qubits during a two-qubit gate operation between the first and second qubits.

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