Patent Description:
Quantum computing devices can be composed of various arrangements of superconducting qubits. In various instances, the qubits can have fixed operational frequencies (e.g., a transmon qubit with a single Josephson junction can have a fixed operational frequency) and can be arranged in two-dimensional arrays on any suitable quantum computing substrate. In various aspects, any qubit in such a two-dimensional array can be coupled to some and/or all of its nearest-neighbor qubits and/or to some and/or all of its next-nearest neighbor qubits. Various techniques and/or systems exist for implementing or building two-qubit gates by driving qubits with microwave tones or signals at a frequency of one or more neighboring qubits. Two-qubit gates implemented using such microwave drive tones can exhibit high coherence and/or strong ZX interaction from cross resonance, which can improve the performance and/or functioning of the quantum computing device.

A number of two-qubit gates implemented using microwave drive tones, including cross-resonance, can have entanglement rates that can be proportional to an exchange coupling strength J between coupled qubits. As such, increasing the exchange coupling strength J can increase the speed of such two-qubit gates. However, increasing the exchange coupling strength J can also increase a known source of idle gate error and multi-qubit circuit infidelity - an always-on, spurious ZZ interaction between the coupled qubits. A competition can therefore exist between obtaining a desired exchange coupling strength J and an always-on, spurious ZZ interaction between the coupled qubits, which can degrade circuit performance. The publication of <NPL>), discloses two-qubit gate schemes that maximize the gate fidelity and draw minimal resources, in order to avoid the weak anharmonicity of transmons which imposes profound constraints on the gate design, leads to increased complexity of devices and control protocols, a resource-efficient control over the interaction of strongly-anharmonic fluxonium qubits is described. By applying an off-resonant drive to non-computational transitions in a pair of capacitively-coupled fluxoniums a ZZ-interaction due to unequal ac-Stark shifts of the computational levels is induced. The drive can either cancel the static ZZ-term or increase it by an order of magnitude to enable a controlled-phase (CP) gate with an arbitrary programmed phase shift. <NPL>, disclose prior art of fast two-qubit gates using a parity-violated superconducting qubit consisting of a capacitively-shunted asymmetric Josephson-junction loop under a finite magnetic flux bias. The second-order nonlinearity manifesting in the qubit enables the interaction with a neighboring single-junction transmon qubit via first-order inter-qubit sideband transitions with Rabi frequencies up to <NUM>. Simultaneously, the unwanted static longitudinal (ZZ) interaction is eliminated with ac Stark shifts induced by a continuous microwave drive near-resonant to the sideband transitions.

The following presents a summary to provide a basic understanding of one or more embodiments of the invention. In one or more embodiments described herein. systems, devices, computer-implemented methods, and/or computer program products that facilitate dynamic control of ZZ interactions for quantum computing devices are described.

According to an aspect of the invention, a quantum device comprises a biasing component that is operatively coupled to first and second qubits via respective first and second drive lines, wherein the first qubit is coupled to the second qubit. The biasing component facilitates dynamic control of ZZ interactions between the first and second qubits using continuous wave (CW) tones applied via the respective first and second drive lines. One aspect of such a quantum device is that the quantum device can facilitate dynamic control of ZZ interactions.

According to another aspect of the invention, a computer-implemented method comprises operatively coupling, by a system operatively coupled to a processor, a biasing component to first and second qubits via respective first and second drive lines. The computer-implemented method further comprises using, by the system, the biasing component to dynamically control ZZ interactions between the first and second qubits with CW tones applied via the respective first and second drive lines. One aspect of such a computer-implemented method is that the computer-implemented method can facilitate dynamic control of ZZ interactions for quantum devices.

According to another aspect of the invention, a computer program product comprises a computer readable storage medium having program instructions embodied therewith. The program instructions are executable by a processor to cause the processor to perform operations. The operations include operatively coupling, by the processor, a biasing component to first and second qubits via respective first and second drive lines. The operations further include using, by the processor, the biasing component to facilitate dynamic control of ZZ interactions between the first and second qubits with CW tones applied via the respective first and second drive lines. One aspect of such a computer program product is that the computer program product can facilitate dynamic control of ZZ interactions for quantum devices.

According to another aspect of the invention, a quantum device comprises a biasing component that is operatively coupled to first and second qubits via respective first and second drive lines. The biasing component facilitates dynamic control of ZZ interactions between the first and second qubits by dynamically adjusting a relative phase difference between CW tones applied via the respective first and second drive lines. One aspect of such a quantum device is that the quantum device can facilitate dynamic control of ZZ interactions.

According to another aspect of the invention, a quantum device comprises a biasing component that is operatively coupled to first and second qubits via respective first and second drive lines. The biasing component facilitates dynamic control of ZZ interactions between the first and second qubits by dynamically adjusting a first amplitude of a first 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. One aspect of such a quantum device is that the quantum device can facilitate dynamic control of ZZ interactions.

One or more embodiments are now described with reference to the drawings, wherein like referenced numerals are used to refer to like elements throughout. In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a more thorough understanding of the one or more embodiments.

The following definitions are used throughout the present disclosure, unless specifically indicated otherwise. "CR" denotes a cross-resonance gate. "CW" denotes continuous wave (e.g., always on). "Anharmonicity" (α) denotes a difference between the second and first excited state energy levels and the qubit transition (e.g., the lowest two energy levels). "On-resonance" refers to when a drive field is at the same frequency as a transition frequency in the quantum system. "Hamiltonian" denotes an energy of the quantum system expressed in terms of quantum operators. "Stark shift" denotes a shift in the energy levels of a quantum system due to an off-resonance drive field. "Stark drive" denotes an off-resonant drive that causes an ac Stark shift. "ZZ" denotes the shift in energy of the state when two qubits are excited. "Gate" denotes an operation on the quantum system that transforms the quantum state. "Single-qubit gate" denotes a gate that transforms the state of a single qubit (e.g., typically with a microwave drive). "Two-qubit gate" denotes a gate that transforms the joint state of two qubits, which involves some form of interaction between the two qubits.

Classical computers operate on binary digits (or bits) that store or represent information as binary states to perform computing and information processing functions. In contrast, quantum computing devices operate on quantum bits (or qubits) that store or represent information as both the binary states and superpositions of the binary states. To that end, quantum computing devices utilize quantum-mechanical phenomena, such as entanglement and interference.

A quantum computation uses a qubit as its essential unit instead of a classical computing bit. The qubit (e.g., quantum binary digit) is the quantum-mechanical analog of the classical bit. Whereas classical bits can employ on only one of two basis states (e.g., <NUM> or <NUM>), qubits can employ on superpositions of those basis states (e.g., α|<NUM>〉 + β|<NUM>〉, where α and β are complex scalars such that |α|<NUM>+|β|<NUM> = <NUM>), allowing a number of qubits to theoretically hold exponentially more information than a same number of classical bits. Thus, quantum computers (e.g., computers that employ qubits instead of solely classical bits) can, in theory, quickly solve problems that can be extremely difficult for classical computers. The bits of a classical computer are simply binary digits, with a value of either <NUM> or <NUM>. Almost any device with two distinct states can serve to represent a classical bit: a switch, a valve, a magnet, a coin, etc. Qubits, operating under the principles of quantum mechanics, can occupy a superposition of <NUM> and <NUM> states, as described above with the complex scalars α and β. However, when the state of the qubit is measured, the result is either <NUM> or <NUM>. But in the course of a computation, a qubit evolves in the superposition state and there can be interference effects between these complex coefficients. This is very distinct from strictly classical probabilistic computing. General quantum programs require coordination of quantum and classical parts of a computation. One way to think about general quantum programs is to identify processes and abstractions involved in specifying a quantum algorithm, transforming the algorithm into executable form, running an experiment or simulation, and analyzing the results. By processing information using laws of quantum mechanics, quantum computers offer novel ways to perform computation tasks such as molecular calculations, financial risk calculations, optimization and many more.

One common type of quantum circuit implemented in quantum computing devices comprise fixed frequency transmon qubits with fixed coupling. Transmons can be viewed as leading candidates toward creating quantum bits (or qubits) for advancing scalability of quantum computing devices. Each qubit of such quantum circuits can have a microwave drive line that operatively couples that qubit to a biasing component. In an embodiment, a Hamiltonian of such quantum circuits can be approximated using the Hamiltonian defined by Equation <NUM>: <MAT>.

In accordance with Equation <NUM> above, ωi denotes the qubit frequency for transmon i (e.g., the energy splitting between the lowest two levels), αi denotes the anharmonicity for transmon i (e.g., the difference between the energy splitting between the first and second energy levels and ωi), n̂i denotes the number operator for transmon i, Ωd,i denotes the microwave drive strength on transmon i, ϕd,i denotes the drive phase on qubit i, <MAT> denotes the creation operator for transmon i, α̂i denotes the annihilation operator for qubit i, ωd,i denotes the microwave drive frequency on transmon i, J is the exchange coupling between the qubits, and t denotes time. In an embodiment, Equation <NUM> can be a duffing oscillator approximation. The Hamiltonian defined by Equation <NUM> includes a qubit frequency term, an anharmonicity term, a drive term, and a coupling term that relates to a coupling between qubits. In Equation <NUM>, the qubit frequency term corresponds to ωin̂i the anharmonicity term corresponds to <MAT>, the drive term corresponds to Ωd,i cos(ωd,it + ϕd,i), and the coupling term corresponds to <MAT>.

In some instances, application of an "on-resonance" drive signal (e.g., ωd,i = ωi) can facilitate single-qubit gates. That is, applying an "on-resonance" drive signal can facilitate manipulating a state of a particular qubit. For example, the particular qubit can modulate between a |<NUM>〉 ground state and a |<NUM>〉 excited state. In some instances, cross-resonance can be performed by applying a drive signal that is resonant with a neighboring qubit. For example, cross-resonance can be performed if ωd,<NUM> = ω<NUM> or vice-versa. Performing such cross-resonance can facilitate an all-microwave method for performing two-qubit gates.

One aspect of the form of the fixed coupling Hamiltonian defined by Equation <NUM> is that in the "dressed frame" (e.g., the frame after diagonalizing the Hamiltonian to account for the coupling term), there can be residual unwanted ZZ coupling. In an embodiment, the residual unwanted ZZ coupling can be approximated using the expression defined by Equation <NUM>: <MAT>.

A number of microwave-only two-qubit gates, including cross-resonance, can have entanglement rates that can be proportional to J, the exchange coupling between qubits. Therefore, increasing J can speed up a two-qubit gate. However, increasing J can also lead to increasing ZZ, which is a known source of idle error and multi-qubit circuit infidelity. This competition between two-qubit gate speed and spurious crosstalk can be remedied by sophisticated coupling schemes that can utilize multiple coupling paths for engineering energy shifts that can lead to cancellation of ZZ while maintaining a relatively sizeable J coupling strength. However, in a fixed frequency architecture, enhancements in the J/ZZ ratio can be sensitive to placement of qubit frequencies in the straddling regime.

In some instances, a CW drive near-resonant to side band transitions can be used to cancel ZZ. Moreover, drives can be used simultaneously at the same frequency on a pair of coupled qubits to drive a Stark induced ZZ gate. In an embodiment, a three-level model of a transmon, excluding counter rotating terms in the coupling Hamiltonian, can be approximated in a high-power limit using the expression defined by Equation <NUM>: <MAT>.

In accordance with Equation <NUM> above, ṽZZ,s denotes the static ZZ interaction term given by Equation <NUM>, αi denotes the anharmonicity of the ith qubit (as in Equation <NUM>), Ωi denotes the Stark drive strength applied to qubit i, ϕi denotes the Stark phase of the drive applied to qubit i, and Δi,d denotes a difference between a frequency of an off-resonance drive tone and an operational frequency of qubit i.

Equation <NUM> shows that a ZZ activation and/or cancellation by Stark can be effectively set by a ratio of the drive power to detuning. Equation <NUM> further shows that the Stark can be a function of the relative phase between the drive tones and can also be proportional to J, the exchange coupling between qubits. Equation <NUM> also shows that ZZ cancellation can be achieved for a wide range of operating parameters (e.g., frequency, drive amplitude, and/or phase difference) that satisfy the relationship defined by Equation <NUM>: <MAT>.

Unlike instances in which a CW drive near-resonant to sideband transitions are used to cancel ZZ, dual driving can facilitate a wide range of frequencies and generally does not involve driving near-resonant to sideband transitions. Furthermore, dual driving can introduce an additional parameter to facilitate ZZ cancellation - a phase difference.

<FIG> illustrates a block diagram of an example, non-limiting quantum device <NUM> that can facilitate dynamic control of ZZ interactions for quantum computing devices, in accordance with one or more embodiments described herein. As illustrated by the example embodiment depicted in <FIG>, quantum device <NUM> includes a biasing component <NUM>, a first qubit <NUM>, and a second qubit <NUM>. First qubit <NUM> and second qubit <NUM> can be operatively coupled to biasing component <NUM> via first drive line <NUM> and second drive line <NUM>, respectively. Examples of qubits that are suitable for implementing first qubit <NUM> and/or second qubit <NUM> include, but are not limited to: a fixed frequency qubit, a tunable qubit, a transmon qubit, a fixed frequency transmon qubit, a tunable transmon qubit, and the like. In an embodiment, first qubit <NUM> and/or second qubit <NUM> can be fixed-frequency, non-tunable qubits. As described in greater detail below, biasing component <NUM> can facilitate dynamic control of ZZ interactions between qubits (e.g., first qubit <NUM> and/or second qubit <NUM>) using continuous wave (CW) tones applied via respective drive lines (e.g., first drive line <NUM> and/or second drive line <NUM>). By modifying aspects of such CW tones, embodiments of biasing component <NUM> can provide tunable coupling <NUM> between first qubit <NUM> and second qubit <NUM>.

<FIG> illustrates example, non-limiting qubit drive tones (or drive signals), in accordance with one or more embodiments described herein. In particular, <FIG> illustrates graphs <NUM> and <NUM> that depict example, non-limiting drive tones that biasing component <NUM> can apply to first qubit <NUM> and second qubit <NUM>, respectively, via corresponding drive lines. In an embodiment, the drive tones that biasing component <NUM> applies can be microwave drive tones. A Y-axis (e.g., the vertical axis of graph <NUM>) of each graph depicted in <FIG> represents drive amplitude (or drive strength) and an X-axis (e.g., the horizontal axis of graph <NUM>) of each graph depicted in <FIG> represents time.

As shown by <FIG>, biasing component <NUM> can apply single-qubit pulse tones (e.g., single-qubit pulse tones <NUM>, <NUM>, <NUM>, <NUM>, <NUM>, and/or <NUM>) to first qubit <NUM> and/or second qubit <NUM> via drive first drive line <NUM> and second drive line <NUM>, respectively. Application of the single-qubit pulse tones can induce single-qubit gate operations on first qubit <NUM> and/or second qubit <NUM>. <FIG> further shows that biasing component <NUM> can apply two-qubit entangling pulse tones (e.g., two-qubit entangling pulse tones <NUM> and/or <NUM>) to one qubit among first qubit <NUM> and second qubit <NUM> via a corresponding drive line. Application of a two-qubit entangling pulse tone to one qubit among first qubit <NUM> and second qubit <NUM> can induce a two-qubit gate operation (e.g., a CNOT gate via cross resonance) between first qubit <NUM> and second qubit <NUM>.

Biasing component <NUM> can also apply CW tones to first qubit <NUM> and second qubit <NUM> via corresponding drive lines. For example, biasing component <NUM> can apply CW tone <NUM> and CW tone <NUM> to first qubit <NUM> and second qubit <NUM>, respectively. CW tone <NUM> comprises a first frequency (e.g., f_stark), a first drive amplitude Ω<NUM>, and a first drive phase ϕ<NUM>. CW tone <NUM> comprises a second frequency (e.g., f_stark), a second drive amplitude Ω<NUM>, and a second drive phase ϕ<NUM>. In the example of <FIG>, CW tone <NUM> and CW tone <NUM> can comprise a common frequency (e.g., f_stark). That is, the first frequency of CW tone <NUM> and the second frequency of CW tone <NUM> can be substantially similar. In an embodiment, the common frequency can be defined using a frequency that is off-resonant from respective transitions of first qubit <NUM> and/or second qubit <NUM>. As discussed in greater detail below, biasing component <NUM> can utilize CW tones (e.g., CW tone <NUM> and/or CW tone <NUM>) to facilitate dynamic control of ZZ interactions between qubits. That is, biasing component <NUM> can utilize such CW tones to facilitate tunable ZZ interaction between qubits.

In an embodiment, biasing component <NUM> can facilitate dynamic control of ZZ interactions between first qubit <NUM> and second qubit <NUM> by dynamically adjusting (or controlling) a relative phase difference between CW tone <NUM> and/or CW tone <NUM>. In this embodiment, biasing component <NUM> can dynamically adjust first drive phase ϕ<NUM> and/or second drive phase ϕ<NUM> such that a phase difference between first drive phase ϕ<NUM> and second drive phase ϕ<NUM> changes. For example, CW tone <NUM> and CW tone <NUM> can have a phase difference of π/<NUM> radians. In this example, biasing component <NUM> can facilitate dynamic control of ZZ interactions between first qubit <NUM> and second qubit <NUM> by dynamically adjusting first drive phase ϕ<NUM> and/or second drive phase ϕ<NUM> such that the phase difference between CW tone <NUM> and CW tone <NUM> changes from π/<NUM> radians to another phase difference (e.g., π radians). By dynamically adjusting the relative phase difference between CW tone <NUM> and CW tone <NUM>, biasing component <NUM> can cancel, mitigate, or substantially reduce a static ZZ interaction between first qubit <NUM> and second qubit <NUM>.

In an embodiment, biasing component <NUM> can facilitate dynamic control of ZZ interactions between first qubit <NUM> and second qubit <NUM> by calibrating (or tuning) a ZZ interaction between first qubit <NUM> and second qubit <NUM> during a two-qubit gate operation. For example, biasing component <NUM> can dynamically adjust (or control) a relative phase difference between CW tone <NUM> and CW tone <NUM> during application of a two-qubit entangling pulse tone to one qubit among first qubit <NUM> and second qubit <NUM>. In this example, biasing component <NUM> can additionally or alternatively adjust at least one amplitude among first drive amplitude Ω<NUM> and second drive amplitude Ω<NUM> during application of the two-qubit entangling pulse tone.

One skilled in the art will appreciate that two-qubit entangling pulse tones (e.g., cross-resonance pulse tones) can generate ZZ interaction terms during a corresponding two-qubit gate operation that are external to static ZZ interaction terms. Such ZZ interaction terms generated during two-qubit gate operations can be referred to as dynamic ZZ interaction. By dynamically calibrating a ZZ interaction (e.g., a static ZZ interaction) between first qubit <NUM> and second qubit <NUM>, biasing component <NUM> can facilitate cancelling, mitigating, or substantially reducing a net ZZ interaction during the two-qubit gate operation. In an embodiment, the net ZZ interaction can have a magnitude based on an exchange coupling strength J between first qubit <NUM> and second qubit <NUM> during the two-qubit gate operation.

<FIG> illustrate an embodiment in which biasing component <NUM> can facilitate dynamic control of ZZ interactions between first qubit <NUM> and second qubit <NUM> using CW tone <NUM> and CW tone <NUM>. In the embodiment illustrated by <FIG>, first qubit <NUM> and second qubit <NUM> can have resonant frequencies of approximately <NUM> megahertz (MHz) and <NUM>, respectively. CW tone <NUM> and CW tone <NUM> can have a common frequency that can be defined using a frequency that is off-resonant from respective transitions of first qubit <NUM> or second qubit <NUM>. In this embodiment, CW tone <NUM> and CW tone <NUM> can have a common frequency of <NUM>. In <FIG>, first qubit <NUM> and second qubit <NUM> can each also have a qubit anharmonicity of -<NUM> and an exchange coupling strength J of <NUM>.

A Y-axis of graph <NUM> (e.g., the vertical axis of graph <NUM>) represents a relative phase difference between CW tone <NUM> and CW tone <NUM> and an X-axis of graph <NUM> (e.g., the horizontal axis of graph <NUM>) represents a first drive amplitude Ω<NUM> of CW tone <NUM>. that biasing component <NUM> applies to first qubit <NUM> and second qubit <NUM>. As illustrated by graph <NUM>, static ZZ interactions between first qubit <NUM> and second qubit <NUM> can vary based on a relative phase difference between CW tone <NUM> and CW tone <NUM> consistent with Equations <NUM> and <NUM>. For example, graph <NUM> includes a low ZZ static interaction region <NUM> at which static ZZ interactions between first qubit <NUM> and second qubit <NUM> can be substantially zero. Graph <NUM> shows that the low ZZ static interaction region <NUM> is approximately centered about a line <NUM> corresponding to the relative phase difference between CW tone <NUM> and CW tone <NUM> of approximately π radians. As such, biasing component <NUM> can facilitate canceling, mitigating, or substantially reducing static ZZ interactions between first qubit <NUM> and second qubit <NUM> by dynamically adjusting the relative phase difference between CW tone <NUM> and CW tone <NUM> to approximately π radians. In an embodiment, the first drive amplitude Ω<NUM> of CW tone <NUM> and the second drive amplitude Ω<NUM> of CW tone <NUM> can remain constant when (or while) biasing component <NUM> dynamically adjusts the relative phase difference.

Graph <NUM> further shows that, consistent with Equations <NUM> and <NUM>, static ZZ interactions between first qubit <NUM> and second qubit <NUM> can also vary based on the first drive amplitude Ω<NUM> of CW tone <NUM> (or the second drive amplitude Ω<NUM> of CW tone <NUM> to the extent that biasing component maintains a constant ratio of approximately <NUM> between the first drive amplitude Ω<NUM> of CW tone <NUM> and the second drive amplitude Ω<NUM> of CW tone <NUM> in this embodiment). For example, the low ZZ static interation region <NUM> of graph <NUM> corresponds with various values of first drive amplitude Ω<NUM> of CW tone <NUM>. As such, biasing component <NUM> can also facilitate canceling, mitigating, or substantially reducing static ZZ interactions between first qubit <NUM> and second qubit <NUM> by dynamically adjusting the first drive amplitude Ω<NUM> of CW tone <NUM> and/or the second drive amplitude Ω<NUM> of CW tone <NUM>. In an embodiment, the relative phase difference between CW tone <NUM> and CW tone <NUM> can remain constant when (or while) biasing component <NUM> dynamically adjusts the first drive amplitude Ω<NUM> of CW tone <NUM> and/or the second drive amplitude Ω<NUM> of CW tone <NUM>.

<FIG> illustrates an example, non-limiting graph <NUM> depicting ZX rate as a function of cross-resonance drive strength (or amplitude), in accordance with one or more embodiments described herein. As illustrated by graph <NUM>, a relatively fast ZX rate via cross-resonance can be realized in addition to the exchange coupling strength J of <NUM> as biasing component <NUM> facilitates such cancelation or substantial reduction in static interaction between first qubit <NUM> and second qubit <NUM>. In particular, graph <NUM> depicts ZX rates that can be realized when biasing component <NUM> dynamically adjusts the relative phase difference between CW tone <NUM> and CW tone <NUM> to π radians for various values of first drive amplitude Ω<NUM>. For example, line <NUM> corresponds to a first drive amplitude Ω<NUM> of <NUM>, line <NUM> corresponds to a first drive amplitude Ω<NUM> of <NUM>, line <NUM> corresponds to a first drive amplitude Ω<NUM> of <NUM>, line <NUM> corresponds to a first drive amplitude Ω<NUM> of <NUM>, line <NUM> corresponds to a first drive amplitude Ω<NUM> of <NUM>, line <NUM> corresponds to a first drive amplitude Ω<NUM> of <NUM>, line <NUM> corresponds to a first drive amplitude Ω<NUM> of <NUM>, line <NUM> corresponds to a first drive amplitude Ω<NUM> of <NUM>, and line <NUM> corresponds to a first drive amplitude Ω<NUM> of <NUM>.

<FIG> illustrate another embodiment in which biasing component <NUM> can facilitate dynamic control of ZZ interactions between first qubit <NUM> and second qubit <NUM> using CW tone <NUM> and CW tone <NUM>. In the embodiment illustrated by <FIG>, the respective resonant frequencies and qubit anharmonicities of first qubit <NUM> and second qubit <NUM> can remain unchanged from the embodiment illustrated by <FIG>. Moreover, the respective frequencies of CW tone <NUM> and CW tone <NUM> can remain <NUM>. In <FIG>, first qubit <NUM> and second qubit <NUM> can have an exchange coupling strength J of <NUM>.

Graph <NUM> further shows that, consistent with Equations <NUM> and <NUM>, static ZZ interactions between first qubit <NUM> and second qubit <NUM> can also vary based on the first drive amplitude Ω<NUM> of CW tone <NUM> (or the second drive amplitude Ω<NUM> of CW tone <NUM> to the extent that biasing component maintains a constant ratio of approximately <NUM> between the first drive amplitude Ω<NUM> of CW tone <NUM> and the second drive amplitude Ω<NUM> of CW tone <NUM> in this embodiment). For example, the low ZZ static interation region <NUM> of graph <NUM> corresponds with various values of first drive amplitude Ω<NUM> of CW tone <NUM>. As such, biasing component <NUM> can also facilitate canceling, mitigating, or substantially reducing static ZZ interactions between first qubit <NUM> and second qubit <NUM> by dynamically adjusting the first drive amplitude Ω<NUM> of CW tone <NUM> and/or the second drive amplitude Ω<NUM> of CW tone <NUM>. In an embodiment, the relative phase difference between CW tone <NUM> and CW tone <NUM> can remain constant when (or while) biasing component <NUM> dynamically adjusts the first drive amplitude Ω<NUM> of CW tone <NUM> and/or the second drive amplitude Ω<NUM> of CW tone <NUM>. Graph <NUM> further includes counter-rotating terms in the coupling Hamiltonian. In this example, the static ZZ interaction between first qubit <NUM> and second qubit <NUM> can exceed <NUM>.

<FIG> illustrates an example, non-limiting graph <NUM> depicting ZX rate as a function of cross-resonance drive strength (or amplitude), in accordance with one or more embodiments described herein. As illustrated by graph <NUM>, a relatively fast ZX rate via cross-resonance can be realized in addition to the exchange coupling strength J of <NUM> as biasing component <NUM> facilitates such cancelation or substantial reduction in static ZZ interaction between first qubit <NUM> and second qubit <NUM>. In particular, graph <NUM> depicts ZX rates that can be realized when biasing component <NUM> dynamically adjusts the relative phase difference between CW tone <NUM> and CW tone <NUM> to π radians for various values of first drive amplitude Ω<NUM>. For example, line <NUM> corresponds to a first drive amplitude Ω<NUM> of <NUM>, line <NUM> corresponds to a first drive amplitude Ω<NUM> of <NUM>, line <NUM> corresponds to a first drive amplitude Ω<NUM> of <NUM>, line <NUM> corresponds to a first drive amplitude Ω<NUM> of <NUM>, line <NUM> corresponds to a first drive amplitude Ω<NUM> of <NUM>, line <NUM> corresponds to a first drive amplitude Ω<NUM> of <NUM>, line <NUM> corresponds to a first drive amplitude Ω<NUM> of <NUM>, line <NUM> corresponds to a first drive amplitude Ω<NUM> of <NUM>, and line <NUM> corresponds to a first drive amplitude Ω<NUM> of <NUM>.

<FIG> illustrate an example of static ZZ interaction reduction facilitated by CW tones during single-qubit randomized benchmarking (RB) runs, in accordance with one or more embodiments described herein. In particular, graph <NUM> of <FIG> and graph <NUM> of <FIG> illustrate results of simultaneous single-qubit RB runs executed on first qubit <NUM> and second qubit <NUM>, respectively, without biasing component <NUM> using CW tones to facilitate control of ZZ static interactions. Graph <NUM> of <FIG> and graph <NUM> of <FIG> illustrate results of simultaneous single-qubit RB runs executed on first qubit <NUM> and second qubit <NUM>, respectively, with biasing component <NUM> using CW tones to facilitate control of ZZ static interactions. A Y-axis (e.g., the vertical axis of graph <NUM>) of each graph depicted in <FIG> represents a respective |<NUM>〉 excited state population and an X-axis (e.g., the horizontal axis of graph <NUM>) of each graph depicted in <FIG> represents a Clifford Length or a number of Cliffords. In an embodiment, the Y-axis of each graph depicted in <FIG> can correspond to a unitless fraction. In this example, first qubit <NUM> and second qubit <NUM> can have resonant frequencies of <NUM> and <NUM>, respectively. In this example, first qubit <NUM> can have average T1 and T2 coherence times of <NUM> microsecond (µs) and <NUM>, respectively. In this example, second qubit <NUM> can have average T1 and T2 coherence times of <NUM> and <NUM>, respectively.

To execute the simultaneous single-qubit RB runs on first qubit <NUM> and second qubit <NUM>, biasing component <NUM> can simultaneously apply single-qubit pulse tones via first drive line <NUM> and second drive line <NUM>, respectively. That simultaneous application of single-qubit pulse tones can induce <NUM> nanosecond (ns) single-qubit gate operations on first qubit <NUM> and second qubit <NUM>. In this example, first qubit <NUM> and second qubit <NUM> can have an exchange coupling strength J of approximately <NUM>. Without biasing component <NUM> using CW tones to facilitate control of ZZ static interactions, a static ZZ interaction between first qubit <NUM> and second qubit <NUM> of approximately <NUM> kilohertz (kHz) can accompany that exchange coupling strength J of approximately <NUM>. That static ZZ interaction of approximately <NUM> can degrade circuit performance. For example, graphs <NUM> and <NUM> show that first qubit <NUM> and second qubit <NUM> each have an average error-rate or Error per Clifford (EPC) of approximately <NUM>% without biasing component <NUM> using CW tones to facilitate control of ZZ static interactions.

With biasing component <NUM> using CW tones to facilitate control of ZZ static interactions, the exchange coupling strength J of approximately <NUM> can be maintained between first qubit <NUM> and second qubit <NUM>. However, the static ZZ interaction between first qubit <NUM> and second qubit <NUM> can be reduced from approximately <NUM> to approximately <NUM> with biasing component <NUM> using CW tones to facilitate control of ZZ static interactions. Such reduction in static interaction between first qubit <NUM> and second qubit <NUM> can facilitate an improvement in circuit performance. For example, graphs <NUM> and <NUM> show that the average error-rate or EPC of first qubit <NUM> and second qubit <NUM> each improve from approximately <NUM>% to approximately <NUM>% with biasing component <NUM> using CW tones to facilitate control of ZZ static interactions. In this example, biasing component <NUM> can apply CW tones via first drive line <NUM> and second drive line <NUM> that each have a frequency of <NUM> while executing the simultaneous single-qubit RB runs on first qubit <NUM> and second qubit <NUM>.

<FIG> illustrate an example of static ZZ interaction reduction facilitated by CW tones during a two-qubit RB run, in accordance with one or more embodiments described herein. In particular, graph <NUM> of <FIG> and graph <NUM> of <FIG> illustrate results of a two-qubit RB run executed on first qubit <NUM> and second qubit <NUM>, respectively, with biasing component <NUM> using CW tones to facilitate control of ZZ static interactions. A Y-axis (e.g., the vertical axis of graph <NUM>) of each graph depicted in <FIG> represents a respective |<NUM>〉 excited state population and an X-axis (e.g., the horizontal axis of graph <NUM>) of each graph depicted in <FIG> represents a Clifford Length or a number of Cliffords. In an embodiment, the Y-axis of each graph depicted in <FIG> can correspond to a unitless fraction. In this example, first qubit <NUM> and second qubit <NUM> can have resonant frequencies of <NUM> megahertz (MHz) and <NUM>, respectively. In this example, first qubit <NUM> can have average T1 and T2 coherence times of <NUM> microsecond (µs) and <NUM>, respectively. In this example, second qubit <NUM> can have average T1 and T2 coherence times of <NUM> and <NUM>, respectively.

To execute the two-qubit RB run on first qubit <NUM> and second qubit <NUM>, biasing component <NUM> can apply a two-qubit entangling pulse tone to first qubit <NUM> via first drive line <NUM>. That application of the two-qubit entangling pulse tone can induce a two-qubit gate operation (e.g., a CNOT gate via cross resonance) between first qubit <NUM> and second qubit <NUM>. In this example, biasing component <NUM> can also apply CW tones via first drive line <NUM> and second drive line <NUM> that each have a frequency of <NUM> while executing the two-qubit RB run on first qubit <NUM> and second qubit <NUM>. In this example, a static ZZ interaction between first qubit <NUM> and second qubit <NUM> while executing the two-qubit RB run can be approximately <NUM>. Graphs <NUM> and <NUM> show that first qubit <NUM> and second qubit <NUM> can each have an average error-rate per gate (EPC/<NUM>) of approximately <NUM>% with biasing component <NUM> using CW tones to facilitate control of ZZ static interactions.

<FIG> illustrates an example, non-limiting graph <NUM> depicting ZZ interaction strength between first qubit <NUM> and second qubit <NUM> as a function of cross-resonance drive strength (or amplitude), in accordance with one or more embodiments described herein. In graph <NUM>, line <NUM> corresponds to static ZZ interaction between first qubit <NUM> and second qubit <NUM>; line <NUM> corresponds to the ZZ interaction between first qubit <NUM> and second qubit <NUM> after the CW Stark drive tone; and line <NUM> corresponds to the ZZ interaction between first qubit <NUM> and second qubit <NUM> after an additional cross-resonance drive tone. <FIG> illustrates an example, non-limiting graph <NUM> depicting ZX interaction strength as a function of cross-resonance drive strength (or amplitude), in accordance with one or more embodiments described herein. <FIG> illustrate another embodiment in which biasing component <NUM> can facilitate dynamic control of ZZ interactions between first qubit <NUM> and second qubit <NUM> using CW tone <NUM> and CW tone <NUM>.

In the embodiment illustrated by <FIG>, first qubit <NUM> and second qubit <NUM> can have resonant frequencies of approximately <NUM> and <NUM>, respectively. In <FIG>, first qubit <NUM> and second qubit <NUM> can each also have a qubit anharmonicity of -<NUM> and an exchange coupling strength J of <NUM>. CW tone <NUM> and CW tone <NUM> can have a common frequency (e.g., <NUM>) that can be defined using a frequency that is off-resonant from respective transitions of first qubit <NUM> or second qubit <NUM>. Biasing component <NUM> can set the relative phase difference between CW tone <NUM> and CW tone <NUM> at approximately π radians. In <FIG>, biasing component <NUM> can calibrate a ZZ interaction between first qubit <NUM> and second qubit <NUM> to cancel a net ZZ interaction during a two-qubit gate operation. To that end, biasing component <NUM> can tune the first drive amplitude Ω<NUM> of CW tone <NUM> and the second drive amplitude Ω<NUM> of CW tone <NUM> to <NUM> and <NUM>, respectively. In doing so, the net ZZ interaction during the two-qubit gate operation can be substantially zero for ZX operation at approximately <NUM> of cross-resonance tone amplitude, as shown by <FIG>.

In the embodiment illustrated by <FIG>, the respective resonant frequencies and qubit anharmonicities of first qubit <NUM> and second qubit <NUM> can remain unchanged from the embodiment illustrated by <FIG>. Moreover, the respective frequencies of CW tone <NUM> and CW tone <NUM> can remain <NUM>. In <FIG>, first qubit <NUM> and second qubit <NUM> can also have an exchange coupling strength J of <NUM>. Biasing component <NUM> can set the relative phase difference between CW tone <NUM> and CW tone <NUM> at approximately π radians. In <FIG>, biasing component <NUM> can tune CW tone <NUM> and CW tone <NUM> to cancel static ZZ interaction between first qubit <NUM> and second qubit <NUM> during a two-qubit gate operation. To that end, biasing component <NUM> can tune the first drive amplitude Ω<NUM> of CW tone <NUM> and the second drive amplitude Ω<NUM> of CW tone <NUM> to <NUM> and <NUM>, respectively. In doing so, the static ZZ interaction during the two-qubit gate operation can be substantially zero, as shown by <FIG>.

<FIG> illustrates a flow diagram of an example, non-limiting computer-implemented method <NUM> of facilitating dynamic control of ZZ interactions for quantum computing devices, in accordance with one or more embodiments described herein. Repetitive description of like elements employed in other embodiments described herein is omitted for sake of brevity. At <NUM>, the computer-implemented method <NUM> can comprise coupling, by a system operatively coupled to a processor, a biasing component (e.g., biasing component <NUM> of <FIG>) to first and second qubits (e.g., first qubit <NUM> and second qubit <NUM>) via respective first and second drive lines (e.g., first drive line <NUM> and second drive line <NUM>).

At <NUM>, the computer-implemented method <NUM> can comprise using, by the system, the biasing component to dynamically control ZZ interactions between the first and second qubits with CW tones applied via the respective first and second drive lines. In an embodiment, the system can use the biasing component to dynamically control ZZ interactions between the first and second qubits by dynamically adjusting a relative phase difference between the CW tones, wherein dynamically adjusting the relative phase difference cancels a static ZZ interaction between the first and second qubits. In an embodiment, the system can use the biasing component to dynamically control ZZ interactions between the first and second qubits by dynamically adjusting an amplitude of at least one CW tone among the CW tones applied via the respective first and second drive lines tones. In an embodiment, dynamically adjusting the amplitude of the at least one CW tone can cancel a static ZZ interaction between the first and second qubits. In an embodiment, the system can use the biasing component to dynamically control ZZ interactions between the first and second qubits by calibrating a ZZ interaction between the first and second qubits in order to cancel a net ZZ interaction during a two-qubit gate operation between the first and second qubits. In an embodiment, the system can use the biasing component to dynamically control ZZ interactions between the first and second qubits by tuning the CW tones to cancel a ZZ interaction between the first and second qubits.

In an embodiment, the computer-implemented method <NUM> can further comprise recalibrating, by the system, respective operating frequencies of the first and second qubits while the CW tones are tuned to cancel the ZZ interaction. In an embodiment, the system can recalibrate the respective operating frequencies of the first and second qubits using Ramsey pulse sequences.

In order to provide a context for the various aspects of the disclosed subject matter, <FIG> as well as the following discussion are intended to provide a general description of a suitable environment in which the various aspects of the disclosed subject matter can be implemented. <FIG> illustrates a suitable operating environment <NUM> for implementing various aspects of this disclosure can also include a computer <NUM>. The computer <NUM> can also include a processing unit <NUM>, a system memory <NUM>, and a system bus <NUM>. The system bus <NUM> couples system components including, but not limited to, the system memory <NUM> to the processing unit <NUM>. The processing unit <NUM> can be any of various available processors. Dual microprocessors and other multiprocessor architectures also can be employed as the processing unit <NUM>. The system bus <NUM> can be any of several types of bus structure(s) including the memory bus or memory controller, a peripheral bus or external bus, and/or a local bus using any variety of available bus architectures including, but not limited to, Industrial Standard Architecture (ISA), Micro-Channel Architecture (MSA), Extended ISA (EISA), Intelligent Drive Electronics (IDE), VESA Local Bus (VLB), Peripheral Component Interconnect (PCI), Card Bus, Universal Serial Bus (USB), Advanced Graphics Port (AGP), Firewire (IEEE <NUM>), and Small Computer Systems Interface (SCSI). The system memory <NUM> can also include volatile memory <NUM> and nonvolatile memory <NUM>. The basic input/output system (BIOS), containing the basic routines to transfer information between elements within the computer <NUM>, such as during start-up, is stored in nonvolatile memory <NUM>. By way of illustration, and not limitation, nonvolatile memory <NUM> can include read only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), flash memory, or nonvolatile random-access memory (RAM) (e.g., ferroelectric RAM (FeRAM). Volatile memory <NUM> can also include random access memory (RAM), which acts as external cache memory. By way of illustration and not limitation, RAM is available in many forms such as 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.

Computer <NUM> can also include removable/non-removable, volatile/nonvolatile computer storage media. <FIG> illustrates, for example, a disk storage <NUM>. Disk storage <NUM> can also include, but is not limited to, devices like a magnetic disk drive, floppy disk drive, tape drive, Jaz drive, Zip drive, LS-<NUM> drive, flash memory card, or memory stick. The disk storage <NUM> also can include storage media separately or in combination with other storage media including, but not limited to, an optical disk drive such as a compact disk ROM device (CD-ROM), CD recordable drive (CD-R Drive), CD rewritable drive (CD-RW Drive) or a digital versatile disk ROM drive (DVD-ROM). To facilitate connection of the disk storage <NUM> to the system bus <NUM>, a removable or non-removable interface is typically used, such as interface <NUM>. <FIG> also depicts software that acts as an intermediary between users and the basic computer resources described in the suitable operating environment <NUM>. Such software can also include, for example, an operating system <NUM>. Operating system <NUM>, which can be stored on disk storage <NUM>, acts to control and allocate resources of the computer <NUM>. System applications <NUM> take advantage of the management of resources by operating system <NUM> through program modules <NUM> and program data <NUM>, e.g., stored either in system memory <NUM> or on disk storage <NUM>. It is to be appreciated that this disclosure can be implemented with various operating systems or combinations of operating systems. A user enters commands or information into the computer <NUM> through input device(s) <NUM>. Input devices <NUM> include, but are not limited to, a pointing device such as a mouse, trackball, stylus, touch pad, keyboard, microphone, joystick, game pad, satellite dish, scanner, TV tuner card, digital camera, digital video camera, web camera, and the like. These and other input devices connect to the processing unit <NUM> through the system bus <NUM> via interface port(s) <NUM>. Interface port(s) <NUM> include, for example, a serial port, a parallel port, a game port, and a universal serial bus (USB). Output device(s) <NUM> use some of the same type of ports as input device(s) <NUM>. Thus, for example, a USB port can be used to provide input to computer <NUM>, and to output information from computer <NUM> to an output device <NUM>. Output adapter <NUM> is provided to illustrate that there are some output devices <NUM> like monitors, speakers, and printers, among other output devices <NUM>, which require special adapters. The output adapters <NUM> include, by way of illustration and not limitation, video and sound cards that provide a means of connection between the output device <NUM> and the system bus <NUM>. It can be noted that other devices and/or systems of devices provide both input and output capabilities such as remote computer(s) <NUM>.

Computer <NUM> can operate in a networked environment using logical connections to one or more remote computers, such as remote computer(s) <NUM>. The remote computer(s) <NUM> can be a computer, a server, a router, a network PC, a workstation, a microprocessor-based appliance, a peer device or other common network node and the like, and typically can also include many or the elements described relative to computer <NUM>. For purposes of brevity, only a memory storage device <NUM> is illustrated with remote computer(s) <NUM>. Remote computer(s) <NUM> is logically connected to computer <NUM> through a network interface <NUM> and then physically connected via communication connection <NUM>. Network interface <NUM> encompasses wire and/or wireless communication networks such as local-area networks (LAN), wide-area networks (WAN), cellular networks, etc. LAN technologies include Fiber Distributed Data Interface (FDDI), Copper Distributed Data Interface (CDDI), Ethernet, Token Ring and the like. WAN technologies include, but are not limited to, point-to-point links, circuit switching networks like Integrated Services Digital Networks (ISDN) and variations thereon, packet switching networks, and Digital Subscriber Lines (DSL). Communication connection(s) <NUM> refers to the hardware/software employed to connect the network interface <NUM> to the system bus <NUM>. While communication connection <NUM> is shown for illustrative clarity inside computer <NUM>, it can also be external to computer <NUM>. The hardware/software for connection to the network interface <NUM> can also include, for exemplary purposes only, internal and external technologies such as, modems including regular telephone grade modems, cable modems and DSL modems, ISDN adapters, and Ethernet cards.

The present invention may be a system, a method, an apparatus and/or a computer program product at any possible technical detail level of integration. The computer program product can include a computer readable storage medium (or media) having computer readable program instructions thereon for causing a processor to carry out aspects of the present invention. The computer readable storage medium can be, for example, 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 of the foregoing. A non-exhaustive list of more specific examples of the computer readable storage medium can also include the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanically encoded device such as punch-cards or raised structures in a groove having instructions recorded thereon, and any suitable combination of the foregoing.

These computer readable program instructions can be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. These computer readable program instructions can also be stored in a computer readable storage medium that can direct a computer, a programmable data processing apparatus, and/or other devices to function in a particular manner, such that the computer readable storage medium having instructions stored therein comprises an article of manufacture including instructions which implement aspects of the function/act specified in the flowchart and/or block diagram block or blocks. The computer readable program instructions can also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational acts to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process, such that the instructions which execute on the computer, other programmable apparatus, or other device implement the functions/acts specified in the flowchart and/or block diagram block or blocks.

While the subject matter has been described above in the general context of computer-executable instructions of a computer program product that runs on a computer and/or computers, those skilled in the art will recognize that this disclosure also can or can be implemented in combination with other program modules. Generally, program modules include routines, programs, components, data structures, etc. that perform particular tasks and/or implement particular abstract data types. Moreover, those skilled in the art will appreciate that the inventive computer-implemented methods can be practiced with other computer system configurations, including single-processor or multiprocessor computer systems, mini-computing devices, mainframe computers, as well as computers, hand-held computing devices (e.g., PDA, phone), microprocessor-based or programmable consumer or industrial electronics, and the like. The illustrated aspects can also be practiced in distributed computing environments in which tasks are performed by remote processing devices that are linked through a communications network. However, some, if not all aspects of this disclosure can be practiced on stand-alone computers. In a distributed computing environment, program modules can be located in both local and remote memory storage devices. For example, in one or more embodiments, computer executable components can be executed from memory that can include or be comprised of one or more distributed memory units. As used herein, the term "memory" and "memory unit" are interchangeable. Further, one or more embodiments described herein can execute code of the computer executable components in a distributed manner, e.g., multiple processors combining or working cooperatively to execute code from one or more distributed memory units. As used herein, the term "memory" can encompass a single memory or memory unit at one location or multiple memories or memory units at one or more locations.

As used in this application, the terms "component," "system," "platform," "interface," and the like, can refer to and/or can include a computer-related entity or an entity related to an operational machine with one or more specific functionalities. The entities disclosed herein can be either hardware, a combination of hardware and software, software, or software in execution. For example, a component can be, but is not limited to being, a process running on a processor, a processor, an object, an executable, a thread of execution, a program, and/or a computer. By way of illustration, both an application running on a server and the server can be a component. One or more components can reside within a process and/or thread of execution and a component can be localized on one computer and/or distributed between two or more computers. In another example, respective components can execute from various computer readable media having various data structures stored thereon. The components can communicate via local and/or remote processes such as in accordance with a signal having one or more data packets (e.g., data from one component interacting with another component in a local system, distributed system, and/or across a network such as the Internet with other systems via the signal). As another example, a component can be an apparatus with specific functionality provided by mechanical parts operated by electric or electronic circuitry, which is operated by a software or firmware application executed by a processor. In such a case, the processor can be internal or external to the apparatus and can execute at least a part of the software or firmware application. As yet another example, a component can be an apparatus that provides specific functionality through electronic components without mechanical parts, wherein the electronic components can include a processor or other means to execute software or firmware that confers at least in part the functionality of the electronic components. In an aspect, a component can emulate an electronic component via a virtual machine, e.g., within a cloud computing system.

As it is employed in the subject specification, the term "processor" can refer to substantially any computing processing unit or device comprising, but not limited to, single-core processors; single-processors with software multithread execution capability; multi-core processors; multi-core processors with software multithread execution capability; multi-core processors with hardware multithread technology; parallel platforms; and parallel platforms with distributed shared memory. Additionally, a processor can refer to an integrated circuit, an application specific integrated circuit (ASIC), a digital signal processor (DSP), a field programmable gate array (FPGA), a programmable logic controller (PLC), a complex programmable logic device (CPLD), a discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. Further, processors can exploit nanoscale architectures such as, but not limited to, molecular and quantum-dot based transistors, switches and gates, in order to optimize space usage or enhance performance of user equipment. A processor can also be implemented as a combination of computing processing units. In this disclosure, terms such as "store," "storage," "data store," data storage," "database," and substantially any other information storage component relevant to operation and functionality of a component are utilized to refer to "memory components," entities embodied in a "memory," or components comprising a memory. It is to be appreciated that memory and/or memory components described herein can be either volatile memory or nonvolatile memory, or can include both volatile and nonvolatile memory. By way of illustration, and not limitation, nonvolatile memory can include read only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable ROM (EEPROM), flash memory, or nonvolatile random access memory (RAM) (e.g., ferroelectric RAM (FeRAM). Volatile memory can include RAM, which can act as external cache memory, for example. By way of illustration and not limitation, RAM is available in many forms such as 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). Additionally, the disclosed memory components of systems or computer-implemented methods herein are intended to include, without being limited to including, these and any other suitable types of memory.

What has been described above include mere examples of systems and computer-implemented methods. It is, of course, not possible to describe every conceivable combination of components or computer-implemented methods for purposes of describing this disclosure, but one of ordinary skill in the art can recognize that many further combinations and permutations of this disclosure are possible. Furthermore, to the extent that the terms "includes," "has," <NUM>% "possesses," and the like are used in the detailed description, claims, appendices and drawings such terms are intended to be inclusive in a manner similar to the term "comprising" as "comprising" is interpreted when employed as a transitional word in a claim.

Claim 1:
A quantum device (<NUM>), comprising:
a first qubit (<NUM>) and a second qubit (<NUM>), wherein the first qubit (<NUM>) and the second qubit (<NUM>) include a qubit from the group of a fixed frequency qubit, a tunable qubit, a transmon qubit, a fixed frequency transmon qubit, a tunable transmon qubit, and wherein the first qubit (<NUM>) is coupled to the second qubit (<NUM>); and
a biasing component (<NUM>) that is operatively coupled to the first and second qubits (<NUM>, <NUM>) via respective first and second drive lines (<NUM>, <NUM>), wherein the biasing component (<NUM>) facilitates dynamic control of ZZ interactions between the first and second qubits (<NUM>, <NUM>) using continuous wave tones (<NUM>, <NUM>) applied via the respective first and second drive lines (<NUM>, <NUM>),
wherein the continuous wave tones (<NUM>, <NUM>) applied via the respective first and second drive lines (<NUM>, <NUM>) comprise a common frequency, and
either
i)wherein the biasing component (<NUM>) facilitates dynamic control of ZZ interactions between the first and second qubits (<NUM>, <NUM>) by dynamically adjusting a relative phase difference between the continuous wave tones (<NUM>, <NUM>), wherein dynamically adjusting the relative phase difference between the continuous wave tones (<NUM>, <NUM>) cancels a static ZZ interaction between the first and second qubits (<NUM>, <NUM>), and wherein respective amplitudes (Ω<NUM>, Ω<NUM>) of the continuous wave tones (<NUM>, <NUM>) remain constant while the relative phase difference between the continuous wave tones (<NUM>, <NUM>) is dynamically adjusted,
or
ii) wherein the biasing component (<NUM>) facilitates dynamic control of ZZ interactions between the first and second qubits (<NUM>, <NUM>) by dynamically adjusting an amplitude (Ω<NUM>, Ω<NUM>) of at least one continuous wave tone (<NUM>, <NUM>) among the continuous wave tones (<NUM>, <NUM>) applied via the respective first and second drive lines (<NUM>, <NUM>), wherein dynamically adjusting the amplitude (Ω<NUM>, Ω<NUM>) of the at least one continuous wave tone (<NUM>, <NUM>) cancels a static ZZ interaction between the first and second qubits (<NUM>, <NUM>), and wherein the relative phase difference between the continuous wave tones (<NUM>, <NUM>) remains constant while the amplitude (Ω<NUM>, Ω<NUM>) of the at least one of the continuous wave tones (<NUM>, <NUM>) is dynamically adjusted.